The stability of certain image restoration problems: Quantitative results

The problem of restoring randomly distributed sets of missing pixels in band-limited discrete images has been considered by several authors, and iterative and non-iterative algorithms, theoretically capable of error-free restoration, have been proposed for this task. The crucial question of stability, however, has been less often studied. In this work we discuss the well-posedness of this image restoration problem as a function of the positions of the missing pixels. Our results help in clarifying the dependence of the eigenvalues of the interpolation matrix upon the number and location of the missing pixels. We give bounds for these eigenvalues which turn out to be accurate and extremely easy to compute, In fact, they can be found in negligible time. The results given are confirmed by simulation results