Generalized subspace pursuit and an application to sparse poisson denoising

We present a generalization of Subspace Pursuit, which seeks the fc-sparse vector that minimizes a generic cost function. We introduce the Restricted Diagonal Property, which much like RIP in the classical setting, enables to control the convergence of Generalized Subspace Pursuit (GSP). To tackle the problem of Poisson denoising, we propose to use GSP together with the Moreau-Yosida approximation of the Poisson likelihood. Experiments were conducted on synthetic, exact sparse and natural images corrupted by Poisson noise. We study the influence of the different parameters and show that our approach performs better than Subspace Pursuit or ℓ₁-relaxed methods and compares favorably to state-of-art methods.