Journal of Mathematical Imaging and Vision
Image Restoration with Discrete Constrained Total Variation Part I: Fast and Exact Optimization
Journal of Mathematical Imaging and Vision
Approximate methods for constrained total variation minimization
CSR'06 Proceedings of the First international computer science conference on Theory and Applications
Exact optimization of discrete constrained total variation minimization problems
IWCIA'04 Proceedings of the 10th international conference on Combinatorial Image Analysis
Relations between higher order TV regularization and support vector regression
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
A four-pixel scheme for singular differential equations
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
Domain decomposition methods with graph cuts algorithms for total variation minimization
Advances in Computational Mathematics
A fast and exact algorithm for total variation minimization
IbPRIA'05 Proceedings of the Second Iberian conference on Pattern Recognition and Image Analysis - Volume Part I
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We develop computationally efficient procedures for solving certain restoration problems in one dimension, including the one-dimensional (1-D) discrete versions of the total variation regularized problem introduced by Sauer and Bouman and the constrained total variation minimization problem introduced by Rudin et al. The procedures are exact and have time complexity O(NlogN) and space complexity O(N), where N is the number of data samples. They are based on a simple nonlinear diffusion equation proposed by Pollak et al. and related to the Perona-Malik equation. A probabilistic interpretation for this diffusion equation in 1-D is provided by showing that it produces optimal solutions to a sequence of estimation problems. We extend our methods to two dimensions, where they no longer have similar optimality properties; however, we experimentally demonstrate their effectiveness for image restoration.