Recently, considerable research efforts have been devoted to the design ofmethods to learn from data overcomplete dictionaries for sparse coding.However, learned dictionaries require the solution of an optimization problemfor coding new data. In order to overcome this drawback, we propose analgorithm aimed at learning both a dictionary and its dual: a linear mappingdirectly performing the coding. By leveraging on proximal methods, ouralgorithm jointly minimizes the reconstruction error of the dictionary and thecoding error of its dual; the sparsity of the representation is induced by an$\ell_1$-based penalty on its coefficients. The results obtained on syntheticdata and real images show that the algorithm is capable of recovering theexpected dictionaries. Furthermore, on a benchmark dataset, we show that theimage features obtained from the dual matrix yield state-of-the-artclassification performance while being much less computational intensive.
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