{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T04:47:35Z","timestamp":1776142055960,"version":"3.50.1"},"reference-count":45,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12025104"],"award-info":[{"award-number":["12025104"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Signal Processing"],"published-print":{"date-parts":[[2026,8]]},"DOI":"10.1016\/j.sigpro.2026.110600","type":"journal-article","created":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T15:55:35Z","timestamp":1773676535000},"page":"110600","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["A two-stage proximal gradient algorithm for sparse optimization problems"],"prefix":"10.1016","volume":"245","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-2680-5380","authenticated-orcid":false,"given":"Jialu","family":"Shen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5623-4864","authenticated-orcid":false,"given":"Zhongyi","family":"Huang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0151-3938","authenticated-orcid":false,"given":"Wenli","family":"Yang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5352-0251","authenticated-orcid":false,"given":"Wei","family":"Zhu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/j.sigpro.2026.110600_bib0001","series-title":"Proc. Int. Congr. Math.","first-page":"235","article-title":"Mathematics of sparsity (and a few other things)","volume":"123","author":"Cand\u00e8s","year":"2014"},{"issue":"2","key":"10.1016\/j.sigpro.2026.110600_bib0002","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1109\/MSP.2007.914731","article-title":"An introduction to compressive sampling","volume":"25","author":"Cand\u00e8s","year":"2008","journal-title":"IEEE Signal Process. Mag."},{"issue":"6","key":"10.1016\/j.sigpro.2026.110600_bib0003","doi-asserted-by":"crossref","first-page":"906","DOI":"10.1109\/JPROC.2010.2047424","article-title":"Applications of sparse representation and compressive sensing","volume":"98","author":"Baraniuk","year":"2010","journal-title":"Proc. IEEE"},{"key":"10.1016\/j.sigpro.2026.110600_bib0004","doi-asserted-by":"crossref","DOI":"10.1016\/j.sigpro.2025.110020","article-title":"Low-resolution compressed sensing and beyond for communications and sensing: trends and opportunities","volume":"235","author":"Joseph","year":"2025","journal-title":"Signal Process."},{"key":"10.1016\/j.sigpro.2026.110600_bib0005","series-title":"Proc. Eur. Solid-State Circuits Conf. (ESSCIRC)","first-page":"22","article-title":"Compressive sensing: principles and hardware implementations","author":"Cand\u00e8s","year":"2013"},{"issue":"7","key":"10.1016\/j.sigpro.2026.110600_bib0006","doi-asserted-by":"crossref","DOI":"10.1118\/1.4811100","article-title":"Improving IMRT delivery efficiency with reweighted \u21131-minimization for inverse planning","volume":"40","author":"Kim","year":"2013","journal-title":"Med. Phys."},{"issue":"1","key":"10.1016\/j.sigpro.2026.110600_bib0007","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jcp.2004.12.004","article-title":"The type 3 nonuniform FFT and its applications","volume":"206","author":"Lee","year":"2005","journal-title":"J. Comput. Phys."},{"issue":"2","key":"10.1016\/j.sigpro.2026.110600_bib0008","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1137\/S0097539792240406","article-title":"Sparse approximate solutions to linear systems","volume":"24","author":"Natarajan","year":"1995","journal-title":"SIAM J. Comput."},{"issue":"2","key":"10.1016\/j.sigpro.2026.110600_bib0009","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1007\/s10915-021-01557-1","article-title":"A first-order image restoration model that promotes image contrast preservation","volume":"88","author":"Zhu","year":"2021","journal-title":"J. Sci. Comput."