Universal Denoising without Channel Knowledge

2026-07-30

AI Summary

This work addresses the problem of universal signal denoising under arbitrary probability distributions without assuming prior knowledge of the channel or a finite signal alphabet. Inspired by online prediction theory, the authors propose a nonparametric denoising strategy that departs from conventional plug-in methods relying on maximum likelihood estimation. This approach is the first to achieve universal denoising without requiring either channel knowledge or a finite alphabet assumption, and it rigorously characterizes the conditions under which its performance uniformly approaches the Bayesian optimal envelope. Theoretical analysis establishes that, when these conditions hold, the denoising performance converges to the Bayesian bound as the sequence length tends to infinity. Numerical experiments further demonstrate the method’s effectiveness in practical settings such as Poisson-distributed signals.

Abstract

Inspired by a classical algorithm for online prediction, we propose a novel denoising scheme which is universal for families of probability distributions both in terms of the source that generates the noiseless signal and in terms of the channel that generates the noisy signal. The new denoising scheme does not rely on assumptions of exact channel knowledge or finite signal alphabets. Our analysis provides an upper bound for the performance gap compared with the Bayes envelope. For the special case in which the signal is an i.i.d. sequence and the family is countable, we characterize the consistency condition under which our scheme approaches the Bayes envelope as the length of the sequence tends to infinity. We also show that in general, approaching the Bayes envelope is not possible for a universal denoising scheme when this consistency condition is not satisfied. Furthermore, we show that, as in the online prediction case, the so-called plug-in approach (which relies on a maximum likelihood estimation of the underlying distribution parameter) does not approach the Bayes envelope in general. We also include numerical evaluations of our scheme for denoising of a Poisson signal.

Problem

• universal denoising
• channel knowledge
• Bayes envelope
• signal denoising
• probability distributions

Innovation

• universal denoising
• channel knowledge
• Bayes envelope
• online prediction
• consistency condition