{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,21]],"date-time":"2025-10-21T15:22:17Z","timestamp":1761060137313},"reference-count":73,"publisher":"American Institute of Mathematical Sciences (AIMS)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IPI"],"published-print":{"date-parts":[[2016,5]]},"DOI":"10.3934\/ipi.2016008","type":"journal-article","created":{"date-parts":[[2016,5,26]],"date-time":"2016-05-26T16:32:37Z","timestamp":1464280357000},"page":"461-497","source":"Crossref","is-referenced-by-count":11,"title":["Color image processing by vectorial total variation with gradient channels coupling"],"prefix":"10.3934","volume":"10","author":[{"given":"Juan C.","family":"Moreno","sequence":"first","affiliation":[]},{"given":"V. B. Surya","family":"Prasath","sequence":"first","affiliation":[]},{"given":"Jo\u00e3o C.","family":"Neves","sequence":"first","affiliation":[]}],"member":"2321","reference":[{"key":"1","article-title":"<em>Functions of Bounded Variation and Free Discontinuity Problems<\/em>,","author":"L. Ambrosio","year":"2000","journal-title":"Oxford University Press"},{"key":"2","article-title":"<em>Variational Analysis in Sobolev and BV Spaces: Applications to PDEs and Optimization,<\/em>","author":"H. Attouch","year":"2006","journal-title":"Society for Industrial and Applied Mathematics (SIAM)"},{"key":"3","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1007\/s00245-004-0812-z","article-title":"Modelling very oscillating signals. Application to image processing,","volume":"51","author":"G. Aubert","year":"2005","journal-title":"<em>Applied Mathematics and Optimization<\/em>"},{"key":"4","article-title":"<em>Mathematical Problems in Image Processing: Partial Differential Equation and Calculus of Variations<\/em>,","author":"G. Aubert","year":"2006","journal-title":"Springer-Verlag"},{"key":"5","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1007\/s11263-005-4948-3","article-title":"Dual norms and image decomposition models,","volume":"63","author":"J.-F. Aujol","year":"2005","journal-title":"<em>International Journal of Computer Vision<\/em>"},{"key":"6","doi-asserted-by":"publisher","first-page":"1004","DOI":"10.1016\/j.jvcir.2006.02.001","article-title":"Combining geometrical and textured information to perform image classification,","volume":"17","author":"J.-F. Aujol","year":"2006","journal-title":"<em>Journal of Visual Communication and Image Representation<\/em>"},{"key":"7","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1007\/s11263-006-4331-z","article-title":"Structure-texture image decomposition - modeling, algorithms and parameter selection,","volume":"67","author":"J.-F. Aujol","year":"2006","journal-title":"<em>International Journal of Computer Vision<\/em>"},{"key":"8","doi-asserted-by":"publisher","first-page":"916","DOI":"10.1016\/j.jvcir.2005.02.001","article-title":"Color image decomposition and restoration,","volume":"17","author":"J.-F. Aujol","year":"2006","journal-title":"<em>Journal of Visual Communication and Image Representation<\/em>"},{"key":"9","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1007\/11408031_10","article-title":"Image deblurring in the presence of salt-and-pepper noise,","volume":"3459","author":"L. Bar","year":"2005","journal-title":"in <em>Lecture Notes in Computer Science<\/em>"},{"key":"10","doi-asserted-by":"publisher","first-page":"2419","DOI":"10.1109\/TIP.2009.2028250","article-title":"Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems,","volume":"18","author":"A. Beck","year":"2009","journal-title":"<em>IEEE Transactions on Image Processing<\/em>"},{"key":"11","doi-asserted-by":"publisher","first-page":"304","DOI":"10.1109\/83.661180","article-title":"Color TV: Total variation methods for restoration of vector valued images,","volume":"7","author":"P. Blomgren","year":"1998","journal-title":"<em>IEEE Transactions on Image Processing<\/em>"},{"key":"12","doi-asserted-by":"publisher","first-page":"1298","DOI":"10.1109\/TPAMI.2002.1039202","article-title":"Generalized spatio-chromatic diffusion,","volume":"24","author":"G. Boccignone","year":"2002","journal-title":"<em>IEEE Transactions on Pattern Analysis and Machine Intelligence<\/em>"},{"key":"13","doi-asserted-by":"publisher","first-page":"455","DOI":"10.3934\/ipi.2008.2.455","article-title":"Fast dual minimization of the vectorial total variation norm and applications to color image processing,","volume":"2","author":"X. Bresson","year":"2008","journal-title":"<em>Inverse Problem and