{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,4]],"date-time":"2025-10-04T07:54:21Z","timestamp":1759564461917,"version":"3.37.3"},"reference-count":28,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2023,12,27]],"date-time":"2023-12-27T00:00:00Z","timestamp":1703635200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,12,27]],"date-time":"2023-12-27T00:00:00Z","timestamp":1703635200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12171496"],"award-info":[{"award-number":["12171496"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2024,2]]},"DOI":"10.1007\/s40314-023-02560-y","type":"journal-article","created":{"date-parts":[[2023,12,27]],"date-time":"2023-12-27T11:02:16Z","timestamp":1703674936000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Nonconvex $$\\ell _p-\\alpha \\ell _q$$ minimization method and p-RIP condition for stable recovery of approximately k-sparse signals"],"prefix":"10.1007","volume":"43","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-4660-8594","authenticated-orcid":false,"given":"Feng","family":"Gu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0316-5850","authenticated-orcid":false,"given":"Anhua","family":"Wan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,12,27]]},"reference":[{"issue":"4","key":"2560_CR1","doi-asserted-by":"publisher","first-page":"220","DOI":"10.1109\/TCI.2015.2485078","volume":"1","author":"R Ahmad","year":"2015","unstructured":"Ahmad R, Schniter P (2015) Iteratively reweighted $$\\ell _1$$ approaches to sparse composite regularization. IEEE Trans Comput Imaging 1(4):220\u2013235","journal-title":"IEEE Trans Comput Imaging"},{"key":"2560_CR2","doi-asserted-by":"publisher","unstructured":"Ashour AS, Guo Y, Alaa EE, Kasem HM (2020) Discrete cosine transform-based compressive sensing recovery strategies in medical imaging. Advances in Computational Techniques for Biomedical Image Analysis, pp 167\u2013184. https:\/\/doi.org\/10.1016\/B978-0-12-820024-7.00009-8","DOI":"10.1016\/B978-0-12-820024-7.00009-8"},{"issue":"3","key":"2560_CR3","doi-asserted-by":"publisher","first-page":"265","DOI":"10.1016\/j.acha.2009.04.002","volume":"27","author":"T Blumensath","year":"2009","unstructured":"Blumensath T, Davies ME (2009) Iterative hard thresholding for compressed sensing. Appl Comput Harmon Anal 27(3):265\u2013274","journal-title":"Appl Comput Harmon Anal"},{"issue":"1","key":"2560_CR4","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1561\/2200000016","volume":"3","author":"S Boyd","year":"2010","unstructured":"Boyd S, Parikh N, Chu E, Peleato B, Eckstein J (2010) Distributed optimization and statistics via alternating direction method of multipliers. Found Trends Mach Learn 3(1):1\u2013122","journal-title":"Found Trends Mach Learn"},{"issue":"10","key":"2560_CR5","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevFluids.4.103907","volume":"4","author":"J Callaham","year":"2019","unstructured":"Callaham J, Maeda K, Brunton S (2019) Robust flow reconstruction from limited measurements via sparse representation. Phys Rev Fluids 4(10):103907","journal-title":"Phys Rev Fluids"},{"key":"2560_CR6","doi-asserted-by":"crossref","unstructured":"Cand\u00e9s EJ, Tao T (2005) Decoding by linear programming. IEEE Trans Inf Theory 51(12):4203\u20134215","DOI":"10.1109\/TIT.2005.858979"},{"issue":"3","key":"2560_CR7","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/24\/3\/035020","volume":"24","author":"R Chartrand","year":"2008","unstructured":"Chartrand R, Staneva V (2008) Restricted isometry properties and nonconvex compressive sensing. Inverse Probl 24(3):035020","journal-title":"Inverse Probl"},{"key":"2560_CR8","doi-asserted-by":"crossref","unstructured":"Chartrand R, Yin W (2008) Iteratively reweighted algorithms for compressive sensing. In: IEEE international conference on acoustics, speech and signal processing, pp 3869\u20133872","DOI":"10.1109\/ICASSP.2008.4518498"},{"key":"2560_CR9","doi-asserted-by":"publisher","first-page":"306","DOI":"10.1016\/j.neucom.2019.06.047","volume":"363","author":"B