The Potential of using UltraWideBand Microwave

The Potential of using UltraWideBand Microwave technologies in the Breast Cancer Detection

Sanggeetha Venkatesan Department of Signals and Systems Division of Biomedical Engineering CHALMERS UNIVERSITY OF TECHNOLOGY Göteborg, Sweden, 2012 Report Number: EX072/2012 1

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Thesis for the Degree of Master of Science

The Potential of using UltraWideBand Microwave technologies in the Breast Cancer Detection

Sanggeetha Venkatesan

CHALMERS

Department of Signals and Systems Division of communication Engineering CHALMERS UNIVERSITY OF TECHNOLOGY Göteborg, Sweden, 2012 3

The Potential of using UltraWideBand Microwave technologies in the Breast Cancer Detection Sanggeetha Venkatesan Supervisor: Hoi Shun Lui Assistant Professor Biomedical Electromagnetics Group Department of Signals and Systems Chalmers University of Technology © Sanggeetha Venkatesan, 2012 Department of Signals and Systems Chalmers University of Technology SE‐412 96 Gothenburg, Sweden Telephone +46 (0)31‐772 10 00 www.chalmers.se 4

Abstract: Earlier detection of Breast cancer helps in increasing the chances of patients recovery and survival. In this thesis project, the possibilities of using Ultra Wideband (UWB) Microwave technologies for breast cancer detection are investigated. Based on Singularity Expansion Method, resonance‐based target recognition technique, that utilizes the Complex Natural Resonance (CNR) of the breast volumes as a feature set, is considered. These CNRs can be directly extracted from the UWB time domain response using Matrix pencil method (MPM). In this project, three different strategies for CNR extraction from a single and multiple time domain response(s) are studied. The UWB time domain electromagnetic responses of simple breast volumes with different tumor sizes are computed numerically using commercial solver. The extracted CNRs from different breast volumes using different CNR extraction strategies are analysed in details.

Keywords: SEM, Matrix Pencil Method, Complex Natural Resonance, UltraWideBand Microwave, polarization, breast cancer detection.

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List of Abbreviations: SEM Singularity Expansion Method MPM Matrix Pencil Method CNR Comple Natural Resonance UWB Ultra Wideband MRI Magnetic Resonance Imaging MOM Method Of Moment V Vertical H Horizontal R Right L Left ER Energy Ratio TF Time Frequency

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Table of Contents 1.Introduction ............................................................................................................................................... 8 1.1. Problem Statement ............................................................................................................................ 8 1.2. Research Question ............................................................................................................................. 9 1.3.Purpose ............................................................................................................................................... 9 1.4.Disposition .......................................................................................................................................... 9 2.Project Methodology ............................................................................................................................... 11 2.1Literature Study ................................................................................................................................. 11 2.2Test Cases and Breast Cancer Detection ........................................................................................... 12 3. Algorithm ................................................................................................................................................ 16 3.1 Matrix Pencil Method For Single transient response ....................................................................... 16 3.2 Matrix pencil Method for multiple signals ........................................................................................ 18 4. Numerical Study and Results: ................................................................................................................. 20 4.1. Test Case1‐ Damping Exponential Signals: ...................................................................................... 20 4.2. Test Case2‐Wire Data: ...................................................................................................................... 22 4.3 Breast Cancer Detection: .................................................................................................................. 24 4.4 Multiple aspect extraction: ............................................................................................................... 47 4.5 Multiple extraction for breast volume: ............................................................................................. 47 4.6 Multiple Aspect Extraction for breast tumor detection: .................................................................. 48 4.7 Polarimetric data ............................................................................................................................... 51 4.7.a Linear polarization for 18 aspects.(VV,HH,VH,HV)..................................................................... 52 4.7.b Circular polarization (LL, RR, LR, RL) .......................................................................................... 55 4.8 Poles extraction for NO tumor, 10mm and 15mm tumor: ............................................................... 58 5.Discussion: ............................................................................................................................................... 60 6. Conclusion ............................................................................................................................................... 61 7

1.Introduction Early detection of breast cancer can significantly improve the survival rate of the patients. In the past couple of decades, several methods of detection and recovery tectiniques for the breast cancer were continously studied. Most predominontly, imaging approach like X‐Ray mammography and Magnetic Resonant Imaging technique are in use. These two methods have some consequences and limitation, in which X‐Ray is an ionizing radiation and which is not preferred for repeated exposure in short period of time since it may cause other consequences to the patient [1]. Magnetic Resonant Imaging method [8] is an expensive method that limits the patient for frequent examination of the cancer condition. In order to overcome these constraints, my project is to investigate the chances of using resonance based microwave technologies for the breast cancer detection. Resonance based target recognition is a method based on Singularity Expansion Method, where the late‐time time domain transient response is considered as it contains most of the information about the target [9]. Microwave detection techniques are advantageous since they are non ionized and detects the change in dielectric properties of the tissue, which leads to periodic checkup for the patient without any risk and also it provides good contrast between malignant tumors. For the detection of nature of breast cancer, the breast volume is considered as the “target. Electromagnetic signal is impringed on the target. The response signal from the target is computed using a Moment of Method solver called FEKO in frequency domain and Inverse fourier tranform is made to obtain in a time domain [10]. Late time response signal is usually preferred since it holds all the information about the target. Among various detection techniques we choose Matrix pencil method in our project study. Matrix pencil method is linear detection technique, which handles single response and multiple response signals. When the response signal from the target passes through the MPM algorithm, signal parameters such as Complex Natural Resonance (CNR) and residues are extracted which gives information about the desired target. CNR is the key parameter as it is aspect independent, extraction of single set of CNR is possible when considering multiple response signals. Whereas, residues are aspect dependent. Multiple response signals may be of multiple aspect and polarimetric data, multiple aspect response signal can be obtained from the target in many look directions with particular polarization. Polarimetric aspect are the response data from the target in particular look direction with all possible polarizations (4 circular or 4 linear polarization). Here, we considered two set of test cases , damped exponential signal and signal from one meter wire. The parameters are extracted for these targets in an efficient manner with MPM algorithm which handles single transient response and multiple signals. Breast tumor detection is done for three different cases of “No tumor”, “10mm tumor”, “15mm tumor”. The CNR for all three cases are extracted and CNR corresponds to the tumor are obtained.

1.1. Problem Statement To investigate the possibility of using Ultra Wideband Microwave technologies such as Matrix pencil method for the detection of nature of breast cancer, by the developement of MPM algorithm. 8

Numerical study for the extraction of signal parameters such as CNR of test case, breast cancer and discusses the efficiency of MPM towards breast cancer detection.

1.2. Research Question How efficient that the UltraWideband Microwave technology, Matrix Pencil Method is suitable for the extraction of signal parameters for breast cancer detection? The question will be addressed in chapter – of the report where the author discussed with numerical results and explains the efficiency of Matrix Pencil Method.

1.3.Purpose The main goal of the thesis is to analyze the advantages and pitfalls of working with an Matrix pencil method for the detection of nature of breast cancer. Thus this thesis provides a detailed exposure to working of Matrix Pencil method with clear numerical study of simple damped exponential and signal from the wire.

1.4.Disposition The rest of the report describes the following main topics: Project Methodology, Algorithm, Numerical Study, Results, Discussion, Conclusion. Chapter 2. Project MEthodology This chapter describes the methodology used to proceed with the project. The planning of two main parts of the project which are Research methodology and Sample cases are explained well here. A brief overview of the two methodologies that will be performed during the thesis to investigate processes is also provided in this section of report. It includes an overview of two different signals cases, Damped exponential signal and response signal from 1m wire. The breast tumor detection is done for 3 different cases of breast cancer, No tumor, 10mm and 15mm tumor. Chaper 3 Algorithm The third chapters of the report explains about flow of the matrix Pencil Method algorithm for single look direction and also the flow of algorithm which uses Matrix pencil method for Multiple signals in parameter extraction. From this chapter, reader gets good understanding about the working of Matrix pencil method. Furthermore, the chapter explains more about how MPM algorithm of single and multiple signals treats three signal cases and helps in extracting the signal parameters. 9

4. Numerical Study and Results This chapter includes the signal parameters like CNR and residues which are extracted from the signal utilising MPM algorithm. These CNR are clearly explained with tables and clear comparison is made between the reference and obtained parameters for test cases. Extracted CNR for breast cancer detection are clearly tabulated. 5. Discussion This section discusses the CNR extraction with single transient response, multiple aspect and polarimetric data. The advantages of using multiple signal over single transient response at a time and also better extraction with polarimetric data instead of multiple aspect are summarized. For breast canser detection, CNR corresponds to the tumor, difference in CNR od 3 cases od breast tumor are detailed. 6. Conclusion This chapter summarizes the thesis by describing the learning outcome and main experience in the project. The thesis is wrapped up by providing some suggestions for the future work and summarizing the whole research and project.

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2.Project Methodology In this thesis following two strategies will be considered to address the prementioned problems of research and study of suitable solutions. ‘’Research can be termed as a logical and systematic search for new and useful infoemation on a particular topic. The outcome of a research is to verify and test important facts, to discover new facts and to overcome and solve problems occuring in our everyday life’’ [1]. In order to get more information, the study was done with following two methodologies a). Literature Study b). Test Cases and Breast Cancer detection

2.1Literature Study Research on possibility of using UWB microwave technologies for breast cancer detection is accomplished by extensive literature review on available various UWB technologies and understanding the nature of each of them. In the recent decades there were several target detection techniques were discussed and studied. Some of most familiar methods are Prony method, E‐Pulse technique and Matrix Pencil Method. To study the nature of target, an electromagnetic wave must passed through desired target and the late time response must be considered to get all information about the target. That signal have to be studied under UWB techniques so that parameters which has information about the target can be obtained. Prony’s method is most popular and earliest linear method for parameter extraction from the response signal. But, the main difficulties with the Prony’s method are computational complexity (i.e) it is a two step process in finding the poles and notorious for its extreme sensitivity to noise [2]. E‐Pulse is an interesting technique for extraction of natural freqency of a radar target from a measured response. This is a technique which is insensitive to random noise and to estimates of model content [3]. E‐pulse is an technique that helps in extraction of natural frequency of desired target and which is also a target recognition technique. An E‐pulse is defined as a waveform of finite duration e(t) and which extinguishes E(t) in the late time [4]. The convolution of e(t) and E(t) yiels the null result. So, if the natural frequency of a target are known, an E‐pulse for that target can be obtained by demanding E(s) = 0 and the convolution of natural frequency and its E‐pulse will yield zero [3]. Matrix Pencil Method is a relatively new and popular linear technique for extraction of the parameters. It is derived from a method called pencil of funcion approach which was in use for some time [2]. Matrix pencil method is computationally more efficient and simple. When it is compared with another linear method called Prony, it has better advantages than that (i.e) it is two step process for finding the poles but Matrix Pencil Method is an one step process in extracting the value of poles. Apart from that, Matrix pencil Method has a lower variance of the estimates of parameter of interest in the presence of noise 11

than the Prony’s method. In our project Matrix Pencil Method is technique which is chosen and study of possibility of using UltraWideband Microwave in breast cancer detection is made with this technique. We also considered Matrix Pencil Method with multiple look direction, where responses are recorded along multiple look direction. An importance of multiple look direction is that the single estimate of all the poles are done utilizing multiple transient waveforms from target along multiple look direction [5]. The major difference between the waveforms are that the residues at the various poles are of different magnitudes. A single estimate for the poles will be more accurate and robust to effects of noise. An algorithm of MPM and Application of MPM with different look direction are explained clearly in the algorithm part of report. From the Ultrawideband microwave backscatter ranging from 1‐11GHz, characterization of targets features such as shape, size can also be investigated numerically. Generally, Smooth, microbulated and spiculated are the three general category in shape and four size categories which are from 0.5 to 2 cm in diameter were considered [7]. There are basically two different methods for classification in characterization, local discriminant bases and principal component analysis. By using these methods shape and size classification can be done with signal to noise ratio ranging 10dB, target size discrimation was 97% accurate and shape was accurate with 70% for about 360 targets. Figure 1 belows shows the 3 major steps for target recongtiion based on Ultra wideband transient electromagnetic responses.

