A novel method for audio declipping based on sparsity is presented. The method incorporates psychoacoustic information by weighting the transform coefficients in the l1 minimization. Weighting leads to an improved quality of restoration while retaining a low complexity of the algorithm. Three possible constructions of the weights are proposed, based on the absolute threshold of hearing, the global masking threshold and on a quadratic curve. Experiments compare the restoration quality according to the signal-to-distortion ratio (SDR) and PEMO-Q objective difference grade (ODG) and indicate that with correctly chosen weights, the presented method is able to compete, or even outperform, the current state of the art.