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This paper addresses the structurally-constrained sparse decomposition ofmulti-dimensional signals onto overcomplete families of vectors, calleddictionaries. The contribution of the paper is threefold. Firstly, a genericspatio-temporal regularization term is designed and used together with thestandard $\ell_1$ regularization term to enforce a sparse decompositionpreserving the spatio-temporal structure of the signal. Secondly, anoptimization algorithm based on the split Bregman approach is proposed tohandle the associated optimization problem, and its convergence is analyzed.Our well-founded approach yields same accuracy as the other algorithms at thestate-of-the-art, with significant gains in terms of convergence speed.Thirdly, the empirical validation of the approach on artificial and real-worldproblems demonstrates the generality and effectiveness of the method. Onartificial problems, the proposed regularization subsumes the Total Variationminimization and recovers the expected decomposition. On the real-world problemof electro-encephalography brainwave decomposition, the approach outperformssimilar approaches in terms of P300 evoked potentials detection, usingstructured spatial priors to guide the decomposition.

Multi-dimensional signal approximation with sparse structured priors using split Bregman iterations