  This paper addresses the structurally-constrained sparse decomposition of
multi-dimensional signals onto overcomplete families of vectors, called
dictionaries. The contribution of the paper is threefold. Firstly, a generic
spatio-temporal regularization term is designed and used together with the
standard $\ell_1$ regularization term to enforce a sparse decomposition
preserving the spatio-temporal structure of the signal. Secondly, an
optimization algorithm based on the split Bregman approach is proposed to
handle the associated optimization problem, and its convergence is analyzed.
Our well-founded approach yields same accuracy as the other algorithms at the
state-of-the-art, with significant gains in terms of convergence speed.
Thirdly, the empirical validation of the approach on artificial and real-world
problems demonstrates the generality and effectiveness of the method. On
artificial problems, the proposed regularization subsumes the Total Variation
minimization and recovers the expected decomposition. On the real-world problem
of electro-encephalography brainwave decomposition, the approach outperforms
similar approaches in terms of P300 evoked potentials detection, using
structured spatial priors to guide the decomposition.
