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Tractable Learning of Sparsely Used Dictionaries from Incomplete Samples

In dictionary learning, we seek a collection of atoms that sparsely represent a given set of training samples. While this problem is well-studied, relatively less is known about the more challenging case where the samples are incomplete, i.e., we only observe a fraction of their coordinates. In this paper, we develop and analyze an algorithm to solve this problem, provided that the dictionary satisfies additional low-dimensional structure.