Time domain response (SEM) CNR Extraction(MPM)

Target recognition

Figure 1: Three major steps for extraction and detection.

2.2Test Cases and Breast Cancer Detection In our project, an algorithm which is chosen for study of possibility of using Ultrawideband Microwave technology is Matrix Pencil Method. In order to deal with working of algorithm more clearly, algorithm must be executed and tested with some sample cases. For detailed and convinient study two different cases are selected, first sample case is a simple damped exponential signal and second sample case is 12

numerical data from wire scatterer. These two cases are considered for numerical study of MPM and for MPM algorithm with multiple look direction. Damped exponential signals are developed with specific requirement for both single and multiple look direction. Single damped exponential signal is developed for MPM algorithm and Multiple look direction algorithm has two different damped exponential signal for two different looks, which has same poles and different residues magnitude. From the strength of residues the signal can be discriminated. Second sample case was the data from wire scatterer. The specification of this sample is from the reference [6]. The parameters extracted from algorithm with these sample signals helps to know efficiency and accuracy of the MPM algorithm. With the help of numerical study with sample signals we can come to the conclusion for the chances of using UWB technologies for breast cancer detection.

2.2.aTest Case1‐Damping Exponential Signals For better understanding of working of MPM algorithm it is always good to deal with simple case first. A simple damped exponential signal is generated with matlab. The damped exponential signal with known signal parameters is given to developed MPM algorithm. The main property of MPM algorithm is to derive signal parameters such as poles and residues of given known input signal. The verification and testing of matrix pencil method algorithm is made with the simple example cases as shown below. In this case, the synthetic data (damped exponential signal) is taken, s(t)

β)t (1)

s (t) = damped exponential signal Ai = Residue β = ‐α + jωi α = damping factor ω = angular frequencies.

2.2.bTest Case2‐Wire Data of 1m In the second case, numerical data of a wire scatterer is considered. This sample is a bit complicated when compared to case 1, but which provides more detailed study and understands the working and efficiency of MPM algorithm. Here, response from the wire (wired data) with wire length, L = 1m and two different look angles, = 15⁰ and 75⁰ are provided. The data set of wire has frequency range from 4.39MHz to 9GHz with equally spaced 2048 number of samples. The response signal of wire scatterer with above specification is given to MPM algorithm for parameter estimation. In [6] for better understanding of results, parameter extracted using another method called Method of Moments, which is solely depends on the target geometry and dielectric properties are also considered and is included in 13

and explained in numerical study part of the report. Extracted parameters using MPM algorithm for sample case 2 is compared with results of Method of Moments and Matrix Pencil Method for two different angles.

Figure 2: Test Case‐ 1m wire

2.2.cBreast Cancer Detection The breast tumor in the breast volume is studied. Three different cases are considered, breast volume with no tumor, 10mm tumor and 15mm tumor. The breast volume of 6cm hemisphere with tumor is considered with 18 plane wave sources around with seperation of 20° each. The breast volume is illuminated with the frequency of 23MHz to 3GHz with 128 samples in frequency domain (256 samples in time domain). Each time, one plane wave source is considered and the corresponding scattered far‐ field in the 18 directions are computed. [10]. The electromagnetic response is computed in the frequency domain and the time domain response are obtained via an inverse Fourier Transofrm of the frequency data. Both circular and linear polarization are considered. These datas are processed with matrix pencil method by considering multiple aspect and polarimetric data. Multiple aspect datas are considered in a way that the transient responses from all the 18 look direction with certain polarization state. Polarimetric datas are transient response from a particular look direction and by considering the datas from circular or linear polarization state [10]. From this case study, it can be said whether the better parameter extraction can done with multiple aspect data or polarimetric data.

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Figure 3: Simulation setup for Breast Cancer Detection in FEKO

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3. Algorithm This chapter describes the flow of Matrix Pencil method with regards to the case of single and various input signals. The procedure of Matrix pencil method varies according to noise level in an input signal and reacts better even in noisy situation. In absence of noise, parameter of estimation can get through in a simple way and the procedure of algorithm flows an another way for a noisy situation. In our project we include Matrix pencil method which treats single set of data and also use an algorithm multiple look direction for noisy condition which are as follows.

3.1 Matrix Pencil Method For Single transient response The term pencil originated with Gantmacher [2], similar to Gantmacher’s definition for matrix pencil, with another entity wehn combining two functions defined on a common interval, with a scalar parameter, λ [2]. f (t, λ) = g(t) + λh(t) (2) f(t, λ) is called as a pencil of functions g(t) and h(t), parameterized by λ. In the case of parameter extraction, pencil of function contains most important information about poles of given input signal. Total least matrix pencil method is found to be more superior, simple and more robust to noisy signal [2]. The main objective of this method is to findout the poles Z, residues R and model order M of noise contaminated data y(t). In this implemetation of total least square matrix pencil method, initially the noise contaminated response signal collected which is specified as x(k). For the reason of developement of algorithm, data x(k) is replaced by y(k) for the formation of matrix [Y1] and [Y2]. Next, the formation of data matrix [Y] is done from noisy data matrix [Y1] and [Y2] and is obtained as mentioned below.

(3)

Note that, formation of matrix [Y1] and [Y2] is obtained from [Y] by deleting the last column and first column from [Y] matrix respectively. The dimension of data matrix [Y] is given as (N‐L)x(L+1), where N is number of samples taken from the response signal and the parameter L must be choosen between N/3 and N/2 for efficient noise filtering and for these values of L, the variance in the parameter poles because of noise has been found to be minimum [2]. 16

Once after the formation data matrix [Y], singular value decomposition of matrix [Y] must be done. Singular value decompostion is a process of factorizing a matrix in the form

[Y]=[U][∑][V]*

(4)

Here, [U] and [V] are said to be unitary matrices, where [U] comprised of eigen vectors of [Y][Y]* and [V] matrix has eigen vectors of [Y]*[Y] and [∑] is a diagonal matrix which has singular value of [Y]. In this stage, estimation of parameter model order M is done. The procedure of finding M varies according to input m value, when input m value is set greater than zero the model order M that is the number of estimated parameters are same as input model order. The way of finding model order M is different when input m is negative. In case of m less than zero, one consider the ratio of various singular values to the largest one. The singular values are represented as σc and largest singular value which is the first singular value is given as σmax. The model order M can be estimated with the following equation.

σc σ max

≈

(5)

Where p is the number of significant decimal digits in the data. The ratio of singular value to its and those singular values are considered for the maximum must be approximately equal to reconstuction of the data. For example, if the data is accurate up to 4 significant decimal digits, then the singular values for which the ratio less than 10 to the power of ‐4 are considered to be noisy data and these datas must not be used for the reconstuction of the data. So the selection of singular values which is approximated with the above equations helps in parameter estimation effectively. The next process is to find out the matrix [Y1] and [Y2], for this we consider the filtered matrix [V’] which is constructed in a way it comprises only M dominant right singular vectors of matrix [V]. The remaining right singular vectors of matrix (i.e) from M+1 to L are neglected as they are smaller. Inorder to form [Y1] and [Y2] matrix, [V1’] and [V2’] filtered matrix must be derived from [V’] by deleting its last row and first row respectively. So,

[Y1] = [U][∑’][V1’]* (6)

[y2] = [U][∑’][V2’]* (7)

In the above equation, [∑’] is obtained from M columns of [∑] that is by considering only M dominant singular values [2]. Once after finding the matrices [Y1] and [Y2], Matrix pencil equation must be solved to accomplish its eigen values which is described below [2],

{[Y2] – λ[Y1]}LxM => {[Y1]=[Y2] – λ[I]}MxM’ 17

The eigen values which we attained with above equation will be equivalent to the eigen velues of the following matrix,

{[V2’]* – λ[V1’]*}LxM => {[V1]}{[V2]} – λ[I]

An above approach of construe the Matrix pencil equation is more transparent in obtaining poles with minimum variance in the presence of noise, typically up to 20‐25 dB of signal to noise ratio can be handled effectively and simpler than prony method [2]. Once after retrieving the model order M and poles Z, the residues are solved from the following least square problem,

(8)

Therefore, Matrix Pencil Method algorithm for estimating the signal parameters such as poles, residues of the desired target is clearly expained.

3.2 Matrix pencil Method for multiple signals This method is an attempt to study more about the target from many aspects like many look directions and different polarization. In this method, target is surrounded by many antennas placed in certain interval. One antenna acts as transmitter and rest of the antennas take the position of receiver. All the antennas takes a turn as tansmitter and receiver. The data from the target are collected by all the receiver and processed in time domain. The poles recorded are independent of look directions and polarization, so here common single set of poles are obtained with different amplitudes. It is believed that parameter extraction by multiple aspect helps in easy parameter extraction. The following is an MPM algorithm that process these multiple aspect data. For the algorithm development, the transient response of length N+1 and k look directions are considered. the response is the noise contaminated data so Total least square Matrix pencil method is preferrable. The first step is to form a matrix [D] from the noise contaminated data, where [D1] matrix can be obtained from [D] by eliminating the last row and matrix [D2] is by deleting the first row of [D] matrix respectively. The data matrix [D] looks as follows [5],

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(9)

Next step deals with factorization of matrix [D] by singular value decomposition, it is done according to [5]

Where [U]&[V]* are two orthogonal matrix, whereas [Σ] has the singular values of [D] matrix. In order to combat the noise effect, model order M must be obtained for matrix filtering. M can be obtained in the same way as it was discussed in the above algorithm. Singular value filtering is done by retaining the M dominant value in the matrix [Σ]. With the filtered matrix, new matrix [D1], [D2] are formed and processed in the matrix pencil equation,

[D2] ‐ λ[D1]

The poles are obtained from the above equation. Once the poles and model order is known it is easy to find out the amplitude value from the following equation [5],

(10)

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4. Numerical Study and Results: 4.1. Test Case1‐ Damping Exponential Signals: In this case, the synthetic data (damped exponential signal) is taken, (t)

β)t (11)

(t) = damped exponential signal Ai = Residue β = ‐α + jωi α = damping factor ω = angular frequencies. The above damped exponential signal is taken as a sample with order M = 6, amplitude, A = {1, 2, 3}, α = {2, 3, 4} and the frequency, f = {4, 5, 6} with ω=2*pi*f for the better understanding. Input is given to MPM algorithm and the parameters like poles and residues are obtained. The estimation of the parameter is done for the different modes. The number of poles and residues are decided with the factor called Model order with the condition say,

σc σ max

≈

(12)

Where, σc = sigular values of the data matrix σmax = maximum (i.e) the first sigular value p = number of significant decimal digits. The model order is selected, when the fraction of the singular value with its maximum one is less than . For example, consider m= 2 , σmax = 58 and the number of singular values must or equal to the be, σc ≤ 0.58. In the case of M < 0, the fraction of singular value σc and maximum singular value σmax must be greater than M.

