Convex Optimization Approach for Stroke Detection in Microwave ...

2014 Makassar International Conference on Electrical Engineering and Infonnatics (MICEEI) Makassar Golden Hotel, Makassar, South Sulawesi, Indonesia 26-30 November 2014

Convex Optimization Approach for Stroke Detection in Microwave Head Imaging U.T. Ahmed, A.T. Mobashsher, K.S. Bialkowski, A.M. Abbosh School of ITEE, The University of Queensland, Brisbane, Australia u.ahmed [email protected]

Abstract-

Convex

optimization

provides

a

method

imaging algorithm was applied in that system to produce a microwave image of the head. The accuracy of the images obtained using this algorithm requires the knowledge of the average pennittivity of the imaged head, but in reality the exact value of permittivity is still unknown for a certain individual. Moreover, the value of average permittivity changes with the direction of the antenna due to the heterogeneous structure of the head. Convex optimization (CO) is a possible technique for estimating the permittivity of human head. There have been some efforts recently to apply this optimization technique in medical imaging [11]-[13]. In this paper, the CO technique using optimized intensity level of the targeted image is applied in radar based head imaging based on the variation of permittivity of the imaged area. The results are compared favorably with the traditional approach in assuming one constant value for the average permittivity.

of

minimization of a convex objective function subject to a convex domain imposed upon it by the problem. For microwave imaging in medical applications, such as head imaging, this technique is seldom investigated.

In this

paper,

a microwave-based head

imaging method based on convex optimization is presented. Convex

optimization

is

used

to

successfully

estimate

the

distribution of relative permittivity of the imaged objects at different directions and thus to improve the quality of the obtained

microwave

image.

The

obtained

results

using

32

antennas surrounding a realistic head model compare favorably with the images from using the traditional microwave head imaging

algorithm,

which

assumes

a

certain

fixed

average

permittivity for the whole imaged head. The results show that the target

representing

a

bleeding

inside

the

head

is

properly

recovered using the proposed optimization despite using wide range of initial average permittivity values. However, the quality of images produced using the traditional

approach depends

strongly on the assumed average permittivity.

II.

Keywords-Microwave imaging; stroke diagnostic system; head imaging; convex optimization.

I.

Convex optimization can be used for solving linear inverse problem arising in image processing. This class of method is an extension of the classical gradient descent algorithm, which is adequate for solving large scale problems even with dense matrix data. However, such methods are also known to converge slowly [14]-[16]. For brain stroke detection, the target is usually one stroke inside the brain, which is a desirable condition for solving the inverse problem. Fig. 1 shows the general configuration of a microwave imaging system using an antenna array of P elements.

INTRODUCTION

Microwave imaging techniques have been attracting a huge interest from researchers around the world due to their potential as a convenient and efficient medical diagnostic system [1]-[6]. Those techniques have recently been investigated to build portable, low-cost and safe diagnostic tools for different medical applications [1]-[9]. One of those applications is head imaging for stroke detection. Brain stroke occurs when the supply of blood to the brain is either interrupted or reduced. When this happens, the brain does not get enough oxygen or nutrients which cause brain cells to die. It is an emergency situation when any delay in the treatment would lead to permanent disability or even death. The current imaging systems, such as CT scan and MRI, are able to successfully identify the location and type of stroke. However, these techniques do not offer a fast, cost effective and portable system. Therefore, a microwave-based imaging technique is a proper choice that can provide a compact and mobile technology for the immediate diagnosis onsite and can be carried as part of the ambulance equipment [10]. A microwave system for head imaging, which is based on radar techniques and includes an array of sixteen antenna elements, has been recently proposed [1]-[3], [6]. A confocal

978-1-4799-6726-1/14/$31.00

©

2014 Crown

OPTIMIZATION TECHNIQUE FOR HEAD IMAGING

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2'

P/2 • P/2+1 •

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Fig.

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I. A general domain of microwave head imaging using antenna array of

P antenna elements surrounding the head.

