Sparse Regression Using Mixed Norms

Matthieu Kowalski (1)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités

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, multi-layered expansion on unions of dictionaries of signals are also considered. These sparse structured expansions are done subject to an exact reconstruction constraint, using a modified FOCUSS algorithm. When the mixed norms are used in the framework of regularized inverse problem, a thresholded Landweber iteration is used to minimize the corresponding variational problem.

Mots clés: Sparse regression; Structured regression; Mixed norms; FOCUSS; Thresholded Landweber iterations

Domaines: Traitement du signal et de l'image [eess.SP]; Optimisation et contrôle [math.OC]; Traitement du signal et de l'image [eess.SP]

Matthieu Kowalski. Sparse Regression Using Mixed Norms. Applied and Computational Harmonic Analysis, 2009, 27 (3), pp.303-324. ⟨10.1016/j.acha.2009.05.006⟩. ⟨hal-00202904v4⟩