Confidence-constrained joint sparsity recovery under the Poisson noise model

TL;DR

This paper addresses the challenge of recovering joint sparsity patterns in signals corrupted by Poisson noise, proposing a convex relaxation approach to improve reconstruction accuracy.

Contribution

It introduces a confidence-constrained optimization framework for joint sparsity recovery under Poisson noise, with a convex reformulation for practical implementation.

Findings

Convex relaxation effectively recovers sparsity patterns.

Proposed method outperforms existing approaches in simulations.

Conditions for perfect reconstruction are analyzed.

Abstract

Our work is focused on the joint sparsity recovery problem where the common sparsity pattern is corrupted by Poisson noise. We formulate the confidence-constrained optimization problem in both least squares (LS) and maximum likelihood (ML) frameworks and study the conditions for perfect reconstruction of the original row sparsity and row sparsity pattern. However, the confidence-constrained optimization problem is non-convex. Using convex relaxation, an alternative convex reformulation of the problem is proposed. We evaluate the performance of the proposed approach using simulation results on synthetic data and show the effectiveness of proposed row sparsity and row sparsity pattern recovery framework.