Regularized ART with Gibbs Priors for Tomographic Image Reconstruction

The Algebraic Reconstruction Technique (ART), which is based on Kaczmarz’s projection algorithm, is one of the most important tools for tomographic consistent image reconstruction. Moreover, in the inconsistent case, an extension of Kaczmarz’s method (KERP, for short) has been obtained by one of the authors in a previous paper. But, although theoretically very general, this extension cannot always produce an enough accurate reconstruction. In this respect, we consider in the present paper a regularized version of KERP algorithm (RKERP, for short), which demonstrates a very weak susceptibility to noisy perturbations in the data. The regularization is achieved through a penalty term in a least-squares objective to which the Kaczmarz’s method is applied. This term is expressed with a Gibbs prior that incorporates nearest neighbor interactions among adjacent pixels. A special attention is drawn to a quadratic clique energy function that makes the Gibbs prior equivalent to a Gaussian prior. Our results demonstrate a high efficiency of the regularized KERP algorithm with such a prior as regards to a quality of the reconstructed images and a computational cost. In the simulations, we used the data from borehole tomography in which the inversion is very ill-posed due to a limitation of an angular range of the projections.