{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,8]],"date-time":"2026-02-08T15:09:26Z","timestamp":1770563366611,"version":"3.49.0"},"reference-count":41,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2017,2,27]],"date-time":"2017-02-27T00:00:00Z","timestamp":1488153600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"name":"PRES Midi-Pyr\u00e9n\u00e9es","award":["MODIM"],"award-info":[{"award-number":["MODIM"]}]},{"name":"RITC","award":["OPTIMUS"],"award-info":[{"award-number":["OPTIMUS"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Math Imaging Vis"],"published-print":{"date-parts":[[2017,7]]},"DOI":"10.1007\/s10851-017-0714-8","type":"journal-article","created":{"date-parts":[[2017,2,27]],"date-time":"2017-02-27T11:46:26Z","timestamp":1488195986000},"page":"333-348","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Approximation of Integral Operators Using Product-Convolution Expansions"],"prefix":"10.1007","volume":"58","author":[{"given":"Paul","family":"Escande","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pierre","family":"Weiss","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,2,27]]},"reference":[{"issue":"7","key":"714_CR1","doi-asserted-by":"crossref","first-page":"6461","DOI":"10.1364\/OE.18.006461","volume":"18","author":"M Arigovindan","year":"2010","unstructured":"Arigovindan, M., Shaevitz, J., McGowan, J., Sedat, J.W., Agard, D.A.: A parallel product-convolution approach for representing the depth varying point spread functions in 3D widefield microscopy based on principal component analysis. Opt. Express 18(7), 6461\u20136476 (2010)","journal-title":"Opt. Express"},{"issue":"6","key":"714_CR2","doi-asserted-by":"crossref","first-page":"1716","DOI":"10.1137\/0729097","volume":"29","author":"G Beylkin","year":"1992","unstructured":"Beylkin, G.: On the representation of operators in bases of compactly supported wavelets. SIAM J. Numer. Anal. 29(6), 1716\u20131740 (1992)","journal-title":"SIAM J. Numer. Anal."},{"issue":"2","key":"714_CR3","first-page":"141","volume":"44","author":"G Beylkin","year":"1991","unstructured":"Beylkin, G., Coifman, R., Rokhlin, V.: Fast wavelet transforms and numerical algorithms I. Appl. Comput. Harmon. Anal. 44(2), 141\u2013183 (1991)","journal-title":"Appl. Comput. Harmon. Anal."},{"key":"714_CR4","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-3428-7","volume-title":"Variational Theory of Splines","author":"AY Bezhaev","year":"2001","unstructured":"Bezhaev, A.Y., Vasilenko, V.A.: Variational Theory of Splines. Springer, Berlin (2001)"},{"key":"714_CR5","unstructured":"Bigot, J., Escande, P., Weiss, P.: Estimation of linear operators from scattered impulse responses. arXiv preprint arXiv:1610.04056 (2016)"},{"issue":"5","key":"714_CR6","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1016\/S0955-7997(02)00152-2","volume":"27","author":"S B\u00f6rm","year":"2003","unstructured":"B\u00f6rm, S., Grasedyck, L., Hackbusch, W.: Introduction to hierarchical matrices with applications. Eng. Anal. Bound. Elem. 27(5), 405\u2013422 (2003)","journal-title":"Eng. Anal. Bound. Elem."},{"issue":"2","key":"714_CR7","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1090\/S0002-9947-1981-0594411-4","volume":"263","author":"R Busby","year":"1981","unstructured":"Busby, R., Smith, H.: Product-convolution operators and mixed-norm spaces. Trans. Am. Math. Soc. 263(2), 309\u2013341 (1981)","journal-title":"Trans. Am. Math. Soc."},{"key":"714_CR8","volume-title":"An Introduction to Frames and Riesz Bases","author":"O Christensen","year":"2013","unstructured":"Christensen, O.: An Introduction to Frames and Riesz Bases. Springer, New York (2013)"},{"key":"714_CR9","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1016\/S0024-3795(02)00505-0","volume":"366","author":"M Chu","year":"2003","unstructured":"Chu, M., Funderlic, R., Plemmons, R.: Structured low rank approximation. Linear Algebra Appl. 366, 157\u2013172 (2003)","journal-title":"Linear Algebra Appl."