Exact Recovery of Sparsely Used Overcomplete Dictionaries

We consider the problem of learning overcomplete dictionaries in the context of sparse coding, where each sample selects a sparse subset of dictionary elements. Our method consists of two stages, viz., initial estimation of the dictionary, and a clean-up phase involving estimation of the coefficient matrix, and re-estimation of the dictionary. We prove that our method exactly recovers both the dictionary and the coefficient matrix under a set of sufficient conditions.