Abstract
This paper studies the model of minimizing total variation with an L 1-norm fidelity term for decomposing a real image into the sum of cartoon and texture. This model is also analyzed and shown to be able to select features of an image according to their scales.
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References
Alizadeh, F., Goldfarb, D.: Second-order cone programming. Mathematical Programming, Series B 95(1), 3–51 (2003)
Alliney, S.: Digital filters as absolute norm regularizers. IEEE Trans. on Signal Processing 40(6), 1548–1562 (1992)
Alliney, S.: Recursive median filters of increasing order: a variational approach. IEEE Trans. on Signal Processing 44(6), 1346–1354 (1996)
Alliney, S.: A property of the minimum vectors of a regularizing functional defined by means of the absolute norm. IEEE Trans. on Signal Processing, 45 4, 913–917 (1997)
Ambrosio, L., Gigli, N., Savaré, G.: Gradient flows, in metric spaces and in the space of probability measures, Birkhäuser (2005)
Aubert, G., Aujol, J.F.: Modeling very oscillating signals. Application to image processing. Applied Mathematics and Optimization 51(2) (March 2005)
Burger, M., Osher, S., Xu, J., Gilboa, G.: Nonlinear inverse scale space methods for image restoration, UCLA CAM Report, 05-34 (2005)
Chan, T.F., Esedoglu, S.: Aspects of total variation regularized L1 functions approximation, UCLA CAM Report 04-07, to appear in SIAM J. Appl. Math
Chen, T., Yin, W., Zhou, X.S., Comaniciu, D., Huang, T.: Illumination normalization for face recognition and uneven background correction using total variation based image models. In: CVPR 2005 (2005)
Goldfarb, D., Yin, W.: Second-order cone programming methods for total variation-based image restoration, Columbia University CORC Report TR-2004-05
Giusti, E.: Minimal surfaces and functions of bounded variation, Birkhäuser (1984)
Haddad, A., Meyer, Y.: Variantional methods in image processing, UCLA CAM Report 04-52
Le, T., Vese, L.: Image decomposition using the total variation and div(BMO), UCLA CAM Report 04-36
Lieu, L., Vese, L.: Image restoration and decomposition via bounded total variation and negative Hilbert-Sobolev spaces, UCLA CAM Report 05-33
Meyer, Y.: Oscillating Patterns in Image Processing and Nonlinear Evolution Equations. University Lecture Series, vol. 22. AMS (2002)
Nikolova, M.: Minimizers of cost-functions involving nonsmooth data-fidelity terms. SIAM J. Numer. Anal. 40(3), 965–994 (2002)
Nikolova, M.: A variational approach to remove outliers and impulse noise. Journal of Mathematical Imaging and Vision 20(1-2), 99–120 (2004)
Nikolova, M.: Weakly constrained minimization. Application to the estimation of images and signals involving constant regions. Journal of Mathematical Imaging and Vision 21(2), 155–175 (2004)
Osher, S., Burger, M., Goldfarb, D., Xu, J., Yin, W.: An iterative regularization method for total variation-based image restoration. SIAM J. on Multiscale Modeling and Simulation 4(2), 460–489 (2005)
Osher, S., Sole, A., Vese, L.A.: Image decomposition and restoration using total variation minimization and the H− ????1 norm, UCLA C.A.M. Report 02-57 (Oct. 2002)
Rudin, L., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D 60, 259–268 (1992)
Scherzer, O., Yin, W., Osher, S.: Slope and G-set characterization of set-Valued functions and applications to non-Differentiable optimization problems, UCLA CAM Report 05-35
Vese, L., Osher, S.: Modelling textures with total variation minimization and oscillating patterns in image processing, UCLA CAM Report 02-19 (May 2002)
Yin, W., Chen, T., Zhou, X.S., Chakraborty, A.: Background correction for cDNA microarray images using the TV+L 1 model. Bioinformatics 21(10), 2410–2416 (2005)
Yin, W., Goldfarb, D., Osher, S.: Total variation-based image cartoon-texture decomposition, Columbia University CORC Report TR-2005-01, UCLA CAM Report 05-27 (2005)
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Yin, W., Goldfarb, D., Osher, S. (2005). Image Cartoon-Texture Decomposition and Feature Selection Using the Total Variation Regularized L 1 Functional. In: Paragios, N., Faugeras, O., Chan, T., Schnörr, C. (eds) Variational, Geometric, and Level Set Methods in Computer Vision. VLSM 2005. Lecture Notes in Computer Science, vol 3752. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11567646_7
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DOI: https://doi.org/10.1007/11567646_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-29348-4
Online ISBN: 978-3-540-32109-5
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