},{"key":"714_CR10","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898719208","volume-title":"The Finite Element Method for Elliptic Problems","author":"PG Ciarlet","year":"2002","unstructured":"Ciarlet, P.G.: The Finite Element Method for Elliptic Problems, vol. 40. SIAM, Philadelphia (2002)"},{"issue":"1","key":"714_CR11","doi-asserted-by":"crossref","first-page":"235","DOI":"10.4171\/RMI\/345","volume":"19","author":"A Cohen","year":"2003","unstructured":"Cohen, A., Dahmen, W., Daubechies, I., DeVore, R.: Harmonic analysis of the space BV. Rev. Mat. Iberoam. 19(1), 235\u2013263 (2003)","journal-title":"Rev. Mat. Iberoam."},{"issue":"1","key":"714_CR12","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1006\/acha.1993.1005","volume":"1","author":"A Cohen","year":"1993","unstructured":"Cohen, A., Daubechies, I., Vial, P.: Wavelets on the interval and fast wavelet transforms. Appl. Comput. Harmon. Anal. 1(1), 54\u201381 (1993)","journal-title":"Appl. Comput. Harmon. Anal."},{"issue":"3","key":"714_CR13","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1007\/BF02072014","volume":"1","author":"W Dahmen","year":"1993","unstructured":"Dahmen, W., Pr\u00f6\u00dfdorf, S., Schneider, R.: Wavelet approximation methods for pseudodifferential equations II: matrix compression and fast solution. Adv. Comput. Math. 1(3), 259\u2013335 (1993)","journal-title":"Adv. Comput. Math."},{"issue":"1","key":"714_CR14","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1007\/BF02571732","volume":"215","author":"W Dahmen","year":"1994","unstructured":"Dahmen, W., Pr\u00f6ssdorf, S., Schneider, R.: Wavelet approximation methods for pseudodifferential equations: I stability and convergence. Math. Z. 215(1), 583\u2013620 (1994)","journal-title":"Math. Z."},{"issue":"7","key":"714_CR15","doi-asserted-by":"crossref","first-page":"909","DOI":"10.1002\/cpa.3160410705","volume":"41","author":"I Daubechies","year":"1988","unstructured":"Daubechies, I.: Orthonormal bases of compactly supported wavelets. Commun. pur. appl. math. 41(7), 909\u2013996 (1988)","journal-title":"Commun. pur. appl. math."},{"key":"714_CR16","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, vol. 61. SIAM, Philadelphia (1992)"},{"issue":"3","key":"714_CR17","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1007\/s11263-015-0817-x","volume":"115","author":"L Denis","year":"2015","unstructured":"Denis, L., Thi\u00e9baut, E., Soulez, F., Becker, J.-M., Mourya, R.: Fast approximations of shift-variant blur. Int. J. Comput. Vis. 115(3), 253\u2013278 (2015)","journal-title":"Int. J. Comput. Vis."},{"key":"714_CR18","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1017\/S0962492900002816","volume":"7","author":"RA DeVore","year":"1998","unstructured":"DeVore, R.A.: Nonlinear approximation. Acta. Numer. 7, 51\u2013150 (1998)","journal-title":"Acta. Numer."},{"key":"714_CR19","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-02888-9","volume-title":"Constructive Approximation","author":"RA DeVore","year":"1993","unstructured":"DeVore, R.A., Lorentz, G.G.: Constructive Approximation, vol. 303. Springer, Berlin (1993)"},{"issue":"4","key":"714_CR20","doi-asserted-by":"crossref","first-page":"2976","DOI":"10.1137\/151003465","volume":"8","author":"P Escande","year":"2015","unstructured":"Escande, P., Weiss, P.: Sparse wavelet representations of spatially varying blurring operators. SIAM J. Imaging Sci. 8(4), 2976\u20133014 (2015)","journal-title":"SIAM J. Imaging Sci."