Stability Conditions in Image Reconstruction: a New Regularization Principle

Abstract

Owing to systematic and noise-type errors, the inverse problems of Image Reconstruction prove to be unstable (see for instance [1]). To cope with these ill-conditioned situations, we therefore have to develop appropriate regularization methods. The problem is to choose a regularization principle ensuring the stability of the restoration procedures. Intuitively, it is clear that we have to find a compromise between resolution and robustness. It is therefore natural to devise a stabilization principle involving the notion of resolution explicitly. As specified at the end of this paper, this is not the case, in particular, for the regularization principle introduced by Tihonov. In other respects, it must be possible to select the stabilization parameters before setting the reconstruction process in motion. In this context, we have devised and implemented a new method for Partial Deconvolution with Support Constraint. The aim of this communication is to give a survey of the corresponding interactive procedure. For clarity we restrict ourselves to the special case of Band-Limited Extrapolation [1]; the generalization to Partial Deconvolution is straightforward.