},{"key":"10.1016\/j.sigpro.2026.110600_bib0010","doi-asserted-by":"crossref","DOI":"10.1016\/j.sigpro.2024.109523","article-title":"Robust sparse representation based on fitting error decomposition","volume":"222","author":"Wang","year":"2024","journal-title":"Signal Process."},{"key":"10.1016\/j.sigpro.2026.110600_bib0011","doi-asserted-by":"crossref","DOI":"10.1016\/j.sigpro.2024.109617","article-title":"Non-signal components minimization for sparse signal recovery","volume":"226","author":"Xiang","year":"2025","journal-title":"Signal Process."},{"issue":"5\u20136","key":"10.1016\/j.sigpro.2026.110600_bib0012","doi-asserted-by":"crossref","first-page":"877","DOI":"10.1007\/s00041-008-9045-x","article-title":"Enhancing sparsity by reweighted \u21131 minimization","volume":"14","author":"Cand\u00e8s","year":"2008","journal-title":"J. Fourier Anal. Appl."},{"issue":"11","key":"10.1016\/j.sigpro.2026.110600_bib0013","doi-asserted-by":"crossref","first-page":"1413","DOI":"10.1002\/cpa.20042","article-title":"An iterative thresholding algorithm for linear inverse problems with a sparsity constraint","volume":"57","author":"Daubechies","year":"2004","journal-title":"Commun. Pure Appl. Math."},{"issue":"1","key":"10.1016\/j.sigpro.2026.110600_bib0014","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1137\/080716542","article-title":"A fast iterative shrinkage-thresholding algorithm for linear inverse problems","volume":"2","author":"Beck","year":"2009","journal-title":"SIAM J. Imag. Sci."},{"issue":"2","key":"10.1016\/j.sigpro.2026.110600_bib0015","doi-asserted-by":"crossref","first-page":"681","DOI":"10.1007\/s12190-021-01548-3","article-title":"A modified dai\u2013liao conjugate gradient method for solving unconstrained optimization and image restoration problems","volume":"68","author":"Lu","year":"2022","journal-title":"J. Appl. Math. Comput."},{"key":"10.1016\/j.sigpro.2026.110600_bib0016","doi-asserted-by":"crossref","DOI":"10.1016\/j.dsp.2024.104628","article-title":"A nonconvex sparse recovery method for DOA estimation based on the trimmed lasso","volume":"153","author":"Bai","year":"2024","journal-title":"Digit. Signal Process."},{"issue":"10","key":"10.1016\/j.sigpro.2026.110600_bib0017","doi-asserted-by":"crossref","first-page":"707","DOI":"10.1109\/LSP.2007.898300","article-title":"Exact reconstruction of sparse signals via nonconvex minimization","volume":"14","author":"Chartrand","year":"2007","journal-title":"IEEE Signal Process. Lett."},{"issue":"11","key":"10.1016\/j.sigpro.2026.110600_bib0018","doi-asserted-by":"crossref","first-page":"6896","DOI":"10.1109\/TIT.2017.2717585","article-title":"Does \u2113p-minimization outperform \u21131-minimization?","volume":"63","author":"Le","year":"2017","journal-title":"IEEE Trans. Inf. Theory"},{"key":"10.1016\/j.sigpro.2026.110600_bib0019","doi-asserted-by":"crossref","DOI":"10.1016\/j.sigpro.2025.109937","article-title":"Performance analysis of unconstrained \u2113p minimization for sparse recovery","volume":"233","author":"Huang","year":"2025","journal-title":"Signal Process."},{"issue":"456","key":"10.1016\/j.sigpro.2026.110600_bib0020","doi-asserted-by":"crossref","first-page":"1348","DOI":"10.1198\/016214501753382273","article-title":"Variable selection via nonconcave penalized likelihood and its oracle properties","volume":"96","author":"Fan","year":"2001","journal-title":"J. Am. Stat. Assoc."},{"issue":"2","key":"10.1016\/j.sigpro.2026.110600_bib0021","doi-asserted-by":"crossref","first-page":"673","DOI":"10.1214\/07-AOS580","article-title":"SCAD-Penalized regression in high-dimensional partially linear models","volume":"37","author":"Xie","year":"2009","journal-title":"Ann. Stat."},{"key":"10.1016\/j.sigpro.2026.110600_bib0022","article-title":"Multi-stage convex relaxation for learning with sparse regularization","volume":"21","author":"Zhang","year":"2008","journal-title":"Adv. Neural Inf. Process. Syst."