Smoothed $$\ell _1$$ ℓ 1 -regularization-based line search for sparse signal recovery

Smoothed $$\ell _1$$ ℓ 1 -regularization-based line search for sparse signal recovery $$\ell _1$$ ℓ 1 -regularization-based sparse recovery has received a considerable attention over the last decade. In this paper, a solver called SQNSR is proposed to recover signals with high dynamic range. SQNSR utilizes linear search strategy and quasi-Newton step to the solve composite objective function for the sparse recovery problem. Since $$\ell _1$$ ℓ 1 -norm-regularized item is nonsmooth, smoothing technique is introduced to obtain an approximate smoothed function. The sufficient and necessary condition is also derived for the feasible smoothed objective function. By limiting the step length in each iteration, the convergence of SQNSR is guaranteed to obtain the sparsest solution. Numerical simulations are implemented to test the performance of the proposed approach and verify the theoretical analysis. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Soft Computing Springer Journals

Smoothed $$\ell _1$$ ℓ 1 -regularization-based line search for sparse signal recovery

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Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2016 by Springer-Verlag Berlin Heidelberg
Subject
Engineering; Computational Intelligence; Artificial Intelligence (incl. Robotics); Mathematical Logic and Foundations; Control, Robotics, Mechatronics
ISSN
1432-7643
eISSN
1433-7479
D.O.I.
10.1007/s00500-016-2423-4
Publisher site
See Article on Publisher Site

Abstract

$$\ell _1$$ ℓ 1 -regularization-based sparse recovery has received a considerable attention over the last decade. In this paper, a solver called SQNSR is proposed to recover signals with high dynamic range. SQNSR utilizes linear search strategy and quasi-Newton step to the solve composite objective function for the sparse recovery problem. Since $$\ell _1$$ ℓ 1 -norm-regularized item is nonsmooth, smoothing technique is introduced to obtain an approximate smoothed function. The sufficient and necessary condition is also derived for the feasible smoothed objective function. By limiting the step length in each iteration, the convergence of SQNSR is guaranteed to obtain the sparsest solution. Numerical simulations are implemented to test the performance of the proposed approach and verify the theoretical analysis.

Journal

Soft ComputingSpringer Journals

Published: Nov 9, 2016

References

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