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Early Breast Cancer Diagnosis Using Microwave Imaging via Space-Frequency Algorithm

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EARLY BREAST CANCER DIAGNOSIS USING MICROWAVE IMAGING
VIA SPACE-FREQUENCY ALGORITHM
A THESIS IN
Electrical Engineering
Presented to the Faculty of the University
of Missouri-Kansas City in partial fulfillment
of the requirements for the degree
MASTER OF SCIENCE
by
SPANDANA VEMULAPALLI
B.E, Manipal Institute of Technology, 2014
Kansas City, Missouri
2017
ProQuest Number: 10283519
All rights reserved
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SPANDANA VEMULAPALLI
ALL RIGHTS RESERVED
EARLY BREAST CANCER DIAGNOSIS USING MICROWAVE IMAGING VIA
SPACE-FREQUENCY ALGORITHM
Spandana Vemulapalli, Candidate for the Master of Science Degree
University of Missouri-Kansas City, 2017
ABSTRACT
The conventional breast cancer detection methods have limitations ranging from
ionizing radiations, low specificity to high cost. These limitations make way for a suitable
alternative called Microwave Imaging, as a screening technique in the detection of breast
cancer. The discernible differences between the benign, malignant and healthy breast
tissues and the ability to overcome the harmful effects of ionizing radiations make
microwave imaging, a feasible breast cancer detection technique.
Earlier studies have shown the variation of electrical properties of healthy and
malignant tissues as a function of frequency and hence stimulates high bandwidth
requirement. A Ultrawideband, Wideband and Narrowband arrays have been designed,
simulated and optimized for high (44%), medium (33%) and low (7%) bandwidths
respectively, using the EM (electromagnetic software) called FEKO. These arrays are then
used to illuminate the breast model (phantom) and the received backscattered signals are
obtained in the near field for each case. The Microwave Imaging via Space-Time (MIST)
beamforming algorithm in the frequency domain, is next applied to these near field
iii
backscattered monostatic frequency response signals for the image reconstruction of the
breast model.
The main purpose of this investigation is to access the impact of bandwidth and
implement a novel imaging technique for use in the early detection of breast cancer. Earlier
studies show the implementation of the MIST imaging algorithm on the time domain
signals via a frequency domain beamformer. The performance evaluation of the imaging
algorithm on the frequency response signals has been carried out in the frequency domain.
The energy profile of the breast in the spatial domain is created via the frequency domain
Parseval’s theorem. The beamformer weights calculated using these the MIST algorithm
(not including the effect of the skin) has been calculated for Ultrawideband, Wideband and
Narrowband arrays, respectively. Quality metrics such as dynamic range, radiometric
resolution etc. are also evaluated for all the three types of arrays.
iv
APPROVAL PAGE
The faculty listed below, appointed by the Dean of the School of Computing and
Engineering, have examined a thesis titled “Early Breast Cancer Diagnosis using
Microwave Imaging via Space-Frequency Algorithm,” presented by Spandana
Vemulapalli, candidate for the Master of Science degree, and certify that in their opinion
it is worthy of acceptance.
Supervisory Committee
Deb Chatterjee, Ph.D., Committee Chair
Department of Computer Science and Electrical Engineering
Ghulam Chaudhry, Ph.D.
Department of Computer Science and Electrical Engineering
Ahmad Hassan, Ph.D.
Department of Computer Science and Electrical Engineering
Masud Chowdhary, Ph.D.
Department of Computer Science and Electrical Engineering
v
CONTENTS
ABSTRACT ....................................................................................................................... iii
LIST OF ILLUSTRATIONS ........................................................................................... viii
ACKNOWLEDGMENTS .................................................................................................. x
Chapter
1. INTRODUCTION .......................................................................................................... 1
1.1
Mammography .................................................................................................... 2
1.2
Breast MRI .......................................................................................................... 3
1.3
Ultrasound ........................................................................................................... 4
1.4
Microwave Imaging ............................................................................................ 4
2. BURIED OBJECT DETECTION USING EM WAVES ............................................... 8
2.1 Ground Penetrating Radar......................................................................................... 8
2.2 Electrical Properties of the Breast............................................................................. 9
2.3 3D Modelling of the Breast in FEKO ..................................................................... 12
3. SENSOR DESIGN AND ANALYSIS IN FEKO ........................................................ 15
3.1 Design of Ultrawideband Antenna.......................................................................... 16
3.2 Design of Wideband Array ..................................................................................... 17
3.3 Design of Narrowband Array.................................................................................. 19
4. NOVEL IMAGING ALGORITHM ............................................................................. 21
vi
4.1 MISF beamforming technique ................................................................................ 21
4.2 Formulation of the Weights of the MISF Beamformer .......................................... 22
5. RESULTS ..................................................................................................................... 27
5.1 Tumor detection using UWB antenna..................................................................... 27
5.2 Tumor detection using WB array ............................................................................ 33
5.3 Tumor detection using NB array............................................................................. 34
6. CONCLUSION ............................................................................................................. 37
6.1 Summary ................................................................................................................. 37
6.2 Future Trend............................................................................................................ 38
APPENDIX ....................................................................................................................... 40
REFERENCES ................................................................................................................. 48
VITA ................................................................................................................................. 57
vii
LIST OF ILLUSTRATIONS
Figure
Page
1. 3D breast model with an embedded tumor in CADFEKO ........................................... 12
2. Relative permittivity of the breast fat and the tumor with respect to frequency........... 13
3. Conductivity of the breast fat and the tumor with respect to frequency ....................... 14
4. UWB antenna array and embedded element ................................................................. 16
5. The UWB embedded element VSWR vs frequency plot shows a bandwidth of 44% . 17
6. The UWB antenna gain vs frequency graph ................................................................. 17
7. Wideband Antenna array and embedded element ........................................................ 18
8. The WB embedded element VSWR vs Frequency plot shows a bandwidth of 33% ... 18
9. The WB embedded element gain vs frequency plot ..................................................... 19
10. Narrowband antenna array and embedded element .................................................... 19
11. The NB embedded element VSWR vs frequency plot shows a bandwidth of 7% ..... 20
12. The NB embedded element gain vs Frequency graph ................................................ 20
13. Block diagram of the MIST algorithm in the frequency domain................................ 22
14. Breast Phantom with tumor in front of a 3X3 UWB sensor array .............................. 28
15. Real part of the filter weights...................................................................................... 28
16. Imaginary part of the filter weights ............................................................................ 29
17. Near field backscattered electric field signals from center element for a breast
phantom with 5mm and 10mm tumors ..................................................................... 30
viii
18. The absolute value of the adaptive weights with respect to frequency for a breast
phantom with 5mm and 10mm tumors ..................................................................... 30
19. The 2D breast images with (a) 10mm and (b) 5mm tumor respectively .................... 31
20. Backscattered electric field signals with breast phantom at 42.8mm, 214mm and
428mm from the UWB sensor array. ........................................................................ 31
21. The magnitude of weights with respect to frequency for different distances of the
breast phantom from the UWB sensor array............................................................. 32
22. The 2D breast images with breast phantom located at (a) 42.8mm, (b) 214mm and (c)
428mm from the UWB sensor array. ........................................................................ 33
23. The 2D reconstructed breast image using a WB sensor array and MISF beamforming
algorithm. .................................................................................................................. 33
24. The 2D reconstructed breast image using a NB sensor array and MISF beamforming
algorithm. .................................................................................................................. 34
25. The signal to mean ratio for UWB, WB and NB sensor arrays using the MISF
algorithm. .................................................................................................................. 36
26. The dynamic range for UWB, WB and NB sensor arrays using the MISF algorithm.
................................................................................................................................... 36
ix
ACKNOWLEDGMENTS
I would like to express my deep gratitude towards my advisor and guide Dr.Deb
Chatterjee who has always been a guiding force behind this research. His highly influential
personality has provided me constant encouragement to tackle any difficult task assigned.