Imaging<\/em>"},{"key":"14","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1007\/s10851-007-0002-0","article-title":"Fast global minimization of the active contour\/snake model,","volume":"28","author":"X. Bresson","year":"2007","journal-title":"<em>Journal of Mathematical Imaging and Vision<\/em>"},{"key":"15","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1023\/A:1022895410391","article-title":"Variational restoration and edge detection for color images,","volume":"18","author":"A. Brook","year":"2003","journal-title":"<em>Journal of Mathematical Imaging and Vision<\/em>"},{"key":"16","doi-asserted-by":"publisher","first-page":"490","DOI":"10.1137\/040616024","article-title":"A review of image denoising methods, with a new one,","volume":"4","author":"A. Buades","year":"2005","journal-title":"<em>Multiscale Modeling and Simulation<\/em>"},{"key":"17","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/BF01385685","article-title":"A geometric model for active contours in image processing,","volume":"66","author":"V. Caselles","year":"1993","journal-title":"<em>Numerische Mathematik<\/em>"},{"key":"18","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1023\/A:1013943314097","article-title":"Geometry and color in natural images,","volume":"16","author":"V. Caselles","year":"2002","journal-title":"<em>Journal of Mathematical Imaging and Vision<\/em>"},{"key":"19","doi-asserted-by":"publisher","first-page":"694","DOI":"10.1109\/ICCV.1995.466871","article-title":"Geodesic active contours,","author":"V. Caselles","year":"1995","journal-title":"<em>International Journal of Computer Vision<\/em>"},{"key":"20","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1023\/B:JMIV.0000011321.19549.88","article-title":"An algorithm for total variation minimization and applications,","volume":"20","author":"A. Chambolle","year":"2004","journal-title":"<em>Journal of Mathematical Imaging and Vision<\/em>"},{"key":"21","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1007\/s10851-010-0251-1","article-title":"A first-order primal-dual algorithm for convex problems with applications to imaging,","volume":"40","author":"A. Chambolle","year":"2011","journal-title":"<em>Journal of Mathematical Imaging and Vision<\/em>"},{"key":"22","doi-asserted-by":"publisher","first-page":"1817","DOI":"10.1137\/040604297","article-title":"Aspects of total variation regularized $L^{1}$ function approximation,","volume":"65","author":"T. F. Chan","year":"2005","journal-title":"<em>SIAM Journal on Applied Mathematics<\/em>"},{"key":"23","doi-asserted-by":"publisher","first-page":"1632","DOI":"10.1137\/040615286","article-title":"Algorithms for finding global minimizers of image segmentation and denoising models,","volume":"66","author":"T. F. Chan","year":"2006","journal-title":"<em>SIAM Journal on Applied Mathematics<\/em>"},{"key":"24","doi-asserted-by":"publisher","first-page":"1964","DOI":"10.1137\/S1064827596299767","article-title":"A nonlinear primal-dual method for total variation-based image restoration,","volume":"20","author":"T. F. Chan","year":"1999","journal-title":"<em>SIAM Journal on Scientific Computing<\/em>"},{"key":"25","doi-asserted-by":"publisher","first-page":"579","DOI":"10.1002\/cpa.20075","article-title":"Variational image inpainting,","volume":"58","author":"T. F. Chan","year":"2005","journal-title":"<em>Communications on Pure and Applied Mathematics<\/em>"},{"key":"26","doi-asserted-by":"publisher","first-page":"313","DOI":"10.1109\/ICIP.2007.4378954","article-title":"Color image denoising via sparse 3d collaborative filtering with grouping constraint in luminance-chrominance space,","volume":"1","author":"K. Dabov","year":"2007","journal-title":"in <em>IEEE International Conference on Image Processing<\/em>"},{"key":"27","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1109\/ISPA.2005.195413","article-title":"Total variation minimization with $L^{1}$ data fidelity as a contrast invariant filter,","author":"J. Darbon","year":"2005","journal-title":"in <em>4th Symposium on Image and Signal Processing and Analysis (ISPA)<\/em>"},{"key":"28","doi-asserted-by":"publisher","first-page":"296","DOI":"10.1007\/s11263-010-0359-1","article-title":"A multi-scale vectorial $L^\\tau$-TV framework for color image restoration,","volume":"92","author":"Y. Dong","year":"2011","journal-title":"<em>International Journal of Computer Vision<\/em>"},{"key":"29","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1007\/s10851-009-0180-z","article-title":"Multiplicative