Robust regularized image restoration

Many image processing applications involve long-tailed noise processes, which introduce outliers in the gray-level distribution of the image. The performance of conventional restoration algorithms is highly degraded by such noise processes. In this paper, a novel restoration approach is introduced, which combines the properties of regularized and robust estimation schemes. Most prominent regularized approaches attempt to compensate for the ill-posedness of the pseudo-inverse solution. Regularization is achieved by constraining the least squares solution in terms of a smoothing criterion. The optimization approach introduced in this paper, further modifies the regularized criterion according to the notion of M-estimation. Thus, an influence function is employed in restraining the contribution of large estimate-deviations in the optimization criterioa The modified criterion provides nonlinear estimates, which do not suffer from artifacts due to the presence of long-tailed noise. The computation of the robust regularized estimate is based on the simple structure of a steepest-descent iterative procedure. One of the most important factors associated with the concept of regularization, is the regularization parameter. Adaptive schemes concerning the selection of this parameter at every iteration step are introduced. The convergence properties of the robust and the adaptive algorithms introduced are extensively studied. The capabilities of the robust regularized algorithms are demonstrated through restoration examples.