I am indebted to him for his invaluable advice and for propelling me further in every aspect
of my academic life. His depths of knowledge, crystal clear concepts have made this
research a cake walk. I consider it my good fortune to have got an opportunity to work with
such a wonderful personality. I am grateful to Dr. Dhivya Ketharnath for providing me
necessary information about the research and helping me learn various tough concepts. She
has always been a great source of inspiration to me and I would like to convey my deep
regards to her.
I would like to thank my colleague Mahrukh Khan for the design of ultrawideband
antenna and for all the thought provoking discussions we had, which inspired me to think
beyond the obvious. My fellow graduate students at the MSEE Department of the School
of Computing and Engineering at the University of Missouri-Kansas City, who dedicated
their time to help and encourage me.
I would like to acknowledge the Interdisciplinary and Intercampus (IDIC) research
grant for providing me the financial support. I am also grateful for the School of Graduate
Studies (SGS) travel grant for supporting me to present my research findings at the IEEE
International Symposium on Antennas and Propagation and USNC- URSI North American
Radio Science Meeting in Vancouver, British Columbia, Canada, 19-26 July, 2015. I would
x
like to extend my appreciation to the MSEE Department of the School of Computing and
Engineering at the University of Missouri-Kansas City.
This thesis would not have been possible without the love and support of my
parents. I am thankful to my sister, Meghana Vemulapalli and my brother-in-law, Sai Kiran
Analdas for always believing in me. The constant love and encouragement from my friends
Krishna.K.Kota and Deeptej Martheneni, made me fight through all the difficulties. I share
this thesis with all of you.
xi
CHAPTER 1
INTRODUCTION
The expanding numbers of breast cancer cases every year make their early detection
imminent. In the year 2015, around 40,000 deaths due to breast cancer were expected. After
lung cancer, Breast cancer is the second most prominent cause of death [1]. Breast cancers
that are detected from symptoms are usually larger and are more likely to have swept
beyond the breast region. In contrast, breast cancer found during early screening tests are
more likely to be smaller and still restricted to the breast. Hence, the main aim of screening
techniques for breast cancer is to detect it before it starts to show its symptoms.
The wide range of limitations of the present breast cancer detection methods like
mammogram, MRI etc. pave way for an alternate screening method known as, microwave
Imaging. The difference in the electrical properties of the benign, malignant and healthy
tissues along with the utilization of non-ionizing frequencies make microwave imaging a
suitable alternative for the detection of breast cancer [1]. Microwave imaging is a
promising screening technique because both ionizing radiation and breast compression are
prevented. It is also less expensive and has the potential to detect very small tumors.
The remaining of the chapter gives a detailed insight about the present breast cancer
detection techniques and their limitations. Chapter 2 of this thesis discusses about the
buried object detection using microwaves. A brief insight into the electrical properties of
the breast and the simulation of the breast model in FEKO. Chapter 3 introduces the
concept of microstrip patch antenna arrays as sensors and also describes the parameters
involved for the design of the ultrawideband, narrowband and wideband sensors for the
1
microwave imaging system. Chapter 4 talks in detail about the MISF imaging algorithm
for the breast image reconstruction. Chapter 5 presents with the results and observations
while Chapter 6 discusses in detail about the challenges faced in microwave imaging and
future trends.
1.1 Mammography
Mammography is the most frequently used breast cancer detection technique over
the past few years. It is commonly called as the gold standard method for breast cancer
diagnosis. During a mammography, the breast is compressed between two surfaces to
flatten the breasts in order to spread the breast tissue. X-rays are then produced by an Xray machine, which pass through the breast to a detector located on the opposite side. The
detector can be either a photographic film sheet, which captures the x-ray image on film,
or a solid-state detector, which transmits electronic signals to a computer to form a digital
image. The images produced are called mammograms.
On a film mammogram, areas of low density, such as fatty tissue, appear black
whereas areas of high density, such as connective and glandular tissue or tumors, appear
white Standard screening mammograms take 2 views (x-ray pictures taken from different
angles) of each breast. A mammogram cannot prove that an abnormal area is cancer. To
confirm whether cancer is present, a small amount of tissue must be removed and looked
at under a microscope. This procedure is called a biopsy. You should also be aware that
mammograms are done to find cancers that can’t be felt. If you have a breast lump, you
should have it checked by your doctor, who may recommend a biopsy even if your
mammogram result is normal.
2
Mammograms are not perfect at finding breast cancer. They do not work as well in
women with dense breasts, since dense breasts can hide a tumor. Dense breasts are more
common in younger women, pregnant women, and women who are breastfeeding, but any
woman can have dense breasts [2]. Even though mammograms use low energy ionizing xrays, frequent screening could cause cancers. The other drawbacks of mammography is its
low sensitivity (67.8%) and accuracy (70.2%) [3]. Apart from these limitations, many
women find mammography uncomfortable or painful and there are sequential health
concerns from the exposure of ionizing radiations.
1.2 Breast MRI
The magnetic resonance imaging uses radio waves and magnetics instead of X-rays
to produce in depth images of the breast. A typical breast MRI procedure consists of
injecting a contrast agent into the blood veins of the arm of the patient under screening.
For the breast MRI, you will need to expose your breasts and lie in a supine position on a
padded platform with cushioned openings for your breasts. Each opening is encircled by a
breast coil, which receives a signal as a part of the MRI unit to create images. The platform
then slides into the centre of the tube-shaped MRI machine. A magnetic field is created
and pulses of radio waves are sent from the MRI unit. The radio waves push the nuclei of
the atoms in your body out of their normal position. As the nuclei realign into proper
position, they send out radio signals.
These signals are received by a computer that analyses and converts them into a
black and white image of the breasts being examined. This image appears on a viewing
monitor. The contrast agent distinguishes the tumor affected area of the breast (white) from
3
the rest of the breast (black). Although MRI can find tumors which go undetectable by
Mammogram, it gives a lot of false-positives. Also MRI is very expensive and is mostly
not covered by insurance unless having a high-risk of breast cancer. Therefore MRI is not
a suitable early diagnostic tool for cancer imaging [2, 3, 4].