σc σ max

> M (13)

Here the extraction of poles and residues were attained in an efficient manner with MPM. For the verification purpose, reconstruction of the signal is also done and shown with factor called VAF. In the table below, poles and residues are obtained for the various M and the parameter extraction is done more effectively for the M = ‐5, ‐3 ‐1, 4, 6, 8, 10. When we consider the case of M = ‐5, by implementing the value of M in the above condition (3) which leads to the number of poles and 20

residues. For M = 2, the poles and residues are extracted with the condition (2). The extracted poles and residues can be clearly seen in the table 1(a)&1(b). Table 1 : parameters for the damped exponential signal M=‐5 VAF = 100 pole = ‐2.0000 25.1327 ‐2.0000 ‐25.1327 ‐3.0000 31.4159 ‐3.0000 ‐31.4159 ‐4.0000 37.6991 ‐4.0000 ‐37.6991 residue = 1.0000 0.0000 1.0000 ‐0.0000 2.0000 ‐0.0000 2.0000 0.0000 3.0000 0.0000 3.0000 ‐0.0000

M=‐3 VAF = 100 pole = ‐2.0000 25.1327 ‐2.0000 ‐25.1327 ‐3.0000 31.4159 ‐3.0000 ‐31.4159 ‐4.0000 37.6991 ‐4.0000 ‐37.6991 residue = 1.0000 0.0000 1.0000 ‐0.0000 2.0000 ‐0.0000 2.0000 0.0000 3.0000 0.0000 3.0000 ‐0.0000

M=‐1 VAF = 100 pole = ‐2.0000 25.1327 ‐2.0000 ‐25.1327 ‐3.0000 31.4159 ‐3.0000 ‐31.4159 ‐4.0000 37.6991 ‐4.0000 ‐37.6991 residue = 1.0000 0.0000 1.0000 ‐0.0000 2.0000 ‐0.0000 2.0000 0.0000 3.0000 0.0000 3.0000 ‐0.0000

M=2 VAF = 95.8660 pole = ‐6.3272 33.1170 ‐6.3272 ‐33.1170 residue = 6.4034 0.1868 6.4034 ‐0.1868

Table 2 : parameters for the damped exponential signal M=4 VAF = 98.7306 pole = ‐2.4068 24.1538 ‐2.4068 ‐24.1538 ‐5.7587 35.6636 ‐5.7587 ‐35.6636 residue = 0.8223 0.6629 0.8223 ‐0.6629 5.1870 ‐0.8183 5.1870 0.8183

M=6 VAF = 100 pole = ‐2.0000 25.1327 ‐2.0000 ‐25.1327 ‐3.0000 31.4159 ‐3.0000 ‐31.4159 ‐4.0000 37.6991 ‐4.0000 ‐37.6991 residue = 1.0000 0.0000 1.0000 ‐0.0000 2.0000 ‐0.0000 2.0000 0.0000 3.0000 0.0000 3.0000 ‐0.0000

M=8 VAF = 100 pole = ‐2.0000 25.100 ‐2.0000 ‐25.100 ‐3.0000 31.400 ‐3.0000 ‐31.400 ‐4.0000 37.700 ‐4.0000 ‐37.700 residue = 1.0000 0.0000 1.0000 ‐0.0000 2.0000 ‐0.0000 2.0000 0.0000 3.0000 0.0000 3.0000 ‐0.0000

M=10 VAF=100 Pole = ‐2.0000 25.100 ‐2.0000 ‐25.100 ‐3.0000 31.400 ‐3.0000 ‐31.400 ‐4.0000 37.700 ‐4.0000 ‐37.700 residue = 1.0000 0.0000 1.0000 ‐0.0000 2.0000 ‐0.0000 2.0000 0.0000 3.0000 ‐0.0000 3.0000 0.0000 21

4.2. Test Case2‐Wire Data: In case of second example of resonance based target recognition method is taken which also considers late time response from the target scattering based on singularity expansion method(SEM), the target tesonance are purely depends on the target composition and geometry not on the incident aspect angle. In the example, response from the wire (wired data) with L = 1m and the angle = 15⁰ and 75⁰ and frequency range from 4.39MHz to 9GHz with equally spaced 2048 samples in frequency domain. The data set for this wired response is given to MPM algorithm for parameter estimation. Here, the parameter extracted using Method of Moments and MPM, which is solely depends on the target geometry and dielectric properties are taken as the reference from [6] and added in the table.

M MOM o reference d e

1 2 3 4 5 6 7 8 9 1 0

MPM reference

‐0.260±j2.91 ‐0.381±j6.01 ‐0.468±j9.06 ‐0.538±j12.2 ‐0.600±j15.3 ‐0.654±j18.4 ‐0.704±j21.5 ‐0.749±j24.6 ‐0.792±j27.7 ‐0.832±j30.8

‐0.252±j2.87 ‐0.373±j5.93 ‐0.444±j9.05 ‐0.545±j12.1 ‐ ‐0.881±j17.6 ‐0.850±j21.6 ‐ ‐1.005±j28.6 ‐

MPM MPM MPM I/p m = 20 O/p M = 20 I/p m = ‐3 O/p M = 43 I/p m = ‐4 O/p M = 178 VAF = 100% VAF = 99.99% VAF = 100% Poles

Residues

Poles

Residues

Poles

Residues

‐0.2533±j2.8733 ‐0.3733±j5.9333 ‐0.4400±j9.0267 ‐0.5433±j12.110 ‐0.6200±j15.953 ‐0.6400±j18.330 ‐0.6900±j21.526 ‐ ‐0.7933±j28.510 ‐

49.64 13.37 2.044 11.63 1.278 2.804 4.647 ‐ 3.253 ‐

‐0.2533±j2.8733 ‐0.3733±j5.9333 ‐0.4267±j9.0300 ‐0.5567±j12.123 ‐0.5728±j15.217 ‐0.6320±j18.327 ‐0.6900±j21.433 ‐ ‐0.781±j27.688 ‐0.818±j30.838

49.64 13.28 2.155 11.18 1.385 2.993 4.587 ‐ 2.624 2.131

‐0.2533±j2.8733 ‐0.3700±j5.9333 ‐0.4567±j9.0067 ‐0.5267±j12.103 ‐0.5733±j15.216 ‐0.6333±j18.326 ‐0.6900±j21.433 ‐ ‐0.7817±j27.688 ‐0.8167±j30.840

49.69 13.21 2.197 11.14 1.395 2.844 4.635 ‐ 2.792 1.771

Table 3: = 15° CNR for Different M. The extraction of useful parameters are completely based on the strength of the residues and is difficult when the residue value is less or 0. The residue values are also provided in the table below in order to show the strength of the poles. The model order considered here are, M = 20, ‐3, ‐4. Most of the useful poles are aquired better in the case of M = ‐4 and reconstuction of the signal is 100% as shown below in the table(2). Residues here shows the strength of the poles. In the case of M = ‐4, number of resonant 22

poles are approximarely 178. Resonance values are obtained and compared with the verified with reference poles. The reconstruction of the signal and pole extraction is more appropriate when it is compared with the proved one. For the data at the angle 15° and 75° is provided to MPM algorithm with different M values are considered. The number of obtained poles with respect to the input order is also shown clearly. The poles for the different model order is compared and the poles obtained are mentioned. For = 15°, different M values are considered and the poles obtained are mentioned in Table 3. For = 75°, different M values are considered and the poles obtained are mentioned in Table 4.

Mode MOM reference

1 2 3 4 5 6 7 8 9 10

‐0.260±j2.91 ‐0.381±j6.01 ‐0.468±j9.06 ‐0.538±j12.2 ‐0.600±j15.3 ‐0.654±j18.4 ‐0.704±j21.5 ‐0.749±j24.6 ‐0.792±j27.7 ‐0.832±j30.8

MPM reference

MPM I/p m = 55 O/p M = 55 VAF = 99.59%

‐0.252±j2.87 ‐0.372±j5.93 ‐0.455±j9.01 ‐0.525±j12.1 ‐0.585±j15.2 ‐0.637±j18.3 ‐0.692±j21.4 ‐0.733±j24.6 ‐0.785±j27.7 ‐0.817±j30.8

MPM I/p m = ‐2 O/p M = 86 VAF = 100%

MPM I/P m = ‐3 O/p M = 579 VAF = 99.99%

Poles

Residues Poles

Residues Poles

Residues

‐0.2486±j2.8788 ‐0.3849±j5.9277 ‐0.4460±j9.0118 ‐0.5439±j12.112 ‐0.5769±j15.195 ‐0.6557±j18.340 ‐0.6953±j21.410 ‐0.7405±j24.597 ‐0.8161±j27.664 ‐0.8031±j30.869

2.394 4.434 5.467 7.053 7.395 8.509 8.739 8.984 9.792 8.679

2.450 4.254 5.675 6.719 7.639 8.193 8.758 8.978 9.225 9.234

2.441 4.236 5.655 6.732 7.633 8.164 8.846 8.779 9.324 9.123

‐0.2525±j2.8732 ‐0.3703±j5.9312 ‐0.4569±j9.0120 ‐0.5228±j12.105 ‐0.5871±j15.207 ‐0.6362±j18.317 ‐0.6919±j21.436 ‐0.7345±j24.559 ‐0.7818±j27.692 ‐0.8211±j30.832

‐0.2517±j2.8739 ‐0.3711±j5.9342 ‐0.4558±j9.0123 ‐0.5247±j12.105 ‐0.5856±j15.207 ‐0.6352±j18.315 ‐0.6963±j21.438 ‐0.7258±j24.562 ‐0.7873±j27.698 ‐0.8158±j30.833

Table 4: = 75° CNR for Different M.

