Multi-dimensional sparse structured signal approximation using split Bregman iterations

Sparse dictionary-based representations, where each signal involves few atoms, have been thoroughly investigated for their good properties, as they enable robust transmission (compressed sensing [1]) or image in-painting [2]. The dictionary is either given, based on the domain knowledge, or learned from the signals [3]. The so-called sparse approximation algorithm aims at finding a sparse approximate representation of the considered signals using this dictionary, by minimizing a weighted sum of the approximation loss and the representation sparsity (see [4] for a survey). When available, prior knowledge about the application domain can also be used to guide the search toward "plausible" decompositions. This paper focuses on sparse approximation enforcing a structured decomposition property, defined as follows. Let the signals be structured (e.g.