},{"issue":"2","key":"10.1016\/j.sigpro.2026.110600_bib0023","doi-asserted-by":"crossref","first-page":"894","DOI":"10.1214\/09-AOS729","article-title":"Nearly unbiased variable selection under minimax concave penalty","volume":"38","author":"Zhang","year":"2010","journal-title":"Ann. Stat."},{"issue":"1","key":"10.1016\/j.sigpro.2026.110600_bib0024","first-page":"3498","article-title":"A unified approach to model selection and sparse recovery using regularized least squares","volume":"37","author":"Lv","year":"2009","journal-title":"Ann. Stat."},{"issue":"2","key":"10.1016\/j.sigpro.2026.110600_bib0025","doi-asserted-by":"crossref","first-page":"829","DOI":"10.1109\/TIP.2015.2511584","article-title":"Nonconvex nonsmooth low rank minimization via iteratively reweighted nuclear norm","volume":"25","author":"Lu","year":"2015","journal-title":"IEEE Trans. Image Process."},{"issue":"5","key":"10.1016\/j.sigpro.2026.110600_bib0026","doi-asserted-by":"crossref","first-page":"1123","DOI":"10.1007\/s11425-021-1987-2","article-title":"Improved RIP-based bounds for guaranteed performance of two compressed sensing algorithms","volume":"66","author":"Zhao","year":"2023","journal-title":"Sci. China Math."},{"issue":"1","key":"10.1016\/j.sigpro.2026.110600_bib0027","doi-asserted-by":"crossref","first-page":"18","DOI":"10.4208\/csiam-am.SO-2022-0016","article-title":"Uniform RIP bounds for recovery of signals with partial support information by weighted \u2113p-minimization","volume":"5","author":"Ge","year":"2024","journal-title":"CSIAM Trans. Appl. Math."},{"issue":"1","key":"10.1016\/j.sigpro.2026.110600_bib0028","doi-asserted-by":"crossref","first-page":"43","DOI":"10.4208\/jcm.2307-m2022-0225","article-title":"Stable recovery of sparse signals with non-convex weighted r-norm minus 1-norm","volume":"43","author":"Huang","year":"2025","journal-title":"J. Comput. Math."},{"issue":"2","key":"10.1016\/j.sigpro.2026.110600_bib0029","doi-asserted-by":"crossref","first-page":"749","DOI":"10.1137\/20M1341490","article-title":"Limited-angle CT reconstruction via the \u21131\/\u21132 minimization","volume":"14","author":"Wang","year":"2021","journal-title":"SIAM J. Imag. Sci."},{"issue":"2","key":"10.1016\/j.sigpro.2026.110600_bib0030","doi-asserted-by":"crossref","first-page":"A770","DOI":"10.1137\/20M136801X","article-title":"Minimization of \u21131 over \u21132 for sparse signal recovery with convergence guarantee","volume":"44","author":"Tao","year":"2022","journal-title":"SIAM J. Sci. Comput."},{"issue":"2","key":"10.1016\/j.sigpro.2026.110600_bib0031","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1007\/s10915-024-02497-2","article-title":"Sorted \u21131\/\u21132 minimization for sparse signal recovery","volume":"99","author":"Wang","year":"2024","journal-title":"J. Sci. Comput."},{"key":"10.1016\/j.sigpro.2026.110600_bib0032","doi-asserted-by":"crossref","first-page":"1056","DOI":"10.1109\/TSP.2022.3144948","article-title":"Block-sparse signal recovery via general total variation regularized sparse bayesian learning","volume":"70","author":"Sant","year":"2022","journal-title":"IEEE Trans. Signal Process."},{"key":"10.1016\/j.sigpro.2026.110600_bib0033","doi-asserted-by":"crossref","DOI":"10.1016\/j.knosys.2024.111659","article-title":"Image compressed sensing: from deep learning to adaptive learning","volume":"293","author":"Xie","year":"2024","journal-title":"Knowl.-Based Syst."},{"key":"10.1016\/j.sigpro.2026.110600_bib0034","doi-asserted-by":"crossref","DOI":"10.1016\/j.neucom.2024.129071","article-title":"DSU-NEt: a dynamic stage unfolding network for high-noise image compressive sensing denoising","volume":"618","author":"Zhang","year":"2025","journal-title":"Neurocomputing"},{"issue":"4","key":"10.1016\/j.sigpro.2026.110600_bib0035","doi-asserted-by":"crossref","first-page":"3619","DOI":"10.1007\/s10462-022-10259-5","article-title":"Deep learning for compressive sensing: a ubiquitous systems perspective","volume":"56","author":"Machidon","year":"2023","journal-title":"Artif. Intell. Rev."