Single response extraction is done with matrix Pencil Method algorithm for the data from the wire scartter. The poles obtained are corresponds to the wire target at different look direction of 15° and 75°. The response signals are processed one after one since we could use MPM which can perform single extraction. So for the simplification of this process, the trasient responses from two different look directions are being processed in MPM algorithm which handles multiple signals. The CNR extraction is more straight forward, single set CNR is obained as it is aspect independent and 2 set of residues are obtained which corresponsds to two different look directions (15° and 75°). The ectracted CNR with multiple aspect are explanined in multiple aspect extraction.

23

4.3 Breast Cancer Detection: The data from the breast volume with No tumor, 10 mm tumor and 15 mm tumor are considered. The poles are extracted for no tumor case. Response signal comprises of datas releted to 18 different aspects. Each aspect has its own 8 polarization (4 in Linear and 4 in Circular). All the response signal from 18 aspect with 8 different polarizations are processed and poles are extracted. so, 18*8=144 number of extractions are done. Dominant poles are judged by Energy Ratio (ER) and verified by using Time Frequency analysis plot. Energy ratio of each resonant mode is obtained by dividing energy level of each resonant mode by sum of energy level of all the resonant modes. Dominant poles for no tumor extraction with the energy ratio for all 18 aspects (time_transmit_receiver: time_1_1 to time_1_18) with different polarization (VV, HH, VH, HV, LL, RR, LR, RL) are tabulated below.

Time domain response

Single Extraction

Time_1_1(tvv) Time_1_1(thh) Time_1_1(thv) Time_1_1(tvh) Time_1_1(tvv) Time_1_1(tll) Time_1_1(trr) Time_1_1(tlr) Time_1_1(rl) to time_1_18()

Multiple set of CNR

Figure 4: Strategies for Single response extraction

At the end of extraction, set of CNR are obtained and It is most important to find out the most dominant poles. In our project there are two strategies are implemented to get the most domonant poles corresponds to the required target. Energy Ratio (ER) gives the information about the most dominant poles, it is defined as the enery level of each mode to the sum of energy level of all resonant modes. Mode with higher energy is the most dominant pole of the specific target and represented in percentage. 24

TF analysis is a technique that consist of both time and frequency domain simultaneously. TF plot shows the most intensive frequency component among all the modes which helps in finding the dominant CNR of the target. TF plot looks as follows,

Real part

Signal in time 0.01 0 -0.01 Linear scale

SP, Lh=16, Nf=67.5, lin. scale, imagesc, Threshold=5% 3000

Frequency [MHz]

Energy spectral density

2500 2000 1500 1000 500

15 10

-3

0

5 x 10

0.004 0.006 0.008 0.01 0.012 0.014 0.016 Time [µs]

Figure 4: TF Plot Model

From the above plot, it is very clear that the frequency of 1GHz is more intensive and also it posses higher energy among all the component. So by looking at TF plot the most dominant poles can be identified. The most dominant CNR for No tumor case for all the look directions are tabulated below with its Energy ratio. Time_1_1 Poles ‐3.272±44.306 ‐4.545±33.489 ‐4.603±54.715 ‐8.526±23.571

ER(VV) (%) 5.89 89.21 3.36 1.53

Poles ‐3.425±22.435 ‐3.085±29.99 ‐3.666±53.072 ‐4.611±42.22

ER(HH) 64.17 1.23 0.07 33.62

25

Poles ‐2.591±54.291 ‐4.501±43.719 ‐5.523±25.358 ‐4.182±35.213

ER(VH) 0.03 0.22 0.003 99.76

Poles ‐3.272±44.306 ‐4.545±33.489 ‐4.603±54.715 ‐8.526±23.571

ER(HV) 5.89 89.21 3.36 1.53

Poles ‐3.647±27.892 ‐3.868±43.381 ‐4.200±53.506

ER(LL) 2.339 96.9 0.736

Poles ‐3.652±27.88 ‐3.865±43.386 ‐4.194±53.499

ER(RR) 2.179 97.29 0.49

Poles ‐3.635±52.054 ‐3.979±32.221 ‐4.057±25.021

ER(LR) 0.03 3.7 96.2

Poles ‐3.642±53.061 ‐3.953±32.160 ‐4.057±25.021

ER(RL) 0.028 4.044 95.916

Table 5: time_1_1 dominant CNR for 8 polarizations

Time_1_2 Poles ‐3.361±44.293 ‐4.607±33.607 ‐5.620±54.090 ‐8.593±23.813

ER(VV) 4.39 90.82 2.26 2.45

26

Poles ‐3.512±28.423 ‐4.412±42.146 ‐3.646±51.527 ‐3.337±25.725

ER(HH) 11.45 9.06 0.006 79.484

Poles ‐2.581±53.895 ‐5.923±23.967 ‐4.499±43.725 ‐5.519±34.430

ER(VH) 0.03 0.85 0.003 98.76

Poles ‐3.361±44.293 ‐4.607±33.607 ‐5.620±54.090 ‐8.593±23.813

ER(HV) 4.39 90.82 2.26 2.45

Poles ‐3.561±28.02 ‐4.397±52.917 ‐3.815±43.230

ER(LL) 1.88 0.79 97.2

Poles ‐3.572±27.978 ‐4.410±52.827 ‐3.821±43.241

ER(RR) 2.44 0.78 96.75

Poles ‐3.220±51.183 ‐3.914±23.191 ‐3.627±46.936 ‐4.757±32.352

ER(LR) 0.028 91.16 3.22 5.584

Poles ‐2.632±53.706 ‐4.058±24.187 ‐4.306±31.803

ER(RL) 0.411 93.31 6.26 Table 6: time_1_2 dominant CNR for 8 polarizations 27

Time_1_3 Poles ‐2.032±53.513 ‐4.740±33.373 ‐3.640±42.983 ‐9.365±25.605

ER(VV) 0.003 5.21 0.154 94.56

Poles ‐2.181±53.209 ‐3.580±28.456 ‐4.445±41.442 ‐9.50±22.892

ER(HH) 0.823 95.625 0.982 2.36

Poles ‐2.716±54.199 ‐4.768±43.629 ‐5.820±33.706

ER(VH) 0.05 2.36 97.32

Poles ‐2.032±53.513 ‐4.740±33.373 ‐3.640±42.983 ‐9.365±25.605

ER(HV) 0.003 5.21 0.154 94.56

Poles ‐3.725±42.42 ‐3.562±28.231

ER(LL) 99.68 0.034

Poles ‐3.740±42.411 ‐3.565±28.236

ER(RR) 99.70 0.031

Poles ‐3.304±25.460 ‐3.540±54.728 ‐4.571±36.835 ‐4.955±43.524

ER(LR) 0.026 0.63 74.4 25.48

28

Poles ‐2.939±54.35 ‐3.535±35.259 ‐3.683±43.296 ‐3.872±25.52

ER(RL) 0.69 1.213 0.002 97.94


Time_1_4 Poles ‐2.136±53.663 ‐3.228±44.242 ‐4.8143±33.458 ‐9.4299±25.223

ER(VV) 0.0004 0.0001 2.56 97.43

Poles ‐7.802±22.961 ‐3.648±28.371 ‐3.291±52.143 ‐5.419±40.762

ER(HH) 0.03 98.88 1.01 0.06

Poles ‐4.854±43.155 ‐5.685±33.905 ‐6.102±26.803 ‐5.112±53.555

ER(VH) 0.03 99.87 0.124 0.001

Poles ‐2.136±53.663 ‐3.228±44.242 ‐4.8143±33.458 ‐9.4299±27.223

ER(HV) 0.0004 0.0001 2.56 97.43

Poles ‐2.740±53.172 ‐4.721±40.886 ‐4.346±27.495

ER(LL) 1.36 0.06 98.57

29

Poles ‐2.748±53.150 ‐4.696±40.482 ‐4.377±27.465

ER(RR) 1.29 0.08 98.33

Poles ‐3.212±27.751 ‐4.586±41.931 ‐2.632±54.11 ‐4.881±33.001

ER(LR) 0.21 0.004 1.217 98.54

Poles ER(RL) ‐2.550±53.83 0.82 ‐3.887±28.294 96.53 ‐4.062±43.054 0.02 ‐4.986±32.992 2.34 Table 8: time_1_4 dominant CNR for 8 polarizations Time_1_5 Poles ‐2.330±53.379 ‐3.298±44.045 ‐4.841±33.134 ‐8.256±24.162

ER(VV) 0.003 0.0013 0.198 99.79

Poles ‐3.591±28.415 ‐4.337±51.917 ‐7.1593±40.368

ER(HH) 99.86 0.13 0.013

Poles ‐4.268±24.402 ‐2.576±54.125 ‐4.842±42.017 ‐5.328±33.055

ER(VH) 96.23 0.001 2.03 1.20

30

Poles ‐2.330±53.379 ‐3.298±44.045 ‐4.841±33.134 ‐8.256±24.162

ER(HV) 0.003 0.0013 0.198 99.79

Poles ‐2.590±52.291 ‐3.822±28.500 ‐5.065±43.428

ER(LL) 0.002 3.736 96.26

Poles ‐2.594±52.31 ‐3.819±28.501 ‐5.069±43.423

ER(RR) 0.003 3.600 96.27

Poles ‐3.852±26.211 ‐4.685±34.158

ER(LR) 1.43 98.54

Poles ‐2.550±53.83 ‐3.887±28.294 ‐4.062±43.054 ‐4.986±32.992

ER(RL) 0.08 2.10 0.09 97.41 Table 9: time_1_5 dominant CNR for 8 polarizations

31

Time_1_6 Poles ‐2.699±43.194 ‐4.751±53.67 ‐9.2822±34.201

ER(VV) 0.025 0.06 99.91

Poles ‐2.918±28.488 ‐7.085±42.564

ER(HH) 99.23 0.74

Poles ‐2.430±54.331 ‐2.829±41.186 ‐4.382±34.844 ‐5.112±22.312

ER(VH) 0.0001 0.01 92.52 7.477

Poles ‐2.699±43.194 ‐4.751±53.67 ‐9.2822±34.201

ER(HV) 0.025 0.06 99.91

Poles ‐4.361±27.949 ‐5.266±43.284 ‐7.745±52.144

ER(LL) 99.664 0.3356 0.0001

Poles ‐4.360±27.956 ‐5.28±43.272 ‐7.669±52.163

ER(RR) 99.791 0.27 0.0001

Poles ‐2.610±34.207 ‐3.632±28.26

ER(LR) 99.97 0.02

32

Poles ‐1.549±42.77 ‐3.88±28.66 ‐2.715±35.07

ER(RL) 98.396 0.33 1.09


Time_1_7 Poles ‐2.935±51.326 ‐3.251±40.471 ‐6.281±34.171

ER(VV) 0.0001 0.298 99.57

Poles ‐2.067±52.837 ‐4.104±28.553 ‐5.571±41.890

ER(HH) 0.0001 98.56 1.32

Poles ‐2.698±42.801 ‐5.687±52.830 ‐5.815±30.132

ER(VH) 1.23 0.009 98.23

Poles ‐2.935±51.326 ‐3.251±40.471 ‐6.281±34.171

ER(HV) 0.0001 0.298 99.57

Poles ‐4.525±53.587 ‐3.310±29.296 ‐4.627±42.511

ER(LL) 0.0002 99.90 0.01

Poles ‐4.389±52.981 ‐3.299±29.593 ‐4.587±43.256

ER(RR) 0.0001 99.88 0.02

33

Poles ‐2.317±43.067 ‐3.656±32.828

ER(LR) 0.12 99.879

Poles ER(RL) ‐1.135±52.317 0.41 ‐3.366±42.401 7.99 ‐2.994±37.492 91.52 ‐3.936±28.634 0.01 Table 11: time_1_7 dominant CNR for 8 polarizations Time_1_8 Poles ‐5.341±33.557 ‐5.576±42.889 ‐5.477±58.581

