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G. Aubert and P. Kornprobst. Mathematical problems in image processing, volume 147 of Applied Mathematical Sciences. Springer-Verlag, New York, 2002. Partial differential equations and the calculus of variations, With a foreword by Olivier Faugeras.
V. Bally. Approximation scheme for solutions of BSDE. In Backward stochastic differential equations (Paris, 1995-1996), volume 364 of Pitman Res. Notes Math. Ser., pages 177–191. Longman, Harlow, 1997.
V. Caselles, G. Sapiro, and B. Tang. Diffusion on general data on non-flat manifolds via harmonic maps theory: the direction diffusion case. Int. J. Comput. Vis., 36(2):149–161, 2000.
V. Caselles, G. Sapiro, and . Tang. Color image enhancement via chromaticity diffusion. IEEE Trans. Image Process., 10(5):701–707, 2001.
T. Cecil, S. Osher, and L. Vese. Numerical methods for minimization problems constrained to S 1 and S 2 . J. Comput. Phys., 198(2):567–579, 2004.
T. Chan, S. H. Kang, and J. Shen. Total variation denoising and enhancement of color image based on the CB and HSV color models. J. Vis. Comm. Image Represent., 12(4):422–435, 2001.
T. Chan and J. Shen. Variational restoration of nonflat image features: models and algorithms. SIAM J. Appl. Math., 61(4):1338–1361 (electronic), 2000/01.
D. Chevance. Numerical methods for backward stochastic differential equations. In Numerical methods in finance, Publ. Newton Inst., pages 232–244. Cambridge Univ. Press, Cambridge, 1997.
R. Deriche and D. Tschumperlé. Diffusion PDE’s on vector-valued images: local approach and geometric viewpoint. IEEE Signal Process. Mag., 19(5):16–25, 2002.
S. Di Zenzo. A note on the gradient of a multi-image. Comput. Vis. Graph. Image Process., 33(1):116–125, 1986.
A. Gégout-Petit and E. Pardoux.Équations différentielles stochastiques rétrogrades réfléchies dans un convexe. Stochast. Stochast. Rep., 57(1-2):111-128,1996.
J. Ma, P. Protter, J. San Martin, and S. Torres. Numerical method for backward stochastic differential equations. Ann. Appl. Probab., 12(1):302–316, 2002.
J. Malik and P. Perona. Scale-space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Mach. Intell., 12(7):629–639, 1990.
S. J. Osher and L. A. Vese. Numerical methods for p-harmonic flows and applications to image processing. SIAM J. Numer. Anal., 40(6):2085–2104 (electronic) (2003),2002.
E. Pardoux. Backward stochastic differential equations and viscosity solutions of systems of semilinear parabolic and elliptic PDEs of second order. In Stochastic analysis and related topics, VI (Geilo, 1996), volume 42 of Progr. Probab., pages 79–127. Birkhäuser Boston, Boston, MA, 1998.
Y. Saisho. Stochastic differential equations for multidimensional domain with reflecting boundary. Probab. Theor. Relat. Field., 74(3):455–477, 1987.
H. Tanaka. Stochastic differential equations with reflecting boundary condition in convex regions. Hiroshima Math. J., 9(1):163–177, 1979.
J. Zhang. A numerical scheme for BSDEs. Ann. Appl. Probab., 14(1):459–488, 2004.
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Borkowski, D. (2007). Chromaticity Denoising using Solution to the Skorokhod Problem. In: Tai, XC., Lie, KA., Chan, T.F., Osher, S. (eds) Image Processing Based on Partial Differential Equations. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-33267-1_9
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