{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,9]],"date-time":"2026-07-09T23:56:28Z","timestamp":1783641388247,"version":"3.55.0"},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2011,9,22]],"date-time":"2011-09-22T00:00:00Z","timestamp":1316649600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2012,3]]},"DOI":"10.1007\/s10915-011-9536-9","type":"journal-article","created":{"date-parts":[[2011,9,21]],"date-time":"2011-09-21T11:53:59Z","timestamp":1316606039000},"page":"536-556","source":"Crossref","is-referenced-by-count":19,"title":["Sparsity Enforcing Edge Detection Method for Blurred and Noisy Fourier data"],"prefix":"10.1007","volume":"50","author":[{"given":"W.","family":"Stefan","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"A.","family":"Viswanathan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"A.","family":"Gelb","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"R.","family":"Renaut","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2011,9,22]]},"reference":[{"issue":"1","key":"9536_CR1","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1109\/TMI.1986.4307732","volume":"5","author":"C.B. Ahn","year":"1986","unstructured":"Ahn, C.B., Kim, J.H., Cho, Z.H.: High-speed spiral-scan echo planar NMR imaging-I. IEEE Trans. Med. Imaging 5(1), 2 (1986)","journal-title":"IEEE Trans. Med. Imaging"},{"issue":"8","key":"9536_CR2","doi-asserted-by":"crossref","first-page":"1207","DOI":"10.1002\/cpa.20124","volume":"59","author":"E. Candes","year":"2006","unstructured":"Candes, E., Romberg, J., Tao, T.: Stable signal recovery from incomplete and inaccurate measurements. Commun. Pure Appl. Math. 59(8), 1207\u20131223 (2006)","journal-title":"Commun. Pure Appl. Math."},{"issue":"2","key":"9536_CR3","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1109\/TIT.2005.862083","volume":"52","author":"E. Candes","year":"2006","unstructured":"Candes, E., Romberg, J., Tao, T.: Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans. Inf. Theory 52(2), 489\u2013509 (2006)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"12","key":"9536_CR4","doi-asserted-by":"crossref","first-page":"5406","DOI":"10.1109\/TIT.2006.885507","volume":"52","author":"E. Candes","year":"2006","unstructured":"Candes, E., Tao, T.: Near-optimal signal recovery from random projections: universal encoding strategies? IEEE Trans. Inf. Theory 52(12), 5406\u20135425 (2006)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"9536_CR5","doi-asserted-by":"crossref","unstructured":"Cochran, D., Gelb, A., Wang, Y.: Edge detection from truncated Fourier data using spectral mollifiers, preprint, submitted to Advances in Computational Mathematics (2011)","DOI":"10.1007\/s10444-011-9258-4"},{"issue":"5","key":"9536_CR6","doi-asserted-by":"crossref","first-page":"2620","DOI":"10.1137\/070689899","volume":"46","author":"S. Engelberg","year":"2008","unstructured":"Engelberg, S., Tadmor, E.: Recovery of edges from spectral data with noise\u2014a new perspective. SIAM J. Numer. Anal. 46(5), 2620\u20132635 (2008)","journal-title":"SIAM J. Numer. Anal."},{"issue":"2","key":"9536_CR7","doi-asserted-by":"crossref","first-page":"560","DOI":"10.1109\/TSP.2002.807005","volume":"51","author":"J.A. Fessler","year":"2003","unstructured":"Fessler, J.A., Sutton, B.P.: Nonuniform fast Fourier transforms using min-max interpolation. IEEE Trans. Signal Process. 51(2), 560\u2013574 (2003)","journal-title":"IEEE Trans. Signal Process."},{"issue":"1","key":"9536_CR8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10915-007-9170-8","volume":"36","author":"A. Gelb","year":"2008","unstructured":"Gelb, A., Cates, D.: Detection of edges in spectral data III\u2014refinement of the concentration method. J.\u00a0Sci. Comput. 36(1), 1\u201343 (2008)","journal-title":"J.\u00a0Sci. Comput."