},{"key":"10.1016\/j.sigpro.2026.110600_bib0036","doi-asserted-by":"crossref","DOI":"10.1016\/j.sigpro.2023.109260","article-title":"A reLU-based hard-thresholding algorithm for non-negative sparse signal recovery","volume":"215","author":"He","year":"2024","journal-title":"Signal Process."},{"key":"10.1016\/j.sigpro.2026.110600_bib0037","article-title":"Individual time series and composite forecasting of the chinese stock index","volume":"5","author":"Xu","year":"2021","journal-title":"Mach. Learn. Appl."},{"key":"10.1016\/j.sigpro.2026.110600_bib0038","doi-asserted-by":"crossref","DOI":"10.1142\/S2811034X24500060","article-title":"Forecasts of china mainland new energy index prices through gaussian process regressions","volume":"1","author":"Jin","year":"2024","journal-title":"J. Clean Energy Energy Storage"},{"issue":"ahead-of-print","key":"10.1016\/j.sigpro.2026.110600_bib0039","article-title":"Contemporaneous causal orderings among prices of retail properties: evidence from chinese cities through vector error-correction modeling and directed acyclic graphs","author":"Jin","year":"2025","journal-title":"J. Financ. Manag. Prop. Constr."},{"issue":"3","key":"10.1016\/j.sigpro.2026.110600_bib0040","doi-asserted-by":"crossref","first-page":"595","DOI":"10.1108\/FS-01-2023-0016","article-title":"Peanut oil price change forecasts through the neural network","volume":"27","author":"Jin","year":"2025","journal-title":"Foresight"},{"key":"10.1016\/j.sigpro.2026.110600_bib0041","series-title":"Proc. IEEE Conf. Comput. Vis. Pattern Recognit. (CVPR)","first-page":"1828","article-title":"ISTA-NEt: interpretable optimization-inspired deep network for image compressive sensing","author":"Zhang","year":"2018"},{"issue":"2","key":"10.1016\/j.sigpro.2026.110600_bib0042","doi-asserted-by":"crossref","first-page":"762","DOI":"10.1007\/s10915-019-00955-w","article-title":"Detecting edges from non-uniform fourier data via sparse bayesian learning","volume":"80","author":"Churchill","year":"2019","journal-title":"J. Sci. Comput."},{"issue":"6","key":"10.1016\/j.sigpro.2026.110600_bib0043","doi-asserted-by":"crossref","first-page":"1139","DOI":"10.3934\/ipi.2023011","article-title":"A first-order rician denoising and deblurring model","volume":"17","author":"Yang","year":"2023","journal-title":"Inverse Probl. Imag."},{"key":"10.1016\/j.sigpro.2026.110600_bib0044","series-title":"Convex Optimization","author":"Boyd","year":"2004"},{"issue":"1","key":"10.1016\/j.sigpro.2026.110600_bib0045","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1109\/TMI.2008.927346","article-title":"Highly undersampled magnetic resonance image reconstruction via homotopic \u21130-minimization","volume":"28","author":"Trzasko","year":"2008","journal-title":"IEEE Trans. Med. Imag."}],"container-title":["Signal Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0165168426001143?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0165168426001143?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T04:00:25Z","timestamp":1776139225000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0165168426001143"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,8]]},"references-count":45,"alternative-id":["S0165168426001143"],"URL":"https:\/\/doi.org\/10.1016\/j.sigpro.2026.110600","relation":{},"ISSN":["0165-1684"],"issn-type":[{"value":"0165-1684","type":"print"}],"subject":[],"published":{"date-parts":[[2026,8]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"A two-stage proximal gradient algorithm for sparse optimization problems","name":"articletitle","label":"Article Title"},{"value":"Signal Processing","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.sigpro.2026.110600","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"110600"}}