An iterative method for designing separable Wiener filters

In this paper, we present a technique for designing the optimal (in the mean square error sense) separable 2-D filter for recovering a signal from a noise-corrupted signal when the joint statistics of the signal and noise are known. A set of nonlinear equations in the design parameters is derived, and an iterative algorithm to solve them is presented. The algorithm is shown to be nondivergent in theory and rapidly convergent in practice. The results of applying the separable filter design algorithm to several typical image recovery problems are given. In most cases, the performance of the resulting separable filter is similar to that of the optimal nonseparable filter with the same region of support.