Introduction

The restoration or reconstruction of signals which are degraded by a low pass type system represented by the point spread function and corrupted by noise is a typical ill-posed problem. Nevertheless, image restoration has proven to be a valuable tool to compensate for the degradation of the imaging quality of the Hubble Space Telescope (HST). Fig. 1 schematically shows the generation of the measured data. Basically we want to estimate the signal , e.g., an image written as a vector, from the measured data which contains a noise term . This signal can not be measured directly but only after having passed a linear system represented by the matrix :

In the case of a shift invariant system is a Toeplitz matrix.