Comparative study of some statistical and set-theoretic methods for image restoration

In the last decade, many researchers have devoted considerable effort to the problem of image restoration. However, no recent study has been undertaken for a comparative evaluation of these techniques under conditions where a user may have different kinds of a priori information about the ideal image. To this effect, we briefly survey some recent techniques and compare the performance of a linear space-invariant (LSI) maximum a posteriori (MAP) filter, an LSI reduced update Kalman filter (RUKF), an edge-adaptive RUKF, and an adaptive convex-type constraint-based restoration implemented via the method of projection onto convex sets (POCS). The mean square errors resulting from the LSI algorithms are compared with that of the finite impulse response Wiener filter, which is the theoretical limit in this case. We also compare the results visually in terms of their sharpness and the appearance of artifacts. As expected, the space-variant restoration methods which are adaptive to local image properties obtain the best results.