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ISBN: 978-1-4799-6726-1

2014 Makassar International Conference on Electrical Engineering and Infonnatics (MICEEI) Makassar Golden Hotel, Makassar, South Sulawesi, Indonesia 26-30 November 2014 In the conventional microwave imaging approach, each of The gradient method is designed to solve convex optimization problem of the form the antenna elements in the array is used to transmit continuous signals at N frequency steps from fi to IN , where fi is the starting frequency andlN is the frequency after JIh steps. The same transmitting antenna (monostatic) or all the antennas of the array (multistatic) collect the reflected/scattered signals. The acquired signal at each antenna of pth element, where where, Cn is continuously differentiable convex functions P=I,2, ....32 for the example used in this work, is transformed which is the objective function of the imaging area based on into time domain from frequency domain. Since the head relative permittivity values of the head as the variables. To represents a complex heterogeneous structure, the collected solve this function using gradient descent method, Cn has to be signals are embedded in clutter. Thus, the signals are pre­ a smooth convex function. In order to solve such problems processed to remove the strong background reflections which generally, several algorithms have been developed such as otherwise dominate the target response. An imaging algorithm iterative shrinkage algorithm [18]. The basic idea of this based on confocal delay-sum algorithm is utilized then for the algorithm is to build at each iteration, a regularization of the post-processing of the signal and show a clear image of the linearized differentiable function part in the objective. The object enabling the detection of any target, a brain stroke in smooth convex function is based on � Lipschitz continuous this case [17]. To that end, Fermat's principle is implemented gradient, which states the path that minimizes the travel time of the microwave signal is the real path. This principle is used to L(C): III7C(x) - I7C(y) II ::::'L(C) Ilx-yll/oreveryx,y E RN (2) estimate the correct propagation path from the antenna to boundary points in the head domain, and then from the where L > 0 is a constant and the largest eigenvalue of the boundary points to the scattering points under test, which are Hessian of C is unifonnly upper bounded by L everywhere located inside the head domain. Finally, an image of within the convex set for all X and y to form the convex hull of backscattered signal is obtained from the coherent sum of the all convex combinations [18]. The algorithm initializes a time delay of the spatial difference signals [1]. Obviously, an vector based on the starting point of the algorithm which is, average relative pennittivity of the signal path within the head xO E RN and then until the vector has converged it keeps is needed to estimate the travel time. updating the value of the permittivity based on the In the traditional approach, one average permittivity is reconstruction gradient of hidden units of the sparse area. This assumed for the head irrespective of the signal's travel path. means that the ultimate objective of the optimization is the Accuracy of the image and thus the detection depends on that average of the maximum intensity area compared to the value. If a wrong value is used, the image will show the average in the rest of the head. In this way it identifies the incorrect distribution of scatterers in the head and thus any imaging area with maximum intensity and converges into a stroke might not be detected, or even a false target can be global minimum. shown. On the other hand, the optimization technique III. SIMULATION RESULTS estimates the distribution of relative permittivity of the imaged object at different directions by considering different values of As an investigation of the optimization technique, a permittivity for the whole imaged head. As a result, the heterogeneous head model with realistic shape and size is targeted object can be properly identified based on the constructed considering the frequency dispersive properties of converging criteria of the optimization technique. The key the biological tissues of a real human head. In order to advantage of dealing with convex optimization is that a local accomplish this task, a 3-D image of the human head is minima of the convex function is always a global minima. formulated using MRI-derived model as a CAD file [19]. The To use CO technique to improve the quality of the image, head model includes all the main tissues (skin, fat, muscular the gradient based method is implemented. To apply this parts, skull, Dura, cerebrospinal fluid (CSF), gray matter, method, a real valued function of C is considered on a set X= white matter, cerebellum and spinal cord). N {XI, X2, ... .... xn} of R . This set is called the epigraph of C. The In the simulations, the three-dimensional antenna function C is convex if its epigraph is a convex set in R, where presented in [20] is utilized. To achieve wideband operation, the line joining any two points X and y from the set C lies the utilized antenna employs a slotted dipole element and a inside C as shown in Fig. 2. folded parasitic structure on two blocks of low cost GIL 1023 substrates (relative permittivity lOr =3.32, loss tangent tanG = 0.003 and thickness hs = 1.524 mm ) [20]. The dipole element of the antenna is responsible for the high resonant frequencies. On the other hand, the folded parasitic structure is responsible for the lower operating band for the unidirectional radiation pattern of the antenna. Fig. 2. The convex set contains the line joining any two points that belong to the set.