},{"key":"9536_CR9","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1006\/acha.1999.0262","volume":"7","author":"A. Gelb","year":"1999","unstructured":"Gelb, A., Tadmor, E.: Detection of edges in spectral data. Appl. Comput. Harmon. Anal. 7, 101\u2013135 (1999)","journal-title":"Appl. Comput. Harmon. Anal."},{"issue":"4","key":"9536_CR10","doi-asserted-by":"crossref","first-page":"1389","DOI":"10.1137\/S0036142999359153","volume":"38","author":"A. Gelb","year":"2000","unstructured":"Gelb, A., Tadmor, E.: Detection of edges in spectral data II. Nonlinear enhancement. SIAM J. Numer. Anal. 38(4), 1389\u20131408 (2000)","journal-title":"SIAM J. Numer. Anal."},{"issue":"2\u20133","key":"9536_CR11","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1007\/s10915-006-9088-6","volume":"28","author":"A. Gelb","year":"2006","unstructured":"Gelb, A., Tadmor, E.: Adaptive edge detectors for piecewise smooth data based on the minmod limiter. J. Sci. Comput. 28(2\u20133), 279\u2013306 (2006)","journal-title":"J. Sci. Comput."},{"issue":"4","key":"9536_CR12","doi-asserted-by":"crossref","first-page":"644","DOI":"10.1137\/S0036144596301390","volume":"39","author":"D. Gottlieb","year":"1997","unstructured":"Gottlieb, D., Shu, C.W.: On the Gibbs phenomenon and its resolution. SIAM Rev. 39(4), 644\u2013668 (1997)","journal-title":"SIAM Rev."},{"key":"9536_CR13","unstructured":"Grant, M., Boyd, S.: CVX: Matlab software for disciplined convex programming, version 1.21 (2010)"},{"key":"9536_CR14","first-page":"155","volume-title":"Nonconvex Optimization and its Applications","author":"M. Grant","year":"2006","unstructured":"Grant, M., Boyd, S., Ye, Y.: Disciplined convex programming. In: Nonconvex Optimization and its Applications, pp. 155\u2013210. Springer, Berlin (2006)"},{"key":"9536_CR15","doi-asserted-by":"crossref","unstructured":"Guo, W., Yin, W.: EdgeCS: edge guided compressive sensing reconstruction. Technical report, Rice CAAM Report TR10-02, 2010","DOI":"10.1117\/12.863354"},{"issue":"1","key":"9536_CR16","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1002\/mrm.1910380117","volume":"38","author":"R.D. Hoge","year":"1997","unstructured":"Hoge, R.D., Kwan, R.K., Pike, G.B.: Density compensation functions for spiral MRI. Magn. Reson. Med. 38(1), 117\u2013128 (1997)","journal-title":"Magn. Reson. Med."},{"key":"9536_CR17","first-page":"559","volume":"5","author":"M.I. Kadec","year":"1964","unstructured":"Kadec, M.I.: The exact value of the Paley-Wiener constant. Sov. Math. Dokl. 5, 559\u2013561 (1964)","journal-title":"Sov. Math. Dokl."},{"issue":"4","key":"9536_CR18","doi-asserted-by":"crossref","first-page":"200","DOI":"10.1109\/TMI.1985.4307723","volume":"4","author":"J.D. O\u2019Sullivan","year":"1985","unstructured":"O\u2019Sullivan, J.D.: A fast sinc function griding algorithm for Fourier inversion in computer tomography. IEEE Trans. Med. Imaging 4(4), 200\u2013207 (1985)","journal-title":"IEEE Trans. Med. Imaging"},{"issue":"1","key":"9536_CR19","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1002\/(SICI)1522-2594(199901)41:1<179::AID-MRM25>3.0.CO;2-V","volume":"41","author":"J.G. Pipe","year":"1999","unstructured":"Pipe, J.G., Menon, P.: Sampling density compensation in MRI: Rationale and an iterative numerical solution. Magn. Reson. Med. 41(1), 179\u2013186 (1999)","journal-title":"Magn. Reson. Med."},{"issue":"4","key":"9536_CR20","doi-asserted-by":"crossref","first-page":"306","DOI":"10.1109\/42.848182","volume":"19","author":"H. Sedarat","year":"2000","unstructured":"Sedarat, H., Nishimura, D.G.: On the optimality of the griding reconstruction algorithm. IEEE Trans. Med. Imaging 19(4), 306\u2013317 (2000)","journal-title":"IEEE Trans. Med. Imaging"},{"issue":"1","key":"9536_CR21","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/S0377-0427(03)00500-4","volume":"161","author":"B. Shizgal","year":"2003","unstructured":"Shizgal, B., Jung, J.H.: Towards the resolution of the Gibbs phenomena. J. Comput. Appl. Math. 161(1), 41\u201365 (2003)","journal-title":"J. Comput. Appl. Math."