{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T12:47:37Z","timestamp":1785415657307,"version":"3.56.0"},"reference-count":26,"publisher":"Optica Publishing Group","issue":"14","license":[{"start":{"date-parts":[[2026,7,8]],"date-time":"2026-07-08T00:00:00Z","timestamp":1783468800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/doi.org\/10.1364\/OA_License_v2#VOR-OA"},{"start":{"date-parts":[[2026,7,8]],"date-time":"2026-07-08T00:00:00Z","timestamp":1783468800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/opg.optica.org\/policies\/opg-tdm-policy.json"}],"funder":[{"DOI":"10.13039\/100007847","name":"Natural Science Foundation of Jilin Province","doi-asserted-by":"crossref","award":["20240101341JC"],"award-info":[{"award-number":["20240101341JC"]}],"id":[{"id":"10.13039\/100007847","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["opg.optica.org"],"crossmark-restriction":false},"short-container-title":["Opt. Express"],"published-print":{"date-parts":[[2026,7,13]]},"abstract":"<jats:p>Lensless coded aperture polarization imaging offers a highly promising avenue for compact optical systems. However, high-fidelity imaging is severely hindered by traditional mask designs that cause spectral zeros in the modulation transfer function (MTF), coupled with the inherently ill-posed reconstruction process that amplifies noise during nonlinear polarization computations. To address these issues, we develop a differentiable physical model to optimize the spatial arrangement of the sub-aperture, avoiding the formation of contiguous transparent regions. This approach effectively eliminates MTF zeros and boosts the energy in mid-to-high frequency bands, providing a solid physical foundation for mitigating noise in the reconstructed images. Furthermore, we propose a total generalized variation momentum primal-dual hybrid gradient (TGV-MPDHG) algorithm by incorporating a second-order regularization into the MPDHG framework to solve the ill-posed reconstruction problem. Experimental results demonstrate that this integrated methodology significantly enhances reconstruction fidelity, reduces background noise, and achieves both faster convergence and stable reconstruction quality across various object sizes.<\/jats:p>","DOI":"10.1364\/oe.601473","type":"journal-article","created":{"date-parts":[[2026,6,23]],"date-time":"2026-06-23T13:00:32Z","timestamp":1782219632000},"page":"26290","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["High-fidelity lensless polarization imaging enabled by differentiable mask optimization and second-order regularized reconstruction"],"prefix":"10.1364","volume":"34","author":[{"given":"Wenbo","family":"Wang","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/007mntk44","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8543-2694","authenticated-orcid":true,"given":"Wenjun","family":"He","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/007mntk44","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pengjun","family":"Xu","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/007mntk44","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3815-6559","authenticated-orcid":true,"given":"Zhencong","family":"Xiong","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/007mntk44","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"285","published-online":{"date-parts":[[2026,7,8]]},"reference":[{"key":"oe-34-14-26290-R1","doi-asserted-by":"publisher","first-page":"12215","DOI":"10.1364\/OE.421287","type":"journal-article","volume":"29","author":"Usmani","year":"2021","journal-title":"Opt. Express"},{"key":"oe-34-14-26290-R2","doi-asserted-by":"publisher","first-page":"10659","DOI":"10.3390\/app142210659","type":"journal-article","volume":"14","author":"Liu","year":"2024","journal-title":"Appl. Sci."},{"key":"oe-34-14-26290-R3","doi-asserted-by":"publisher","first-page":"5","DOI":"10.3847\/1538-4357\/ac6fce","type":"journal-article","volume":"933","author":"Ignace","year":"2022","journal-title":"Astrophys. J."},{"key":"oe-34-14-26290-R4","doi-asserted-by":"publisher","first-page":"1297","DOI":"10.1364\/PRJ.452968","type":"journal-article","volume":"10","author":"Li","year":"2022","journal-title":"Photonics Res."},{"key":"oe-34-14-26290-R5","doi-asserted-by":"publisher","first-page":"076101","DOI":"10.1063\/5.0057625","type":"journal-article","volume":"6","author":"Liu","year":"2021","journal-title":"APL Photon."},{"key":"oe-34-14-26290-R6","doi-asserted-by":"publisher","first-page":"685","DOI":"10.1080\/713820903","type":"journal-article","volume":"29","author":"Azzam","year":"1982","journal-title":"Opt. Acta"},{"key":"oe-34-14-26290-R9","doi-asserted-by":"publisher","first-page":"13634","DOI":"10.1364\/OE.24.013634","type":"journal-article","volume":"24","author":"Morel","year":"2016","journal-title":"Opt. Express"},{"key":"oe-34-14-26290-R10","doi-asserted-by":"publisher","first-page":"108589","DOI":"10.1016\/j.optlaseng.2024.108589","type":"journal-article","volume":"184","author":"Ma","year":"2025","journal-title":"Opt. Lasers Eng."},{"key":"oe-34-14-26290-R11","doi-asserted-by":"publisher","first-page":"19087","DOI":"10.1364\/OE.18.019087","type":"journal-article","volume":"18","author":"Gruev","year":"2010","journal-title":"Opt. Express"},{"key":"oe-34-14-26290-R13","doi-asserted-by":"publisher","first-page":"931","DOI":"10.1364\/AO.11.000931","type":"journal-article","volume":"11","author":"Groh","year":"1972","journal-title":"Appl. Opt."