A CLASS OF ROBUST IMAGE-PROCESSORS

In this paper robust recursive estimators for image restoration are de veloped. Image restoration for images corrupted by noise is carried ou t in two steps. To preserve true edges while restoring, edge detection using a 5 x 5 x 5 x 5 Graeco-Latin square is carried out as a first s tep. An edge is localized using an F-test on contrasts. The center pix el is then estimated as a second step. The method of estimation of a c enter pixel uses a multiple linear regression model fitted to the nois y image part on the same side of the edge. Parameters of a multiple li near regression model are estimated recursively using the Robbins-Monr o Stochastic Approximation procedure applied to the least-squares esti mator. When noise departs from a Gaussian assumption, robust technique s for restoration are sought. The recursive least-squares estimator is robustized using Huber's maximum likelihood estimator of location par ameter of the -f'/f type, where -f'/f is approximated by an M-interval polynomial approximation algorithm, and f is the p.d.f. of noise. A m inimax estimator based on a soft limiter is used to robustize the recu rsive least-squares estimator as a computationally simpler but slightl y less efficient alternative. The theory developed in this paper was t ested using computer simulations which verified the theory and evaluat ed the computational complexity/simplicity of the methods.