ITR: Universal Discrete Denoising

在这份提案中，我们描述了一个具有非常广泛应用的新研究领域的综合研究计划：离散序列的滤波或去噪问题。这种统计信号处理问题自然而然地出现在广泛的应用中，涉及计算机科学、统计学、工程学、天文学、生物学和信息论等领域的各种信息技术应用。考虑从已被已知通道破坏的噪声版本中恢复信号的问题。根据应用，恢复可以采用两种主要模式：非因果，即一旦整个信号可用就开始；因果，即必须在接收到每个符号之后立即作出决定。连续情况，其中输入和输出字母表是实线(或其他欧几里得空间)，半个多世纪以来受到了不可估量的关注，正如Wiener，Kolmogorov和Kalman对线性变换以及Donoho和Johnstone对非线性变换的主要贡献所证明的那样。

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.