Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Numerical Methods for p-Harmonic Flows and Applications to Image Processing
SIAM Journal on Numerical Analysis
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
Error Analysis for Image Inpainting
Journal of Mathematical Imaging and Vision
Image Processing Based on Partial Differential Equations: Proceedings of the International Conference on PDE-Based Image Processing and Related Inverse ... 8-12, 2005 (Mathematics and Visualization)
Spatial error concealment: A novel exemplar-based approach using segmentation
Computers and Electrical Engineering
Simultaneously inpainting in image and transformed domains
Numerische Mathematik
L0-Norm and Total Variation for Wavelet Inpainting
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
A Variational Framework for Non-local Image Inpainting
EMMCVPR '09 Proceedings of the 7th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
The Split Bregman Method for L1-Regularized Problems
SIAM Journal on Imaging Sciences
Using the complex Ginzburg-Landau equation for digital inpainting in 2D and 3D
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
Filling-in by joint interpolation of vector fields and gray levels
IEEE Transactions on Image Processing
Simultaneous structure and texture image inpainting
IEEE Transactions on Image Processing
Region filling and object removal by exemplar-based image inpainting
IEEE Transactions on Image Processing
A novel kernel-based limited-view computerized tomography reconstruction via anisotropic diffusion
Computers and Electrical Engineering
Texture segmentation using vector-valued Chan-Vese model driven by local histogram
Computers and Electrical Engineering
Computers & Mathematics with Applications
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In this paper, we propose a fast algorithm to solve the well known total variation (TV) inpainting model. Classically, the Euler-Lagrange equation deduced from TV inpainting model is solved by the gradient descent method and discretized by an explicit scheme, which produces a slow inpainting process. Sometimes an implicit scheme is also used to tackle the problem. Although the implicit scheme is several times faster than the explicit one, it is still too slow in many practical applications. In this paper, we propose to use an operator splitting method by adding new variables in the Euler-Lagrange equation of TV inpainting model such that the equation is split into a few very simple subproblems. Then we solve these subproblems by an alternate iteration. Numerically, the proposed algorithm is very easy to implement. In the numerical experiments, we mainly compare our algorithm with the existing implicit TV inpainting algorithms. It is shown that our algorithm is about ten to twenty times faster than the implicit TV inpainting algorithms with similar inpainting quality. The comparison of our algorithm with harmonic inpainting algorithm also shows some advantages and disadvantages of the TV inpainting model.