Mô hình phục hồi ảnh xám dựa trên PDE bậc bốn tuyến tính

Aubert G, Kornprobst P (2006) Mathematical problems in image processing: partial differential equations and the calculus of variations, vol 147. Springer, Bwelin Bertalmio M, Sapiro G, Caselles V, Ballester C (2000) Image inpainting. In: Proceedings of the 27th annual conference on Computer graphics and interactive techniques (SIGGRAPH ’00), New Orleans, LU, pp 417–424 Bertalmio M, Bertozzi AL, Sapiro G (2001) Navier–Stokes, fluid dynamics, and image and video inpainting. In: Proceedings of the 2001 IEEE computer society conference on computer. Vision and pattern recognition. CVPR 2001, vol 1, pp 355–362 Bertozzi AL, Esedoglu S, Gillette A (2007a) Inpainting of binary images using the Cahn–Hilliard equation. IEEE Trans Image Process 16(1):285–291 Bertozzi AL, Esedoglu S, Gillette A (2007b) Analysis of a two-scale Cahn–Hilliard model for image inpainting. Multiscale Model Simul 6(3):913–936 Burger M, He L, Schönlieb CB (2009) Cahn–Hilliard inpainting and a generalization for grayvalue images. SIAM J Imaging Sci 2(4):1129–1167 Chan TF, Shen J (2001a) Mathematical models for local non-texture inpaintings. SIAM J Appl Math 62(3):1019–1043 Chan TF, Shen J (2001b) Non-texture inpainting by curvature driven diffusions (CDD). J Vis Commun Image Rep 12(4):436–449 Chan TF, Kang SH, Shen J (2002) Euler’s elastica and curvature-based inpainting. SIAM J Appl Math 63(2):564592 Chan TF, Shen JH, Zhou HM (2006) Total variation wavelet inpainting. J Math Imaging Vis 25(1):107–125 Cherfils L, Fakih H, Miranville A (2017) A complex version of the Cahn–Hilliard equation for grayscale image inpainting. Multiscale Model Simul 15:575–605 Criminisi A, Perez P, Toyama K (2003) Object removal by exemplar-based inpainting. IEEE Int Conf Comput Vis Pattern Recognit 2:721–728 Deo SG, Lakshmikantham V, Raghavendra V (1997) Textbook of ordinary differential equations. Tata McGraw-Hill, New York Dobrosotskaya JA, Bertozzi AL (2008) A wavelet-laplace variational technique for image deconvolution and inpainting. IEEE Trans Image Process 17(5):657–663 Efros AA, Leung TK (1999) Texture synthesis by non-parametric sampling. In: IEEE international conference on computer vision, Corfu, Greece Esedoglu S, Shen JH (2002) Digital inpainting based on the Mumford–Shah–Euler image model. Eur J Appl Math 13(4):353–370 Evans LC (2010) Partial differential equations. Graduate studies in mathematics. American Mathematical Society, Providence Eyre D (1998) An unconditionally stable one-step scheme for gradient systems. Unpublished Fife PC (2000) Models for phase separation and their mathematics. Electron J Differ Equ 48:1–26 Gillette A (2006) Image Inpainting using a modified Cahn–Hilliard equation. PhD thesis, University of California, Los Angeles Kašpar R, Zitová B (2003) Weighted thin-plate spline image denoising. Pattern Recognit 36:3027–3030 Li X (2011) Image recovery via hybrid sparse representations: a deterministic annealing approach. IEEE J Sel Top Signal Process 5(5):953–962 Masnou S, Morel J (1998) Level lines based disocclusion. In: 5th IEEE international conference on image processing, Chicago, pp 259–263 Mumford D, Shah J (1989) Optimal approximations by piecewise smooth functions and associated variational problems. Commun Pure Appl Math 42:577–685 Nitzberg N, Mumford D, Shiota T (1993) Filtering, segmentation, and depth. Lecture notes in computer science. Springer, Berlin Papafitsoros K, Schönlieb CB, Sengul B (2013) Combined first and second order total variation inpainting using split Bregman. Image Process. Line 3:112136 Perona P, Malik J (1990) Scale-space and edge detection using anisotropic diffusion. IEEE Trans Pattern Anal Mach Intell 12(7):629–639 Rudin LI, Osher S, Fatemi E (1992) Nonlinear total variation based noise removal algorithms. Physica D 60:259–268 Sch önlieb CB (2009) Modern PDE techniques for image inpainting. PhD thesis, DAMTP, University of Cambridge Schönlieb, (2012) Higher-order total variation inpainting. File Exchange, MATLAB Central Schönlieb CB, Bertozzi A (2011) Unconditionally stable schemes for higher order inpainting. Commun Math Sci 9(2):413–457 Temam R (1997) Infinite dimensional dynamical systems in mechanics and physics, vol 68. Springer, Berlin Theljani A, Belhachmi Z, Kallel M, Moakher M (2017) Multiscale fourth order model for image inpainting and low-dimensional sets recovery. Math Methods Appl Sci 40:3637–3650 Vijayakrishna R (2015) A unified model of Cahn–Hilliard greyscale inpainting and multiphase classification. PhD thesis, IIT Kanpur, India Wang Z, Bovik AC (2002) A universal image quality index. IEEE Signal Process Lett 9(3):81–84