ER(VV) 93.43 6.56 0.0002

Poles ‐4.321±28.575 ‐5.373±40.783 ‐4.554±52.259

ER(HH) 98.19 1.726 0.077

Poles ‐2.568±54.304 ‐2.430±43.250 ‐5.053±35.158 ‐5.143±22.453

ER(VH) 0.001 0.29 56.02 43.66

Poles ‐5.341±33.557 ‐5.576±42.889 ‐5.477±58.581

ER(HV) 93.43 6.56 0.0002

Poles ‐2.994±29.184 ‐5.1062±41.95 ‐5.956±53.994

ER(LL) 99.02 0.91 0.0002

34

Poles ‐3.045±29.296 ‐5.141±41.932 ‐5.821±54.121

ER(RR) 99.04 0.87 0.0002

Poles ‐3.799±29.434 ‐4.298±42.200

ER(LR) 99.498 0.5

Poles ER(RL) ‐2.205±32.257 97.96 ‐2.803±53.219 1.34 ‐3.035±42.966 0.52 Table 12: time_1_8 dominant CNR for 8 polarizations Time_1_9 Poles ‐3.272±56.127 ‐4.026±43.915 ‐5.392±33.064

ER(VV) 0.012 9.60 90.25

Poles ‐4.434±28.441 ‐5.396±40.562 ‐5.614±55.101

ER(HH) 99.78 0.21 0.005

Poles ‐2.530±43.874 ‐3.080±54.513 ‐4.672±22.957 ‐4.821±35.894

ER(VH) 0.03 0.001 59.39 40.59

Poles ‐3.272±56.127 ‐4.026±43.915 ‐5.392±33.064

ER(HV) 0.012 9.60 90.25

35

Poles ‐‐4.789±55.562 ‐4.526±43.714 ‐4.992±29.282

ER(LL) 0.01 19.99 79.99

Poles ‐4.882±55.591 ‐4.426±43.158 ‐4.725±29.782

ER(RR) 0.009 20.32 79.54

Poles ‐3.811±29.294 ‐3.940±42.755

ER(LR) 99.87 0.098

Poles ‐2.871±53.752 ‐3.120±43.478 ‐3.949±29.350

ER(RL) 0.09 2.02 97.85


Time_1_10 Poles ‐2.796±54.666 ‐3.999±43.954 ‐5.280±33.088

ER(VV) 0.23 16.78 82.99

Poles ‐3.161±54.577 ‐4.437±28.531 ‐5.705±43.497

ER(HH) 0.0038 95.61 4.38

Poles ‐2.530±43.874 ‐3.080±54.513 ‐4.672±23.994 ‐5.213±34.213

ER(VH) 0.32 0.002 2.63 97.53

36

Poles ‐2.796±54.666 ‐3.999±43.954 ‐5.280±33.088

ER(HV) 0.23 16.78 82.99

Poles ‐4.105±54.694 ‐4.268±44.086 ‐4.953±29.051

ER(LL) 0.39 18.09 81.45

Poles ‐4.113±54.698 ‐4.589±44.254 ‐5.012±29.531

ER(RR) 0.4 18.52 81.01

Poles ‐3.349±43.137 ‐3.896±29.308

ER(LR) 1.194 98.532

Poles ‐3.040±43.135 ‐3.896±29.306

ER(RL) 2.89 97.02


Time_1_11 Poles ‐3.275±56.134 ‐4.026±43.915 ‐5.329±33.064

ER(VV) 0.26 16.71 83.02

Poles ‐4.434±28.44 ‐5.396±40.563 ‐5.611±55.099

ER(HH) 97.78 2.213 0.005

37

Poles ‐2.531±43.878 ‐3.095±52.521 ‐4.622±21.121 ‐4.832±35.912

ER(VH) 1.23 0.01 60.78 38.02

Poles ‐3.275±56.134 ‐4.026±43.915 ‐5.329±33.064

ER(HV) 0.26 16.71 83.02

Poles ‐2.542±52.030 ‐4.958±43.704 ‐3.089±29.297

ER(LL) 0.41 18.98 80.45

Poles ‐2.567±30.084 ‐4.789±55.49 ‐4.723±43.753

ER(RR) 0.48 19.49 79.99

Poles ‐2.874±53.760 ‐3.122±43.482 ‐3.950±29.359

ER(LR) 1.001 0.89 97.76

Poles ER(RL) ‐3.937±42.758 1.12 ‐3.812±29.290 98.86 Table 15: time_1_11 dominant CNR for 8 polarizations Time_1_12 Poles ‐5.343±33.556 ‐5.572±42.881 ‐5.461±51.571

ER(VV) 88.89 9.98 1.15

38

Poles ‐4.322±28.573 ‐5.371±40.785 ‐4.553±55.250

ER(HH) 98.38 1.58 0.0001

Poles ‐2.567±54.309 ‐2.4316±43.241 ‐5.048±35.150

ER(VH) 0.002 56.46 43.53

Poles ‐5.343±33.556 ‐5.572±42.881 ‐5.461±51.571

ER(HV) 88.89 9.98 1.15

Poles ‐3.018±29.27 ‐5.143±41.92 ‐5.569±53.994

ER(LL) 98.67 1.22 0.001

Poles ‐2.997±29.210 ‐5.124±41.961 ‐5.463±53.874

ER(RR) 99.02 0.92 0.001

Poles ‐2.801±53.21 ‐3.038±42.96 ‐4.844±35.488

ER(LR) 1.99 3.02 94.968

Poles ER(RL) ‐3.806±30.431 99.51 ‐4.268±42.180 0.49 Table 16: time_1_12 dominant CNR for 8 polarizations 39

Time_1_13 Poles ‐3.247±40.474 ‐6.278±34.166

ER(VV) 0.35 99.56

Poles ‐2.076±52.827 ‐4.102±28.551 ‐5.574±41.888

ER(HH) 0.0002 99.65 0.24

Poles ‐2.698±42.798 ‐5.699±52.806 ‐5.983±35.977

ER(VH) 9.3 0.03 90.23

Poles ‐3.247±40.474 ‐6.278±34.166

ER(HV) 0.35 99.56

Poles ‐4.531±53.586 ‐3.321±29.288 ‐4.615±42.522

ER(LL) 0.0001 99.64 0.29

Poles ‐3.329±29.292 ‐4.721±42.991 ‐4.951±52.785

ER(RR) 99.82 0.17 0.0001

Poles ‐1.152±52.334 ‐5.988±25.492 ‐3.374±42.397 ‐3.934±32.641

ER(LR) 0.42 0.29 89.12 9.06

40

Poles ‐3.408±33.135 ‐2.311±43.073

ER(RL) 93.25 6.67


Time_1_14 Poles ‐2.701±43.194 ‐4.749±55.679 ‐5.296±34.192

ER(VV) 1.005 0.05 98.75

Poles ‐3.917±28.488 ‐5.080±42.565

ER(HH) 97.89 2.10

Poles ‐2.430±54.340 ‐2.837±41.182 ‐4.387±34.829

ER(VH) 0.05 92.76 7.23

Poles ‐2.701±43.194 ‐4.749±55.679 ‐5.296±34.192

ER(HV) 1.005 0.05 98.75

Poles ‐4.362±27.952 ‐5.288±43.288 ‐5.689±52.100

ER(LL) 99.69 0.21 0.0002

Poles ‐4.372±27.949 ‐5.381±43.279 ‐5.221±52.186

ER(RR) 99.71 0.17 0.0001

41

Poles ‐2.531±42.689 ‐3.895±28.64 ‐4.212±36.285

ER(LR) 0.097 1.90 97.99

Poles ER(RL) ‐3.577±33.574 99.89 ‐2.61±44.187 0.0001 ‐3.627±28.26 0.002 Table 18: time_1_14 dominant CNR for 8 polarizations Time_1_15 Poles ‐2.288±53.368 ‐3.273±44.10 ‐4.839±33.065 ‐7.238±23.920

ER(VV) 0.36 0.002 3.99 95.65

Poles ‐3.591±28.418 ‐4.332±51.92 ‐5.079±40.371

ER(HH) 99.85 0.003 0.14

Poles ‐2.576±54.126 ‐4.845±42.016 ‐5.333±33.043 ‐5.053±23.125

ER(VH) 0.02 1.03 98.99 0.001

Poles ‐2.288±53.368 ‐3.273±44.10 ‐4.839±33.065 ‐7.238±23.920

ER(HV) 0.36 0.002 3.99 95.65

Poles ‐2.596±52.328 ‐3.818±28.501 ‐3.915±43.421

ER(LL) 0.01 97.06 2.93

42

Poles ‐2.583±52.307 ‐3.820±28.499 ‐3.992±43.582

ER(RR) 0.04 96.35 3.61

Poles ‐2.551±53.828 ‐3.891±28.291 ‐4.048±46.050 ‐4.893±37.523

ER(LR) 0.02 1.01 0.25 98.53

Poles ER(RL) ‐2.125±35.603 99.72 ‐3.206±27.151 0.04 Table 19: time_1_15 dominant CNR for 8 polarizations Time_1_16 Poles ‐2.145±53.684 ‐3.294±44.226 ‐4.820±33.460 ‐7.289±27.531