1.3 Ultrasound
Ultrasound which is also known as sonography uses sound waves for imaging
purposes. A gel is put on the skin of the breast and an instrument called a transducer is
moved across the skin to show the underlying tissue structure. The transducer emits sound
waves and picks up the echoes as they bounce off body tissues. The echoes are converted
into an image on a computer screen. This test is painless and does not expose you to
radiation. Ultrasounds aren’t used by themselves for screening because they can miss some
cancers [2, 4].
1.4 Microwave Imaging
Microwave Imaging is a non-invasive breast cancer screening method which
primarily uses microwaves (300MHz-30GHz) to detect malignant tumors. It takes
advantages of the difference in dielectric properties between malignant, benign and healthy
breast tissues. The non-ionizing radiations and the non-invasive nature of this technique
makes it a capable domain in the area of breast cancer detection. Even though microwave
imaging has been around for quite some time, its applications in the medical industry are
not explored entirely. Microwave imaging for breast cancer is mainly of three types:
passive, hybrid and active [5].
4
1.4.1 Passive Microwave Imaging
Passive microwave imaging is built on the concept of temperature differences
between a tumor and a healthy tissue when illuminated by microwaves. Typical passive
microwave imaging system consists of a radiometer that measures the temperature
differences. The main limitation of this approach is the low-power radiation of these tumors
which lead to technical difficulties. Another drawback is its ineffectiveness to differentiate
a cool substance close to the surface of the body and a hot tumor located deep inside it.
1.4.2 Hybrid Microwave Imaging
Hybrid technique consists of illuminating the breast tissue with microwaves and
recording the change in the pressure waves generated by the expansion of heated tissue
using an ultrasound transducer. The heterogeneity of the breast shape and the close
proximity of the skin to the transducer are some major challenges to this method. The skin
tissue have higher conductivity in comparison to the tumor causing stronger reflections.
1.4.3 Active Microwave Imaging
The active microwave imaging approach is based on the differences in the electrical
properties of different tissues under microwave illumination. The microwave travelling
through the breast, tend to scatter due to the change in the electrical properties. This
scattering in turn causes a change in energy detected by a receiver. This method is further
subdivided into two groups: tomography and UWB radar imaging.
1.4.3.1 Microwave Tomography
Microwave tomography is also called transmission-reflection imaging. The
scattered signals from the breast are used to form a dielectric profile of the breast under
5
examination using inversion algorithms. The breast is surrounded by a number of antennas
that receive the scattered signals through the breast. A single antenna is used to transmit
microwaves, while other antennas act as receivers. The position of the transmitting antenna
is changed and the process is repeated. The image is formed from the information obtained
from the incident and the forward scattered signals using imaging algorithms. One of the
problems encountered by this technique is inverse-scattering. Due to the heterogeneity of
the breast shape, the transmitted microwaves undergo many unwanted reflections leading
to inverse-scattering which is difficult to solve because of the non-linear relationship
between the recorded scattered signals and the dielectric profile of the breast [6].
1.4.3.2 UWB Radar Microwave Imaging
In this approach an ultrawideband transceiver is used to measure the backscattered
signals. The basic concept of UWB radar imaging in breast cancer detection is the same as
in the ground penetrating radar. A major advantage of this method over microwave
tomography is that it avoids the inverse scattering problem. Unlike tomography which
maps the dielectric profile of the breast, the UWB radar microwave imaging uses the
measured backscattered energy and imaging algorithms for image reconstruction purposes
[7].
In our approach, we use the UWB radar microwave imaging method for the early
detection of the breast cancer using EM simulation software called FEKO. The sensor used
to record the backscattered signals is a 3X3 uniform planar array designed using FEKO.
Each element in the array is a V-slot, L-probe fed, rectangular microstrip patch antenna.
To analyse the impact of the sensor bandwidth and to justify the use of UWB sensor for
6
early diagnosis of breast cancer, a simple wideband and narrowband sensor arrays were
also designed for comparison. A multistatic radar approach where the central antenna
transmits while all the antennas receive the backscattered signals is implemented. These
near electric field signals recorded are then used to form a breast profile using a novel
imaging approach called Microwave Imaging via Space Frequency (MISF). The
limitations as well as the future trends of this application is also discussed in the end.
7
CHAPTER 2
BURIED OBJECT DETECTION USING EM WAVES
2.1 Ground Penetrating Radar
The concept of ground penetrating radar (GPR) commonly called as subsurface
radar originates from geophysics. In GPR, electromagnetic waves are applied in order to
obtain the subsurface profile [8]. Since then the concept of GPR has been applied
successfully for geology and many other domains. One of the major uses of GPR is in the
case of landmine detection, it senses the electrical variations of the metals or even dielectric
landmines inside a less conducting soil. However, one must understand that GPR is not
just a landmine sensor but an electrical contrast sensor which has many applications.
The received signals in the case of landmine detection is largely affected by the
change in soil properties. Other materials inside the soil, such as rocks, roots, etc. and soil
heterogeneity also produces a strong overlapping signal, which has to be eliminated using
pre-processing techniques. Earlier studies show that the received signal is often very weak,
which suggests that the reflection that is caused by the buried landmine is very trivial [8].
This is because of the strong reflection obtained as a result of ground bounce which is
primarily observed at the air-soil interface. Earlier studies show that the bandwidth of the
radar considerably affects the the ability of the GPR’s to detect buried objects.
The same concept is utilized in the case of microwave imaging of breast cancer.
The tumor is considered to be a buried object in the presence of various biological tissues.
The first medical application using the concept of GPR came forward in 1998 by Hagness
8
[7] and her colleagues for breast cancer detection. This method is favored more in
comparison to earlier microwave imaging systems like tomography to avoid the nonlinear
inverse scattering methods. As mentioned earlier, even though it does not provide the
dielectric profiles of the permittivity, it detects the regions of different dielectrics based on
the scattered fields.
The data collection involves the breast being illuminated with an ultra-wideband
pulse, and the receiver collects the backscattered waves. This process is repeated for
different positions of the sensors. The signals obtained at the receiver undergo a time shift
and add algorithm. The time delay for the round trip from the antenna to the breast and
back is calculated for each antenna position. The tumor signature can be detected, if it has
sufficiently large contrast compared to the surrounding tissues.
One of the significant advantages of this approach is that high resolution can be
obtained provided that a sufficiently wideband pulse can be used. In the system introduced
by Hagness and colleagues, the woman to be screened lies in a supine position and sensors
are placed on the flattened breast surface. Finite different time domain (FDTD) method is
used for complex numerical calculation of the performance of this system. Initial work has
suggested the feasibility of detecting tumors as small as 2 mm [8].
