Stopping rules for iterative methods in nonnegatively constrained deconvolution

We consider the two-dimensional discrete nonnegatively constrained deconvolution problem, whose goal is to reconstruct an object x⁎ from its image b obtained through an optical system and affected by noise. When the large size of the problem prevents regularization through a direct method, iterative methods enjoying the semi-convergence property, coupled with suitable strategies for enforcing nonnegativity, are suggested. For these methods an accurate detection of the stopping index is essential. In this paper we analyze various stopping rules and, with the aid of a large experimentation, we test their effect on three different widely used iterative regularizing methods.