A class of robust image processors

摘要

In this paper robust recursive estimators for image restoration are developed. Image restoration for images corrupted by noise is carried out in two steps. To preserve true edges while restoring, edge detection using a 5 × 5 × 5 × 5 Graeco-Latin square is carried out as a first step. An edge is localized using an F-test on contrasts. The center pixel is then estimated as a second step. The method of estimation of a center pixel uses a multiple linear regression model fitted to the noisy image part on the same side of the edge. Parameters of a multiple linear regression model are estimated recursively using the Robbins-Monro Stochastic Approximation procedure applied to the least-squares estimator. When noise departs from a Gaussian assumption, robust techniques for restoration are sought. The recursive least-squares estimator is robustized using Huber's maximum likelihood estimator of location parameter 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 minimax estimator based on a soft limiter is used to robustize the recursive least-squares estimator as a computationally simpler but slightly less efficient alternative.The theory developed in this paper was tested using computer simulations which verified the theory and evaluated the computational complexity/simplicity of the methods.