Universal minimax discrete denoising under channel uncertainty

The assumption of a known channel was inherent in the structure of the denoising under channel uncertainty (DUDE). There are many scenarios where the DUDE is effective for denoising. A denoising scheme is sought, which will accommodate uncertainty in the statistical characteristics of the noisy medium. Unfortunately, it can be shown that in this setting the task of attaining the performance of the optimum nonuniversal distribution-dependent scheme is impossible, even for a "genie-aided" scheme with complete knowledge of the noisy signal statistics. In this paper, the noise-corrupted signal with the clean components and their values in the finite alphabet are assumed. The corruption mechanism is a discrete memoryless channel (DMC) with an associated invertible channel matrix. It lies in a given uncertainty set.