Chen","year":"2019","unstructured":"Chen B, Wan A (2019) General RIP bounds of $$\\delta _{tk}$$ for sparse signal recovery by $$\\ell _p$$ minimization. Neurocomputing 363:306\u2013312","journal-title":"Neurocomputing"},{"issue":"4","key":"2560_CR10","doi-asserted-by":"publisher","first-page":"1289","DOI":"10.1109\/TIT.2006.871582","volume":"52","author":"DL Donoho","year":"2006","unstructured":"Donoho DL (2006) Compressed sensing. IEEE Trans Inf Theory 52(4):1289\u20131306","journal-title":"IEEE Trans Inf Theory"},{"issue":"1","key":"2560_CR11","doi-asserted-by":"publisher","first-page":"6","DOI":"10.1109\/TIT.2005.860430","volume":"52","author":"DL Donoho","year":"2005","unstructured":"Donoho DL, Elad M, Temlyakov VN (2005) Stable recovery of sparse overcomplete representations in the presence of noise. IEEE Trans Inf Theory 52(1):6\u201318","journal-title":"IEEE Trans Inf Theory"},{"issue":"6","key":"2560_CR12","doi-asserted-by":"publisher","first-page":"1137","DOI":"10.4208\/jcm.2207-m2022-0058","volume":"41","author":"B Du","year":"2023","unstructured":"Du B, Wan A (2023) Stable and robust recovery of approximately $$k$$-sparse signals with partial support information in noise settings via weighted $$\\ell _p\\, (0<p\\le 1)$$ minimization. J Comput Math 41(6):1137\u20131170","journal-title":"J Comput Math"},{"issue":"4","key":"2560_CR13","doi-asserted-by":"publisher","first-page":"2010","DOI":"10.1137\/13090540X","volume":"6","author":"E Esser","year":"2013","unstructured":"Esser E, Lou Y, Xin J (2013) A method for finding structured sparse solutions to non-negative least squares problems with applications. SIAM J Imaging Sci 6(4):2010\u20132046","journal-title":"SIAM J Imaging Sci"},{"key":"2560_CR14","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-8176-4948-7","volume-title":"A mathematical introduction to compressive sensing","author":"S Foucart","year":"2013","unstructured":"Foucart S, Rauhut H (2013) A mathematical introduction to compressive sensing. Birkh\u00e4user, Boston"},{"issue":"1","key":"2560_CR15","doi-asserted-by":"publisher","first-page":"82","DOI":"10.1137\/090775397","volume":"21","author":"M Lai","year":"2011","unstructured":"Lai M, Wang J (2011) An unconstrained $$\\ell _q$$ minimization with $$0<q\\le 1$$ for sparse solution of underdetermined linear systems. SIAM J Optim 21(1):82\u2013101","journal-title":"SIAM J Optim"},{"issue":"5","key":"2560_CR16","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6420\/ab750c","volume":"36","author":"P Li","year":"2020","unstructured":"Li P, Chen W, Ge H, Ng MK (2020) $$\\ell _1-\\alpha \\ell _2$$ minimization methods for signal and image reconstruction with impulsive noise removal. Inverse Probl 36(5):055009","journal-title":"Inverse Probl"},{"issue":"1","key":"2560_CR17","doi-asserted-by":"publisher","first-page":"536","DOI":"10.1137\/140952363","volume":"37","author":"Y Lou","year":"2015","unstructured":"Lou Y, Qi Y, Xin P (2015) Minimization of $$\\ell _1-\\ell _2$$ for compressed sensing. SIAM J Sci Comput 37(1):536\u2013563","journal-title":"SIAM J Sci Comput"},{"issue":"3","key":"2560_CR18","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1016\/j.acha.2008.07.002","volume":"26","author":"D Needell","year":"2009","unstructured":"Needell D, Tropp JA (2009) CoSaMP: iterative signal recovery from incomplete and inaccurate samples. Appl Comput Harmon Anal 26(3):301\u2013321","journal-title":"Appl Comput Harmon Anal"},{"key":"2560_CR19","doi-asserted-by":"crossref","unstructured":"Park SW, Park J, Jung BC (2013) On the sparse signal recovery with parallel orthogonal matching pursuit. IEICE Trans Fundam E96-A(12):2728\u20132730","DOI":"10.1587\/transfun.E96.A.2728"},{"issue":"1","key":"2560_CR20","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1515\/nuka-2016-0012","volume":"61","author":"L Raczy\u0144ski","year":"2016","unstructured":"Raczy\u0144ski L, Moskal