{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,21]],"date-time":"2025-10-21T15:11:13Z","timestamp":1761059473849},"reference-count":47,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2013,2,21]],"date-time":"2013-02-21T00:00:00Z","timestamp":1361404800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Math Imaging Vis"],"published-print":{"date-parts":[[2014,2]]},"DOI":"10.1007\/s10851-013-0422-y","type":"journal-article","created":{"date-parts":[[2013,2,20]],"date-time":"2013-02-20T20:41:06Z","timestamp":1361392866000},"page":"205-234","source":"Crossref","is-referenced-by-count":34,"title":["Analysis of Inpainting via Clustered Sparsity and Microlocal Analysis"],"prefix":"10.1007","volume":"48","author":[{"given":"Emily J.","family":"King","sequence":"first","affiliation":[]},{"given":"Gitta","family":"Kutyniok","sequence":"additional","affiliation":[]},{"given":"Xiaosheng","family":"Zhuang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2013,2,21]]},"reference":[{"key":"422_CR1","doi-asserted-by":"crossref","first-page":"4311","DOI":"10.1109\/TSP.2006.881199","volume":"54","author":"M. Aharon","year":"2006","unstructured":"Aharon, M., Elad, M., Bruckstein, A.: K-SVD: an algorithm for designing overcomplete dictionaries for sparse representation. IEEE Trans. Signal Process. 54, 4311\u20134322 (2006)","journal-title":"IEEE Trans. Signal Process."},{"issue":"8","key":"422_CR2","doi-asserted-by":"crossref","first-page":"1200","DOI":"10.1109\/83.935036","volume":"10","author":"C. Ballester","year":"2001","unstructured":"Ballester, C., Bertalmio, M., Caselles, V., Sapiro, G., Verdera, J.: Filling-in by joint interpolation of vector fields and gray levels. IEEE Trans. Image Process. 10(8), 1200\u20131211 (2001)","journal-title":"IEEE Trans. Image Process."},{"key":"422_CR3","first-page":"I355","volume-title":"Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition 2001 (CVPR 2001)","author":"M. Bertalmio","year":"2001","unstructured":"Bertalmio, M., Bertozzi, A., Sapiro, G.: Navier-Stokes, fluid dynamics, and image and video inpainting. In: Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition 2001 (CVPR 2001), pp.\u00a0I355\u2013I362. IEEE Press, New York (2001)"},{"key":"422_CR4","first-page":"417","volume-title":"Proceedings of SIGGRAPH 2000","author":"M. Bertalm\u00edo","year":"2000","unstructured":"Bertalm\u00edo, M., Sapiro, G., Caselles, V., Ballester, C.: Image inpainting. In: Proceedings of SIGGRAPH 2000, New Orleans, pp.\u00a0417\u2013424 (2000)"},{"issue":"3","key":"422_CR5","doi-asserted-by":"crossref","first-page":"379","DOI":"10.3934\/ipi.2010.4.379","volume":"4","author":"J.F. Cai","year":"2010","unstructured":"Cai, J.F., Cha, R.H., Shen, Z.: Simultaneous cartoon and texture inpainting. Inverse Probl. Imaging 4(3), 379\u2013395 (2010)","journal-title":"Inverse Probl. Imaging"},{"key":"422_CR6","doi-asserted-by":"crossref","first-page":"1033","DOI":"10.1090\/S0894-0347-2012-00740-1","volume":"25","author":"J.F. Cai","year":"2012","unstructured":"Cai, J.F., Dong, B., Osher, S., Shen, Z.: Image restoration: Total variation, wavelet frames, and beyond. J. Am. Math. Soc. 25, 1033\u20131089 (2012)","journal-title":"J. Am. Math. Soc."},{"issue":"2","key":"422_CR7","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1002\/cpa.10116","volume":"57","author":"E.J. Cand\u00e8s","year":"2004","unstructured":"Cand\u00e8s, E.J., Donoho, D.L.: New tight frames of curvelets and optimal representations of objects with piecewise C 2 singularities. Commun. Pure Appl. Math. 57(2), 219\u2013266 (2004)","journal-title":"Commun. Pure Appl. Math."