A comparison of three total variation based texture extraction models
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Computer Vision and Image Understanding
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International Journal of Computer Vision
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Some First-Order Algorithms for Total Variation Based Image Restoration
Journal of Mathematical Imaging and Vision
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IEEE Transactions on Signal Processing
Efficient minimization method for a generalized total variation functional
IEEE Transactions on Image Processing
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IEEE Transactions on Image Processing
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SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
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Computational Optimization and Applications
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Journal of Biomedical Imaging
A Multilevel Algorithm for Simultaneously Denoising and Deblurring Images
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
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SIAM Journal on Imaging Sciences
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International Journal of Bioinformatics Research and Applications
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In this paper we present optimization algorithms for image restoration based on the total variation (TV) minimization framework of Rudin, Osher, and Fatemi (ROF). Our approach formulates TV minimization as a second-order cone program which is then solved by interior-point algorithms that are efficient both in practice (using nested dissection and domain decomposition) and in theory (i.e., they obtain solutions in polynomial time). In addition to the original ROF minimization model, we show how to apply our approach to other TV models, including ones that are not solvable by PDE-based methods. Numerical results on a varied set of images are presented to illustrate the effectiveness of our approach.