Universal Minimax Discrete Denoising Under Channel Uncertainty

Abstract

The goal of a denoising algorithm is to recover a signal from its noise-corrupted observations. Perfect recovery is seldom possible and performance is measured under a given single-letter fidelity criterion. For discrete signals corrupted by a known discrete memoryless channel (DMC), the Discrete Universal DEnoiser (DUDE) was recently shown to perform this task asymptotically optimally, without knowledge of the statistical properties of the source. In the present work, we address the scenario where, in addition to the lack of knowledge of the source statistics, there is also uncertainty in the channel characteristics. We propose a family of discrete denoisers and establish their asymptotic optimality under a minimax performance criterion which we argue is appropriate for this setting. As we show elsewhere, the proposed schemes can also be implemented computationally efficiently