},{"issue":"2","key":"422_CR8","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1016\/j.acha.2005.02.003","volume":"19","author":"E.J. Cand\u00e8s","year":"2005","unstructured":"Cand\u00e8s, E.J., Donoho, D.L.: Continuous curvelet transform. I. Resolution of the wavefront set. Appl. Comput. Harmon. Anal. 19(2), 162\u2013197 (2005)","journal-title":"Appl. Comput. Harmon. Anal."},{"issue":"1\u20132","key":"422_CR9","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1007\/s10851-006-6865-7","volume":"26","author":"T.F. Chan","year":"2006","unstructured":"Chan, T.F., Kang, S.H.: Error analysis for image inpainting. J.\u00a0Math. Imaging Vis. 26(1\u20132), 85\u2013103 (2006)","journal-title":"J.\u00a0Math. Imaging Vis."},{"issue":"2","key":"422_CR10","first-page":"564","volume":"63","author":"T.F. Chan","year":"2002","unstructured":"Chan, T.F., Kang, S.H., Shen, J.: Euler\u2019s elastica and curvature based inpainting. SIAM J. Appl. Math. 63(2), 564\u2013592 (2002)","journal-title":"SIAM J. Appl. Math."},{"issue":"3","key":"422_CR11","doi-asserted-by":"crossref","first-page":"1019","DOI":"10.1137\/S0036139900368844","volume":"62","author":"T.F. Chan","year":"2002","unstructured":"Chan, T.F., Shen, J.: Mathematical models for local nontexture inpaintings. SIAM J. Appl. Math. 62(3), 1019\u20131043 (2002) (electronic)","journal-title":"SIAM J. Appl. Math."},{"key":"422_CR12","series-title":"Applied and Numerical Harmonic Analysis","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-8176-8224-8","volume-title":"An Introduction to Frames and Riesz Bases","author":"O. Christensen","year":"2003","unstructured":"Christensen, O.: An Introduction to Frames and Riesz Bases. Applied and Numerical Harmonic Analysis. Birkh\u00e4user, Boston (2003)"},{"issue":"1","key":"422_CR13","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1137\/0524017","volume":"24","author":"C.K. Chui","year":"1993","unstructured":"Chui, C.K., Shi, X.L.: Inequalities of Littlewood-Paley type for frames and wavelets. SIAM J. Math. Anal. 24(1), 263\u2013277 (1993)","journal-title":"SIAM J. Math. Anal."},{"key":"422_CR14","series-title":"CBMS-NSF Regional Conference Series in Applied Mathematics","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611970104","volume-title":"Ten Lectures on Wavelets","author":"I. Daubechies","year":"1992","unstructured":"Daubechies, I.: Ten Lectures on Wavelets. CBMS-NSF Regional Conference Series in Applied Mathematics, vol.\u00a061. SIAM, Philadelphia (1992)"},{"issue":"2","key":"422_CR15","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1016\/j.acha.2011.06.001","volume":"32","author":"B. Dong","year":"2012","unstructured":"Dong, B., Ji, H., Li, J., Shen, Z., Xu, Y.: Wavelet frame based blind image inpainting. Appl. Comput. Harmon. Anal. 32(2), 268\u2013279 (2012)","journal-title":"Appl. Comput. Harmon. Anal."},{"issue":"5","key":"422_CR16","doi-asserted-by":"crossref","first-page":"2197","DOI":"10.1073\/pnas.0437847100","volume":"100","author":"D.L. Donoho","year":"2003","unstructured":"Donoho, D.L., Elad, M.: Optimally sparse representation in general (nonorthogonal) dictionaries via l 1 minimization. Proc. Natl. Acad. Sci. USA 100(5), 2197\u20132202 (2003) (electronic)","journal-title":"Proc. Natl. Acad. Sci. USA"},{"issue":"7","key":"422_CR17","doi-asserted-by":"crossref","first-page":"2845","DOI":"10.1109\/18.959265","volume":"47","author":"D.L. Donoho","year":"2001","unstructured":"Donoho, D.L., Huo, X.: Uncertainty principles and ideal atomic decomposition. IEEE Trans. Inf. Theory 47(7), 2845\u20132862 (2001)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"422_CR18","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1002\/cpa.21418","volume":"66","author":"D.L. Donoho","year":"2013","unstructured":"Donoho, D.L., Kutyniok, G.: Microlocal analysis of the geometric separation problem. Commun. Pure Appl. Math. 66, 1\u201347 (2013)","journal-title":"Commun. Pure Appl. Math."