Nonlinear image filtering: trade-off between optimality and practicality

The high sensitivity of many specific filters to an accurate modeling of the noise that is to be removed led us to investigate the existence of a new class of filters using the theory of robust estimation. The latter class includes a large number of filters whose optimality when given a specific noise distribution is attained by merely adjusting weights. We also show that a convex combination of the mean and relaxed median filters exhibits many good properties. Some deterministic and asymptotic properties are studied, and comparisons with other filtering schemes are performed. Experimental results showing a much improved performance of the proposed filters in the presence of mixed Gaussian and heavy-tailed noise are analyzed and illustrated