ITR: Universal Discrete Denoising

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ABSTRACT0312839Verdu, SergioPrinceton UIn this proposal we describe an integrated research program on a new research area with a very richarray of applications: the problem of .ltering or denoising of discrete sequences. This statisticalsignal processing problem arises naturally in a wide range of applications spanning a variety ofinformation technology applications in .elds as varied as computer science, statistics, engineering,astronomy, biology, and information theory.Consider the problem of recovering a signal from a noisy version, which has been corruptedby a known channel. The recovery can assume two major modes depending on the application:noncausal, i.e. it starts once the entire signal is available;and causal, i.e. decisions must be madeimmediately after each symbol is received.The continuous case, where the input and output alphabets are the real line (or other Euclideanspaces), has received immeasurable attention for over half a century, as witnessed by major contributionsto linear .ltering by Wiener, Kolmogorov and Kalman, and to nonlinear .ltering byDonoho and Johnstone.