2.2 Electrical Properties of the Breast
The differences in the dielectric properties effects the propagation of the microwave
signal through the breast tissue by altering its amplitude or phase and results in alterations
of the microwave signal. In general, the conductivity is defined by the free path length and
speed of the electrons inside the material while the value of the permittivity is associated
9
with the molecule dipole moment per volume. The permeability is similar to that of free
space since the breast tissues are non-magnetic in nature. When the breast tissues are
affected by diseases, temperature etc., there is a variation in the dielectric properties with
respect to a healthy tissue. By monitoring these variations, we can identify anomalies or
use the information for treatment of the disease. This is the foundation for microwave
imaging of breast cancer.
The dielectric properties of human tissues have been examined for a long time [9].
One of the characteristics of these properties are the substantial changes that they undergo
over a widespread frequency spectrum. In 1996, Gabriel and Gabriel [9, 10, 11] measured
the dielectric properties of 20 types of human tissues over the frequency band from 10 Hz
to 20 GHz. They could observe that:
1. The dispersion property of human tissues and frequency do not have a simple linear
relationship. A staircase relationship is observed which can be defined by a Cole-Cole
relaxation mechanism;
2. Different tissues may have substantially different permittivity and conductivity
properties at different frequencies.
Several studies were conducted that show the ex vivo measurements over various
frequency bands in terms of the dielectric properties of female breast tissue. A significant
variation was observed in the dielectric properties with varying frequency. This is mainly
due to the various breast layers and the associated variations in water content. In the
microwave frequency band, it is noticed that the variations in the conductivity and
10
permittivity of the breast tumor tissues deviate significantly from those of the normal breast
tissue.
These fascinating discoveries have led to uncharted research utilizing microwaves
to detect tumors by reconstructing dielectric profiles. The experiments in [10, 12] and many
other studies utilized ex vivo tissue, meaning the tissues used in the measurements were
excised from the body but measured as freshly as possible. Recent in vivo breast tissue
measurements at Dartmouth College have demonstrated that the dielectric properties of the
in vivo tissue are substantially different from the ex vivo cases reported by previous studies
[13].
The high contrast justified by many previous studies provides a major incentive to
the use of microwave imaging in breast cancer detection. However, other advantages
include nonionizing radiation which is safer than ionizing radiation in the case of X-rays
used in mammography. Finally, no compression is needed in microwave imaging making
the exams more comfortable than mammography.
Also the low cost, low illumination power levels and non-invasiveness associated
with microwave imaging, makes it a feasible technique for regular check-ups. The
microwave imaging has not been explored completely to its potential. Preliminary studies
show that microwave imaging is not only used to create the dielectric profile of the breast,
other physical or biological properties that have strong associations to dielectric properties
can also be concluded from the reconstructed dielectric profile. The thermal dependence
of the dielectric properties have been studied by Meaney et al.[14] since 1993. Research in
this domain makes use of the linear relationship between conductivity and temperature. By
11
reconstructing the dielectric profiles, the variations of the temperature profiles can be
retrieved from the dielectric-temperature linear relationship. Temperature monitoring is
especially necessary in hyperthermia. In hyperthermia, the malignant tissue is heated to
facilitate cancer cell death in addition with radiation treatment. An efficient treatment and
minimization of the damage to normal tissue is a consequence of the temperature control.
Non-invasive microwave thermometry is a novel field which is being investigated to make
use of the characteristics of microwave imaging for the detection and cure of breast cancer.
2.3 3D Modelling of the Breast in FEKO
Based on the previous studies [15] of the modelling of the dielectric properties of
the breast, we create a homogenous breast tissue with a tumor embedded at the center of
it. Our main aim being the proof of concept of using the developed MISF imaging
algorithm, we model the breast in its simplest form (breast fat and tumor).
Figure 1. 3D breast model with an embedded tumor in CADFEKO
The hemispherical breast tissue is 60mm of radius while the size of the spherical
tumor is 5 and 10mm respectively as shown in Fig 1. The reason behind this specific tumor
12
size is that the breast cancer can be cured if the tumor as early as 5-10mm is detected. The
full wave simulation software, FEKO has a built-in feature enabling the use of Debye
relaxation for the modelling of the 3D breast. As observed earlier, the dielectric properties
of the breast fat tissue and the tumor vary with frequency. We need to make sure to
incorporate these different permittivity and conductivity values at different microwave
frequencies to our breast model. The Debye relaxation is known as the dielectric relaxation
response of the material at the microwave frequencies. It is a frequency dependent
modelling technique of the dielectric properties. The wide contrast between the breast fat
and tumor dielectric properties enables the huge difference in the scattered energy. Fig 2
and 3 show the permittivity and conductivity values, we have used for breast fat and tumor
while modelling in CADFEKO.
Relative permittivity vs Frequency
70
60
Relative Permittivity
50
40
30
20
10
0
1
2
3
4
5
6
7
8
9
10
Frequency
tumor
healthy breast fat
Figure 2 Relative permittivity of the breast fat and the tumor with respect to frequency
13
Conductivity vs Frequency
14
12
Conductivity [S/m]
10
8
6
4
2
0
1
2
3
4
5
6
7
8
9
10
Frequency
tumor
healthy breast fat
Figure 3 Conductivity of the breast fat and the tumor with respect to frequency
14
CHAPTER 3
SENSOR DESIGN AND ANALYSIS IN FEKO
The FCC authorized frequency band for ultrawideband medical imaging systems is
from 3.1GHz-10GHz [15]. Therefore, we designed our sensor within this range. The
primary reason for the selection of microstrip patch antennas for design purposes is its lowcost, low profile and easy fabrication. However, one of the major limitations of microstrip
patch antennas is its narrow bandwidth. To overcome this problem and to enhance the
bandwidth and the gain, many techniques are employed [16]
One of the ways to increase the bandwidth is to increase the height of the substrate
on which the patch is mounted on. This destroys the low-profile nature of the microstrip
patch antennas. The improvised patch antennas using slots is a substantial way of
improving the bandwidth without a tradeoff.
Preliminary studies [17] show the use of u-slot increasing the bandwidth and gain
of a rectangular microstrip patch antenna [25-30%]. Among different studies pertaining to
different slot configurations, observed that bandwidth can be further increased by changing
the arm angle of the u-slot to make it a v-slot. Recent study [18] achieves an optimized
bandwidth and gain by employing L-probe feeding technique.
In our sensor design for cancer detection sing microwaves, we use a uniform planar
arrays with a v-slot, L-probe rectangular microstrip patch antenna. The array consists of
total of 9 elements (3X3). The center elements is used for transmitting while all elements
are used to receive the backscattered energy. A simple wideband and narrowband,
15
rectangular microstrip patch arrays with a simple feeding technique (straight) have also
been designed using CADFEKO, to compare the performance of the microwave imaging
system based on its bandwidth. All the designs were under compliance with the FCC rules
on the bandwidth allocated for the UWB medical imaging systems.
The received, near electric field by sensor is visualized using the MOM solver
option. These measurements are then imported into MATLAB for post-processing using
MISF algorithm to create a profile of the breast.
