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Total variation
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== External links == <!-- Most of these are not External links in the sense of [[WP:EL]] --> '''One variable''' * "[http://planetmath.org/encyclopedia/TotalVariation.html Total variation]" on [[PlanetMath]]. '''One and more variables''' *[http://www.encyclopediaofmath.org/index.php/Function_of_bounded_variation Function of bounded variation] at [http://www.encyclopediaofmath.org/ Encyclopedia of Mathematics] '''Measure theory''' *{{MathWorld |author=Rowland, Todd |title=Total Variation |urlname=TotalVariation }}. *{{PlanetMath|urlname=JordanDecomposition|title=Jordan decomposition}}. *[http://www.encyclopediaofmath.org/index.php/Jordan_decomposition_%28of_a_signed_measure%29 Jordan decomposition] at [http://www.encyclopediaofmath.org/ Encyclopedia of Mathematics] === Applications === *{{Citation |last1 = Caselles |first1 = Vicent |last2 = Chambolle |first2 = Antonin |last3 = Novaga |first3 = Matteo |title = The discontinuity set of solutions of the TV denoising problem and some extensions |url = http://cvgmt.sns.it/papers/caschanov07/ |publisher = [[Society for Industrial and Applied Mathematics|SIAM]], Multiscale Modeling and Simulation, vol. 6 n. 3 |year = 2007 |url-status = dead |archive-url = https://web.archive.org/web/20110927172158/http://cvgmt.sns.it/papers/caschanov07/ |archive-date = 2011-09-27 }} (a work dealing with total variation application in denoising problems for [[image processing]]). *{{Citation | last1 = Rudin | first1 = Leonid I. | last2 = Osher | first2 = Stanley | last3 = Fatemi | first3 = Emad | title = Nonlinear total variation based noise removal algorithms | journal = Physica D: Nonlinear Phenomena | volume = 60 | issue = 1β4 | pages = 259β268 | publisher = Physica D: Nonlinear Phenomena 60.1: 259-268 | year = 1992| doi = 10.1016/0167-2789(92)90242-F | bibcode = 1992PhyD...60..259R }}. *{{Citation | last1 = Blomgren | first1 = Peter | last2 = Chan | first2 = Tony F. | title = Color TV: total variation methods for restoration of vector-valued images | journal = IEEE Transactions on Image Processing | volume = 7 | issue = 3 | pages = 304β309 | publisher = Image Processing, IEEE Transactions on, vol. 7, no. 3: 304-309 | year = 1998| bibcode = 1998ITIP....7..304B | doi = 10.1109/83.661180 | pmid = 18276250 }}. *[[Tony F. Chan]] and Jackie (Jianhong) Shen (2005), [https://web.archive.org/web/20080117220948/http://jackieneoshen.googlepages.com/ImagingNewEra.html ''Image Processing and Analysis - Variational, PDE, Wavelet, and Stochastic Methods''], [[Society for Industrial and Applied Mathematics|SIAM]], {{isbn|0-89871-589-X}} (with in-depth coverage and extensive applications of Total Variations in modern image processing, as started by Rudin, Osher, and Fatemi). {{DEFAULTSORT:Total Variation}} [[Category:Mathematical analysis]]
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