},{"key":"422_CR19","doi-asserted-by":"crossref","DOI":"10.1155\/2007\/20248","volume":"2007","author":"I. Drori","year":"2007","unstructured":"Drori, I.: Fast \u2113 1 minimization by iterative thresholding for multidimensional NMR spectroscopy. EURASIP J. Adv. Signal Process. 2007, 020248 (2007)","journal-title":"EURASIP J. Adv. Signal Process."},{"issue":"9","key":"422_CR20","doi-asserted-by":"crossref","first-page":"2558","DOI":"10.1109\/TIT.2002.801410","volume":"48","author":"M. Elad","year":"2002","unstructured":"Elad, M., Bruckstein, A.M.: A generalized uncertainty principle and sparse representation in pairs of bases. IEEE Trans. Inf. Theory 48(9), 2558\u20132567 (2002)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"3","key":"422_CR21","doi-asserted-by":"crossref","first-page":"340","DOI":"10.1016\/j.acha.2005.03.005","volume":"19","author":"M. Elad","year":"2005","unstructured":"Elad, M., Starck, J.L., Querre, P., Donoho, D.L.: Simultaneous cartoon and texture image inpainting using morphological component analysis (MCA). Appl. Comput. Harmon. Anal. 19(3), 340\u2013358 (2005)","journal-title":"Appl. Comput. Harmon. Anal."},{"key":"422_CR22","first-page":"2443","volume-title":"IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP\u00a0\u201999)","author":"K. Engan","year":"1999","unstructured":"Engan, K., Aase, S., Hakon Husoy, J.: Method of optimal directions for frame design. In: IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP\u00a0\u201999), vol.\u00a05, pp.\u00a02443\u20132446 (1999)"},{"key":"422_CR23","volume-title":"Proceedings of SampTA 2011","author":"S. Foucart","year":"2011","unstructured":"Foucart, S.: Recovering jointly sparse vectors via hard thresholding pursuit. In: Proceedings of SampTA 2011, Singapore (2011)"},{"issue":"4","key":"422_CR24","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1007\/s00605-010-0264-2","volume":"164","author":"P. Grohs","year":"2011","unstructured":"Grohs, P.: Continuous shearlet frames and resolution of the wavefront set. Monatshefte Math. 164(4), 393\u2013426 (2011)","journal-title":"Monatshefte Math."},{"key":"422_CR25","unstructured":"Grohs, P., Kutyniok, G.: Parabolic molecules. Preprint (2012)"},{"issue":"2","key":"422_CR26","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1016\/j.acha.2010.08.004","volume":"30","author":"K. Guo","year":"2011","unstructured":"Guo, K., Labate, D.: Analysis and detection of surface discontinuities using the 3D continuous shearlet transform. Appl. Comput. Harmon. Anal. 30(2), 231\u2013242 (2011)","journal-title":"Appl. Comput. Harmon. Anal."},{"issue":"1","key":"422_CR27","first-page":"32","volume":"8","author":"K. Guo","year":"2013","unstructured":"Guo, K., Labate, D.: The construction of smooth parseval frames of shearlets. Math. Model. Nat. Phenom. 8(1), 32\u201355 (2013)","journal-title":"Math. Model. Nat. Phenom."