noise removal using $L^1$ fidelity on frame coefficients,","volume":"36","author":"S. Durand","year":"2010","journal-title":"<em>Journal of Mathematical Imaging and Vision<\/em>"},{"key":"30","doi-asserted-by":"publisher","first-page":"154","DOI":"10.1137\/090757083","article-title":"The TVL1 model: A geometrical point of view,","volume":"8","author":"V. Duval","year":"2009","journal-title":"<em>Multiscale Modelling & Simulation<\/em>"},{"key":"31","doi-asserted-by":"publisher","first-page":"232","DOI":"10.1007\/s10851-010-0203-9","article-title":"Mathematical modelling of textures: Application to color image decomposition with a projected gradient algorithm,","volume":"37","author":"V. Duval","year":"2010","journal-title":"<em>Journal of Mathematical Imaging and Vision<\/em>"},{"key":"32","doi-asserted-by":"publisher","first-page":"9","DOI":"10.1109\/TIP.2013.2277775","article-title":"Vector-valued image processing by parallel level sets,","volume":"23","author":"M. J. Ehrhardt","year":"2014","journal-title":"<em>IEEE Transactions on Image Processing<\/em>"},{"key":"33","doi-asserted-by":"publisher","first-page":"1937","DOI":"10.1137\/130930704","article-title":"A total variation spectral framework for scale and texture analysis,","volume":"7","author":"G. Gilboa","year":"2014","journal-title":"<em>Multiscale Modelling and Simulation<\/em>"},{"key":"34","doi-asserted-by":"publisher","first-page":"285","DOI":"10.1007\/s10851-007-0020-y","article-title":"Noisy image decomposition: A new structure, texture and noise model based on local adaptivity,","volume":"28","author":"J. Gilles","year":"2007","journal-title":"<em>Journal of Mathematical Imaging and Vision<\/em>"},{"key":"35","doi-asserted-by":"publisher","first-page":"1409","DOI":"10.1137\/120881579","article-title":"Multiscale texture separation,","volume":"10","author":"J. Gilles","year":"2012","journal-title":"<em>Multiscale Modeling & Simulation<\/em>"},{"key":"36","doi-asserted-by":"publisher","first-page":"537","DOI":"10.1137\/110823766","article-title":"The natural vectorial total variation which arises from geometric measure theory,","volume":"5","author":"B. Goldluecke","year":"2012","journal-title":"<em>SIAM Journal on Imaging Sciences<\/em>"},{"key":"37","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1137\/080725891","article-title":"The split Bregman algorithm for L1 regularized problems,","volume":"2","author":"T. Goldstein","year":"2009","journal-title":"<em>SIAM Journal on Imaging Sciences<\/em>"},{"key":"38","doi-asserted-by":"publisher","first-page":"38","DOI":"10.1137\/S0036141003427373","article-title":"Traveling wave solutions of fourth order PDEs for image processing,","volume":"36","author":"J. B. Greer","year":"2004","journal-title":"<em>SIAM Journal on Mathematical Analysis<\/em>"},{"key":"39","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1007\/BF00133570","article-title":"Snakes: Active contour models,","volume":"1","author":"M. Kass","year":"1988","journal-title":"<em>International Journal of Computer Vision<\/em>"},{"key":"40","doi-asserted-by":"publisher","first-page":"390","DOI":"10.1137\/040610052","article-title":"Image decomposition using total variation and div(BMO),","volume":"4","author":"T. M. Le","year":"2005","journal-title":"<em>Multiscale Modelling & Simulation<\/em>"},{"key":"41","doi-asserted-by":"publisher","first-page":"1282","DOI":"10.1016\/j.aml.2011.01.028","article-title":"Adaptive fourth-order partial differential equation filter for image denoising,","volume":"24","author":"X. Liu","year":"2011","journal-title":"<em>Applied Mathematics Letters<\/em>"},{"key":"42","doi-asserted-by":"publisher","DOI":"10.1090\/ulect\/022","article-title":"<em>Oscillating Patterns in Image Processing and Nonlinear Evolution Equations<\/em>,","author":"Y. Meyer","year":"2001","journal-title":"American Mathematical Society"},{"key":"43","article-title":"<em>Adaptive Diffusion Constrained Total Variation Scheme with Application to Cartoon + Texture + Edge Image Decomposition<\/em>,","author":"J. C. Moreno","year":"1505","journal-title":"Technical Report 1505.00866"},{"key":"44","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1007\/s10107-004-0552-5","article-title":"Smooth minimization of non-smooth functions,","volume":"103","author":"Y. Nesterov","year":"2005","journal-title":"<em>Mathematical Programming<\/em>"},{"key":"45","doi-asserted-by":"publisher","first-page":"965","DOI":"10.1137\/S0036142901389165","article-title":"Minimizers of cost-function