},{"key":"oe-34-14-26290-R14","doi-asserted-by":"publisher","first-page":"2411","DOI":"10.1109\/23.983251","type":"journal-article","volume":"48","author":"Accorsi","year":"2001","journal-title":"IEEE Trans. Nucl. Sci."},{"key":"oe-34-14-26290-R15","doi-asserted-by":"publisher","first-page":"34","DOI":"10.1016\/j.radmeas.2015.04.014","type":"journal-article","volume":"77","author":"Sun","year":"2015","journal-title":"Radiat. Meas."},{"key":"oe-34-14-26290-R17","doi-asserted-by":"publisher","first-page":"023102","DOI":"10.1117\/1.OE.54.2.023102","type":"journal-article","volume":"54","author":"DeWeert","year":"2015","journal-title":"Opt. Eng."},{"key":"oe-34-14-26290-R18","doi-asserted-by":"publisher","first-page":"384","DOI":"10.1109\/TCI.2016.2593662","type":"journal-article","volume":"3","author":"Asif","year":"2017","journal-title":"IEEE Trans. Comput. Imaging"},{"key":"oe-34-14-26290-R19","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1364\/OPTICA.5.000001","type":"journal-article","volume":"5","author":"Antipa","year":"2018","journal-title":"Optica"},{"key":"oe-34-14-26290-R20","doi-asserted-by":"publisher","first-page":"37395","DOI":"10.1364\/OE.500097","type":"journal-article","volume":"31","author":"Xiong","year":"2023","journal-title":"Opt. Express"},{"key":"oe-34-14-26290-R21","doi-asserted-by":"publisher","first-page":"26742","DOI":"10.1364\/OE.564256","type":"journal-article","volume":"33","author":"Wang","year":"2025","journal-title":"Opt. Express"},{"key":"oe-34-14-26290-R22","doi-asserted-by":"publisher","first-page":"116102","DOI":"10.1063\/5.0120465","type":"journal-article","volume":"7","author":"Baek","year":"2022","journal-title":"APL Photon."},{"key":"oe-34-14-26290-R23","doi-asserted-by":"publisher","first-page":"758","DOI":"10.1364\/OL.549538","type":"journal-article","volume":"50","author":"Xiong","year":"2025","journal-title":"Opt. Lett."},{"key":"oe-34-14-26290-R24","doi-asserted-by":"publisher","first-page":"30248","DOI":"10.1364\/OE.400486","type":"journal-article","volume":"28","author":"Zhou","year":"2020","journal-title":"Opt. Express"},{"key":"oe-34-14-26290-R25","doi-asserted-by":"publisher","first-page":"1843","DOI":"10.1364\/OL.455378","type":"journal-article","volume":"47","author":"Pan","year":"2022","journal-title":"Opt. Lett."},{"key":"oe-34-14-26290-R26","doi-asserted-by":"publisher","first-page":"28075","DOI":"10.1364\/OE.27.028075","type":"journal-article","volume":"27","author":"Monakhova","year":"2019","journal-title":"Opt. Express"},{"key":"oe-34-14-26290-R27","first-page":"1934","type":"journal-article","volume":"44","author":"Khan","year":"2020","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"oe-34-14-26290-R28","doi-asserted-by":"publisher","first-page":"492","DOI":"10.1137\/090769521","type":"journal-article","volume":"3","author":"Bredies","year":"2010","journal-title":"SIAM J. Imaging Sci."},{"key":"oe-34-14-26290-R29","doi-asserted-by":"publisher","first-page":"480","DOI":"10.1002\/mrm.22595","type":"journal-article","volume":"65","author":"Knoll","year":"2011","journal-title":"Magn. Reson. Med."},{"key":"oe-34-14-26290-R30","doi-asserted-by":"publisher","first-page":"600","DOI":"10.1109\/TIP.2003.819861","type":"journal-article","volume":"13","author":"Wang","year":"2004","journal-title":"IEEE Trans. on Image Process."}],"container-title":["Optics Express"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/opg.optica.org\/viewmedia.cfm?URI=oe-34-14-26290&seq=0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,7,8]],"date-time":"2026-07-08T19:38:07Z","timestamp":1783539487000},"score":1,"resource":{"primary":{"URL":"https:\/\/opg.optica.org\/abstract.cfm?URI=oe-34-14-26290"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,7,8]]},"references-count":26,"journal-issue":{"issue":"14","published-online":{"date-parts":[[2026]]},"published-print":{"date-parts":[[2026]]}},"URL":"https:\/\/doi.org\/10.1364\/oe.601473","relation":{},"ISSN":["1094-4087"],"issn-type":[{"value":"1094-4087","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,7,8]]},"assertion":[{"value":"Optica Publishing Group","name":"publisher","label":"This article is maintained by"},{"value":"https:\/\/doi.org\/10.1364\/OE.601473","name":"articlelink","label":"Crossref DOI link to publisher maintained version"},{"value":"research-article","name":"content_type","label":"Article type"},{"value":"Screened by Similarity Check","name":"cross_check","label":"Similarity check"},{"value":"Yes","order":0,"name":"peer_reviewed","label":"Peer reviewed","group":{"name":"peer_review","label":"Peer review"}},{"value":"Single blind","order":1,"name":"review_process","label":"Review process","group":{"name":"peer_review","label":"Peer review"}},{"value":"13 April 2026","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"19 June 2026","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"8 July 2026","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}},{"value":"\u00a9 2026 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement","name":"copyright","label":"Copyright"}]}}