On regularization parameters estimation in edge-preserving image reconstruction

Abstract

The image restoration problem is a well known ill-posed inverse problem. Thus, to solve it some regularization techniques are necessary. By these techniques the solution of the problem is defined as the minimum of an energy function. This function is given by the sum of two terms: the first one is due to the data consistency condition, the second one is related to the a priori smoothness condition on the solution. A regularization parameter regulate the degree of strength of the two terms. A right estimation of this parameter is very important to obtain a correct image reconstruction. Dealing with an edge-preserving image reconstruction, another free parameter is introduced. This parameter controls the number of discontinuities presenting in the restored image. In this paper we deal with joint estimation of these two parameters, proposing a novel technique for a correct second order reconstruction. © 2008 Springer-Verlag Berlin Heidelberg.