IMAGE-RESTORATION USING RECURSIVE ESTIMATORS

In this paper, edge preserving recursive estimators are proposed for r estoring images corrupted by noise, Edge detection using a 5x5 Graeco- Latin squares (GLS) mask is carried out as the first step for preservi ng edges, The GLS mask preprocessor determines the orientation of edge s in horizontal, vertical, 45 degrees diagonal, or 135 degrees diagona l directions, The actual removal of noise is done in the second step, If the noise is Gaussian, the center pixel in the 5x5 mask is estimate d using a multiple linear regression model fitted to the noisy image o n the same side of the edge, The parameters of the regression model ar e estimated using the least squares estimator, The least squares estim ator is made recursive using the Robbins-Monro stochastic approximatio n (RMSA) algorithm, The RMSA guarantees convergence of the estimate in the mean square sense and with probability one, If the Gaussian noise is contaminated by a small percentage of heavy tailed (impulsive) noi se (salt and pepper noise), the recursive least square estimator is ro bustized using a symmetrical version of Wilcoxon signed rank statistic , The GLS mask for edge detection uses an F-ratio test which is robust for small deviations from normality assumption of the noise, The math ematical properties and various forms of convergence of the robustized algorithm are shown in the appendix, The efficacy of the proposed res toration procedures are demonstrated on two types of images (''girl'' and ''house'').