combines nonconvex Lipschitzian-type mappings with canonical orthogonal projectors. The former are aimed at uniformly enhancing the sparsity level by shrinkage effects, the latter are used to project back onto the space of feasible solutions. The iterative process is driven by an increasing sequence of a scalar parameter that mainly contributes to approach the sparsest solutions. It is shown that the minima are locally asymptotically stable for a specific smooth . ℓ0-norm. Furthermore, it is shown that the points yielded by this iterative strategy are related to the optimal solutions measured in terms of a suitable smooth . ℓ1-norm. Numerical simulations on phase transition show that the performances of the proposed technique overcome those yielded by well known methods for sparse recovery.

Sparse decomposition by iterating Lipschitzian-type mappings / A. Adamo, G. Grossi, R. Lanzarotti, J. Lin. - In: THEORETICAL COMPUTER SCIENCE. - ISSN 0304-3975. - 664(2017 Feb 15), pp. 12-28. [Epub ahead of print] [10.1016/j.tcs.2016.04.025]

Sparse decomposition by iterating Lipschitzian-type mappings

A. Adamo
Primo
;
G. Grossi
;
R. Lanzarotti
Penultimo
;
J. Lin
Ultimo
2017

Abstract

combines nonconvex Lipschitzian-type mappings with canonical orthogonal projectors. The former are aimed at uniformly enhancing the sparsity level by shrinkage effects, the latter are used to project back onto the space of feasible solutions. The iterative process is driven by an increasing sequence of a scalar parameter that mainly contributes to approach the sparsest solutions. It is shown that the minima are locally asymptotically stable for a specific smooth . ℓ0-norm. Furthermore, it is shown that the points yielded by this iterative strategy are related to the optimal solutions measured in terms of a suitable smooth . ℓ1-norm. Numerical simulations on phase transition show that the performances of the proposed technique overcome those yielded by well known methods for sparse recovery.
fixed-point iteration scheme; Lipschitzian mappings; Smooth ℓ0-norm; Smooth ℓ1-norm; sparse recovery; underdetermined linear systems
Settore INF/01 - Informatica
26-apr-2016
Article (author)
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/426526
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