{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:38:13Z","timestamp":1787323093334,"version":"build-2736575974"},"reference-count":41,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Imaging Sci."],"published-print":{"date-parts":[[2011,1]]},"abstract":"<jats:p>This paper deals with the parameter choice for the nonlocal means (NLM) algorithm. After basic computations on toy models highlighting the bias of the NLM, we study the bias-variance trade-off of this filter so as to highlight the need of a local choice of the parameters. Relying on Stein's unbiased risk estimate, we then propose an efficient algorithm to locally set these parameters, and we compare this method with the NLM with optimal global parameter.<\/jats:p>","DOI":"10.1137\/100790902","type":"journal-article","created":{"date-parts":[[2011,6,28]],"date-time":"2011-06-28T18:10:02Z","timestamp":1309284602000},"page":"760-788","source":"Crossref","is-referenced-by-count":69,"title":["A Bias-Variance Approach for the Nonlocal Means"],"prefix":"10.1137","volume":"4","author":[{"given":"Vincent","family":"Duval","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jean-Fran\u00e7ois","family":"Aujol","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yann","family":"Gousseau","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2011,6,28]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2006.64"},{"key":"R2","doi-asserted-by":"crossref","unstructured":"N. Azzabou, N. Paragios, and F. Guichard,\n                      Uniform and textured regions separation in natural images towards MPM adaptive denoising\n                      , in Proceedings of the 1st International Conference on Scale Space and Variational Methods in Computer Vision, Springer-Verlag, Berlin, Heidelberg, 2007, pp. 418\u2013429.","DOI":"10.1007\/978-3-540-72823-8_36"},{"key":"R3","doi-asserted-by":"crossref","unstructured":"N. Azzabou, N. Paragios, F. Guichard, and F. Cao,\n                      Variable bandwidth image denoising using image-based noise models\n                      , in Proceedings of the IEEE International Conference on Computer Vision and Pattern Recognition, 2007, pp. 1\u20137.","DOI":"10.1109\/CVPR.2007.383216"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2007.906002"},{"key":"R5","doi-asserted-by":"crossref","unstructured":"T. Brox and D. Cremers,\n                      Iterated nonlocal means for texture restoration\n                      , in Proceedings of the 1st International Conference on Scale Space and Variational Methods in Computer Vision, Lecture Notes in Comput. Sci. 4485, F. Sgallari, A. Murli, and N. Paragios, eds., Springer-Verlag, Berlin, 2007, pp. 13\u201324.","DOI":"10.1007\/978-3-540-72823-8_2"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2008.924281"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1137\/040616024"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1142\/S0219691304000688"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2007.901238"},{"key":"R10","doi-asserted-by":"crossref","unstructured":"J. Darbon, A. Cunha, T.F. Chan, S. Osher, and G. Jensen,\n                      Fast nonlocal filtering applied to electron cryomicroscopy\n                      , in Proceedings of the 5th IEEE International Symposium on Biomedical Imaging: From Nano to Macro, 2008, pp. 1331\u20131334.","DOI":"10.1109\/ISBI.2008.4541250"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2009.2029593"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1995.10476626"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2008.2011832"},{"key":"R14","doi-asserted-by":"crossref","unstructured":"A. A. Efros and T. K. Leung,\n                      Texture synthesis by non-parametric sampling\n                      , in Proceedings of the IEEE International Conference on Computer Vision, Corfu, Greece, 1999, pp. 1033\u20131038.","DOI":"10.1109\/ICCV.1999.790383"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1137\/060669358"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1137\/070698592"},{"key":"R17","unstructured":"B. Goossens, Q. Luong, A. Pizurica, and W. Philips,\n                      An improved non-local denoising algorithm\n                      , in Proceedings of the International Workshop on Local and Non-Local Approximation in Image Processing, 2008."