{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:52:43Z","timestamp":1787323963258,"version":"3.56.0"},"reference-count":36,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","funder":[{"DOI":"10.13039\/100010661","name":"Horizon 2020 Framework Programme","doi-asserted-by":"publisher","award":["646804-ERC-COG-BNYQ"],"award-info":[{"award-number":["646804-ERC-COG-BNYQ"]}],"id":[{"id":"10.13039\/100010661","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>In traditional optical imaging systems, the spatial resolution is limited by the physics of diffraction, which acts as a low-pass filter. The information on subwavelength features is carried by evanescent waves, never reaching the camera, thereby posing a hard limit on resolution: the so-called diffraction limit. Modern microscopic methods enable super-resolution, by employing fluorescence techniques. State-of-the-art localization based fluorescence subwavelength imaging techniques such as PALM and STORM achieve subdiffraction spatial resolution of several tens of nanometers. However, they require tens of thousands of exposures, which limits their temporal resolution. We have recently proposed sparsity based super-resolution correlation microscopy (SPARCOM), which exploits the sparse nature of the fluorophore distribution, alongside a statistical prior of uncorrelated emissions, and showed that SPARCOM achieves spatial resolution comparable to PALM\/STORM, while capturing the data hundreds of times faster. Here, we provide a detailed mathematical formulation of SPARCOM, which in turn leads to an efficient numerical implementation, suitable for large-scale problems. We further extend our method to a general framework for sparsity based super-resolution imaging, in which sparsity can be assumed in other domains such as wavelet or discrete-cosine, leading to improved reconstructions in a variety of physical settings.<\/jats:p>","DOI":"10.1137\/18m1174921","type":"journal-article","created":{"date-parts":[[2019,2,19]],"date-time":"2019-02-19T11:35:46Z","timestamp":1550576146000},"page":"392-419","source":"Crossref","is-referenced-by-count":33,"title":["SPARCOM: Sparsity Based Super-resolution Correlation Microscopy"],"prefix":"10.1137","volume":"12","author":[{"given":"Oren","family":"Solomon","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yonina C.","family":"Eldar","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Maor","family":"Mutzafi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mordechai","family":"Segev","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2019,2,19]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1137\/080716542"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2009.2028250"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2016.04.077"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1126\/science.1127344"},{"key":"atypb5","doi-asserted-by":"crossref","unstructured":"M. Born and E. Wolf,\n                      Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light\n                      , Cambridge University Press Archive, Cambridge, UK, 2000.","DOI":"10.1063\/1.1325200"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1109\/MSP.2007.914731"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1023\/B:JMIV.0000011325.36760.1e"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2014.2331613"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160410705"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0907866106"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1364\/OE.18.018875"},{"key":"atypb12","doi-asserted-by":"crossref","unstructured":"Y. C. Eldar,\n                      Sampling Theory: Beyond Bandlimited Systems\n                      , Cambridge University Press, Cambridge, UK, 2015.","DOI":"10.1017\/CBO9780511762321"},{"key":"atypb13","first-page":"2633","author":"Figueiredo M. A.","year":"2006","journal-title":"Proceedings of the IEEE International Conference on Image Processing"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1186\/2192-2853-1-4"},{"key":"atypb15","unstructured":"J. Goodman,\n                      Introduction to Fourier Optics\n                      , 3rd ed., Roberts and Company, Englewood, CO, 2005."},{"key":"atypb16","doi-asserted-by":"crossref","unstructured":"R. M. Gray,\n                      Toeplitz and Circulant Matrices: A Review\n                      , Now Publishers, Hanover, MA, 2006.","DOI":"10.1561\/9781933019680"},{"key":"atypb17","doi-asserted-by":"crossref","unstructured":"P. C. Hansen, J. G. Nagy, and D. P. O'Leary,\n                      Deblurring Images: Matrices, Spectra, and Filtering\n                      , Fundam. Algorithms 3, SIAM, Philadelphia, 2006,https:\/\/doi.org\/10.1137\/1.9780898718874.","DOI":"10.1137\/1.9780898718874"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1111\/j.1365-2818.2012.03675.x"},{"key":"atypb19","unstructured":"H. Kirshner, D. Sage, and M. Unser, 3\n                      D PSF models for fluorescence microscopy in ImageJ\n                      , in Proceedings of the Twelfth International Conference on Methods and Applications of Fluorescence Spectroscopy, Imaging and Probes (MAF), 2011, p. 54."},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1109\/5.75086"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1038\/srep04577"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.24033\/bsmf.1625"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1137\/15M1016552"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1137\/040605412"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1093\/bioinformatics\/btu202"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2014.2385033"},{"key":"atypb27","doi-asserted-by":"crossref","unstructured":"D. P. Palomar and Y. C. Eldar,\n                      Convex Optimization in Signal Processing and Communications\n                      , Cambridge University Press, Cambridge, UK, 2010.","DOI":"10.1017\/CBO9780511804458"},{"key":"atypb28","doi-asserted-by":"crossref","unstructured":"J. Rietdorf,\n                      Microscopy Techniques\n                      , Adv. Biochem. Eng. Biotechnol. 95, Springer, Berlin, Heidelberg, 2005.","DOI":"10.1007\/b14097"},{"key":"atypb29","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(92)90242-F"},{"key":"atypb30","doi-asserted-by":"publisher","DOI":"10.1038\/nmeth929"},{"key":"atypb31","doi-asserted-by":"publisher","DOI":"10.1038\/nmeth.2844"},{"key":"atypb32","first-page":"6215","author":"Solomon O.","year":"2017","journal-title":"Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)"},{"key":"atypb33","doi-asserted-by":"publisher","DOI":"10.1364\/OE.26.018238"},{"key":"atypb34","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2014.2304932"},{"key":"atypb35","doi-asserted-by":"publisher","DOI":"10.1111\/j.2517-6161.1996.tb02080.x"},{"key":"atypb36","unstructured":"T. Wimalajeewa, Y. C. Eldar, and P. K. Varshney,\n                      Recovery of Sparse Matrices via Matrix Sketching\n                      , preprint,https:\/\/arxiv.org\/abs\/1311.2448v1, 2013."}],"container-title":["SIAM Journal on Imaging Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/18M1174921","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:16:33Z","timestamp":1787321793000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/18M1174921"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1]]},"references-count":36,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2019,1]]}},"alternative-id":["10.1137\/18M1174921"],"URL":"https:\/\/doi.org\/10.1137\/18m1174921","relation":{},"ISSN":["1936-4954"],"issn-type":[{"value":"1936-4954","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,1]]}}}