3.1 Design of Ultrawideband Antenna
An ultrawideband antenna array is designed in a commercial electromagnetic
software called FEKO. Each rectangular microstrip patch antenna in the array has
dimensions, L=13.6947mm and
Figure 4 UWB antenna array and embedded element
W=18.9671mm. The array is designed on a substrate of thickness 4.15mm and
dielectric value of 2.2. The array has a uniform element spacing of 21.4mm. Each antenna
element is excited using an L-probe feed. The embedded element bandwidth is 44% with
16
an upper frequency 8.91GHz and lower frequency 5.67GHz. An embedded element gain
of 7.81dBi is achieved with this array.
Figure 5 The UWB embedded element VSWR vs frequency plot shows a bandwidth of
44%
Figure 6 The UWB antenna gain vs frequency graph
3.2 Design of Wideband Array
A wideband antenna array is designed as shown in fig 6 with each rectangular
microstrip patch antenna in the array having dimensions, L=11.228mm and W=16.823mm.
17
Figure 7 Wideband Antenna array and embedded element
The array is designed on a substrate of thickness 4.15mm and dielectric value of
2.2 and a uniform element spacing of 21.4mm. Each antenna element is excited using a
probe feed. The embedded element bandwidth is 33% with an upper frequency 8.12GHz
and lower frequency 5.8GHz. An embedded element gain of 7.81dBi is achieved with this
array.
Figure 8 The WB embedded element VSWR vs Frequency plot shows a bandwidth of
33%
18
Figure 9 The WB embedded element gain vs frequency plot
3.3 Design of Narrowband Array
A narrowband antenna element is designed with dimensions as L=8.421mm and
W=12.632mm. The array has uniform elements with uniform spacing of 21.4mm simulated
on a substrate of 4.15mm and a dielectric value of 2.2.
Figure 10 Narrowband antenna array and embedded element
The elements of an array are excited using a probe fed placed at a distance of 2.5mm
from the radiating end and 2.1mm from the non-radiating end. The embedded element
19
bandwidth is 7% with an upper frequency 7.642GHz and lower frequency 7.111GHz. An
embedded element gain of 6.199dBi is achieved with this array.
Figure 11 The NB embedded element VSWR vs frequency plot shows a bandwidth of 7%
Figure 12 The NB embedded element gain vs Frequency graph
20
CHAPTER 4
NOVEL IMAGING ALGORITHM
4.1 MISF beamforming technique
The Microwave imaging via space frequency beamforming technique uses the
backscattered electric field signals, obtained as a function of frequency for the image
reconstruction of the breast, because it avoids the use of fourier transform and inverse
fourier transform stages in the imaging system as shown in earlier studies [19,20,21]. The
near field backscattered electric field signals are in sequence phase-shifted and weighted,
and further used to create the energy profiles of the interior of the breast. Fig 12 shows the
block diagram of the frequency domain implementation of the microwave imaging via
space frequency beamforming algorithm.
The output of the beamformer is calculated using (1)
=
Where
from the
,
1
( ,f) is the monostatic frequency response related with the propagation
antenna through the breast to the scatterer located at
we delay the phase of the backscattered electric field signal by
(
the frequency responses of each channel are aligned in phase. Here
and back. As in (2),
=
-
) so that
is the maximum
(worst case) propagation delay over all the locations and channels and also the reference
phase to which all the received signals are aligned The round-trip propagation delay
from the Mth antenna to the scatterer located at
21
)
and back, is computed by dividing the
round-trip propagation distance with the speed of propagation. The beamformer weights
are obtained using
Figure 13 Block diagram of the MIST algorithm in the frequency domain
=
Where
|
,
!
,
|#1 + ∑
&
,
&'
2
is the average time delay due to the beamformer. The backscattered
energy for the location
is evaluated using the Parseval’s theorem in the frequency
domain using
)
= * ∑*
∗
(3)
Similarly, p( ) is calculated for each location inside the breast and the
backscattered energy as a function of location is plotted in order to reconstruct the breast
model.
4.2 Formulation of the Weights of the MISF Beamformer
Since we did not consider the effect of skin, electric field signal received in the
frequency domain is assumed to be the signal after the skin artifact removal due to a lesion
located at
.
22
, -./ = 0 12
, 12 , 1≤
≤45 61≤.≤7
4
Where , -./ is the received electric field signal in the frequency domain by the
antenna, 12 is the .
frequency. 0 12 is the transmitted frequency signal and
, 12 is the backscattered signal to the
antenna. While modeling the microwave
imaging system in FEKO, it has the option of obtaining only the backscattered signal
, 12 while neglecting the transmitted signal. The signals received by each antenna
have to be aligned in phase by
(
channel are aligned in phase. Here
=
-
) so that the frequency responses of each
is the maximum (worst case) propagation delay over
all the locations and channels and also the reference phase to which all the received signals
) from the Mth antenna to the scatterer
are aligned The round-trip propagation delay
located at
and back, is computed by dividing the round-trip propagation distance with
the speed of propagation.. These signals are then weighted and summed across all the
frequencies and the corresponding energy is calculated using the Parseval’s theorem. In
order to compensate for the propagation to and from location
, we need the output to have
gain 1 and a linear phase as shown as:
=
>?
, 12
=
DDDD
@A BC
∗ -./
=
=
DDDD
>? !
, 12
>? ! E F BC
BC
>?
@A BC
∗ -./
5
, 12 is the frequency response due to propagation after removing the linear
phase shift related with round-trip propagation delay. The value
delay introduced by the beamformer as is equal to
Hence we obtain design limitations on
23
*
is the average time
and HI is the sampling interval.
-./ as:
=
DDDD
>?
, 12
=
DDDD
F
∗ -./
BC
∗ -./
, 12
>? ! E F BC
=
>? ! BC
=
6
7
This can be written in vector form as
O
L-./M N
Qℎ
O
N
>? ! BC
, 12 =
, 12 = -DDD
L-./ = -
, 12 DDD
-./
8
, 12 … DDDD
-./ …
, 1 2 /B
-./ /B
If these constraints are satisfied then the beamformer output at .
frequency is
given as:
12 =
OM
Multiply N
O
L-./M N
>? ! E F BC
9
, 12 on both sides to get
OM
, 12 N
, 12 =
>? ! BC O M
N
, 12
10
Taking Hermitian transpose on both sides we get
OM
N
O
, 12 N
O
, 12 L-./ = N
L-./ =
O
N
OM
N
, 12
>? ! BC
, 12 >? ! BC
O , 12
, 12 N
However the above solution is not robust since the magnitude of beamformer can
OM
be very large when N
O
, 12 N
, 12 is very small. This is challenging especially at
higher frequencies and deeper scan locations where attenuation results in small values of
O
N
, 12 . The robustness of a beamformer to errors between actual and estimated models
and to background noise is proportional to the norm of the weight vector or noise gain.
