An EM-algorithm approach for the design of orthonormal bases adapted to sparse representations

In this paper, we consider the problem of dictionary learning for sparse representations. Several algorithms dealing with this problem can be found in the literature. One of them, introduced by Sezer et al. in optimizes a dictionary made up of the union of orthonormal bases. In this paper, we propose a probabilistic interpretation of Sezer's algorithm and suggest a novel optimization procedure based on the EM algorithm. Comparisons of the performance in terms of missed detection rate show a clear superiority of the proposed approach.