Universal Minimax Discrete Denoising Under Channel Uncertainty
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Publication:3548111
DOI10.1109/TIT.2006.878234zbMATH Open1309.94098arXivcs/0504060MaRDI QIDQ3548111
Tsachy Weissman, Styrmir Sigurjonsson, George M. Gemelos
Publication date: 21 December 2008
Published in: IEEE Transactions on Information Theory (Search for Journal in Brave)
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, the 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.
Full work available at URL: https://arxiv.org/abs/cs/0504060
Minimax procedures in statistical decision theory (62C20) Statistical aspects of information-theoretic topics (62B10) Channel models (including quantum) in information and communication theory (94A40)
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