Gauss-Seidel based spatially varying optimal regularization improves reconstruction in diffuse optical tomography

The inverse problem associated with Diffuse optical tomography image reconstruction is known to be highly nonlinear, under-determined, and ill-posed. The Levenberg-Marquardt technique is employed in solving it and is known to produce low-resolution reconstructed images. To stabilize the inversion of the large matrix, a heuristically chosen regularization parameter is used. A novel methodology is developed using Gauss-Seidel, Modified Richardson, and Kaczmarz recursive methods to solve the inverse problem and to obtain spatially varying regularization parameters, which are optimally obtained for every node automatically, which is otherwise not possible. The proposed methods are thoroughly compared with the existing traditional methods in both 2-D and 3-D imaging domains using numerically simulated noisy data and also real-life phantom data. Of all the proposed methods, the Gauss-Seidel-based method provides a quantitatively accurate estimation of spatially varying regularization using the model-resolution-matrix-based method and hence improves the quality of the reconstructed images with better resolution characteristics.