Multiple descriptions using sparse decompositions

In this paper, we consider the design of multiple descriptions (MDs) using sparse decompositions. In a description erasure channel only a subset of the transmitted descriptions is received. The MD problem concerns the design of the descriptions such that they individually approximate the source and furthermore are able to refine each other. In this paper, we form descriptions using convex optimization with l₁-norm minimization and Euclidean distortion constraints on the reconstructions and show that with this method we can obtain non-trivial descriptions. We give an algorithm based on recently developed first-order method to the proposed convex problem such that we can solve large-scale instances for image sequences.