  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.
