Information theoretic regularization in diffuse optical tomography.

Diffuse optical tomography (DOT) retrieves the spatially distributed optical characteristics of a medium from external measurements. Recovering the parameters of interest involves solving a nonlinear and highly ill-posed inverse problem. This paper examines the possibility of regularizing DOT via the introduction of a priori information from alternative high-resolution anatomical modalities, using the information theory concepts of mutual information (MI) and joint entropy (JE). Such functionals evaluate the similarity between the reconstructed optical image and the prior image while bypassing the multimodality barrier manifested as the incommensurate relation between the gray value representations of corresponding anatomical features in the two modalities. By introducing structural information, we aim to improve the spatial resolution and quantitative accuracy of the solution. We provide a thorough explanation of the theory from an imaging perspective, accompanied by preliminary results using numerical simulations. In addition we compare the performance of MI and JE. Finally, we have adopted a method for fast marginal entropy evaluation and optimization by modifying the objective function and extending it to the JE case. We demonstrate its use on an image reconstruction framework and show significant computational savings.