ER(VV) 0.64 0.0002 2.89 96.26

Poles ‐3.799±45.946 ‐3.648±28.367 ‐3.288±52.143 ‐5.422±23.562

ER(HH) 0.85 96.89 1.96 0.14

Poles ‐4.859±43.158 ‐5.704±33.897 ‐5.986±52.846 ‐5.987±24.856

ER(VH) 0.001 99.98 0.002 0.001

Poles ‐2.145±53.684 ‐3.294±44.226 ‐4.820±33.460 ‐7.289±27.531

ER(HV) 0.64 0.0002 2.89 96.26

43

Poles ‐2.749±53.149 ‐4.365±27.467 ‐2.292±43.153

ER(LL) 1.125 97.34 0.24

Poles ‐2.755±53.165 ‐4.335±27.506 ‐4.745±43.903

ER(RR) 1.90 98.008 0.17

Poles ‐3.3524±54.795 ‐3.7135±24.915 ‐4.325±34.523 ‐3.953±42.625

ER(LR) 0.06 98.88 1.01 0.03


ER(VV) 1.652 0.192 8.98 89.17

Poles ‐4.928±21.325 ‐2.175±53.206 ‐4.445±41.442 ‐3.580±28.454 Poles ‐2.715±54.21 ‐4.751±43.632 ‐5.820±33.757 ‐5.923±26.262

ER(HH) 8.03 0.124 0.208 91.619 ER(VH) 0.02 1.23 97.01 1.03

44

Poles ‐2.021±53.501 ‐3.662±42.984 ‐4.74±33.37 ‐6.846±25.359

ER(HV) 1.652 0.192 8.98 89.17

Poles ‐3.743±42.422 ‐4.183±33.107

ER(LL) 3.22 96.69

Poles ‐3.745±42.433 ‐3.559±32.230

ER(RR) 2.31 97.68

Poles ‐2.926±54.371 ‐3.582±43.278 ‐3.555±28.252 ‐3.981±37.125

ER(LR) 0.12 0.03 97.85 1.894


ER(VV) 6.89 88.21 3.36 1.53

Poles ‐3.513±28.428 ‐4.413±42.148 ‐3.638±51.230 ‐4.328±25.716

ER(HH) 11.43 9.24 0.006 79.254

45

Poles ‐2.583±53.886 ‐4.487±43.713 ‐5.542±25.702 ‐5.543±34.373

ER(VH) 0.006 2.03 0.03 97.21

Poles ‐3.356±44.289 ‐4.609±33.605 ‐5.638±54.086 ‐9.254±26.317

ER(HV) 6.89 88.21 3.36 1.53

Poles ‐2.855±55.469 ‐3.822±43.241 ‐3.372±28.002

ER(LL) 0.339 96.9 2.36

Poles ‐3.819±43.233 ‐3.569±27.999 ‐2.998±54.891

ER(RR) 96.61 2.55 0.394

Poles ‐2.633±53.708 ‐4.295±31.732 ‐3.171±43.621 ‐4.077±28.206

ER(LR) 94.00 0.027 5.62 0.365

Poles ER(RL) ‐3.216±55.189 91.31 ‐3.609±46.905 3.47 ‐4.668±32.381 0.041 ‐3.922±28.156 5.167 Table 22: time_1_18 dominant CNR for 8 polarizations From the above tables, the most dominant poles obtained but it is time consuming process. So it is preferrable to do multiple extraction with MPM algorithm which handles multiple signals.

46

4.4 Multiple aspect extraction: The CNR extracted with single transient are time consuming process. So the extraction can be done by utilizing multiple signals at once through MPM algorithm. For test case of 1m wire, the response from the two aspect 15° and 75° are processed through the Matrix pencil method and poles extraction is made. The major advantage with this method is time consumption. The extracted single set of CNRand residues for 15° and 75° are tabulated below, MOM reference MPM reference

MPM

MPM (15°)

MPM(75°)

(m = ‐2 & M = 55)

Residues (A1)

Residues(A2)

Poles (VAF=100%) ‐0.260±j2.91

‐0.252±j2.87

‐0.2486±j2.8788

49.64

2.394

‐0.381±j6.01

‐0.373±j5.93

‐0.3849±j5.9277

13.28

4.434

‐0.468±j9.06

‐0.444±j9.05

‐0.4460±j9.0118

2.155

5.467

‐0.538±j12.2

‐0.545±j12.1

‐0.5439±j12.112

11.18

7.053

‐0.600±j15.3

‐

‐0.5769±j15.195

1.385

7.395

‐0.654±j18.4

‐0.881±j17.6

‐0.6557±j18.340

2.993

8.509

‐0.704±j21.5

‐0.850±j21.6

‐0.6953±j21.410

4.587

8.739

‐0.749±j24.6

‐

‐0.7405±j24.597 3.629

8.984

‐0.792±j27.7

‐1.005±j28.6

‐0.8161±j27.664

2.624

9.792

‐0.832±j30.8

‐

‐0.8031±j30.869 2.131

8.679

Table 23: CNR WITH Multiple aspect (wire)

Multiple aspect extraction leads to better extraction of CNR when compared with single response extraction. When 15° aspect was under extraction, some poles are not excited and missed. But when utilising two aspect, the chances of getting poles related to target increases. Multiple extraction helps in better pole extraction and target identification.

4.5 Multiple extraction for breast volume: The response data from the breast volume has 18 aspects with 8 different polarization. The possibilities of poles extraction can be done in two ways, Multiple aspect (18 look direction with 8 polarizations 47

each) and polarimetric data (4 linear and 4 circular polarization for all the 18 aspects). Poles extraction with multiple aspect and polarimetric datas are tabulated below,

Time domain response

Single Extraction

Extraction with multiple signals

Multiple Aspect

Polarimetric

Time_1_1(tvv) Time_1_1(thh) Time_1_1(thv) Time_1_1(tvh) Time_1_1(tvv) Time_1_1(tll) Time_1_1(trr) Time_1_1(tlr) Time_1_1(rl)‐ time_1_18()

Tvv(time_1_1‐..) Thh(time_1_1‐..) Tvh(time_1_1‐..) Thv(time_1_1‐..) Tll(time_1_1‐..) Trr(time_1_1‐..) Tlr(time_1_1‐..)

Time_1_1(tvv,tvh,thh,t hv) Time_1_1(tll,trr,tlr,trl) ...... time_1_18(tvv,tvh,thh ,thv) time_1_18(tll,trr,tlr,trl )

Multiple set of CNR

Single set of CNR

Single set of CNR

Fig5: Various ways of CNR extraction [11]

4.6 Multiple Aspect Extraction for breast tumor detection: Poles are extracted using Multiple aspect for data time_1_1 of No tumor case are tabulated below,

48

Time_1, TLR Poles ‐2.764±54.105 ‐3.825±24.533 ‐4.414±45.427 ‐5.104±33.746

ER 0.04 97.99 0.0001 1.88

ER 0.0001 94.36 2.045 3.574

ER 0.05 0.034 22.23 77.85

ER 1.36 0.29 0.001 98.36

ER 0.0001 1.39 0.0001 98.57

ER 0.0001 0.03 0.0001 99.98

ER 0.0001 0.0000 0.15 99.86

ER 0.0001 99.48 0.49 0.0001

ER 0.0001 99.87 0.089 0.0001

ER 0.0001 98.54 1.18 0.0001

ER 1.003 97.85 0.88 0.0001

ER ER ER ER ER 1.89 0.39 0.0001 0.02 0.059 0.0001 0.3 1.99 1.0 98.78 2.99 89.35 0.08 0.3 0.03 94.968 8.99 97.53 98.51 1.00 Table 24: CNR of 18 aspect with Polarization LR

ER 0.12 97.82 0.03 1.89

ER 0.32 94.06 5.33 0.03

Time_1,TRL Poles ‐2.75±54.096 ‐3.872±24.52 ‐4.4023±45.43 ‐5.128±33.76

ER 0.03 95.62 0.0001 3.99

ER 0.39 94.00 0.0001 6.25

ER 0.7 97.53 0.002 1.24

ER 0.79 96.52 0.02 2.33

ER 0.08 2.1 0.07 97.39

ER 0.0001 0.32 98.39 1.09

ER 0.39 0.01 7.89 91.56

ER 1.29 0.0001 0.53 97.93

ER 0.09 97.86 2.00 0.0001

ER 0.0001 98.22 1.69 0.0001

ER 0.00012 97.66 2.35 0.0001

ER ER ER ER ER 0.0001 0.0001 0.0001 0.0001 1.78 0.0001 0.0001 0.003 0.03 0.04 0.5 5.37 0.0001 0.0001 0.16 99.38 94.55 99.89 99.75 97.896 Table 25: CNR of 18 aspect with Polarization RL

ER 3.25 1.83 4.98 89.73

ER 93.31 3.16 2.47 0.04

Time_1,TLL Poles ‐3.827 ±30.285 ‐3.865 ±53.399 ‐4.4727±43.082

ER 1.36 0.83 97.62

ER 0.88 0.65 98.01

ER 0.04 0.0001 99.69

ER 97.47 2.46 0.06

ER 1.52 0.002 98.45

ER 99.66 0.0001 0.34

ER 99.90 0.0002 0.01

ER 99.18 0.0002 0.75

ER 78.79 0.01 20.65

ER 83.39 0.45 16.10

ER 82.45 0.39 16.98

ER ER ER ER ER 97.55 99.62 98.64 98.26 97.34 0.001 0.0001 0.0002 0.01 1.125 2.34 0.3 1.26 1.73 0.24 Table 26: CNR of 18 aspect with Polarization LL

ER 97.69 0.0001 2.22

ER 2.36 0.33 96.9

49

Time_1,TRR Poles ‐3.828 ±30.275 ‐3.864 ±53.399 ‐4.4728±43.081

ER 2.36 0.73 98.62

ER 3.44 0.86 95.75

ER 0.04 0.0001 99.82

ER 98.47 1.46 0.08

ER 2.59 0.002 97.27

ER 99.70 0.0001 0.28

ER 99.91 0.0002 0.01

ER 99.09 0.0002 0.65

ER 77.79 0.01 21.65

ER 82.41 0.25 17.10

ER 0.04 19.49 79.77

ER ER ER ER ER 99.35 99.52 96.64 97.26 98.34 0.001 0.0001 0.0002 0.03 1.74 0.45 0.39 3.26 2.73 0.19 Table 27: CNR of 18 aspect with Polarization RR

ER 97.71 0.0001 2.39

ER 2.22 0.19 97.12

Time_1_x (x = 1 to 18),TVV Poles ‐3.338±43.8823 ‐4.501±33.2407 ‐2.855±53.4440 ‐6.521±23.1334 ER 14.69 84.99 0.23 0.0001

ER 4.79 91.41 2.81 0.98

ER 15.71 84.02 0.26 0.0001

ER 5.14 91.57 1.51 1.7

ER 0.20 6.21 0.029 93.56

ER 0.0001 1.76 0.0005 98.23

ER 0.0013 1.178 0.003 98.89

ER 0.035 99.89 0.08 0.0001

ER 0.502 99.35 0.0001 0.0001

ER ER ER ER ER 10.02 0.44 2.12 0.002 0.0002 87.77 99.46 97.75 3.79 1.89 1.20 0.0001 0.05 0.66 0.64 0.0001 0.0001 0.0001 95.55 97.26 Table 28: CNR of 18 aspect with Polarization VV

