Information theoretic regularization in diffuse optical tomography

Diffuse optical tomography (DOT) retrieves the spatially distributed optical characteristics of a medium from external measurements. Recovering these parameters of interest involves solving a non-linear and severely ill-posed inverse problem. In this thesis we propose methods towards the regularization of DOT via the introduction of spatially unregistered, a priori information from alternative high resolution anatomical modalities, using the information theory concepts of joint entropy (JE) and mutual information (MI). Such functionals evaluate the similarity between the reconstructed optical image and the prior image, while bypassing the multi-modality barrier manifested as the incommensurate relation between the gray value representations of corresponding anatomical features in the modalities involved. By introducing structural a priori information in the image reconstruction process, we aim to improve the spatial resolution and quantitative accuracy of the solution. A further condition for the accurate incorporation of a priori information is the establishment of correct alignment between the prior image and the probed anatomy in a common coordinate system. However, limited information regarding the probed anatomy is known prior to the reconstruction process. In this work we explore the potentiality of spatially registering the prior image simultaneously with the solution of the reconstruction process. We provide a thorough explanation of the theory from an imaging perspective, accompanied by preliminary results obtained by numerical simulations as well as experimental data. In addition we compare the performance of MI and JE. Finally, we propose a method for fast joint entropy evaluation and optimization, which we later employ for the information theoretic regularization of DOT. The main areas involved in this thesis are: inverse problems, image reconstruction & regularization, diffuse optical tomography and medical image registration