Smoothed ℓp-ℓ2 solvers for signal denoising

The basis pursuit denoising refers to the solution of an ℓ₁-ℓ₂ minimization formulation which is well known as an effective method for signal denoising. In this paper we investigate an ℓ_p-ℓ₂ formulation with p ∈ (0, 1) for denoising. Based on an analysis of the discontinuity of the global minimizer of the ℓ_p-ℓ₂ problem with respect to regularization parameter, we propose two smoothed ℓ_p-ℓ₂ solvers for orthogonal basis and overcomplete dictionary respectively. Experimental studies that evaluate the performance of the proposed solvers with various parameter settings are also presented.