SALMON , Joseph

Sparsity priors are commonly used in denoising and image reconstruction. For analysis-type priors, a dictionary defines a representation of signals that is likely to be sparse. In most situations, this dictionary is not known, and is to be recovered from pairs of ground-truth signals and measurements, by minimizing the reconstruction error....

For composite nonsmooth optimization problems, which are "regular enough", proximal gradient descent achieves model identification after a finite number of iterations. For instance, for the Lasso, this implies that the iterates of proximal gradient descent identify the non-zeros coefficients after a finite number of steps. The identification...