This paper addresses an innovative approach to informed enhancement of damaged sound. It uses sparse approximations with a learned dictionary of atoms modeling the main components of the undamaged source spectra. The decomposition process aims at finding which of the atoms could constitute the decomposition of the undamaged source in order to recover it. The decomposition of the damaged signal is done with a Matching Pursuit algorithm and involves an adaptation of the dictionary learned on undamaged sources. Evaluation is performed on a bandwidth extension task for various classes of signals.