Generalized maximum a posteriori processing of multichannel images and applications

This paper considers several aspects of robust estimation in the restoration of mutichannel images. Robust functionals emerging from a generalized maximum a posteriori (MAP) approach are employed for the representation of both the noise and the signal statistics. Several linear multichannel techniques can be derived as special cases of the approach presented. In addition, the robust approach derives nonlinear algorithms that simultaneously account for the suppression of nominal noise and outliers, and for the efficient reconstruction of sharp detailed structure in the estimate. The robust multichannel approach is presented as a general approach for the regularization of the ill-posed restoration problem. From this perspective, we develop a method for the selection of the regularization parameter, which can be used in a wide variety of applications that may or may not involve noise outliers. We consider several issues associated with the application of robust algorithms to multichannel images, we discuss computational inefficiencies of such algorithms, and we propose approximations that are appropriate for their cost-efficient multichannel implementation. We demonstrate the robust approach in two examples from the rapidly developing fields of color image processing and multiresolution image processing in the wavelet domain.The research presented in this paper was partially supported by the Graduate School of the University of Minnesota under Summer Research Fellowship no. 15556 and Grant-in-Aid Award no. 15987.