},{"issue":"6","key":"422_CR28","doi-asserted-by":"crossref","first-page":"WB203","DOI":"10.1190\/1.3494032","volume":"75","author":"G. Hennenfent","year":"2010","unstructured":"Hennenfent, G., Fenelon, L., Herrmann, F.J.: Nonequispaced curvelet transform for seismic data reconstruction: a sparsity-promoting approach. Geophysics 75(6), WB203\u2013WB210 (2010)","journal-title":"Geophysics"},{"key":"422_CR29","volume-title":"SEG International Exposition and 76th Annual Meeting","author":"G. Hennenfent","year":"2006","unstructured":"Hennenfent, G., Herrmann, F.J.: Application of stable signal recovery to seismic interpolation. In: SEG International Exposition and 76th Annual Meeting. SEG, Tulsa (2006)"},{"key":"422_CR30","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1111\/j.1365-246X.2007.03698.x","volume":"173","author":"F.J. Herrmann","year":"2008","unstructured":"Herrmann, F.J., Hennenfent, G.: Non-parametric seismic data recovery with curvelet frames. Geophys. J. Int. 173, 233\u2013248 (2008)","journal-title":"Geophys. J. Int."},{"key":"422_CR31","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-61497-2","volume-title":"The Analysis of Linear Partial Differential Operators. I. Classics in Mathematics","author":"L. H\u00f6rmander","year":"2003","unstructured":"H\u00f6rmander, L.: The Analysis of Linear Partial Differential Operators. I. Classics in Mathematics. Springer, Berlin (2003). Distribution theory and Fourier analysis. Reprint of the second (1990) edition [Springer, Berlin; MR1065993 (91m:35001a)]"},{"issue":"1","key":"422_CR32","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1007\/BF01274192","volume":"5","author":"Z. Jing","year":"1999","unstructured":"Jing, Z.: On the stability of wavelet and Gabor frames (Riesz bases). J. Fourier Anal. Appl. 5(1), 105\u2013125 (1999)","journal-title":"J. Fourier Anal. Appl."},{"key":"422_CR33","unstructured":"King, E.J.: Wavelet and frame theory: frame bound gaps, generalized shearlets, Grassmannian fusion frames, and p-adic wavelets. Ph.D. thesis, University of Maryland, College Park (2009)"},{"key":"422_CR34","volume-title":"SPIE Proceedings: Wavelets and Sparsity XIV","author":"E.J. King","year":"2011","unstructured":"King, E.J., Kutyniok, G., Zhuang, X.: Analysis of data separation and recovery problems using clustered sparsity. In: SPIE Proceedings: Wavelets and Sparsity XIV, vol.\u00a08138 (2011)"},{"key":"422_CR35","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1007\/s11760-008-0076-1","volume":"3","author":"M. Kowalski","year":"2009","unstructured":"Kowalski, M., Torr\u00e9sani, B.: Sparsity and persistence: mixed norms provide simple signal models with dependent coefficients. Signal Image Video Process. 3, 251\u2013264 (2009)","journal-title":"Signal Image Video Process."},{"key":"422_CR36","unstructured":"Kutyniok, G.: Geometric separation by single pass alternating thresholding. Appl. Comput. Harmon. Anal. (to appear)"},{"issue":"5","key":"422_CR37","doi-asserted-by":"crossref","first-page":"2719","DOI":"10.1090\/S0002-9947-08-04700-4","volume":"361","author":"G. Kutyniok","year":"2009","unstructured":"Kutyniok, G., Labate, D.: Resolution of the wavefront set using continuous shearlets. Trans. Am. Math. Soc. 361(5), 2719\u20132754 (2009)","journal-title":"Trans. Am. Math. Soc."},{"key":"422_CR38","series-title":"Applied and Numerical Harmonic Analysis","volume-title":"Shearlets: Multiscale Analysis for Multivariate Data","year":"2012","unstructured":"Kutyniok, G., Labate, D. (eds.): Shearlets: Multiscale Analysis for Multivariate Data. Applied and Numerical Harmonic Analysis. Birkh\u00e4user, Boston (2012)"},{"key":"422_CR39","volume-title":"Approximation Theory XIII","author":"G. Kutyniok","year":"2010","unstructured":"Kutyniok, G., Lemvig, J., Lim, W.: Compactly supported shearlets. In: Approximation Theory XIII, San Antonio, TX, 2010. Springer, Berlin (2010)"},{"key":"422_CR40","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-8176-8316-0","volume-title":"Shearlets: Multiscale Analysis for Multivariate