{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:48:06Z","timestamp":1787320086326,"version":"build-2736575974"},"reference-count":28,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Imaging Sci."],"published-print":{"date-parts":[[2020,1]]},"abstract":"<jats:p>Vector fields arise in a variety of quantity measure and visualization techniques, such as fluid flow imaging, motion estimation, deformation measures, and color imaging, leading to a better understanding of physical phenomena. Recent progress in vector field imaging technologies has emphasized the need for efficient noise removal and reconstruction algorithms. A key ingredient in the successful extraction of signals from noisy measurements is prior information, which can often be represented as a parameterized model. In this work, we extend the overparameterization variational framework in order to perform model-based reconstruction of vector fields. The overparameterization methodology combines local modeling of the data with global model parameter regularization. By considering the vector field as a linear combination of basis vector fields and appropriate scale and rotation coefficients, we can reduce the denoising problem to a simpler form of coefficient recovery. We introduce two versions of the overparameterization framework: a total variation-based method and a sparsity-based method, which relies on the cosparse analysis model. We demonstrate the efficiency of the proposed frameworks for two- and three-dimensional vector fields with linear and quadratic overparameterization models.<\/jats:p>","DOI":"10.1137\/19m1280697","type":"journal-article","created":{"date-parts":[[2020,8,25]],"date-time":"2020-08-25T12:54:36Z","timestamp":1598360076000},"page":"1386-1414","source":"Crossref","is-referenced-by-count":0,"title":["Overparameterized Models for Vector Fields"],"prefix":"10.1137","volume":"13","author":[{"given":"Keren","family":"Rotker","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dafna Ben","family":"Bashat","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alex M.","family":"Bronstein","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2020,8,25]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1287\/moor.1100.0449"},{"key":"atypb2","doi-asserted-by":"crossref","unstructured":"H. Attouch, G. Buttazzo, and G. Michaille,\n                      Variational Analysis in Sobolev and BV Spaces: Applications to PDEs and Optimization\n                      , 2nd ed., MOS-SIAM Ser. Optim. 17, SIAM, 2014,https:\/\/doi.org\/10.1137\/1.9781611973488.","DOI":"10.1137\/1.9781611973488"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2007.891805"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1109\/83.661180"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1109\/LSP.2014.2369212"},{"key":"atypb6","first-page":"836","author":"Bostan E.","year":"2013","journal-title":"IEEE"},{"key":"atypb7","doi-asserted-by":"crossref","unstructured":"S. Boyd, N. Parikh, and E. Chu,\n                      Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers\n                      , Now Publishers, Inc., 2011.","DOI":"10.1561\/9781601984616"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1109\/TMI.2005.844159"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1023\/B:JMIV.0000011324.14508.fb"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1137\/140998585"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1007\/s10851-008-0127-9"},{"key":"atypb12","unstructured":"B. C. Hall,\n                      Lie Groups, Lie Algebras, and Representations: An Elementary Introduction\n                      , 2nd ed., Grad. Texts in Math. 222, Springer, 2015,http:\/\/gen.lib.rus.ec\/book\/index.php?md5=170209c3008e99f226bcc911c4ee7fe9."},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1002\/jmri.23632"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1002\/jmri.20871"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1109\/TBME.2011.2163070"},{"key":"atypb16","doi-asserted-by":"crossref","unstructured":"S. Nam, M. E. Davies, M. Elad, and R. Gribonval,\n                      Recovery of cosparse signals with greedy analysis pursuit in the presence of noise\n                      , in Proceedings of the 2011 4th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), IEEE, 2011, pp. 361-364.","DOI":"10.1109\/CAMSAP.2011.6136026"},{"key":"atypb17","first-page":"1","author":"Nir T.","year":"2007","journal-title":"IEEE"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1007\/s11263-007-0051-2"},{"key":"atypb19","first-page":"761","author":"Rosman G.","year":"2011","journal-title":"Springer"},{"key":"atypb20","first-page":"19","author":"Rosman G.","year":"2014","journal-title":"Springer"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(92)90242-F"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1109\/83.541429"},{"key":"atypb23","first-page":"379","author":"Shem-Tov S.","year":"2013","journal-title":"Springer"},{"key":"atypb24","first-page":"861","author":"Sochen N.","year":"2003","journal-title":"IEEE"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1109\/83.661181"},{"key":"atypb26","first-page":"1061","author":"Tafti P. 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