Optimal restoration of multichannel images based on constrained mean-square estimation

In this paper, we present an efficient algorithm for the problem of multichannel image restoration. Existing multichannel techniques do not provide sufficient flexibility for the simultaneous suppression of the noise process and the preservation of sharp detailed structure in the estimate. The approach introduced overcomes this inefficiency by introducing the prototype Wiener structure in the smoothing process of the estimate. The corresponding algorithm is obtained from the optimization of theconstrained mean-square-error (CMSE) criterion, which is interpreted as a structured regularized criterion. The CMSE estimate always has a meaningful structure and lies between the minimum mean-square error estimate and the pseudo-inverse solution. In addition, the CMSE approach enables the suppression of streak artifacts, which are often experienced due to the amplification of the noise process. In particular, the paper focuses on the selection of the regularization parameter, which can significantly affect the quality of the regularized estimate. Two selection techniques are introduced. The first technique develops the equivalence between the minimization of the weighted least-squares function and the solution of a set of nonlinear equations in the case of unstructured space-varying and nonstationary problem formulations. The second selection method is based on the Cramer-Rao bound on the expected variation of the stabilizing term. The CMSE approach is demonstrated through a multichannel restoration example and is compared to other restoration techniques.