Data","author":"G. Kutyniok","year":"2012","unstructured":"Kutyniok, G., Lemvig, J., Lim, W.: Shearlets and optimally sparse approximations. In: Shearlets: Multiscale Analysis for Multivariate Data. Springer, Berlin (2012)"},{"key":"422_CR41","doi-asserted-by":"crossref","first-page":"2962","DOI":"10.1137\/110844726","volume":"44","author":"G. Kutyniok","year":"2012","unstructured":"Kutyniok, G., Lemvig, J., Lim, W.Q.: Optimally sparse approximations of 3d functions by compactly supported shearlet frames. SIAM J. Appl. Math. 44, 2962\u20133017 (2012)","journal-title":"SIAM J. Appl. Math."},{"key":"422_CR42","doi-asserted-by":"crossref","first-page":"1564","DOI":"10.1016\/j.jat.2011.06.005","volume":"163","author":"G. Kutyniok","year":"2011","unstructured":"Kutyniok, G., Lim, W.: Compactly supported shearlets are optimally sparse. J. Approx. Theory 163, 1564\u20131589 (2011)","journal-title":"J. Approx. Theory"},{"issue":"4","key":"422_CR43","first-page":"209","volume":"145\u2013146","author":"Y. Meyer","year":"1987","unstructured":"Meyer, Y.: Principe d\u2019incertitude, bases hilbertiennes et alg\u00e8bres d\u2019op\u00e9rateurs. Ast\u00e9risque 145\u2013146(4), 209\u2013223 (1987). S\u00e9minaire Bourbaki, Vol.\u00a01985\/86","journal-title":"Ast\u00e9risque"},{"key":"422_CR44","series-title":"University Lecture Series","doi-asserted-by":"crossref","DOI":"10.1090\/ulect\/022","volume-title":"Oscillating Patterns in Image Processing and Nonlinear Evolution Equations","author":"Y. Meyer","year":"2001","unstructured":"Meyer, Y.: Oscillating Patterns in Image Processing and Nonlinear Evolution Equations. University Lecture Series, vol.\u00a022. Am. Math. Soc., Providence (2001). The fifteenth Dean Jacqueline B. Lewis memorial lectures"},{"key":"422_CR45","volume-title":"International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2011)","author":"S. Nam","year":"2011","unstructured":"Nam, S., Davies, M., Elad, M., Gribonval, R.: Cosparse analysis modeling\u2014uniqueness and algorithms. In: International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2011). IEEE Press, New York (2011)"},{"issue":"1","key":"422_CR46","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1016\/j.acha.2012.03.006","volume":"34","author":"S. Nam","year":"2013","unstructured":"Nam, S., Davies, M.E., Elad, M., Gribonval, R.: The cosparse analysis model and algorithms. Appl. Comput. Harmon. Anal. 34(1), 30\u201356 (2013)","journal-title":"Appl. Comput. Harmon. Anal."},{"issue":"23","key":"422_CR47","doi-asserted-by":"crossref","first-page":"3311","DOI":"10.1016\/S0042-6989(97)00169-7","volume":"37","author":"B.A. Olshausen","year":"1997","unstructured":"Olshausen, B.A., Field, D.J.: Sparse coding with an overcomplete basis set: a strategy employed by V1? Vis. Res. 37(23), 3311\u20133325 (1997)","journal-title":"Vis. Res."}],"container-title":["Journal of Mathematical Imaging and Vision"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10851-013-0422-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10851-013-0422-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10851-013-0422-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T02:26:22Z","timestamp":1559269582000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10851-013-0422-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,2,21]]},"references-count":47,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2014,2]]}},"alternative-id":["422"],"URL":"https:\/\/doi.org\/10.1007\/s10851-013-0422-y","relation":{},"ISSN":["0924-9907","1573-7683"],"issn-type":[{"value":"0924-9907","type":"print"},{"value":"1573-7683","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,2,21]]}}}