Coarse-to-fine reconstruction in linear inverse problems with application to limited-angle computerized tomography

Abstract

The goal of this paper is to propose and test an iterative coarse-to-fine reconstruction procedure for a certain class of linear inverse problems. This procedure is based on preconditioned iterative regularization through the conjugate gradient (CG) method, through Tikhonov preconditioning, as well as through wavelet low-pass filtering. A quadratic minimization problem associated with a linear inverse problem, can be very problematic if the quadratic form is not diagonal or nearly (block) diagonal. In the present reconstruction strategy, a nearly block diagonal representation of a quadratic form is obtained due to wavelet filtering and preconditioning. In the numerical experiments, the proposed procedure is successfully applied to limited-angle computerized tomography (limited-angle CT). The results of these experiments show that a combined use of wavelet filters and preconditioning can be effective within the present problem class.