24
The noise gain for our beamformer is defined as
V-./ = L-./M L-./
DDDD
OM
N
V-./ = L-./ L-./ = M
O
N
, 12
O
, 12 N
M
V-./ =
OM
N
>? ! BC
, 12
1
O
, 12 N
The noise gain increases as |DDDD
O
N
OM
N
, 12
=
, 12 >? ! BC
= M
O , 12
O
, 12 N
N
∑=
1
|DDDD
1
O
, 12 N
, 12
, 12 |
, 12 | decreases. In order to control the noise
gain and obtain a robust beamformer, assume a penalized least squares problem:
MO
W-./ = arg minL-2/ - |L-./ N
, 12 −
>? ! BC ]
| +
=
^ -./|
_ -./|
/
where ^ -./ is the penalty weight and is selected in such a way that the norm of
_ -./
is traded against the approximation error. The penalty weights can be represented as
a diagonal matrix P[l].
O
W-./ = arg minL-2/ - |L-./M N
, 12 −
>? ! BC ]
| + L-./M `-./L-.//
We know that the above equation will have one minimum as the function W-./ is a
parabola.
Taking the derivative of W-./ with respect to L-./ and equating it to zero, we can
find the value of L-./ for which the function W-./ has a minimum.
6W-./
O
= 2aL-./M N
6L-./
O
L-./M N
OM
, 12 N
, 12 −
>? ! BC
OM
bN
, 12 + 2L-./M `-./ = 0
OM
, 12 + L-./M `-./ = N
, 12
>? ! BC
Applying Hermitian transpose on both sides we get:
O
N
OM
, 12 N
O
, 12 + `-./ L-./ = N
25
, 12
>? ! BC
L-./ =
O
N
O , 12
N
OM
, 12 N
>? ! BC
, 12 + `-./
This equation can also be written as:
L-./ =
O , 12
` -./N
O M , 12 ` -./N
O
N
>? ! BC
, 12 + 1
It can be observed that as ^ -./ decreases, the approximation error decreases but
the norm of
-./ increases. To compensate for these effects, the penalty weights are
selected as ^ -./ = |DDDD
, 12 |. This reduces the beamformer coefficients as:
-./ =
|DDDD
DDDD
, 12 >? ! BC
, 12 | 1 + ∑= |DDDD , 12 |
The beamformer weights are calculated in MATLAB using the imported near
electric field values. The images are formed, visualized and compared using MATLAB.
26
CHAPTER 5
RESULTS
5.1 Tumor detection using UWB antenna
The Microwave imaging via space frequency (MISF) algorithm was used for the
2D image reconstruction of the breast phantom using an UWB 3X3 array sensor. The breast
phantom with a 10mm tumor is placed in the near field region of the sensor array. It is an
adaptive beamforming filter. The weights of the beamforming filter are data dependent in
nature that is it depends on the backscattered electric field signals. Equation (2) can be
rewritten as
Wd (f) =
|eff ( ,f)|g hi g hjklm
|eff ( ,f)| n E∑hop&ehh ( ,f)&q
(7)
The real and the imaginary parts of the weights are hence derived as
Re Wd (f)) =
Im Wd (f)) =
stu vf E wxy
(8)
u{| vf E wxy
(9)
n E∑hop&ehh ( ,f)&q
n E∑hop&ehh ( ,f)&q
The weights are visualized for the 4 elements of the array since all others are
symmetric in nature with respect to the breast phantom as shown in fig 13. The visual
representation of the real and imaginary parts of the adaptive filter weights are shown in
fig 14 and 15.
27
Figure 14 Breast Phantom with tumor in front of a 3X3 UWB sensor array
0.08
Real part of the Weights
0.06
0.04
0.02
0
-0.02
-0.04
-0.06
6
6.5
7
Frequency
7.5
Figure 15 Real part of the filter weights
28
8
x 10
9
Figure 16 Imaginary part of the filter weights
The MISF algorithm was applied on two types of 3D breast phantoms with 5mm
and 10mm tmors repectively. Fig 16 shows the near field backscattered electric field
signals from a breast phantom with 5 and 10mm tumors. The backscattered signal from a
breast phantom with 10mm tumor has a higher signal strength when compared to the
phantom with 5mm tumor. Fig 17 shows that the magnitude of adaptive weights
irrespective of the embedded element in the array considered, will be inversely proportional
to the backscattered signal received by the element. This is theoretically proved by the
following equation derived from equation 7.
29
R=10mm
R=5mm
Absolute value of Weights
Figure 17 Near field backscattered electric field signals from center element for a breast
phantom with 5mm and 10mm tumors
Figure 18 The absolute value of the adaptive weights with respect to frequency for a
breast phantom with 5mm and 10mm tumors
Using this beamforming algorithm the images of the interior of the breast are
reconstructed. Since MISF is a spatio-frequency filter, the backscattered energy for each
location inside the breast is visualized using the MATLAB software. The image is 2D since
a coronal slice that cuts exactly through the center of the breast is mapped with respect to
the spatial location. The following figures 18 (a) and (b) show the 2D image of the breast
30
phantom with 10mm and 5mm tumors respectively electronically scanned from -60mm to
60mm via X and Y axis. The reconstructed images show that the tumor is located at the
center of the breast phantom.
60
20
50
18
40
16
30
14
X (mm)
20
10
12
0
10
-10
8
-20
6
-30
4
-40
-50
2
-60
-60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60
Y (mm)
0
(a)
(b)
Figure 19 The 2D breast images with (a) 10mm and (b) 5mm tumor respectively
To prove that the imaging works only in the near field region of the sensor array,
we kept varying the distance of the breast phantom with 10mm tumor from the UWB sensor
array. We observed as in fig 19 that the backscattered electric field signal strength
decreases as distance increases.
D=42.8mm
D=214mm
D=428mm
Figure 20 Backscattered electric field signals with breast phantom at 42.8mm, 214mm
and 428mm from the UWB sensor array.
31
Since the magnitude of weights of the beamforming filter is inversely proportional
to the backscattered electric field signal. We observed that the magnitude of weights of the
filter increase with the increase in the distance as shown in fig 20.
Figure 21 The magnitude of weights with respect to frequency for different distances of
the breast phantom from the UWB sensor array
The 2D reconstructed breast images for different distances are shown in fig 21. It
clearly is observed that as distance of the phantom from the sensor array increases the
detection of the tumor becomes difficult due to the decrease in the backscattered electric
field signal strength.
32
Figure 22 The 2D breast images with breast phantom located at (a) 42.8mm, (b) 214mm
and (c) 428mm from the UWB sensor array.
5.2 Tumor detection using WB array
A wideband antenna sensor array is designed with 9 elements (3X3). The embedded
element bandwidth is 33%. The breast phantom is placed in the near field region of the
sensor array. The data dependent MISF algorithm is used for the image reconstructed of
the breast using the signals
Figure 23 The 2D reconstructed breast image using a WB sensor array and MISF
beamforming algorithm.
33
received by the WB array. The image is reconstructed for a coronal slice cutting
through the center of the 3D breast phantom with 10mm tumor. We detected from fig 22
that the tumor is located at the center of the breast phantom.
