Comparison of the main forms of half-quadratic regularization

We consider the reconstruction of images by minimizing regularized cost-functions. To accelerate the computation of the estimate, two forms of half-quadratic regularization, multiplicative and additive, are often used. The goal of this paper is to compare both theoretically and experimentally the efficiency of these two forms. We provide a theoretical and experimental analysis of the speed of convergence that they allow. We show that the multiplicative form gives rise to a better rate of convergence.