Noise reduction in signal processing using binary couplings

TL;DR

This paper extends a noise reduction model in signal processing with binary couplings, providing practical improvements, an annealed approximation for noise source limits, and a universal behavior of the RSB Parisi solution.

Contribution

It introduces a practical extension of an existing noise reduction model with binary couplings and analyzes its theoretical properties including an annealed approximation and universality of the Parisi solution.

Findings

Annealed approximation provides an upper bound on noise sources.

Full RSB Parisi solution is universal for symmetric distributions.

Model extension improves practical applicability.

Abstract

We report a simple extension of a model for noise reduction in signal processing, already introduced by Mourik et al., in the presence of binary coupling vectors, which turns to be more useful for practical and engineering implementations. We also compute annealed approximation which gives an upper bound of the correct critical number of noise-sources. Finally, we also find that the full RSB Parisi solution just above the AT line is an universal function for any symmetric distribution of the coupling vectors.