Matthieu Kowalski

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Sparse regression often uses `p norm priors (with p < 2). This paper demonstrates that the introduction of mixed-norms in such contexts allows one to go one step beyond in signal models, and promote some different, structured, forms of sparsity. It is shown that the particular case of the `1,2 and `2,1 norms leads to new group shrinkage operators. Mixed(More)
Magnetoencephalography (MEG) and electroencephalography (EEG) allow functional brain imaging with high temporal resolution. While solving the inverse problem independently at every time point can give an image of the active brain at every millisecond, such a procedure does not capitalize on the temporal dynamics of the signal. Linear inverse methods(More)
Mixed norms are used to exploit in an easy way, both structure and sparsity in the framework of regression problems, and introduce implicitly couplings between regression coefficients. Regression is done through optimization problems, and corresponding algorithms are described and analyzed. Beside the classical sparse regression problem, multilayered(More)
Magneto- and electroencephalography (M/EEG) measure the electromagnetic fields produced by the neural electrical currents. Given a conductor model for the head, and the distribution of source currents in the brain, Maxwell's equations allow one to compute the ensuing M/EEG signals. Given the actual M/EEG measurements and the solution of this forward(More)
Imaging inverse problems can be formulated as an optimization problem and solved thanks to algorithms such as forward-backward or ISTA (Iterative Shrinkage/Thresholding Algorithm) for which non smooth functionals with sparsity constraints can be minimized efficiently. However, the soft thresholding operator involved in this algorithm leads to a biased(More)
We consider the problem of extracting the source signals from an under-determined convolutive mixture assuming known mixing filters. State-of-the-art methods operate in the time-frequency domain and rely on narrowband approximation of the convolutive mixing process by complex-valued multiplication in each frequency bin. The source signals are then estimated(More)
We consider the audio declipping problem by using iterative thresholding algorithms and the principle of social sparsity. This recently introduced approach features thresholding/shrinkage operators which allow to model dependencies between neighboring coefficients in expansions with time-frequency dictionaries. A new unconstrained convex formulation of the(More)
Sparse and structured signal expansions on dictionaries can be obtained through explicit modeling in the coefficient domain. The originality of the present article lies in the construction and the study of generalized shrinkage operators, whose goal is to identify structured significance maps and give rise to structured thresholding. These generalize(More)
The inverse problem with distributed dipoles models in M/EEG is strongly ill-posed requiring to set priors on the solution. Most common priors are based on a convenient l2 norm. However such methods are known to smear the estimated distribution of cortical currents. In order to provide sparser solutions, other norms than l2 have been proposed in the(More)