},{"issue":"3","key":"714_CR21","doi-asserted-by":"crossref","first-page":"504","DOI":"10.1364\/JOSAA.22.000504","volume":"22","author":"RC Flicker","year":"2005","unstructured":"Flicker, R.C., Rigaut, F.J.: Anisoplanatic deconvolution of adaptive optics images. J. Opt. Soc. Am. A 22(3), 504\u2013513 (2005)","journal-title":"J. Opt. Soc. Am. A"},{"issue":"1","key":"714_CR22","doi-asserted-by":"crossref","first-page":"326","DOI":"10.1016\/j.jcp.2005.12.003","volume":"216","author":"E Gilad","year":"2006","unstructured":"Gilad, E., Von Hardenberg, J.: A fast algorithm for convolution integrals with space and time variant kernels. J. Comput. Phys. 216(1), 326\u2013336 (2006)","journal-title":"J. Comput. Phys."},{"issue":"4","key":"714_CR23","doi-asserted-by":"crossref","first-page":"742","DOI":"10.1190\/1.1440743","volume":"42","author":"LJ Griffiths","year":"1977","unstructured":"Griffiths, L.J., Smolka, F.R., Trembly, L.D.: Adaptive deconvolution: a new technique for processing time-varying seismic data. Geophysics 42(4), 742\u2013759 (1977)","journal-title":"Geophysics"},{"issue":"4","key":"714_CR24","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1007\/BF01396324","volume":"54","author":"W Hackbusch","year":"1989","unstructured":"Hackbusch, W., Nowak, Z.P.: On the fast matrix multiplication in the boundary element method by panel clustering. Numer. Math. 54(4), 463\u2013491 (1989)","journal-title":"Numer. Math."},{"issue":"2","key":"714_CR25","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1137\/090771806","volume":"53","author":"N Halko","year":"2011","unstructured":"Halko, N., Martinsson, P.-G., Tropp, J.A.: Finding structure with randomness: probabilistic algorithms for constructing approximate matrix decompositions. SIAM Rev. 53(2), 217\u2013288 (2011)","journal-title":"SIAM Rev."},{"key":"714_CR26","doi-asserted-by":"crossref","DOI":"10.1090\/mmono\/233","volume-title":"Lectures and Exercises on Functional Analysis","author":"AY Helemskii","year":"2006","unstructured":"Helemskii, A.Y.: Lectures and Exercises on Functional Analysis, vol. 233. American Mathematical Society, Providence (2006)"},{"key":"714_CR27","doi-asserted-by":"crossref","unstructured":"Hirsch, M., Sra, S., Scholkopf, B., Harmeling, S.: Efficient filter flow for space-variant multiframe blind deconvolution. In: Proc. CVPR IEEE (2010)","DOI":"10.1109\/CVPR.2010.5540158"},{"issue":"11","key":"714_CR28","doi-asserted-by":"crossref","first-page":"5706","DOI":"10.1109\/TSP.2010.2063426","volume":"58","author":"T Hrycak","year":"2010","unstructured":"Hrycak, T., Das, S., Matz, G., Feichtinger, H.G.: Low complexity equalization for doubly selective channels modeled by a basis expansion. IEEE Trans. Signal Process. 58(11), 5706\u20135719 (2010)","journal-title":"IEEE Trans. Signal Process."},{"key":"714_CR29","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781139165372","volume-title":"An Introduction to Harmonic Analysis","author":"Y Katznelson","year":"2004","unstructured":"Katznelson, Y.: An Introduction to Harmonic Analysis. Cambridge University Press, Cambridge (2004)"},{"issue":"3","key":"714_CR30","doi-asserted-by":"crossref","first-page":"867","DOI":"10.1137\/S0036141003433437","volume":"37","author":"W Kozek","year":"2005","unstructured":"Kozek, W., Pfander, G.E.: Identification of operators with bandlimited symbols. SIAM J. Math. Anal. 37(3), 867\u2013888 (2005)","journal-title":"SIAM J. Math. Anal."