},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1007\/s11263-007-0096-2"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1137\/050622249"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2006.878172"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1137\/100785855"},{"key":"R22","doi-asserted-by":"crossref","unstructured":"J. Mairal, F. Bach, J. Ponce, G. Sapiro, and A. Zisserman,\n                      Non-local sparse models for image restoration\n                      , in Proceedings of the 12th IEEE International Conference on Computer Vision, 2009, pp. 2272\u20132279.","DOI":"10.1109\/ICCV.2009.5459452"},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1137\/07068881X"},{"key":"R24","doi-asserted-by":"publisher","DOI":"10.1016\/j.cviu.2008.09.003"},{"key":"R25","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2008.2001404"},{"key":"R26","doi-asserted-by":"publisher","DOI":"10.1109\/LSP.2009.2038954"},{"key":"R27","doi-asserted-by":"crossref","unstructured":"J. Salmon and E. Le Pennec,\n                      An aggregator point of view on NL-Means\n                      , in Wavelets XIII, Proceedings of the SPIE, Vol. 7446, 2009, 74461E.","DOI":"10.1117\/12.826881"},{"key":"R28","doi-asserted-by":"crossref","unstructured":"J. Salmon and Y. Strozecki,\n                      From patches to pixels in non-local methods: Weighted-average reprojection\n                      , in Proceedings of the 17th IEEE International Conference on Image Processing, 2010, pp. 1929\u20131932.","DOI":"10.1109\/ICIP.2010.5650780"},{"key":"R29","doi-asserted-by":"publisher","DOI":"10.1137\/070712146"},{"key":"R30","doi-asserted-by":"crossref","unstructured":"V. Solo,\n                      A sure-fired way to choose smoothing parameters in ill-conditioned inverse problems\n                      , in Proceedings of the IEEE International Conference on Image Processing, 1996, pp. 89\u201392.","DOI":"10.1109\/ICIP.1996.560376"},{"key":"R31","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176345632"},{"key":"R32","unstructured":"A. Szlam,\n                      Non-Stationary Analysis on Datasets and Applications\n                      , Ph.D. thesis, Yale University, New Haven, CT, 2006."},{"key":"R33","unstructured":"A. Szlam,\n                      Non-Local Means for Audio Denoising\n                      , UCLA CAM Report 08-56, University of California, Los Angeles, CA, 2008."},{"key":"R34","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2009.2028259"},{"key":"R35","unstructured":"D. Tschumperl\u00e9 and L. Brun,\n                      Image denoising and registration by PDE's on the space of patches\n                      , in Proceedings of the International Workshop on Local and Non-Local Approximation in Image Processing (LNLA'08), Lausanne, Switzerland, 2008."},{"key":"R36","doi-asserted-by":"crossref","unstructured":"D. Tschumperl\u00e9 and L. Brun,\n                      Non-local image smoothing by applying anisotropic diffusion PDE's in the space of patches\n                      , in Proceedings of the 16th IEEE International Conference on Image Processing (ICIP'09), Cairo, Egypt, 2009.","DOI":"10.1109\/ICIP.2009.5413453"},{"key":"R37","doi-asserted-by":"publisher","DOI":"10.1109\/LSP.2009.2027669"},{"key":"R38","unstructured":"D. Van De Ville and M. Kocher,\n                      Non-local means with dimensionality reduction and SURE-based parameter selection\n                      , IEEE Trans. Image Process., to appear."},{"key":"R39","first-page":"600","volume":"13","author":"Wang Z.","year":"2004","journal-title":"IEEE Trans. Signal Process.","ISSN":"https:\/\/id.crossref.org\/issn\/1053-587X","issn-type":"print"},{"key":"R40","doi-asserted-by":"publisher","DOI":"10.1016\/j.patcog.2009.09.023"},{"key":"R41","doi-asserted-by":"crossref","unstructured":"X.P. Zhang and Z.Q. Luo,\n                      A new time-scale adaptive denoising method based on wavelet shrinkage\n                      , in ICASSP '99: Proceedings of the 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing, IEEE Computer Society, Washington, DC, 1999, pp. 1629\u20131632.","DOI":"10.1109\/ICASSP.1999.756302"}],"container-title":["SIAM Journal on Imaging Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/100790902","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:41:38Z","timestamp":1787319698000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/100790902"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,1]]},"references-count":41,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2011,1]]}},"alternative-id":["10.1137\/100790902"],"URL":"https:\/\/doi.org\/10.1137\/100790902","relation":{},"ISSN":["1936-4954"],"issn-type":[{"value":"1936-4954","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,1]]}}}