involving nonsmooth data-fidelity terms,","volume":"40","author":"M. Nikolova","year":"2002","journal-title":"<em>SIAM Journal on Numerical Analysis<\/em>"},{"key":"46","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1023\/B:JMIV.0000011920.58935.9c","article-title":"A variational approach to remove outliers and impulse noise,","volume":"20","author":"M. Nikolova","year":"2004","journal-title":"<em>Journal of Mathematical Imaging and Vision<\/em>"},{"key":"47","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1023\/B:JMIV.0000035180.40477.bd","article-title":"Weakly constrained minimization: application to the estimation of images and signals involving constant regions,","volume":"21","author":"M. Nikolova","year":"2004","journal-title":"<em>Journal of Mathematical Imaging and Vision<\/em>"},{"key":"48","doi-asserted-by":"publisher","first-page":"4090","DOI":"10.1109\/CVPR.2014.521","article-title":"Decorrelated vectorial total variation,","author":"S. Ono","year":"2014","journal-title":"in <em>IEEE Conference on Computer Vision and Pattern Recognition<\/em>"},{"key":"49","doi-asserted-by":"publisher","first-page":"237","DOI":"10.4310\/CMS.2004.v2.n2.a6","article-title":"G-norm properties of bounded variation regularization,","volume":"2","author":"S. Osher","year":"2004","journal-title":"<em>Communications in Mathematical Sciences<\/em>"},{"key":"50","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1109\/ICCV.2001.937500","article-title":"Gradient vector flow fast geodesic active contours,","volume":"1","author":"N. Paragios","year":"2001","journal-title":"<em>Computer Vision"},{"key":"51","doi-asserted-by":"publisher","first-page":"4042","DOI":"10.1109\/IGARSS.2011.6050119","article-title":"Weighted Laplacian differences based multispectral anisotropic diffusion,","author":"V. B. S. Prasath","year":"2011","journal-title":"in <em>IEEE International Geoscience and Remote Sensing Symposium (IGARSS)<\/em>"},{"key":"52","doi-asserted-by":"publisher","first-page":"769","DOI":"10.2478\/v10006-011-0061-7","article-title":"A well-posed multiscale regularization scheme for digital image denoising,","volume":"21","author":"V. B. S. Prasath","year":"2011","journal-title":"<em>International Journal of Applied Mathematics and Computer Science<\/em>"},{"key":"53","article-title":"<em>Color image denoising by chromatic edges based vector valued diffusion<\/em>,","author":"V. B. S. Prasath","year":"1304","journal-title":"Technical Report 1304.5587"},{"key":"54","first-page":"9","article-title":"Multichannel image restoration using combined channel information and robust M-estimator approach,","volume":"12","author":"V. B. S. Prasath","year":"2010","journal-title":"<em>International Journal Tomography and Statistics<\/em>"},{"key":"55","doi-asserted-by":"publisher","first-page":"2091","DOI":"10.1080\/01431160903260965","article-title":"Multispectral image denoising by well-posed anisotropic diffusion scheme with channel coupling,","volume":"31","author":"V. B. S. Prasath","year":"2010","journal-title":"<em>International Journal of Remote Sensing<\/em>"},{"key":"56","article-title":"Well-posed inhomogeneous nonlinear diffusion scheme for digital image denoising,","volume":"2010","author":"V. B. S. Prasath","year":"2010","journal-title":"<em>Journal of Applied Mathematics<\/em>"},{"key":"57","doi-asserted-by":"publisher","DOI":"10.1142\/S0219467812500039","article-title":"An adaptive anisotropic diffusion scheme for image restoration and selective smoothing,","volume":"12","author":"V. B. S. Prasath","year":"2012","journal-title":"<em>International Journal of Image and Graphics<\/em>"},{"key":"58","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1016\/0167-2789(92)90242-F","article-title":"Nonlinear total variation based noise removal algorithms,","volume":"60","author":"L. Rudin","year":"1992","journal-title":"<em>Physica D<\/em>"},{"key":"59","doi-asserted-by":"publisher","first-page":"1582","DOI":"10.1109\/83.541429","article-title":"Anisotropic diffusion of multivalued images with application to color filtering,","volume":"5","author":"G. Sapiro","year":"1996","journal-title":"<em>IEEE Transactions on Image Processing<\/em>"},{"key":"60","doi-asserted-by":"publisher","first-page":"479","DOI":"10.4310\/CMS.2005.v3.n4.a1","article-title":"Slope and $G$-set characterization of set-valued functions and applications to non-differentiable optimization problems,","volume":"3","author":"O. Scherzer","year":"2005","journal-title":"<em>Communications in