Diffuse optical tomography (DOT) is a functional imaging modality which aims to retrieve the optical characteristics of the probed tissue, namely light absorption and diffusion. The accurate retrieval of the spatial distribution for each optical characteristic involves the solution of a highly-ill posed, non-linear inverse problem, thus employing a regularization is essential. In this work, we propose an entropic regularization scheme for DOT reconstruction that uses a priori structural information through mutual information (MI) and joint entropy (JE).We compare MI and JE through simulations that illustrate their behavior when the reference and DOT images are not identical in structure. We propose an efficient implementation of these regularizers based on fast Fourier transforms. The method is tested through numerical simulations.
[Show abstract][Hide abstract] ABSTRACT: We present a review of methods for the forward and inverse problems in optical tomography. We limit ourselves to the highly scattering case found in applications in medical imaging, and to the problem of absorption and scattering reconstruction. We discuss the derivation of the diffusion approximation and other simplifications of the full transport problem. We develop sensitivity relations in both the continuous and discrete case with special concentration on the use of the finite element method. A classification of algorithms is presented, and some suggestions for open problems to be addressed in future research are made.
[Show abstract][Hide abstract] ABSTRACT: We propose a non-parametric method for incorporating information from co-registered anatomical images into PET image reconstruction through priors based on mutual information. Mutual information between feature vectors extracted from the anatomical and functional images is used as a priori information in a Bayesian framework for the reconstruction of the PET image. The computation of mutual information requires an estimate of the joint density of the two images, which is obtained by using the Parzen window method. Preconditioned conjugate gradient with a bent Armijo line-search is used to maximize the resulting posterior density. The performance of this method is compared with that using a Gaussian quadratic penalty, which does not use anatomical information. Simulation results are presented for PET and MR images generated from a slice of the Hoffman brain phantom. These indicate that mutual information based penalties can potentially provide superior quantitation compared to Gaussian quadratic penalties
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