5.3 Tumor detection using NB array
A 3X3 narrowband antenna sensor array with an embedded element bandwidth of
4% is designed. The breast phantom is placed in the near field region of the sensor array.
The data dependent MISF algorithm is used for the image reconstructed of the breast using
the signals received by the NB array. The image is reconstructed for a coronal slice cutting
through the center of the 3D breast phantom with 10mm tumor. Fig 5.23 shows the 2D
image reconstruction of breast phantom using NB sensor array.
60
50
12
40
10
30
8
X (mm)
20
10
6
0
-10
4
-20
2
-30
0
-40
-50
-60
-60 -50 -40 -30 -20 -10
-2
0 10
Y(mm)
20
30
40
50
60
Figure 24 The 2D reconstructed breast image using a NB sensor array and MISF
beamforming algorithm.
34
The performance of the sensor arrays with different bandwidths were analyzed
using few quality metrics which are defined as follows:
The Performance of the two algorithms are evaluated based on the following quality
metrics [22]
•
Dynamic Range: The ratio between maximum and minimum
intensities of the reconstructed image.
} = 10.~•
0
0
€
•
Where Id‚ƒ and Id‚ƒ are the maximum and minimum intensities of the
reconstructed image.
•
Signal to mean clutter ratio: It is a measure of the ability of the
algorithm to discriminate, or resolve, areas of different scattering properties.
„ = 10.~•
†
…1 + ˆ
‡
Where σ= standard deviation and µ= mean of the image intensities
Using these quality metrics it was observed that the UWB has the highest
performance when compared to WB and NB sensor arrays as shown in fig 24 and 25 [23].
35
Signal to Mean clutter ratio
6.6
6.5
6.4
6.3
6.2
6.1
UWB
WB
NB
Figure 25 The signal to mean ratio for UWB, WB and NB sensor arrays using the MISF
algorithm.
Dynamic range
20.2
20.1
20
19.9
19.8
19.7
19.6
19.5
UWB
WB
NB
Figure 26 The dynamic range for UWB, WB and NB sensor arrays using the MISF
algorithm.
36
CHAPTER 6
CONCLUSION
6.1 Summary
An active microwave system using the UWB radar approach was developed.
Nowadays, with the available commercial EM simulation tools like FEKO, one can
develop microwave imaging system. These simulation tools enable us to research, design,
analyze and validate complex medical imaging systems before their fabrication to provide
a cost-effective system at the developmental stage. In our research, we developed a lowcost, low profile, UWB microstrip patch uniform planar array with an enhanced embedded
antenna bandwidth (44%) and gain (7.81dBi) using FEKO. The central element of this
array is used to illuminate the 3D breast model designed using the MOM solver option in
FEKO. The received near electric field signals by all the antenna elements in the array are
imported into MATLAB for post-processing methods. A novel imaging approach called
the MISF algorithm was developed using the MATLAB programming language for the
breast profile reconstruction.
For performance comparison and also to justify the use of UWB microwave
imaging sensor arrays for the early detection of breast cancer, wideband and narrowband
microstrip patch antenna arrays were designed (within the same frequency range) and used
to form images of the breast. Two different quality measurements namely dynamic range
and signal to mean clutter ratio were compared for the different sensor arrays. The UWB
sensor array is proved to be a better sensor in an active microwave imaging system. One
37
of the major advantages of this system is the exclusion of the coupling liquid which makes
it completely non-invasive.
The MISF beamforming algorithm formulated was also visualized using
MATLAB. The results show the inverse dependence of the adaptive weights of the
beamformer on the received electric field signals. The sensor distance from the breast has
a huge effect on the imaging system, it is seen that as the distance increases the resolution
decreases. This justifies our approach of measuring the electric field signals in the nearfield.
6.2 Future Trend
The main aim of our research was to develop an UWB microwave imaging system
at a simulation level. Our assumptions exclude the inclusion of the skin and other tissues
during the modelling of the breast which is a limitation. The skin reflections are stronger
than that of the tumor and hence proper reconstruction would not be possible until we
include a pre-processing filter in order to remove the effects of the skin.
The homogeneous shape of the breast as well as the tumor makes the imaging
problem fairly simple. In general, the breast has a heterogeneous shape which could be one
of the major challenges encountered by microwave imaging systems. Another problem
faced by cancer detection using microwaves, is the low contrast scenarios of the breast
tissues.
These challenges and limitations can be taken care of by further improvising our
imaging system which is still at a simulation level. The improvisations made at a simulation
38
level before fabricating the system does not include extra costs and ensures better
feasibility.
Furthermore, the comparison between time domain and frequency domain imaging
algorithms can be studied. The potential of microwave imaging is yet to be explored
completely while facing its challenges. A microwave imaging system which overcomes all
its limitations will be the first non-invasive, low-cost, portable commercial breast cancer
screening technique.
39
APPENDIX
MATLAB Algorithm for MISF implementation
•
The near field backscattered electric field signal intensity with respect to frequency
from each antenna is simulated using FEKO. These backscattered signal intensities
with respect to frequencies are calculated when the centre element of the 3x3
antenna array is transmitting and all other antenna arrays are receiving.
•
Load the above backscattered electric field signal intensity with respect to
frequency (at 32 frequencies) into MATLAB.
•
As the signal received are out of phase, they have to be aligned. Calculate the phase
delay to align the signals in phase using the equation:
(
Here
=
-
)
is the maximum (worst case) propagation delay over all the locations and
channels and also the reference phase to which all the received signals are aligned
) from the Mth antenna to the scatterer
The round-trip propagation delay
located at
and back, is computed by dividing the round-trip propagation distance
with the speed of propagation (speed of light).
•
Adaptive weights are calculated and then applied to these phase aligned signals to
compensate for the propagation to and from location
, we need the output to have
gain 1 and a linear phase.
-./ =
|DDDD
DDDD
, 12 >? ! BC
, 12 | 1 + ∑= |DDDD , 12 |
40
DDDD
, 12 is the backscattered electric field signal at 12 frequency, M antenna and
r location of the breast due to propagation after removing the linear phase shift related
with round-trip propagation delay. The value
the beamformer as is equal to
•
*
and HI is the sampling interval. Here N=32, HI =1.
The output of the beamformer is calculated using
=
•
is the average time delay introduced by
,
The backscattered energy for the location
is evaluated using the Parseval’s
theorem in the frequency domain using
)
1
=
7
*
∗
Similarly, p( ) is calculated for each location inside the breast and the backscattered
energy as a function of location is plotted in order to get a 2D map of the breast model.
Here N=32 in our case.
MATLAB Code for MISF implementation
%% Load the backscattered near field signals from 4 antennas and for the rest the values
will be symmetrical as the breast model and the array is symmetrical.