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ISBN: 978-1-4799-6726-1

2014 Makassar International Conference on Electrical Engineering and Infonnatics (MICEEI) Makassar Golden Hotel, Makassar, South Sulawesi, Indonesia 26-30 November 2014

(a)

(a)

30mm

70 nun

(b)

(b) Fig. 3. The antenna utilized in the simulation: (a) 3D view and (b) top view.

The antenna is finally optimized after completing the initial design using 'Quasi Newton' algorithm [21] in the finite element method based electromagnetic simulator HFSS. As a result, the optimized widest bandwidth of the antenna is obtained based on the local maxima and minima of the stationary point of a function. The reflection coefficient of the antenna is obtained as below -10dB over 102.2% fractional bandwidth (1.1-3.4 GHz) and an average of 9 dB front to back ratio covering the band 1.1 -3.4 GHz, which is suitable for head imaging. The antenna depicted in Fig. 3 has the overall dimensions of 70x30x15 mm3. At the time of data acquisition, the distance between the antenna and head phantom is maintained at 15 mm. Initially the number of antennas is taken as 32 with interval angle of 11.25°. One stroke is assumed in the head model with a size of 20 mm x 20 mm. At first, the traditional confocal imaging algorithm is used to get an image of the head. To that end, a certain average permittivity is assumed for the whole head. Then, the proposed CO technique is implemented and the obtained results are compared with those from the traditional confocal algorithm as shown in Fig. 4. It can be seen from Fig. 4 that by performing a traditional approach in confocal algorithm, the position of the target can be detected but it has a low intensity compared with the remaining healthy tissue regions. The ratio of the target intensity to several healthy areas within the head changes with the different assumed constant value for the relative permittivity. However, after using the convex optimization technique with the similar assumed initial values of the permittivity, the position of the target is successfulIy detected with very clear image.

(c)

(d)

(e)

Fig. 4. Images obtained using the traditional (left) and proposed (right) convex optimization algorithm for the following values of initial average relative permittivity: (a) 30, (b) 35, (c) 40, (d) 45, and (e) 50.

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ISBN: 978-1-4799-6726-1

2014 Makassar International Conference on Electrical Engineering and Infonnatics (MICEEI) Makassar Golden Hotel, Makassar, South Sulawesi, Indonesia 26-30 November 2014 IEEE MTT-S Int. Microwave Workshop Series RF Wireless Tech.

The strong intensity color as shown in Fig. 4 indicates the location of the significant scattering object. The objective func­ tion has converged into global minimum, indicating the correct detection of the target for any reasonable initial value for the average pennittivity. Therefore, using this optimization technique in microwave based head imaging can result in a successful de­ tection of the brain stroke even with variations of relative per­ mittivity of imaged individuals. The presented work in this paper is an initial effort in using convex optimization in microwave-based head imaging. The work needs further improvements in several aspects. In future works, multiple layers of the head similar to the actual head tissues will be considered in the optimization environment for the average permittivity and thus the optimization technique will be tested to get the ultimate global minimum for the imag­ ing area. Moreover, the proposed optimization algorithm of the imaging system will be tested on human subjects based on the ethical clearance to confirm the realistic approach of the opti­ mization technique.

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ISBN: 978-1-4799-6726-1