{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,9]],"date-time":"2024-09-09T17:02:53Z","timestamp":1725901373724},"publisher-location":"Berlin, Heidelberg","reference-count":13,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642335631"},{"type":"electronic","value":"9783642335648"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2012]]},"DOI":"10.1007\/978-3-642-33564-8_5","type":"book-chapter","created":{"date-parts":[[2012,10,17]],"date-time":"2012-10-17T15:22:27Z","timestamp":1350487347000},"page":"38-47","source":"Crossref","is-referenced-by-count":3,"title":["Application of Backward Stochastic Differential Equations to Reconstruction of Vector-Valued Images"],"prefix":"10.1007","author":[{"given":"Dariusz","family":"Borkowski","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Katarzyna","family":"Ja\u0144czak-Borkowska","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"5_CR1","doi-asserted-by":"publisher","first-page":"184","DOI":"10.1051\/ps:2006005","volume":"10","author":"R. Abraham","year":"2006","unstructured":"Abraham, R., Riviere, O.: Forward-backward stochastic differential equations and PDE with gradient dependent second order coefficients. ESAIM P&S\u00a010, 184\u2013205 (2006)","journal-title":"ESAIM P&S"},{"key":"5_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"262","DOI":"10.1007\/978-3-642-21227-7_25","volume-title":"Image Analysis","author":"F. \u00c5str\u00f6m","year":"2011","unstructured":"\u00c5str\u00f6m, F., Felsberg, M., Lenz, R.: Color Persistent Anisotropic Diffusion of Images. In: Heyden, A., Kahl, F. (eds.) SCIA 2011. LNCS, vol.\u00a06688, pp. 262\u2013272. Springer, Heidelberg (2011)"},{"key":"5_CR3","doi-asserted-by":"crossref","unstructured":"Aubert, G., Kornprobst, P.: Mathematical problems in image processing, 2nd edn. Applied Mathematical Sciences, vol.\u00a0147. Springer (2006)","DOI":"10.1007\/978-0-387-44588-5"},{"key":"5_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"233","DOI":"10.1007\/978-3-642-15910-7_26","volume-title":"Computer Vision and Graphics","author":"D. Borkowski","year":"2010","unstructured":"Borkowski, D.: Smoothing, Enhancing Filters in Terms of Backward Stochastic Differential Equations. In: Bolc, L., Tadeusiewicz, R., Chmielewski, L.J., Wojciechowski, K. (eds.) ICCVG 2010, Part I. LNCS, vol.\u00a06374, pp. 233\u2013240. Springer, Heidelberg (2010)"},{"issue":"5","key":"5_CR5","doi-asserted-by":"publisher","first-page":"16","DOI":"10.1109\/MSP.2002.1028349","volume":"19","author":"R. Deriche","year":"2002","unstructured":"Deriche, R., Tschumperl\u00e9, D.: Diffusion PDE\u2019s on vector-valued images: local approach and geometric viewpoint. IEEE Signal Processing Magazine\u00a019(5), 16\u201325 (2002)","journal-title":"IEEE Signal Processing Magazine"},{"issue":"1","key":"5_CR6","doi-asserted-by":"publisher","first-page":"116","DOI":"10.1016\/0734-189X(86)90223-9","volume":"33","author":"S. Zenzo Di","year":"1986","unstructured":"Di Zenzo, S.: A note on the gradient of a multi-image. Comput. Vis. Graph. Image Process.\u00a033(1), 116\u2013125 (1986)","journal-title":"Comput. Vis. Graph. Image Process."},{"key":"5_CR7","doi-asserted-by":"crossref","unstructured":"Pardoux, \u00c9.: Backward stochastic differential equations and viscosity solutions of systems of semilinear parabolic and elliptic PDEs of second order. In: Stochastic Analysis and Related Topics, VI, Geilo, vol.\u00a042, pp. 79\u2013127 (1998)","DOI":"10.1007\/978-1-4612-2022-0_2"},{"issue":"7","key":"5_CR8","doi-asserted-by":"publisher","first-page":"629","DOI":"10.1109\/34.56205","volume":"12","author":"P. Perona","year":"1990","unstructured":"Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Mach. Intell.\u00a012(7), 629\u2013639 (1990)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"issue":"1\u20134","key":"5_CR9","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1016\/0167-2789(92)90242-F","volume":"60","author":"L.I. Rudin","year":"1992","unstructured":"Rudin, L.I., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D\u00a060(1\u20134), 259\u2013268 (1992)","journal-title":"Physica D"},{"issue":"11","key":"5_CR10","doi-asserted-by":"publisher","first-page":"1582","DOI":"10.1109\/83.541429","volume":"5","author":"G. Sapiro","year":"1996","unstructured":"Sapiro, G., Ringach, D.L.: Anisotropic diffusion of multivalued images with applications to color filtering. IEEE Trans. Image Process.\u00a05(11), 1582\u20131585 (1996)","journal-title":"IEEE Trans. Image Process."},{"issue":"1","key":"5_CR11","doi-asserted-by":"crossref","first-page":"163","DOI":"10.32917\/hmj\/1206135203","volume":"9","author":"H. Tanaka","year":"1979","unstructured":"Tanaka, H.: Stochastic differential equations with reflecting boundary condition in convex regions. Hiroshima Math. J.\u00a09(1), 163\u2013177 (1979)","journal-title":"Hiroshima Math. J."},{"issue":"4","key":"5_CR12","doi-asserted-by":"publisher","first-page":"600","DOI":"10.1109\/TIP.2003.819861","volume":"13","author":"Z. Wang","year":"2004","unstructured":"Wang, Z., Bovik, A.C., Sheikh, H.R., Simoncelli, E.P.: Image quality assessment: From error visibility to structural similarity. IEEE Trans. Image Process.\u00a013(4), 600\u2013612 (2004)","journal-title":"IEEE Trans. Image Process."},{"key":"5_CR13","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1007\/978-3-7091-6586-7_13","volume":"11","author":"J. Weickert","year":"1996","unstructured":"Weickert, J.: Theoretical Foundations Of Anisotropic Diffusion In Image Processing. Computing Suppement\u00a011, 221\u2013236 (1996)","journal-title":"Computing Suppement"}],"container-title":["Lecture Notes in Computer Science","Computer Vision and Graphics"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-33564-8_5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,7,4]],"date-time":"2019-07-04T19:05:17Z","timestamp":1562267117000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-33564-8_5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012]]},"ISBN":["9783642335631","9783642335648"],"references-count":13,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-33564-8_5","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2012]]}}}