Application of the multiplicative regularized contrast source inversion method to real biological data

Abstract

In this paper we applied the so-called Multi- plicative Regularized Contrast Source Inversion (MR-CSI) method for imaging of real biological microwave tomography data. By using this method we show that the inversion of three-dimensional high contrast biological object which involves 175616 complex dielectric permittivity unknowns is feasible with a present day computer power. Index Terms—Biomedical, Three-dimensional, Inversion. Electromagnetic microwave tomography is a promising tool to carry out medical diagnostic by producing image of an object in its dielectrical properties. It is known that dielectrical properties (complex permittivity) of tissues with high (muscle) and low (fat and bone) water content are significantly different (1). Further it has been demon- strated that the permittivity of tumors and normal tissue are different in breast (2), in lung (3), in colon (3) and in liver (4). Changes in permittivity were observed during cerebral edema (5), spreading depression in cortex (6) and heart myocardial infraction (7). The value of the changes in the permittivity varies with frequency, type of tissues and diseases from a few (6) up to five hundreds (2) percentage points. There are two significant bottlenecks in the development of microwave tomography technology for biomedical ap- plications. The first is the high attenuation of the elec- tromagnetic wave field within the body. The attenuation can be reduced by employing a low frequency, however spatial resolution is also reduced. The compromise be- tween attenuation and spatial resolution forms an optimum frequency for microwave tomography system. Numerical experiment indicates that microwave imaging of whole scale biological objects with reasonable acquisition time and spatial resolution of 6-8 mm can be performed at frequencies near 1 GHz (8), (14). The second difficulty is the wave character of the electromagnetic field within and around the body. The processing of these type of data required the solution of nonlinear inverse scattering problem. Advanced nonlinear imaging approaches have been developed and applied for imaging of biological objects by several research groups (9), (10), (11), (12). In this paper we applied the so-called Multiplicative reg- ularized contrast source inversion (MR-CSI) method (13) for imaging of real two- (2D) and three-dimensional (3D) biological data. These data are collected at Carolina Med- ical Center using a prototype of microwave tomography system (14). In this MR-CSI method we reconstruct the complex permittivity contrast and the so-called contrast sources (the product of the contrast and the fields) by minimizing a cost functional. This minimization is carried out alternatingly. In each iterative step we update the contrast and the contrast sources each using one conjugate gradient step so that the total computational complexity of the method is equal to the complexity of solving only two forward problems. By operating in this manner solving a full three-dimensional vector nonlinear inverse scattering problem is feasible. Further this method is equipped with total variation type regularization. This regularization is included as a multiplicative constraint, so that the regu- larization parameter needed in the minimization process is determined automatically. The multiplicative type of regularization seems to handle noisy as well as limited data in a robust way without the usually necessary ap riori information.