Projected Nesterov’s Proximal-Gradient Algorithm for Sparse Signal Recovery

dc.contributor.author Gu, Renliang
dc.contributor.author Dogandzic, Aleksandar
dc.contributor.author Dogandžić, Aleksandar
dc.contributor.department Electrical and Computer Engineering
dc.date 2018-01-29T20:54:44.000
dc.date.accessioned 2020-06-30T02:02:09Z
dc.date.available 2020-06-30T02:02:09Z
dc.date.copyright Sun Jan 01 00:00:00 UTC 2017
dc.date.issued 2017-07-01
dc.description.abstract <p>We develop a projected Nesterov's proximal-gradient (PNPG) approach for sparse signal reconstruction that combines adaptive step size with Nesterov's momentum acceleration. The objective function that we wish to minimize is the sum of a convex differentiable data-fidelity (negative log-likelihood (NLL)) term and a convex regularization term. We apply sparse signal regularization where the signal belongs to a closed convex set within the closure of the domain of the NLL; the convex-set constraint facilitates flexible NLL domains and accurate signal recovery. Signal sparsity is imposed using the ℓ<sub>1</sub> -norm penalty on the signal's linear transform coefficients. The PNPG approach employs a projected Nesterov's acceleration step with restart and a duality-based inner iteration to compute the proximal mapping. We propose an adaptive step-size selection scheme to obtain a good local majorizing function of the NLL and reduce the time spent backtracking. Thanks to step-size adaptation, PNPG converges faster than the methods that do not adjust to the local curvature of the NLL. We present an integrated derivation of the momentum acceleration and proofs of O(k−2) objective function convergence rate and convergence of the iterates, which account for adaptive step size, inexactness of the iterative proximal mapping, and the convex-set constraint. The tuning of PNPG is largely application independent. Tomographic and compressed-sensing reconstruction experiments with Poisson generalized linear and Gaussian linear measurement models demonstrate the performance of the proposed approach.</p>
dc.description.comments <p>This is a manuscript of an article published as Gu, Renliang, and Aleksandar Dogandžić. "Projected Nesterov's Proximal-Gradient Algorithm for Sparse Signal Recovery." <em>IEEE Transactions on Signal Processing</em> 65, no. 13 (2017): 3510-525. doi:<a href="http://dx.doi.org/10.1109/TSP.2017.2691661" target="_blank">10.1109/TSP.2017.2691661</a>. Posted with permission.</p>
dc.format.mimetype application/pdf
dc.identifier archive/lib.dr.iastate.edu/ece_pubs/125/
dc.identifier.articleid 1125
dc.identifier.contextkey 9982430
dc.identifier.s3bucket isulib-bepress-aws-west
dc.identifier.submissionpath ece_pubs/125
dc.identifier.uri https://dr.lib.iastate.edu/handle/20.500.12876/20945
dc.language.iso en
dc.source.bitstream archive/lib.dr.iastate.edu/ece_pubs/125/2017_Dogandzic_Projected_Nesterov_s.pdf|||Fri Jan 14 19:23:08 UTC 2022
dc.source.uri 10.1109/TSP.2017.2691661
dc.subject.disciplines Electrical and Computer Engineering
dc.subject.disciplines Signal Processing
dc.subject.keywords Convex optimization
dc.subject.keywords Nesterov's momentum acceleration
dc.subject.keywords sparse signal reconstruction
dc.subject.keywords Poisson compressed sensing
dc.subject.keywords proximal-gradient methods
dc.title Projected Nesterov’s Proximal-Gradient Algorithm for Sparse Signal Recovery
dc.type article
dc.type.genre article
dspace.entity.type Publication
relation.isAuthorOfPublication c910f7d3-c386-4c37-8143-4e653a539aa9
relation.isOrgUnitOfPublication a75a044c-d11e-44cd-af4f-dab1d83339ff
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