{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:34:32Z","timestamp":1787337272470,"version":"build-2736575974"},"reference-count":38,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2006,1]]},"abstract":"<jats:p>\n                    A new algorithm for the characterization of engineering surface topographies with line singularities is proposed. It is based on thresholding complex ridgelet coefficients combined with total variation (TV) minimization. The discrete ridgelet transform is designed by first using a discrete Radon transform based on the nonequispaced fast Fourier transform (NFFT) and then applying a dual-tree complex wavelet transform (DT CWT). The NFFT-based approach of the Radon transform completely avoids linear interpolations of the Cartesian-to-polar grid and requires only O(n\n                    <jats:sup>2<\/jats:sup>\n                    log n) arithmetic operations for n by n arrays, while its inverse preserves the good reconstruction quality of the filtered backprojection. The DT CWT in the second step of the ridgelet transform provides approximate shift invariance on the projections of the Radon transform. After hard thresholding the ridgelet coefficients, they are restored using TV minimization to eliminate the pseudo-Gibbs artifacts near the discontinuities. Numerical experiments demonstrate the remarkable ability of the methodology to extract line scratches.\n                  <\/jats:p>","DOI":"10.1137\/05062737x","type":"journal-article","created":{"date-parts":[[2008,2,6]],"date-time":"2008-02-06T16:45:19Z","timestamp":1202316319000},"page":"984-1000","source":"Crossref","is-referenced-by-count":24,"title":["Combined Complex Ridgelet Shrinkage and Total Variation Minimization"],"prefix":"10.1137","volume":"28","author":[{"given":"Jianwei","family":"Ma","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Markus","family":"Fenn","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,8,4]]},"reference":[{"key":"R1","unstructured":"A. Averbuch, R. Coifman, D. Donoho, M. Israeli, and J. Wald\u00e9n,\n                      Fast Slant Stack: A Notion of Radon Transform for Data in a Cartesian GridWhich Is Rapidly Computable, Algebraically Exact, Geometrically Faithful and Invertible\n                      , http:\/\/www\u2010stat.stanford.edu\/\u223cdonoho\/Reports\/2001\/FastSlantStack.pdf (2001)."},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1006\/acha.1995.1026"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1006\/acha.1998.0248"},{"key":"R4","unstructured":"E. Cand\u00e8s, L. Demanet, D. Donoho, and L. Ying,\n                      Fast discrete curvelet transforms\n                      , Multiscale Model. Simul., to appear."},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1098\/rsta.1999.0444"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1006\/jath.2001.3624"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1016\/j.sigpro.2004.07.009"},{"key":"R8","unstructured":"T. Chan and H. Zhou,\n                      Optimal Constructions of Wavelet Coefficients Using Total Variation Regularization in Image Compression\n                      , CAM Tech. Report 00\u201027, UCLA, Los Angeles, CA, 2000."},{"key":"R9","unstructured":"M. Do, M. Vetterli, Contourlets, Stud. Comput. Math., Vol. 10, Academic Press\/Elsevier, San Diego, CA, 2003, 83\u20131052136839"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2002.806252"},{"key":"R11","doi-asserted-by":"crossref","unstructured":"D. Donoho, A. Flesia, Digital ridgelet transform based on true ridge functions, Stud. Comput. Math., Vol. 10, Academic Press\/Elsevier, San Diego, CA, 2003, 1\u2013302136836","DOI":"10.1016\/S1570-579X(03)80029-0"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827501397792"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1137\/0914081"},{"key":"R14","unstructured":"Benedikte Elbel, Gabriele Steidl, Fast Fourier transforms for nonequispaced data, Innov. Appl. Math., Vanderbilt Univ. Press, Nashville, TN, 1998, 39\u2013461743031"},{"key":"R15","unstructured":"J. A. Fessler and B. P. Sutton,\n                      NUFFT\u2014Nonuniform FFT Toolbox for Matlab\n                      , http:\/\/www.eecs.umich.edu\/\u223cbpsutton\/MR\/Code\/NUFFT\/ (2002)."},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2002.807005"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1007\/s00041-003-0021-1"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1137\/S003614450343200X"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1098\/rsta.1999.0447"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1006\/acha.2000.0343"},{"key":"R21","unstructured":"S. Kunis and D. Potts,\n                      NFFT, Software Package, C Subroutine Library\n                      , http:\/\/www.math.uni\u2010luebeck.de\/potts\/nfft\/ (2002)."},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2005.843753"},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2004.12.053"},{"key":"R24","unstructured":"J. Ma, X. Jiang, and L. Blunt,\n                      Complex wavelet transform for extraction of morphological features on surface topography\n                      , in Euspen\u2019s 4th International Conference, Glasgow, UK, 2004, pp. 350\u2013351."},{"key":"R25","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2005.06.091"},{"key":"R26","doi-asserted-by":"publisher","DOI":"10.1006\/acha.2002.0379"},{"key":"R27","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-663-01409-6"},{"key":"R28","doi-asserted-by":"publisher","DOI":"10.1142\/S0219691305000749"},{"key":"R29","doi-asserted-by":"publisher","DOI":"10.1007\/s00041-002-0025-2"},{"key":"R30","doi-asserted-by":"crossref","unstructured":"Daniel Potts, Gabriele Steidl, Manfred Tasche, Fast Fourier transforms for nonequispaced data: a tutorial, Appl. Numer. Harmon. 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Report 03\u201059, UCLA, Los Angeles, CA, 2003."}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/05062737X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:53:54Z","timestamp":1787334834000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/05062737X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,1]]},"references-count":38,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2006,1]]}},"alternative-id":["10.1137\/05062737X"],"URL":"https:\/\/doi.org\/10.1137\/05062737x","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,1]]}}}