An infeasible Predictor-Corrector Interior Point Method Applied to Image Denoising

Projet PROMATH; Image recovery problems can be solved using optimization techniques. In this case, they often lead to the resolution of either a large scale quadratic program, or, equivalently, to a nondifferentiable minimization problem. Interior point methods are widely known for their efficiency in linear programming. Lately, they have been extended with success to the resolution of linear complementary problems, (LCP), which include convex quadratic programming. We present an infeasible predictor-corrector interior point method, in the general framework of monotone (LCP). The algorithm has polynomial complexity. We also prove it converges globally, with asymptotic quadratic rate. We apply this method to the denoising of images. In the implementation we take advantage of the underlying structure of the problem, specially its sparsity. We obtain good performances, that we assess by comparing the method with a variable-metric proximal bundle algorithm applied to the resolution of the equivalent nonsmooth problem.