{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:50:33Z","timestamp":1787323833070,"version":"build-2736575974"},"reference-count":74,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","funder":[{"name":"MIS-FNRS","award":["AlterSense"],"award-info":[{"award-number":["AlterSense"]}]},{"DOI":"10.13039\/501100003134","name":"Fonds pour la Formation \u00e0 la Recherche dans l'Industrie et dans l'Agriculture","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100003134","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002661","name":"Fonds De La Recherche Scientifique - FNRS","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100002661","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Imaging Sci."],"published-print":{"date-parts":[[2019,1]]},"abstract":"<jats:p>Fourier transform interferometry (FTI) is an appealing hyperspectral (HS) imaging modality for many applications demanding high spectral resolution, e.g., in fluorescence microscopy. However, the effective resolution of FTI is limited by the durability of biological elements when exposed to illuminating light. Overexposed elements are indeed subject to photo-bleaching and become unable to fluoresce. In this context, the acquisition of biological HS volumes based on sampling the optical path difference axis at Nyquist rate leads to unpleasant trade-offs between spectral resolution, quality of the HS volume, and light exposure intensity. In this paper we propose two variants of the FTI imager, i.e., coded illumination-FTI (CI-FTI) and structured illumination FTI (SI-FTI), based on the theory of compressive sensing (CS). These schemes efficiently modulate light exposure temporally (in CI-FTI) or spatiotemporally (in SI-FTI). Leveraging a variable density sampling strategy recently introduced in CS, we provide near-optimal illumination strategies, so that the light exposure imposed on a biological specimen is minimized while the spectral resolution is preserved. Our theoretical analysis focuses on two criteria: (i) a trade-off between exposure intensity and the quality of the reconstructed HS volume for a given spectral resolution; (ii) maximizing HS volume quality for a fixed spectral resolution and constrained light exposure budget. Our contributions can be adapted to an FTI imager without hardware modifications. The reconstruction of HS volumes from CS FTI measurements relies on an $\\ell_1$-norm minimization problem promoting a spatiospectral sparsity prior. Numerically, we support the proposed methods on synthetic data and simulated CS measurements (from actual FTI measurements) under various scenarios. In particular, the biological HS volumes considered in this work can be reconstructed with a three-to-tenfold reduction in the light exposure.<\/jats:p>","DOI":"10.1137\/18m1214111","type":"journal-article","created":{"date-parts":[[2019,4,2]],"date-time":"2019-04-02T14:23:00Z","timestamp":1554214980000},"page":"671-715","source":"Crossref","is-referenced-by-count":6,"title":["A Variable Density Sampling Scheme for Compressive Fourier Transform Interferometry"],"prefix":"10.1137","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6751-2698","authenticated-orcid":true,"given":"A.","family":"Moshtaghpour","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6261-0328","authenticated-orcid":true,"given":"L.","family":"Jacques","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"V.","family":"Cambareri","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"P.","family":"Antoine","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"M.","family":"Roblin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2019,4,2]]},"reference":[{"key":"atypb1","unstructured":"Fluorophores.org - Database of Fluorescent Dyes, Properties and Applications\n                      ,http:\/\/www.fluorophores.tugraz.at, retrieved on Jan. 5, 2018."},{"key":"atypb2","unstructured":"B. Adcock, C. Boyer, and S. Brugiapaglia,\n                      On Oracle-Type Local Recovery Guarantees in Compressed Sensing\n                      , preprint,arXiv:1806.03789, 2018."},{"key":"atypb3","first-page":"5","author":"Adcock B.","year":"2017","journal-title":"Sigma"},{"key":"atypb4","first-page":"143","author":"Adcock B.","year":"2015","journal-title":"New York"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1109\/LSP.2016.2550101"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1364\/JOSAA.28.002400"},{"key":"atypb7","unstructured":"R. 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Degraux, V. Cambareri, B. Geelen, L. Jacques, and G. Lafruit,\n                      Multispectral Compressive Imaging Strategies Using Fabry-P\u00e9rot Filtered Sensors\n                      , preprint,arXiv:1802.02040, 2018.","DOI":"10.1109\/TCI.2018.2864659"},{"key":"atypb19","first-page":"690","author":"Diaspro A.","year":"2006","journal-title":"New York"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2006.871582"},{"key":"atypb21","doi-asserted-by":"crossref","unstructured":"D. L. Donoho and I. M. 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Freedman,\n                      University Physics: With Modern Physics\n                      , Addison-Wesley, Reading, MA, 2007."},{"key":"atypb73","doi-asserted-by":"publisher","DOI":"10.1177\/193229681000400508"},{"key":"atypb74","doi-asserted-by":"publisher","DOI":"10.1364\/AO.50.004417"},{"key":"atypb75","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2011.2162263"}],"container-title":["SIAM Journal on Imaging Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/18M1214111","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:14:21Z","timestamp":1787321661000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/18M1214111"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1]]},"references-count":74,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2019,1]]}},"alternative-id":["10.1137\/18M1214111"],"URL":"https:\/\/doi.org\/10.1137\/18m1214111","relation":{},"ISSN":["1936-4954"],"issn-type":[{"value":"1936-4954","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,1]]}}}