Microwave Tomographic Imaging Reconstruction Algorithm Research

Microwave tomography is a promising nondestructive evaluation method, which exploit microwave as incidence to irradiate the object and reconstruct the internal complex permittivity image of the object by applying the scattered data from receivers settled outside of the object. Complex permittivity includes abundant information, since its real part is the dielectric constant, and the imaginary part is proportional to conductivity. Moreover, permittivity has close relationship with some physiological parameters, such as temperature, water content, blood content, blood oxygenation, and so on. Therefore microwave tomography can produce the internal information of not only morphology but also physiology. Thus it will be a potential imaging technique for medical diagnosis, as either an independent system competitive with other sophisticated imaging methods or merely a complementary method.Microwave tomography belongs to electromagnetic inverse scattering problems, where the word "scattering" is a generalized concept, which includes transmission, reflection, refraction, diffraction, and scattering. This kind of problems is quite difficult to develop to its full potential because of its nonlinearity and ill-posedness. Fortunately, the problem of a weakly scattering object can be linearized by Born or Rytov approximation and thus resolved in Fourier domain with methods similar to those in X-CT. However, these methods would not be valid in biomedical field, in which most tissues or media have high contrast of permittivity. A possible solution is to apply spatial methods, which discretize the integrate equations into matrix equations and solve them iteratively in the framework of optimization problem. The conspicuous advantage of these methods is the capability to improve the inherent ill-posedness of the inverse scattering problem by introducing some a priori knowledge of the object, such as the external structure, the lower and upper limit of permittivity, etc. It is these spatial methods that encourage the development of microwave tomography and make a lot of achievements.After the brief explanation of the principle of microwave tomography and introduction of some basic reconstruction algorithms several spatial methods are proposed, including the extended local search reconstruction (ELSR), the neural network reconstruction (NNR), and the trust region reconstruction (TRR). ELSR focuses on not only the errors of scattered data, but also the errors of coefficient matrix coming from computing. Hence, ELSR is to search the global optimum solution of the total least squres problem and apply Tikhonov regularization to improve the ill-posedness of the problem. NNR is to resolve a mixed-variable problem, since a Morkov random field model is introduced and there are binary line processes, together with the continuous permittivity, in the edge-preserving regularization. Here, NNR includes two neural networks, coupled Hopfield network (CHN) and augmented Hopfield network (AHN), both of which are composed with two sub-networks to deal with continuous and binary variables, respectively. Inaddition, these two sub-networks interact with each other. The sub-networks to continuous variables of CHN and AHN are based on the continuous Hopfield network and have the same structure and neurons. The difference between CHN and AHN exists in the other sub-network of handling the binary variables. For CHN, the subnetwork is also a continuous Hopfield network, for the line processes have been expanded into continuous one with the range from 0 to 1. A specific penalty term is incorporated into the energy function to penalize the continuous line processes back to binary variables. Situation is quite different in AHN. The sub-network of binary variable is composed of binary neurons with binary input and output, and thus can deal with binary variable directly. TRR resolve the problem with constrained least squares criterion, where the constrained condition comes from a priori knowledge. In each iteration the problem can be transformed as...