Universal discrete denoising

Tsachy Weissman, Erik Ordentlich, Gadiel Seroussi, Sergio Verdú, Marcelo J. Weinberger

Abstract: We propose a discrete denoising algorithm, that, based on the observation of the output of a known discrete memoryless channel (DMC), estimates the input sequence to minimize a given fidelity criterion. The algorithm is universal in the sense that it requires no knowledge of the input sequence or its statistical properties. Yet, asymptotically it performs as well as the optimum denoiser that knows the input sequence distribution. The proposed denoising algorithm is practical, and can be implemented in O(n log n) time and O(n/sup 2/3/ log n) storage complexity. Extensions to the case of delay-constrained denoising, and to the case of channel uncertainty, are briefly discussed.