{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,6]],"date-time":"2026-06-06T17:09:47Z","timestamp":1780765787162,"version":"3.54.1"},"reference-count":32,"publisher":"Association for Computing Machinery (ACM)","issue":"1","license":[{"start":{"date-parts":[[2014,12,29]],"date-time":"2014-12-29T00:00:00Z","timestamp":1419811200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2014,12,29]]},"abstract":"<jats:p>\n            Sparsity in the Fourier domain is an important property that enables the dense reconstruction of signals, such as 4D light fields, from a small set of samples. The sparsity of natural spectra is often derived from continuous arguments, but reconstruction algorithms typically work in the discrete Fourier domain. These algorithms usually assume that sparsity derived from continuous principles will hold under discrete sampling. This article makes the critical observation that sparsity is much greater in the\n            <jats:italic>continuous<\/jats:italic>\n            Fourier spectrum than in the\n            <jats:italic>discrete<\/jats:italic>\n            spectrum. This difference is caused by a windowing effect. When we sample a signal over a finite window, we convolve its spectrum by an infinite sinc, which destroys much of the sparsity that was in the continuous domain. Based on this observation, we propose an approach to reconstruction that optimizes for sparsity in the continuous Fourier spectrum. We describe the theory behind our approach and discuss how it can be used to reduce sampling requirements and improve reconstruction quality. Finally, we demonstrate the power of our approach by showing how it can be applied to the task of recovering non-Lambertian light fields from a small number of 1D viewpoint trajectories.\n          <\/jats:p>","DOI":"10.1145\/2682631","type":"journal-article","created":{"date-parts":[[2015,1,5]],"date-time":"2015-01-05T13:27:09Z","timestamp":1420464429000},"page":"1-13","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":207,"title":["Light Field Reconstruction Using Sparsity in the Continuous Fourier Domain"],"prefix":"10.1145","volume":"34","author":[{"given":"Lixin","family":"Shi","sequence":"first","affiliation":[{"name":"Massachusetts Institute of Technology, Cambridge, MA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Haitham","family":"Hassanieh","sequence":"additional","affiliation":[{"name":"Massachusetts Institute of Technology, Cambridge, MA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Abe","family":"Davis","sequence":"additional","affiliation":[{"name":"Massachusetts Institute of Technology, Cambridge, MA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dina","family":"Katabi","sequence":"additional","affiliation":[{"name":"Massachusetts Institute of Technology, Cambridge, MA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fredo","family":"Durand","sequence":"additional","affiliation":[{"name":"Massachusetts Institute of Technology, Cambridge, MA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2014,12,29]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1109\/34.121783"},{"key":"e_1_2_2_2_1","volume-title":"Proceedings of the IEEE International Conference on Computational Photography (ICCP'09)","author":"Bishop T. E.","unstructured":"T. E. Bishop , S. Zanetti , and P. Favaro . 2009. Light field superesolution . In Proceedings of the IEEE International Conference on Computational Photography (ICCP'09) . T. E. Bishop, S. Zanetti, and P. Favaro. 2009. Light field superesolution. In Proceedings of the IEEE International Conference on Computational Photography (ICCP'09)."},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/383259.383309"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2005.862083"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.20124"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2012.03009.x"},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2006.871582"},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/1073204.1073320"},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/1531326.1531399"},{"key":"e_1_2_2_10_1","doi-asserted-by":"publisher","DOI":"10.5555\/2383894.2383927"},{"key":"e_1_2_2_11_1","doi-asserted-by":"crossref","unstructured":"B. Ghazi H. Hassanieh P. Indyk D. Katabi E. Price and L. Shi. 2013. Sample-optimal average-case sparse fourier transform in two dimensions. http:\/\/people.csail.mit.edu\/lixin\/files\/ALLER13_0252_FI.pdf.  