ER 7.36 92.62 0.0004 0.0001

ER 0.189 9.98 1.552 88.24

ER 9.32 90.42 0.010 0.0001

ER 5.77 88.32 3.36 1.53

Time_1,THH Poles ‐3.683±29.992 ‐3.692±42.001 ‐3.718±52.953 ‐5.444±25.195

ER 1.23 33.62 0.79 64.17

ER 11.56 9.822 0.143 78.46

ER 95.05 0.958 1.235 2.56

ER 97.75 0.06 2.12 0.03

ER 99.34 0.0125 0.413 0.0001

ER 98.90 1.01 0.0001 0.0001

ER 97.48 2.368 0.008 0.0001

ER 98.86 1.09 0.07 0.0001

ER 99.339 0.12 0.002 0.0001

ER 96.88 3.04 0.0059 0.0001

ER 96.34 2.97 0.659 0.0001

ER ER ER ER ER 98.86 98.48 96.90 98.358 97.254 1.02 1.375 1.582 1.118 0.2242 0.003 0.0660 0.0001 0.412 1.390 0.0001 0.0001 0.0001 0.0001 0.1300 Table 29: CNR of 18 aspect with Polarization HH

ER 94.016 0.267 0.004 5.71

ER 15.565 5.812 0.143 78.478 50

Time_1,TVH Poles ‐2.655±33.219 ‐4.084±44.308 ‐4.705±52.647 ‐6.245±22.442

ER 99.43 0.321 0.006 0.0016

ER 98.96 0.005 0.02 0.65

ER 98.91 2.20 0.04 0.0003

ER 99.75 0.6 0.004 0.160

ER 2.05 3.012 0.001 94.56

ER 91.98 0.014 0.0002 7.322

ER 98.04 1.42 0.009 0.045

ER 55.98 0.18 0.0002 43.98

ER 38.112 0.0332 0.0001 62.56

ER 96.96 0.0506 0.0002 3.02

ER 40.23 0.99 0.0003 58.23

ER ER ER ER ER 42.66 89.56 5.96 4.01 95.883 56.46 10.02 93.55 0.004 3.74 0.0002 0.045 0.0003 0.0001 0.205 0.0001 0.046 0.0001 95.65 0.163 Table 30: CNR of 18 aspect with Polarization VH

ER 99.90 0.0804 0.0002 0.0001

ER 99.96 0.035 0.0002 0.0001

Time_1,THV Poles ‐3.338±43.8823 ‐4.501±33.2407 ‐2.855±53.4440 ‐6.521±23.1334

ER 4.79 91.41 2.81 0.98

ER 5.14 91.57 1.51 1.7

ER 0.20 6.21 0.029 93.56

ER 0.0001 1.76 0.0005 98.23

ER 0.0013 1.178 0.003 98.89

ER 0.035 99.89 0.08 0.0001

ER 0.502 99.35 0.0001 0.0001

ER 7.36 92.62 0.0004 0.001

ER 9.32 90.42 0.010 0.0001

ER 14.69 84.99 0.23 0.0001

ER 15.71 84.02 0.26 0.0001

ER ER ER ER ER 10.02 0.44 2.12 0.002 0.0002 87.77 99.46 97.75 3.79 1.89 1.20 0.0001 0.05 0.66 0.64 0.001 0.0001 0.0001 95.55 97.26 Table 31: CNR of 18 aspect with Polarization HV

ER 0.189 9.98 1.552 88.24

ER 5.77 88.32 3.36 1.53

4.7 Polarimetric data The poles are extracted for all aspect with particular polarization, when extracting the poles with particular polarization there is possibility of missing dominant poles so it is necessary to extract for all polarization in linear or circular. Poles extracted with polarimetric data for (time_1_1 to time_1_18 for 4 linear and 4 circular polarizations) are tabulated below,

51

4.7.a Linear polarization for 18 aspects.(VV,HH,VH,HV) Time_1_1 Poles ‐2.433±54.888 ‐4.108 ±42.51 ‐4.6003±33.53 ‐3.8475±27.96

ER 1.64 5.16 90.43 1.02

ER 0.75 33.92 1.22 63.17

ER 1.06 0.231 98.76 0.001

ER 1.98 5.01 89.99 1.67

ER 1.7 90.5 5.63 1.80

ER 79.07 12.56 8.96 0.14

ER 0.01 98.96 1.03 0.0001

ER 1.7 90.5 5.14 2.51

ER 0.02 92.26 6.21 1.34

ER 2.23 2.56 93.05 0.958

ER 0.05 0.0001 97.85 1.95

ER 1.02 91.56 6.21 1.20

Poles ‐4.312 ±42.38 ‐5.121±32.78 ‐2.323±53.25 ‐3.876 ±28.18

ER 0.0001 3.76 0.0005 96.23

ER 0.06 95.45 2.12 1.03

ER 0.02 98.25 0.924 0.001

Time_1_5 Poles ‐4.231±43.66 ‐4.323±33.255 ‐2.416±54.267 ‐3.632±28.443

ER 0.0013 1.178 1.003 97.89

ER 0.0125 95.34 1.417 1.0001

Time_1_2 Poles ‐3.889±28.021 ‐4.797 ±33.488 ‐4.242±42.618 ‐2.559 ±54.077

Time_1_3 Poles ‐2.278±54.19 ‐3.871 ±28.158 ‐4.538±33.707 ‐4.985±42.035

Time_1_4

ER 0.244 1.30 0.07 97.56

ER 0.0001 3.76 0.0005 95.23

ER 0.0013 1.178 2.003 96.89

52

Time_1_6 Poles ‐3.156 ±42.089 ‐4.223±35.319 ‐2.445±54.86 ‐3.722±28.332

Time_1_7 Poles ‐3.831±43.431 ‐3.510 ±33.898 ‐3.306±54.61 ‐3.767±28.686 Time_1_8 Poles ‐3.742 ±44.19 ‐3.221±33.59 ‐2.964±54.23 ‐3.751±28.90

Time_1_9 Poles ‐4.120 ±44.498 ‐4.902±33.050 ‐3.545±54.732 ‐4.130±29.108

Time_1_10 Poles ‐4.1307±45.52 ‐5.3651±32.55 ‐4.117±55.256 ‐4.485±29.188 Time_1_1 1 Poles ‐4.102±44.48 ‐5.105±33.08 ‐3.553±54.735 ‐4.131±29.108

ER 0.035 98.89 1.08 0.001

ER 2.56 0.0001 1.0001 95.90

ER 0.01 92.62 0.0038 6.88

ER 0.035 97.89 1.08 0.001

ER 1.502 97.35 0.0001 0.0001

ER 2.36 97.48 0.0008 0.0002

ER 1.03 97.25 0.08 1.25

ER 0.502 99.35 0.0001 0.0001

ER 7.36 92.62 0.0004 0.0001

ER 1.09 97.86 1.07 0.0001

ER 1.56 64.36 0.05 33.88

ER 9.32 90.42 0.010 0.001

ER 0.12 99.33 0.0002 0.0001

ER 2.36 83.64 0.075 13.96

ER 9.32 90.42 0.010 0.0001

ER 10.69 87.99 1.23 0.0001

ER 3.04 95.88 1.005 0.0001

ER 1.38 95.66 0.09 2.89

ER 14.03 84.12 0.23 0.0001

ER 15.71 83.02 0.26 0.0001

ER 2.97 95.34 1.659 0.0001

ER 1.56 42.56 0.06 56.05

ER 15.71 84.02 0.26 0.0001

ER 8.36 91.62 0.0004 0.0001

53

Time_1_12 Poles ‐3.815±44.246 ‐5.441±33.66 ‐3.013±54.271 ‐3.749±28.902

ER 10.02 87.77 1.20 0.0001

ER 1.02 98.86 0.003 0.0001

ER 33.59 65.26 0.12 0.0114

ER 10.02 86.77 2.20 0.0001

Time_1_13 Poles ‐3.817±43.42 ‐3.51±33.590 ‐3.29±54.192 ‐3.758±28.688

ER 2.44 97.46 0.0001 0.0001

ER 1.37 98.04 0.06 0.0001

ER 0.3 92.36 0.07 6.89

ER 2.44 97.46 0.0001 0.0001

ER 2.12 97.43 0.05 0.0001

ER 1.58 96.90 0.0001 0.0001

ER 87.76 12.212 0.0238 0.0001

ER 2.12 97.75 0.05 0.0001

ER 0.002 3.79 0.66 95.02

ER 1.118 98.35 0.412 0.0001

ER 0.023 4.59 0.177 94.62

ER 0.002 3.79 0.66 95.03

ER 0.0002 2.89 1.64 95.26

ER 0.22 97.25 1.39 0.13

ER 0.02 99.63 0.0004 0.001

ER 0.0002 1.89 0.64 96.26

ER 0.189 9.98 1.552 88.24

ER 0.26 94.06 0.004 5.71

Time_1_14 Poles ‐3.155±42.101 ‐4.238±36.142 ‐2.368±54.87 ‐3.706±28.33 Time_1_15 Poles ‐4.126±43.595 ‐5.238±35.236 ‐2.1961±54.194 ‐3.635±28.45

Time_1_16 Poles ‐4.982±42.395 ‐5.123±32.838 ‐2.305±53.291 ‐3.871 ±28.176 Time_1_17 Poles ‐5.096±41.994 ‐4.478±33.881 ‐2.101±54.138 ‐3.869±28.155

ER 2.23 96.98 0.0032 0.014

ER 1.189 9.98 1.552 87.24

54

Time_1_18 Poles ‐4.368±42.32 ‐4.568±33.66 ‐2.552±54.149 ‐3.8908±28.008

ER ER ER ER 5.77 5.81 0.03 5.77 88.01 15.565 98.89 87.32 3.08 0.143 0.0898 4.36 2.53 78.47 0.0534 1.53 Table 32: CNR extraction with Linear polarizations

4.7.b Circular polarization (LL, RR, LR, RL) Time_1_1 Poles ‐3.7424±26.084 ‐2.621±53.958 ‐3.720±42.56 ‐4.146±35.463 Time_1_2 Poles ‐3.749±28.244 ‐2.037±53.964 ‐4.160±42.234 ‐4.146±35.463 Time_1_3 Poles ‐3.733±28.144 ‐2.793±54.573 ‐4.620±42.828 ‐4.146±35.463 Time_1_4 Poles ‐3.778±28.204 ‐2.797±53.108 ‐4.586±41.931 ‐4.146±35.463 Time_1_5 Poles ‐3.723±28.403 ‐2.894±54.55 ‐4.028±43.751 ‐4.146±35.463

