Confidence-constrained joint sparsity recovery under the Poisson noise model
This work addresses a domain-specific problem in signal processing for applications like imaging or spectroscopy where Poisson noise is common, but it appears incremental as it builds on existing sparsity recovery methods with a new noise model.
The paper tackles the joint sparsity recovery problem under Poisson noise by formulating confidence-constrained optimization in least squares and maximum likelihood frameworks, and proposes a convex relaxation method, showing effectiveness in recovering row sparsity and its pattern in simulations on synthetic data.
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.