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

, Volume 21 (16) – Nov 9, 2016
16 pages

/lp/springer_journal/smoothed-ell-1-1-regularization-based-line-search-for-sparse-signal-1yjEIMhRyA
Publisher
Springer 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

DeepDyve is your personal research library

It’s your single place to instantly
that matters to you.

over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month Explore the DeepDyve Library Search Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly Organize Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place. Access Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals. Your journals are on DeepDyve Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more. All the latest content is available, no embargo periods. DeepDyve Freelancer DeepDyve Pro Price FREE$49/month
\$360/year

Save searches from
PubMed

Create lists to

Export lists, citations