Multi-dimensional signal approximation with sparse structured priors using split Bregman iterations
This work addresses the challenge of preserving spatio-temporal structure in signal decomposition for applications like EEG analysis, representing an incremental improvement with specific gains.
The paper tackles the problem of decomposing multi-dimensional signals with spatio-temporal structure using sparse structured priors, achieving state-of-the-art accuracy with significant gains in convergence speed. It demonstrates effectiveness on artificial and real-world tasks, such as outperforming similar approaches in P300 evoked potentials detection for EEG brainwave decomposition.
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.