Recently, considerable research efforts have been devoted to the design of methods to learn from data overcomplete dictionaries for sparse coding. However, learned dictionaries require the solution of a sparse approximation problem for coding new data. In order to overcome this drawback, we propose an algorithm aimed at learning both a dictionary and its dual: a linear mapping directly performing the coding. Our algorithm is based on proximal methods and jointly minimizes the reconstruction error of the dictionary and the coding error of its dual; the sparsity of the representation is induced by an ℓ_1-based penalty on its coefficients. Experimental results show that the algorithm is capable of recovering the expected dictionaries. Furthermore, on a benchmark dataset the image features obtained from the dual matrix yield state-of-the-art classification performance while being much less computational intensive.
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