P, Kowalski P, Wi\u015blicki W et al (2016) Application of the compress sensing theory for improvement of the TOF resolution in a novel J-PET instrument. Nukleonika 61(1):35\u201339","journal-title":"Nukleonika"},{"issue":"12","key":"2560_CR21","doi-asserted-by":"publisher","first-page":"4655","DOI":"10.1109\/TIT.2007.909108","volume":"53","author":"JA Tropp","year":"2007","unstructured":"Tropp JA, Gilbert AC (2007) Signal recovery from random measurements via orthogonal matching pursuit. IEEE Trans Inf Theory 53(12):4655\u20134666","journal-title":"IEEE Trans Inf Theory"},{"key":"2560_CR22","doi-asserted-by":"crossref","unstructured":"Wan A (2020a) Stable recovery of approximately $$k$$-sparse signals in noisy cases via $$\\ell _p$$ minimization. Neurocomputing 406:159\u2013168","DOI":"10.1016\/j.neucom.2020.04.014"},{"key":"2560_CR23","doi-asserted-by":"crossref","unstructured":"Wan A (2020b) Unified RIP conditions for recovery of sparse signals by $$\\ell _p\\, (0<p\\le 1)$$ minimization. IEEE Trans Signal Process 68:5379\u20135394","DOI":"10.1109\/TSP.2020.3022822"},{"key":"2560_CR24","doi-asserted-by":"publisher","first-page":"2927","DOI":"10.1109\/TSP.2023.3296197","volume":"71","author":"R Xiao","year":"2023","unstructured":"Xiao R, Fu Y, Wan A (2023) Upper bound of null space constant $$\\rho (p, t, A, k)$$ and high-order restricted isometry constant $$\\delta _{tk}$$ for sparse recovery via $$\\ell _p$$ minimization. IEEE Trans Signal Process 71:2927\u20132935","journal-title":"IEEE Trans Signal Process"},{"issue":"3","key":"2560_CR25","doi-asserted-by":"publisher","first-page":"566","DOI":"10.1016\/j.acha.2017.10.004","volume":"47","author":"A Zhang","year":"2017","unstructured":"Zhang A, Li S (2017) Optimal RIP bounds for sparse signals recovery via $$\\ell _p$$ minimization. Appl Comput Harmon Anal 47(3):566\u2013584","journal-title":"Appl Comput Harmon Anal"},{"key":"2560_CR26","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2022.114800","volume":"393","author":"X Zhang","year":"2022","unstructured":"Zhang X, Ji T, Xie F, Zheng H, Zheng Y (2022) Unsteady flow prediction from sparse measurements by compressed sensing reduced order modeling. Comput Methods Appl Mech Eng 393:114800","journal-title":"Comput Methods Appl Mech Eng"},{"key":"2560_CR27","doi-asserted-by":"publisher","DOI":"10.1016\/j.sigpro.2022.108754","volume":"202","author":"Z Zhou","year":"2023","unstructured":"Zhou Z (2023) RIP analysis for the weighted $$\\ell _r-\\ell _1$$ minimization method. Signal Process 202:108754","journal-title":"Signal Process"},{"key":"2560_CR28","doi-asserted-by":"publisher","first-page":"14","DOI":"10.3389\/fams.2019.00014","volume":"5","author":"Z Zhou","year":"2019","unstructured":"Zhou Z, Yu J (2019) A new nonconvex sparse recovery method for compressive sensing. Front Appl Math Stat 5:14","journal-title":"Front Appl Math Stat"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-023-02560-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-023-02560-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-023-02560-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,11]],"date-time":"2024-02-11T11:22:09Z","timestamp":1707650529000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-023-02560-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12,27]]},"references-count":28,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2024,2]]}},"alternative-id":["2560"],"URL":"https:\/\/doi.org\/10.1007\/s40314-023-02560-y","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"type":"print","value":"2238-3603"},{"type":"electronic","value":"1807-0302"}],"subject":[],"published":{"date-parts":[[2023,12,27]]},"assertion":[{"value":"20 January 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 October 2023","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 November 2023","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 December 2023","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"29"}}