Mathematical Sciences<\/em>"},{"key":"61","doi-asserted-by":"publisher","first-page":"2223","DOI":"10.1016\/j.cam.2011.09.043","article-title":"Geometry of total variation regularized $L^p$-model,","volume":"236","author":"Y. Shi","year":"2012","journal-title":"<em>Journal of Computational and Applied Mathematics<\/em>"},{"key":"62","article-title":"<em>Adaptive Total Variation Minimizing Image Restoration<\/em>,","author":"D. Strong","year":"1997","journal-title":"PhD thesis"},{"key":"63","doi-asserted-by":"publisher","first-page":"165","DOI":"10.1088\/0266-5611\/19\/6\/059","article-title":"Edge-preserving and scale-dependent properties of total variation regularization,","volume":"19","author":"D. Strong","year":"2003","journal-title":"<em>Inverse Problems<\/em>"},{"key":"64","first-page":"96","article-title":"<em>Spatially and Scale Adaptive Total Variation Based Regularization and Anisotropic Diffusion in Image Processing<\/em>,","author":"D. M. Strong","year":"1996","journal-title":"Technical Report 96-46"},{"key":"65","doi-asserted-by":"publisher","first-page":"554","DOI":"10.1137\/030600448","article-title":"A multiscale image representation using hierarchical ($BV,L^{2}$) decomposition,","volume":"2","author":"E. Tadmor","year":"2004","journal-title":"<em>Multiscale Modeling and Simulation<\/em>"},{"key":"66","doi-asserted-by":"publisher","first-page":"701","DOI":"10.1109\/83.918563","article-title":"Color image enhancement via chromaticity diffusion,","volume":"10","author":"B. Tang","year":"2001","journal-title":"<em>IEEE Transactions on Pattern Analysis Machine Intelligence<\/em>"},{"key":"67","doi-asserted-by":"publisher","first-page":"148","DOI":"10.1007\/s10851-012-0351-1","article-title":"Multiscale texture extraction with hierarchical $(BV,G_p,L^{2})$,","volume":"45","author":"L. Tang","year":"2013","journal-title":"<em>Journal of Mathematical Imaging and Vision<\/em>"},{"key":"68","doi-asserted-by":"publisher","first-page":"651","DOI":"10.1109\/CVPR.2003.1211415","article-title":"Vector-valued image regularization with PDE's: A common framework for different applications,","volume":"1","author":"D. Tschumperle","year":"2003","journal-title":"<em>Computer Vision and Pattern Recognition"},{"key":"69","doi-asserted-by":"publisher","first-page":"553","DOI":"10.1023\/A:1025384832106","article-title":"Modeling textures with total variation minimization and oscillating patterns in image processing,","volume":"19","author":"L. A. Vese","year":"2003","journal-title":"<em>Journal of Scientific Computing<\/em>"},{"key":"70","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1109\/SYNASC.2006.24","article-title":"Color texture modeling and color image decomposition in variational PDE approach,","author":"L. A. Vese","year":"2006","journal-title":"in <em>Proceedings of the Eighth International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC '06)<\/em>"},{"key":"71","doi-asserted-by":"publisher","first-page":"600","DOI":"10.1109\/TIP.2003.819861","article-title":"Image quality assessment: from error visibility to structural similarity,","volume":"13","author":"Z. Wang","year":"2004","journal-title":"<em>IEEE Transactions on Image Processing<\/em>"},{"key":"72","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1007\/11567646_7","article-title":"Image cartoon-texture decomposition and feature selection using total variation regularized $L^1$ functional,","volume":"3752","author":"W. Yin","year":"2005","journal-title":"in <em>Variational"},{"key":"73","doi-asserted-by":"publisher","first-page":"190","DOI":"10.1137\/060663027","article-title":"The total variation regularized $L^1$ model for multiscale decomposition,","volume":"6","author":"W. Yin","year":"2007","journal-title":"<em>Multiscale Modeling & Simulation<\/em>"}],"container-title":["Inverse Problems and Imaging"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.aimsciences.org\/journals\/displayArticlesnew.jsp?paperID=12614","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,24]],"date-time":"2017-06-24T15:07:16Z","timestamp":1498316836000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.aimsciences.org\/journals\/displayArticlesnew.jsp?paperID=12614"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,5]]},"references-count":73,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2016,5]]}},"URL":"https:\/\/doi.org\/10.3934\/ipi.2016008","relation":{},"ISSN":["1930-8337"],"issn-type":[{"value":"1930-8337","type":"print"}],"subject":[],"published":{"date-parts":[[2016,5]]}}}