B. Ghazi H. Hassanieh P. Indyk D. Katabi E. Price and L. Shi. 2013. Sample-optimal average-case sparse fourier transform in two dimensions. http:\/\/people.csail.mit.edu\/lixin\/files\/ALLER13_0252_FI.pdf.","DOI":"10.1109\/Allerton.2013.6736670"},{"key":"e_1_2_2_12_1","volume-title":"Proc. SPIE 5914","author":"Gilbert A.","unstructured":"A. Gilbert , M. Muthukrishnan , and M. Strauss . 2005. Improved time bounds for near-optimal sparse fourier representations . Proc. SPIE 5914 . A. Gilbert, M. Muthukrishnan, and M. Strauss. 2005. Improved time bounds for near-optimal sparse fourier representations. Proc. SPIE 5914."},{"key":"e_1_2_2_13_1","volume-title":"Introduction to Fourier Optics","author":"Goodman J. W.","unstructured":"J. W. Goodman . 1996. Introduction to Fourier Optics . McGraw-Hill . J. W. Goodman. 1996. Introduction to Fourier Optics. 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Fundamentals of texture mapping and image warping. https:\/\/www.cs.cmu.edu\/&sim;ph\/texfund\/texfund.pdf."},{"key":"e_1_2_2_18_1","volume-title":"Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR'10). 1831","author":"Levin A.","year":"1838","unstructured":"A. Levin and F. Durand . 2010. Linear view synthesis using a dimensionality gap light field prior . In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR'10). 1831 -- 1838 . A. Levin and F. Durand. 2010. Linear view synthesis using a dimensionality gap light field prior. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR'10). 1831--1838."},{"key":"e_1_2_2_19_1","doi-asserted-by":"publisher","DOI":"10.1145\/1276377.1276464"},{"key":"e_1_2_2_20_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-88693-8_7"},{"key":"e_1_2_2_21_1","doi-asserted-by":"publisher","DOI":"10.1145\/1360612.1360670"},{"key":"e_1_2_2_22_1","doi-asserted-by":"publisher","DOI":"10.1145\/1531326.1531403"},{"key":"e_1_2_2_23_1","doi-asserted-by":"publisher","DOI":"10.1145\/237170.237199"},{"key":"e_1_2_2_24_1","doi-asserted-by":"publisher","DOI":"10.1145\/2461912.2461914"},{"key":"e_1_2_2_25_1","doi-asserted-by":"publisher","DOI":"10.1145\/127719.122736"},{"key":"e_1_2_2_26_1","doi-asserted-by":"publisher","DOI":"10.1145\/1073204.1073256"},{"key":"e_1_2_2_27_1","unstructured":"R. Ng M. Levoy M. Bredif G. Duval M. Horowitz and P. Hanrahan. 2005. Light field photography with a hand-held plenoptic camera. https:\/\/graphics.stanford.edu\/papers\/lfcamera\/lfcamera-150dpi.pdf.  R. Ng M. Levoy M. Bredif G. Duval M. Horowitz and P. Hanrahan. 2005. Light field photography with a hand-held plenoptic camera. https:\/\/graphics.stanford.edu\/papers\/lfcamera\/lfcamera-150dpi.pdf."},{"key":"e_1_2_2_28_1","doi-asserted-by":"publisher","DOI":"10.1145\/280814.280927"},{"key":"e_1_2_2_29_1","unstructured":"Stanford. 2008. Stanford light field archive. http:\/\/lightfield.stanford.edu\/.  Stanford. 2008. Stanford light field archive. http:\/\/lightfield.stanford.edu\/."},{"key":"e_1_2_2_30_1","doi-asserted-by":"publisher","DOI":"10.1145\/1276377.1276463"},{"key":"e_1_2_2_31_1","doi-asserted-by":"publisher","DOI":"10.1145\/1073204.1073259"},{"key":"e_1_2_2_32_1","volume-title":"Proceedings of the IEEE International Conference on Computational Photography (ICCP'09)","author":"Zhang Z.","unstructured":"Z. Zhang and M. Levoy . 2009. Wigner distributions and how they relate to the light field . In Proceedings of the IEEE International Conference on Computational Photography (ICCP'09) . 1--10. Z. Zhang and M. Levoy. 2009. Wigner distributions and how they relate to the light field. In Proceedings of the IEEE International Conference on Computational Photography (ICCP'09). 1--10."}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2682631","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2682631","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T06:16:53Z","timestamp":1750227413000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2682631"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,12,29]]},"references-count":32,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2014,12,29]]}},"alternative-id":["10.1145\/2682631"],"URL":"https:\/\/doi.org\/10.1145\/2682631","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"value":"0730-0301","type":"print"},{"value":"1557-7368","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,12,29]]},"assertion":[{"value":"2014-02-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2014-05-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2014-12-29","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}