Recently there has been a growing interest in the sparse representation of signals. Particularly, many new multi-scale transforms have been proposed in this direction. Instead of using fixed transforms such as wavelets, curvelets etc., an alternative way is to train a dictionary from the image itself. This paper presents a novel despeckling scheme for medical ultrasound images using such a sparse and redundant representation. It is shown that the proposed algorithm can be used effectively for removal of multiplicative speckle noise by introducing a simple preprocessing stage before an adaptive dictionary is learned from the image patches (called atoms) for sparse representation. This learning process, called the K-SVD, is efficiently performed using an Orthogonal Matching Pursuit (OMP) and a Singular Value Decomposition (SVD). Results are evaluated both on US images and artificially speckled photographic images.