},{"issue":"2","key":"9536_CR22","doi-asserted-by":"crossref","first-page":"232","DOI":"10.1137\/080730251","volume":"3","author":"W. Stefan","year":"2010","unstructured":"Stefan, W., Renaut, R.A., Gelb, A.: Improved total variation-type regularization using higher-order edge detectors. SIAM J. Imaging Sci. 3(2), 232\u2013251 (2010)","journal-title":"SIAM J. Imaging Sci."},{"issue":"3","key":"9536_CR23","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1023\/A:1018901926283","volume":"9","author":"G. Steidl","year":"1998","unstructured":"Steidl, G.: A note on fast Fourier transforms for nonequispaced grids. Adv. Comput. Math. 9(3), 337\u2013352 (1998)","journal-title":"Adv. Comput. Math."},{"key":"9536_CR24","doi-asserted-by":"crossref","first-page":"625","DOI":"10.1080\/10556789908805766","volume":"11\u201312","author":"J.F. Sturm","year":"1999","unstructured":"Sturm, J.F.: Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optim. Methods Softw. 11\u201312, 625\u2013653 (1999). Special issue on Interior Point Methods (CD supplement with software), http:\/\/sedumi.mcmaster.ca\/","journal-title":"Optim. Methods Softw."},{"key":"9536_CR25","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1017\/S0962492906320016","volume":"16","author":"E. Tadmor","year":"2007","unstructured":"Tadmor, E.: Filters, mollifiers and the computation of the Gibbs phenomenon. Acta Numer. 16, 305\u2013378 (2007)","journal-title":"Acta Numer."},{"issue":"5\u20136","key":"9536_CR26","doi-asserted-by":"crossref","first-page":"744","DOI":"10.1007\/s00041-008-9038-9","volume":"14","author":"E. Tadmor","year":"2008","unstructured":"Tadmor, E., Zou, J.: Three novel edge detection methods for incomplete and noisy spectral data. J.\u00a0Fourier Anal. Appl. 14(5\u20136), 744\u2013763 (2008)","journal-title":"J.\u00a0Fourier Anal. Appl."},{"key":"9536_CR27","unstructured":"Toh, K., T\u00fct\u00fcnc\u00fc, R., Todd, M.: SDPT3 4.0 (beta) (software package). Technical report, Department of Mathematics National University of Singapore, September 2006. http:\/\/www.math.nus.edu.sg\/mattohkc\/sdpt3.html"},{"key":"9536_CR28","unstructured":"Viswanathan, A.: Imaging from Fourier spectral data: problems in discontinuity detection, non-harmonic Fourier reconstruction and point-spread function estimation. PhD thesis, Arizona State University (2010)"},{"key":"9536_CR29","doi-asserted-by":"crossref","unstructured":"Viswanathan, A., Gelb, A., Cochran, D.: Iterative design of concentration factors for edge detection. J.\u00a0Sci. Comput. (2011, to appear)","DOI":"10.1007\/s10915-011-9524-0"},{"issue":"3","key":"9536_CR30","doi-asserted-by":"crossref","first-page":"248","DOI":"10.1137\/080724265","volume":"1","author":"Y. Wang","year":"2008","unstructured":"Wang, Y., Yin, W., Zhang, Y.: A fast algorithm for image deblurring with total variation regularization. SIAM J. Imaging Sci. 1(3), 248\u2013272 (2008)","journal-title":"SIAM J. Imaging Sci."},{"key":"9536_CR31","volume-title":"An Introduction to Nonharmonic Fourier Analysis","author":"R.M. Young","year":"2001","unstructured":"Young, R.M.: An Introduction to Nonharmonic Fourier Analysis. Academic Press, New York (2001)"}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-011-9536-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-011-9536-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-011-9536-9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,16]],"date-time":"2019-06-16T04:08:02Z","timestamp":1560658082000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-011-9536-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,9,22]]},"references-count":31,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2012,3]]}},"alternative-id":["9536"],"URL":"https:\/\/doi.org\/10.1007\/s10915-011-9536-9","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,9,22]]}}}