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Many natural signals exhibit a sparse representation, whenever a suitabledescribing model is given. Here, a linear generative model is considered, wheremany sparsity-based signal processing techniques rely on such a simplifiedmodel. As this model is often unknown for many classes of the signals, we needto select such a model based on the domain knowledge or using some exemplarsignals. This paper presents a new exemplar based approach for the linear model(called the dictionary) selection, for such sparse inverse problems. Theproblem of dictionary selection, which has also been called the dictionarylearning in this setting, is first reformulated as a joint sparsity model. Thejoint sparsity model here differs from the standard joint sparsity model as itconsiders an overcompleteness in the representation of each signal, within therange of selected subspaces. The new dictionary selection paradigm is examinedwith some synthetic and realistic simulations.

Dictionary Subselection Using an Overcomplete Joint Sparsity Model