Anisotropic Total Variation Filtering

Acar, R., Vogel, C.R.: Analysis of bounded variation penalty methods for ill-posed problems. Inverse Probl. 10(6), 1217–1229 (1994)

Ambrosio, L., Fusco, N., Pallara, D.: Functions of Bounded Variation and Free Discontinuity Problems. Oxford Mathematical Monographs. The Clarendon Press/Oxford University Press, New York (2000)

Aviles, P., Giga, Y.: Variational integrals on mappings of bounded variation and their lower semicontinuity. Arch. Ration. Mech. Anal. 115(3), 201–255 (1991)

Berkels, B., Burger, M., Droske, M., Nemitz, O., Rumpf, M.: Cartoon extraction based on anisotropic image classification. In: Vision, Modeling, and Visualization Proceedings, pp. 293–300. Akademische Verlagsgesellschaft Aka GmbH, Berlin (2006)

Bouchitté, G., Fonseca, I., Mascarenhas, L.: A global method for relaxation. Arch. Ration. Mech. Anal. 145(1), 51–98 (1998)

Brézis, H.: Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert. North-Holland Publishing Co., Amsterdam (1973). North-Holland Mathematics Studies, No. 5. Notas de Matemática (50)

Catté, F., Lions, P.-L., Morel, J.-M., Coll, T.: Image selective smoothing and edge detection by nonlinear diffusion. SIAM J. Numer. Anal. 29(1), 182–193 (1992)

Chan, R.H., Setzer, S., Steidl, G.: Inpainting by flexible Haar-wavelet shrinkage. SIAM J. Imaging Sci. 1(3), 273–293 (2008)

Dacorogna, B.: Direct Methods in the Calculus of Variations. Applied Mathematical Sciences, vol. 78, 2nd edn. Springer, New York (2008)

Dal Maso, G.: Integral representation on BV(Ω) of Γ-limits of variational integrals. Manuscripta Math. 30(4), 387–416 (1979/80)

Demengel, F., Temam, R.: Convex functions of a measure and applications. Indiana Univ. Math. J. 33(5), 673–709 (1984)

Evans, L.C., Gariepy, R.F.: Measure Theory and Fine Properties of Functions. Studies in Advanced Mathematics. CRC Press, Boca Raton (1992)

Fonseca, I., Müller, S.: Relaxation of quasiconvex functionals in BV(Ω,R p ) for integrands f(ξ,u,∇ u). Arch. Ration. Mech. Anal. 123(1), 1–49 (1993)

Giusti, E.: Direct Methods in the Calculus of Variations. World Scientific Publishing, River Edge (2003)

Grasmair, M.: Relaxation of nonlocal integrals with rational integrands. PhD thesis, University of Innsbruck, Austria, Innsbruck, June 2006

Guidotti, P., Lambers, J.V.: Two new nonlinear nonlocal diffusions for noise reduction. J. Math. Imaging Vis. 33(1), 25–37 (2009)

Perona, P., Malik, J.: Scale space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Mach. Intell. 12(7), 629–639 (1990)

Rudin, L.I., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D 60(1–4), 259–268 (1992)

Scherzer, O., Grasmair, M., Grossauer, H., Haltmeier, M., Lenzen, F.: Variational Methods in Imaging. Applied Mathematical Sciences, vol. 167. Springer, New York (2009)

Scherzer, O., Weickert, J.: Relations between regularization and diffusion filtering. J. Math. Imaging Vis. 12(1), 43–63 (2000)

Weickert, J.: Anisotropic Diffusion in Image Processing. Teubner, Stuttgart (1998). European Consortium for Mathematics in Industry

Yosida, K.: Functional Analysis. Die Grundlehren der Mathematischen Wissenschaften, vol. 123. Academic Press Inc., New York (1965)