},{"key":"714_CR31","volume-title":"A Wavelet Tour of Signal Processing","author":"S Mallat","year":"1999","unstructured":"Mallat, S.: A Wavelet Tour of Signal Processing. Academic Press, New York (1999)"},{"key":"714_CR32","volume-title":"Wavelets and Operators","author":"Y Meyer","year":"1995","unstructured":"Meyer, Y.: Wavelets and Operators, vol. 1. Cambridge University Press, Cambridge (1995)"},{"key":"714_CR33","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1186\/1687-6180-2012-100","volume":"2012","author":"D Miraut","year":"2012","unstructured":"Miraut, D., Portilla, J.: Efficient shift-variant image restoration using deformable filtering (Part I). EURASIP J. Adv. Signal Process. 2012, 100 (2012)","journal-title":"EURASIP J. Adv. Signal Process."},{"issue":"4","key":"714_CR34","doi-asserted-by":"crossref","first-page":"1063","DOI":"10.1137\/S106482759528507X","volume":"19","author":"JG Nagy","year":"1998","unstructured":"Nagy, J.G., O\u2019Leary, D.P.: Restoring images degraded by spatially variant blur. SIAM J. Sci. Comput. 19(4), 1063\u20131082 (1998)","journal-title":"SIAM J. Sci. Comput."},{"issue":"1","key":"714_CR35","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1016\/j.laa.2009.07.024","volume":"432","author":"I Oseledets","year":"2010","unstructured":"Oseledets, I., Tyrtyshnikov, E.: TT-cross approximation for multidimensional arrays. Linear Algebra Appl. 432(1), 70\u201388 (2010)","journal-title":"Linear Algebra Appl."},{"key":"714_CR36","volume-title":"N-Widths in Approximation Theory","author":"A Pinkus","year":"2012","unstructured":"Pinkus, A.: N-Widths in Approximation Theory, vol. 7. Springer, Berlin (2012)"},{"key":"714_CR37","unstructured":"Roh, J.C., Rao, B.D.: An efficient feedback method for MIMO systems with slowly time-varying channels. In: IEEE WCNC, vol.\u00a02, pp. 760\u2013764. IEEE (2004)"},{"issue":"7","key":"714_CR38","doi-asserted-by":"crossref","first-page":"854","DOI":"10.1109\/PROC.1972.8784","volume":"60","author":"AA Sawchuk","year":"1972","unstructured":"Sawchuk, A.A.: Space-variant image motion degradation and restoration. Proc. IEEE 60(7), 854\u2013861 (1972)","journal-title":"Proc. IEEE"},{"key":"714_CR39","doi-asserted-by":"crossref","unstructured":"Stockham, T.G.: High-speed convolution and correlation. In: Proceedings of the April 26\u201328, 1966, Spring joint computer conference, pp. 229\u2013233. ACM (1966)","DOI":"10.1145\/1464182.1464209"},{"issue":"1","key":"714_CR40","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1109\/83.128039","volume":"1","author":"J Trussell","year":"1992","unstructured":"Trussell, J., Fogel, S.: Identification and restoration of spatially variant motion blurs in sequential images. IEEE Trans. Image Process. 1(1), 123\u2013126 (1992)","journal-title":"IEEE Trans. Image Process."},{"issue":"2","key":"714_CR41","doi-asserted-by":"crossref","first-page":"821","DOI":"10.1109\/78.193220","volume":"41","author":"M Unser","year":"1993","unstructured":"Unser, M., Aldroubi, A., Eden, M.: B-spline signal processing. Part I\u2014theory. IEEE Trans. Signal Process. 41(2), 821\u2013833 (1993)","journal-title":"IEEE Trans. Signal Process."}],"container-title":["Journal of Mathematical Imaging and Vision"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10851-017-0714-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10851-017-0714-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10851-017-0714-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,19]],"date-time":"2019-09-19T04:04:50Z","timestamp":1568865890000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10851-017-0714-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,2,27]]},"references-count":41,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2017,7]]}},"alternative-id":["714"],"URL":"https:\/\/doi.org\/10.1007\/s10851-017-0714-8","relation":{},"ISSN":["0924-9907","1573-7683"],"issn-type":[{"value":"0924-9907","type":"print"},{"value":"1573-7683","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,2,27]]}}}