{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:59:44Z","timestamp":1787320784313,"version":"3.56.0"},"reference-count":39,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","funder":[{"name":"PMRF","award":["TF\/PMRF-22-5534"],"award-info":[{"award-number":["TF\/PMRF-22-5534"]}]},{"name":"Government of India","award":["CRG\/2020\/000527"],"award-info":[{"award-number":["CRG\/2020\/000527"]}]},{"name":"Government of India","award":["STR\/2021\/000011"],"award-info":[{"award-number":["STR\/2021\/000011"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Imaging Sci."],"published-print":{"date-parts":[[2025,3,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>The effectiveness of denoising-driven regularization for image reconstruction has been widely recognized. Two prominent algorithms in this area are Plug-and-Play (PnP) and Regularization-by-Denoising (RED). We consider two specific algorithms, PnP-FISTA and RED-APG, where regularization is performed by replacing the proximal operator in the FISTA algorithm with a powerful denoiser. The iterate convergence of FISTA is known to be challenging with no universal guarantees. Yet, we show that for linear inverse problems and a class of linear denoisers, global linear convergence of the iterates of PnP-FISTA and RED-APG can be established through simple spectral analysis.<\/jats:p>","DOI":"10.1137\/24m1656530","type":"journal-article","created":{"date-parts":[[2025,2,4]],"date-time":"2025-02-04T04:11:41Z","timestamp":1738642301000},"page":"SC1-SC15","source":"Crossref","is-referenced-by-count":1,"title":["Short Communication: FISTA Iterates Converge Linearly for Denoiser-Driven Regularization"],"prefix":"10.1137","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-7745-1082","authenticated-orcid":true,"given":"Arghya","family":"Sinha","sequence":"first","affiliation":[{"name":"Department of Computational and Data Sciences, Indian Institute of Science, Bangalore, Karnataka, 560012, India."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kunal N.","family":"Chaudhury","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Indian Institute of Science, Bangalore, Karnataka, 560012, India."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2025,2,4]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1109\/LSP.2023.3323248"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-48311-5_31"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611974997"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1137\/080716542"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611977134"},{"key":"ref6","doi-asserted-by":"crossref","unstructured":"A. Buades, B. Coll, and J. M. Morel, A non-local algorithm for image denoising, in Proceedings of CVPR, IEEE, 2005, pp. 60\u201365, https:\/\/doi.org\/10.1109\/CVPR.2005.38.","DOI":"10.1109\/CVPR.2005.38"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-015-0746-4"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1137\/20M1337168"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1137\/23M1545859"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2021.3075092"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1016\/j.sigpro.2023.109100"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1109\/LSP.2020.2986643"},{"key":"ref13","volume-title":"Matrix Computations","author":"Golub G. H.","year":"1983"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1137\/23M1565243"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1007\/s10208-024-09654-x"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2021.09.004"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139020411"},{"key":"ref18","unstructured":"S. Hurault, A. Leclaire, and N. Papadakis, Gradient step denoiser for convergent plug-and-play, in Proceedings of ICLR, 2022."},{"key":"ref19","unstructured":"P. R. Johnstone and P. Moulin, A Lyapunov Analysis of FISTA with Local Linear Convergence for Sparse Optimization, preprint, arXiv:1502.02281, 2015."},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1109\/LSP.2021.3111594"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1007\/s10851-014-0523-2"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1109\/MSP.2011.2179329"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1137\/120875843"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1109\/LSP.2019.2891879"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2022.3211473"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1007\/s10851-024-01181-2"},{"key":"ref27","doi-asserted-by":"crossref","unstructured":"P. Nair, V. Unni, and K. N. Chaudhury, Hyperspectral image fusion using fast high-dimensional denoising, in Proceedings of ICIP, IEEE, 2019, pp. 3123\u20133127, https:\/\/doi.org\/10.1109\/ICIP.2019.8803377.","DOI":"10.1109\/ICIP.2019.8803377"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1007\/s10208-013-9150-3"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1137\/20M1387961"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1109\/TCI.2018.2880326"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1137\/16M1102884"},{"key":"ref32","unstructured":"E. Ryu, J. Liu, S. Wang, X. Chen, Z. Wang, and W. Yin, Plug-and-play methods provably converge with properly trained denoisers, in Proceedings of ICML, 2019, pp. 5546\u20135557."},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-021-01639-w"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1109\/TCI.2016.2599778"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1137\/151004549"},{"key":"ref36","doi-asserted-by":"crossref","unstructured":"M. Terris, T. Moreau, N. Pustelnik, and J. Tachella, Equivariant plug-and-play image reconstruction, in Proceedings of CVPR, IEEE, 2024, pp. 25255\u201325264, https:\/\/doi.org\/10.1109\/CVPR52733.2024.02386.","DOI":"10.1109\/CVPR52733.2024.02386"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1109\/LSP.2020.3006390"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2021.3088914"},{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2017.2662206"}],"container-title":["SIAM Journal on Imaging Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/24M1656530","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:03:22Z","timestamp":1787317402000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/24M1656530"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,2,4]]},"references-count":39,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,3,31]]}},"alternative-id":["10.1137\/24M1656530"],"URL":"https:\/\/doi.org\/10.1137\/24m1656530","relation":{},"ISSN":["1936-4954"],"issn-type":[{"value":"1936-4954","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,2,4]]}}}