Fast and robust EM-based IRLS algorithm for sparse signal recovery from noisy measurements

In this paper, we analyze a new class of iterative re-weighted least squares (IRLS) algorithms and their effectiveness in signal recovery from incomplete and inaccurate linear measurements. These methods can be interpreted as the constrained maximum likelihood estimation under a two-state Gaussian scale mixture assumption on the signal. We show that this class of algorithms, which performs exact recovery in noiseless scenarios under suitable assumptions, is robust even in presence of noise. Moreover these methods outperform classical IRLS for ℓ_τ -minimization with τ ∈ (0; 1] in terms of accuracy and rate of convergence.