RLS Recovery with Asymmetric Penalty: Fundamental Limits and Algorithmic Approaches

TL;DR

This paper explores the limits and algorithms for regularized least squares signal recovery with asymmetric penalties, especially for signals with nonuniform prior distributions like time-variant sparsity, using the replica method and practical tuning strategies.

Contribution

It introduces an asymptotic performance analysis via the replica method and proposes an optimal tuning strategy for algorithmic approaches in asymmetric penalty-based recovery.

Findings

Asymptotic performance characterized for nonidentical prior distributions.

Proposed tuning strategy improves recovery efficiency.

Demonstrated effectiveness with BPSK signal recovery.

Abstract

This paper studies regularized least square recovery of signals whose samples' prior distributions are nonidentical, e.g., signals with time-variant sparsity. For this model, Bayesian framework suggests to regularize the least squares term with an asymmetric penalty. We investigate this problem in two respects: First, we characterize the asymptotic performance via the replica method and then discuss algorithmic approaches to the problem. Invoking the asymptotic characterization of the performance, we propose a tuning strategy to optimally tune the algorithmic approaches for recovery. To demonstrate applications of the results, the particular example of BPSK recovery is investigated and the efficiency of the proposed strategy is depicted in the shadow of results available in the literature