FileID=fopen('sphere1.efe');
A1=textscan(FileID,'%f %f %f %f %f %f %f %f
%f','Delimiter','\t','CommentStyle','#','HeaderLines',15);
B1=cell2mat(A1);
Ex1=(B1(:,4)+1i*B1(:,5));
41
Ey1=(B1(:,6)+1i*B1(:,7));
Ez1=(B1(:,8)+1i*B1(:,9));
FileID=fopen('sphere2.efe');
A2=textscan(FileID,'%f %f %f %f %f %f %f %f
%f','Delimiter','\t','CommentStyle','#','HeaderLines',15);
B2=cell2mat(A2);
Ex2=(B2(:,4)+1i*B2(:,5));
Ey2=(B2(:,6)+1i*B2(:,7));
Ez2=(B2(:,8)+1i*B2(:,9));
FileID=fopen('sphere3.efe');
A3=textscan(FileID,'%f %f %f %f %f %f %f %f
%f','Delimiter','\t','CommentStyle','#','HeaderLines',15);
B3=cell2mat(A3);
Ex3=(B3(:,4)+1i*B3(:,5));
Ey3=(B3(:,6)+1i*B3(:,7));
Ez3=(B3(:,8)+1i*B3(:,9));
FileID=fopen('sphere4.efe');
A4=textscan(FileID,'%f %f %f %f %f %f %f %f
%f','Delimiter','\t','CommentStyle','#','HeaderLines',15);
42
B4=cell2mat(A4);
Ex4=(B4(:,4)+1i*B4(:,5));
Ey4=(B4(:,6)+1i*B4(:,7));
Ez4=(B4(:,8)+1i*B4(:,9));
g=[(Ex1),(Ex2),(Ex3),(Ex4),(Ex1),(Ex2),(Ex1),(Ex3),(Ex1)];
g=g';
%% defining frequency and other variables
f=5.67e9:0.0645e9:8.91e9; % frequency range of the simulation
c=3e8;
% speed of light
z=70;
% z coordinate value of the scan location
[x,y]=meshgrid(-60:60,-60:60);% x and y cooridinate values of the scan locations
%% sensor array position (rectangular coordinates)
xr=[-21.4 0 -21.4 0 -21.4 0 21.4 21.4 21.4];
yr=[-21.4 -21.4 0 0 21.4 21.4 -21.4 0 21.4];
zr=[0 0 0 0 0 0 0 0 0];
%% round trip delay calculation
for m=1:9;
for l=1:size(x,1);
for j=1:size(y,1);
43
d(l,j,m)=2*sqrt((x(l,j)-xr(m)).^2+(y(l,j)-yr(m)).^2+(z-zr(m)).^2); % distance from the
transmitting antenna element to the scatterer in addition to the distance from the scatterer
to the receiving antenna element.
td(l,j,m)=((d(l,j,m)*10^-3)/(c)); % time delay is calculated by the propagation distance
divided by the average speed of propagation inside the breast.
end
end
end
% sampling time
na=(max(max(max(td)))); % worst case propagation delay.
ni=na-td;% time alignment with respect to the reference time na.
Ts=1;
%% Applying the time delay to the backscattered signals in the frequency domain
for m=1:9;
for k=1:32;
for l=1:size(x,1);
for j=1:size(y,1);
S(l,j,m,k)=g(m,k).*exp(-1i*2*pi*f(k)*(ni(l,j,m))*Ts);
R(l,j,m,k)=S(l,j,m,k);
%gs(l,j,m,k)=g(k,m);% removing the linear phase shift associated withh the round trip
propagation delay.
end
44
end
end
end
%% Calculation of the weights in the frequency domain
for m=1:9;
for k=1:32;
v(m,k)=g(m,k).*exp(1i*2*pi.*f(k)*15.5*Ts);
q2(m,k)=v(m,k)/(abs(g(m,k))*(1+abs(g(1,k))+abs(g(2,k))+abs(g(3,k))+abs(g(4,k))+abs(g
(5,k))+abs(g(6,k))+abs(g(7,k))+abs(g(8,k))+abs(g(9,k)))); %calculation of the weights
end
end
for m=1:9;
for k=1:32;
for l=1:size(x,1);
for j=1:size(y,1);
Y(l,j,k,m)=S(l,j,m,k).*ctranspose(q2(m,k));
end
end
end
end
45
%% Summation of all the weighted, time delayed signals in the frequency domain
Yb=zeros(121,121,32,1);
for m=1:9;
Yb =Yb+Y(:,:,:,m);
end
Yk=zeros(121,121);
for k=1:32;
Yk =Yk+(1/32)*Yb(:,:,k)*ctranspose(Yb(:,:,k));
end
% %% image reconstruction
imagesc(x(1,:),y(:,1),((real(Yk))));
46
47
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VITA
Spandana Vemulapalli was born on December 12, 1992. She received her Bachelor of
Engineering degree in Electronics and Communications Engineering from Manipal
Institute of Technology, India. She applied for Master of Science in Electrical Engineering
at UMKC and received an admit with full DISA scholarship. While she was studying at
UMKC, she was a research assistant at Computational Electromagnetics and Antenna
Laboratory and also Computational Intelligence and Bio-Identification Laboratory. She has
presented and published a total of 5 papers in prestigious international conferences and
won many accolades. She has received best paper presentation award at IEEE International
Workshop on Antenna Innovation and Modern Technologies, Ahmedabad, Gujarat, India
(2015), best poster presentation in graduate student category at the SWE conference,
Kansas City (2015), Interdisciplinary and Intercampus research grant (UM system) for
Graduate Assistantship support (2014). She has also received the USNC/URSI Travel
Fellowship Grant Awardee (2015) and School of Graduate Studies Travel Grant, UMKC
(2015-2016) to present a paper at the 2015 APS-URSI conference held in Vancouver,
Canada. She won the outstanding student award for the year 2014-2015 in the graduate
student (MS) category.
LIST OF PUBLICATIONS
1. Investigation of Narrowband, Wideband and Ultrawideband Sensor Arrays for the
Early Detection of Breast Cancer
S.Vemulapalli and D.Chatterjee
57
IEEE International Workshop on Antenna Innovation and Modern Technologies,
Ahmedabad, Gujarat, India, 26-27 December, 2015
2. Evaluation of Ultrawideband Sensor Array in the Detection of Breast Cancer using
Delay-Multiply and Sum Beamforming in the Frequency Domain
S.Vemulapalli and D.Chatterjee
IEEE International Workshop on Antenna Innovation and Modern Technologies,
Ahmedabad, Gujarat, India, 26-27 December, 2015
3. Analysis of Ultrawideband Microwave Imaging via Space Time Beamforming
Algorithm in the Frequency Domain
S.Vemulapalli and D.Chatterjee
5th IEEE Applied Electromagnetics Conference (AEMC-2015), Guwahati, Assam,
India, 18-19 December 2015
4. A Comparative performance of Ultrawideband and Narrowband Microwave
Imaging Sensor Arrays for the Early Detection of Breast Cancer
S.Vemulapalli, D.Ketharnath, D.Chatterjee
IEEE International Symposium on Antennas and Propagation and USNC- URSI
North American Radio Science Meeting in Vancouver, British Columbia, Canada,
19-26 July, 2015
58
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