ER 1.36 1.83 96.62 0.0001

ER 0.36 1.05 98.62 0.0001

ER 97.99 0.04 0.0001 1.88

ER 95.62 0.03 0.0001 3.99

ER 0.88 0.65 98.01 0.0001

ER 3.44 0.86 95.05 0.0001

ER 94.36 0.0001 2.045 1.574

ER 92.00 0.39 0.0001 6.25

ER 0.04 0.0001 99.43 0.0001

ER 0.04 0.0001 98.82 0.0001

ER 0.034 0.05 22.23 77.85

ER 96.53 1.7 0.002 1.24

ER 96.47 2.46 0.32 0.0001

ER 98.02 1.24 0.08 0.0001

ER 0.29 1.36 0.001 97.36

ER 96.52 0.12 0.02 2.33

ER 1.52 0.002 97.45 0.0001

ER 2.59 0.002 96.27 0.0001

ER 1.39 0.0001 0.0001 98.57

ER 2.1 0.08 0.07 96.39 55




ER 99.66 0.0001 0.34 0.0001

ER 99.70 0.0001 0.28 0.0001

ER 0.03 0.0001 0.0001 99.98

ER 0.32 0.0001 98.39 1.09

ER 99.90 0.0002 0.01 0.0001

ER 99.91 0.0002 0.01 0.0001

ER 0.0001 0.0001 0.15 99.86

ER 0.01 0.39 7.89 91.56

ER 99.18 0.0002 0.75 0.0001

ER 99.09 0.0002 0.65 0.0001

ER 99.48 0.0001 0.49 0.0001

ER 0.0001 1.29 0.53 97.93

ER 78.79 0.01 20.65 0.0001

ER 77.79 0.01 21.65 0.0001

ER 99.87 0.0001 0.089 0.0001

ER 97.86 0.09 2.00 0.0001

ER 83.39 0.45 16.10 0.0001

ER 82.41 0.25 17.10 0.0001

ER 98.54 0.0001 1.18 0.0001

ER 98.22 0.0001 1.69 0.0001

ER 82.45 0.39 16.98 0.0001

ER 0.04 19.49 79.77 0.0001

ER 97.85 1.003 0.88 0.0001

ER 97.66 0.0001 2.35 0.0001 56

Time_1_12 Poles ‐4.065±28.88 ‐4.570±53.66 ‐3.813±42.93 ‐5.329±32.25

ER 97.55 0.001 2.34 0.0001

ER 99.35 0.001 0.45 0.0001

ER 0.0001 1.89 2.99 94.968

ER 0.0001 0.0001 0.5 99.38

ER 99.62 0.0001 0.3 0.0001

ER 99.52 0.0001 0.39 0.0001

ER 98.64 0.0002 1.26 0.0001

ER 96.64 0.0002 3.26 0.0001

ER 1.99 0.0001 0.08 97.53

ER 0.003 0.0001 0.0001 99.89

ER 98.26 0.01 1.73 0.0001

ER 97.26 0.03 2.73 0.0001

ER 1.0 0.02 0.3 98.51

ER 0.03 0.0001 0.0001 99.75

ER 97.34 1.125 0.24 0.0001

ER 98.34 1.74 0.19 0.001

ER 98.78 0.059 0.03 1.00

ER 0.04 1.78 0.16 97.896

ER 97.69 0.0001 2.22 0.0001

ER 97.71 0.0001 2.39 0.0001

ER 97.82 0.12 0.03 1.89

ER 1.83 3.25 4.98 89.73

Time_1_13 Poles ‐3.764±28.641 ‐4.0093±53.555 ‐5.162±43.604 ‐4.523±32.814 Time_1_14 Poles ‐3.644±28.358 ‐2.388±54.57 ‐3.697±41.641 ‐4.130±33.435 Time_1_15 Poles ‐3.731±28.416 ‐2.507±54.31 ‐4.037±43.731 ‐4.523±35.629


ER 0.3 0.39 89.35 8.99

ER 0.0001 0.0001 5.37 94.55

57

Time_1_18 Poles ‐4.091±28.070 ‐3.679±55.543 ‐4.127±42.525 ‐4.030±33.925

ER ER ER ER 2.36 2.22 94.06 3.16 0.33 0.19 0.32 93.31 96.9 97.12 5.33 2.47 0.0001 0.000 0.03 0.04 Table 33: CNR extraction with circular polarizations

When the extraction is done with multiple aspect, the response signal corresponds to the target are from many look directions (here 18 look directions) and with particular polarization state. Some poles are excited at the particular polarization and some poles are excited with other. So in order to get the most dominant poles of a certain taget, the poles must be extracted for all the polarizations (Linear or circular). For instance, the poles extracted for multiple aspect (time_1_1 to time_1_18) with polarization LL, the pole 23 is missing but when it is with the polarization LR it appears and it is possible to extract the most dominant poles when we perform extraction with all polarization cases. When the polarimetric data is utilized for a specific look direction, the poles which are excited with all the polarization aspect can be extracted. So, usage of polarimetric data helps in dominant pole extraction better and time consuming.

4.8 Poles extraction for NO tumor, 10mm and 15mm tumor: The response data from No tumor, 10mm and 15mm tumor are processed through Matrix Pencil Method. The poles are extracted for all the three cases, the poles which are extracted from no tumor data corresponds only to the breast volume, while the poles from 10mm and 15mm tumor related to both breast volume and breast tumor. The polarimetric data for all the three cases are utilsed in poles extraction are tabulated below, Poles (No tumor, M = 16)

Poles (10mm tumor, M = 23)

Poles (15mm tumor, M = 36)

‐3.742±j26.084 ‐2.621±j53.958 ‐3.720±j42.561 ‐4.146±j35.463

‐3.357±j28,114 ‐2.896±j53.824 ‐3.353±j41.774 ‐4.473±j32.229 ‐3.473±j40.782 ‐2.094±j45.452

‐2.6905±j27.18 ‐2.645±j54.387 ‐4.114±j42.885 ‐4.921±j33.954 ‐1.981±j40.958 ‐2.108±j30.193 ‐1.924±j51.037 ‐2.186±j37.381

Poles obtained in the first column corresponds to no tumor target and poles corresponds only to breast volume. In the case of 10mm and 15mm, poles are related to both breast volume and tumor. It is 58

noticeable that there are common poles in all three cases which are related to breast volume and new poles represent the tumor.

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5.Discussion: The transient response signal from the target are processed through the MPM algorithm, the extracted CNR corresponds to the target. In order to simplify the process of CNR extraction, multiple signal from the target are processed at once through MPM algorithm which can handles more than one signal. Multiple signal may be of Multiple aspect or polarimetric, when analysing the parameter extraction with response signal from multiple look directions at particular polarization, there are some missing dominant poles since all the modes are not excited at particular polarization. So all the polarization aspects are considered for all the look directions and again it is a time consuming process. But the extracted CNR with the polarimetric data comprises of all dominant poles related to the target since all modes are excited. From the analysis, it is very clear that the polarimetric data possess the good chances of CNR etraction of breast tumor. When the response signal from the No tumor, 10mm tumor and 15mm tumor are processed through the MPM algorithm, CNR extracted for all the 3 cases. The extracted parameter for No tumor corresponds only to the breast volume, whereas the CNR from the 10mm and 15mm tumor corresponds to the breast tumor and breast volume. Better discriminations are seen for 3 different cases of breast tumor.

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6. Conclusion Based on Singularity Expansion Method, resonance based target recognition using Complex Natural Resonance was implemented. Matrix pencil Method is the microwave technique for extraction of parameter CNR has been selected. Algorithm of Matrix Pencil Method which processes the transient response signal was developed and CNR extracted. To make the CNR extraction easy and reduce the extraction time, MPM algorithm which handles multiple signal was developed. Two different cases of multiple signals, multiple aspect and polarimetric data were utilized. CNR extraction was obtained for both the cases and the best method was analysed. Form the numerical analysis, it was shown that the polarimetric datas helps in better target recognition. The test case of 1m wire was considered and poles are extracted using single response and multiple aspect. the breast cancer detection was made by parameter extraction of 3 different cases of breast tumor. No tumor, 10mm and 15mm tumor are considerd for parameter extraction. The extracted CNR are tabulated for all the 3 cases and dominant CNR corresponds to the breast cancer and breast volume are shown. As we could able to see the CNR corresponds to the breast tumor, it gives us a good confidence about the chances of using Ultra Wideband microwave technologies in breast tumor detection. From the project, the clear idea of using microwave technologies for breast cancer detection and uniqueness of microwave technology were shown. As Ultra Wideband microwave technologies has consist of good positive points of non ionizing radiations, good sensitivity and find out the changes in the dielectric properties of tissues it creates the revolution in breast tumor detection. The numerical parameter CNR of the breast tumor are clearly idenified so it makes the bright chances of using this technique in breast cancer detection.

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References: [1] Screeing of breast cancer by Mammography, The Nordic Cochrane Centre. [2] Using the Matrix Pencil Method to Estimate the Parameter of a Sum of Complex Exponentials. By Tapan K.Sarkar and Odilon Pereira. [3] Extraction of the Natural Frequencies of a Radar Target from a Measured Response Using E‐Pulse Techniques by Edward J.Rothwell, Kun‐Mu Chen and Dennis P.Nyquist. [4] Radar Target Discrimination Using the E‐pulse technique by E.J.Rothwell, D.P Nyquist, K.M Chen and B.Drachman. [5] Application of the Matrix Pencil method for Estimating the Singularity Expansion Method Poles of source free transient responses from Multiple look directions by Tapan Kumar sarkar, Sheeyum park, Jinhwan Koh, Sadasiva M. Roa. [6] On the analysis of Electromagnetic Transients from radar Target using SPWVD by Hoi‐Shun Lui, Nicholas V. Shuley. [7] Breast tumor charecterization based on Ultrawideband Backscatter by Shakthi K Davis, D Van Veen and Susan C Hagness. [8] Magnetic Resonance Imaging by Robert R. Edelman and Steven Warach, The New England Journal of Medicine. [9] Singularity Expansion method and its application to target identification by Baun C. E. [10] Analysis of forward scattering data for mirowave breast imaging by Hoi‐Shun Lui and Andears Fhager and Michel perrson. [11] Radar based resonance target identification with multiple polarization by Hoi‐Shun Lui and Nicolas Shuley, School of information technology and Electrical Engineering, University of queensland, Australia. [12] Complex Resonance frequencies of Biological Targets for microwave imaging application by Dewald and R Bansul. [13] M. El‐Shenawee,"Resonant spectra of malignant breast cancer tumors using the three‐dimensional electromagnetic fast multipole model", IEEE Trans. Biomed. Eng., vol. 51, p.35 , 2004. [14] Hoi‐Shun Lui, et al. “Preliminary Investigation of Breast Tumor Detection Using the E‐Pulse Technique”, Proceedings of IEEE AP‐S International Symposium USNC/URSI National Radio Science Meeting, pp.283‐286, 9 – 14 July, 2006, Albuquerque, New Mexico, USA

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The Potential of using UltraWideBand Microwave

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