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| Content Provider | Springer Nature Link |
|---|---|
| Author | Krishnan, D. Pham, Quang Vinh Yip, Andy M. |
| Copyright Year | 2008 |
| Abstract | In this paper, we propose a fast primal-dual algorithm for solving bilaterally constrained total variation minimization problems which subsume the bilaterally constrained total variation image deblurring model and the two-phase piecewise constant Mumford-Shah image segmentation model. The presence of the bilateral constraints makes the optimality conditions of the primal-dual problem semi-smooth which can be solved by a semi-smooth Newton’s method superlinearly. But the linear system to solve at each iteration is very large and difficult to precondition. Using a primal-dual active-set strategy, we reduce the linear system to a much smaller and better structured one so that it can be solved efficiently by conjugate gradient with an approximate inverse preconditioner. Locally superlinear convergence results are derived for the proposed algorithm. Numerical experiments are also provided for both deblurring and segmentation problems. In particular, for the deblurring problem, we show that the addition of the bilateral constraints to the total variation model improves the quality of the solutions. |
| Ending Page | 266 |
| Page Count | 30 |
| Starting Page | 237 |
| File Format | |
| ISSN | 10197168 |
| e-ISSN | 15729044 |
| Journal | Advances in Computational Mathematics |
| Issue Number | 1-3 |
| Volume Number | 31 |
| Language | English |
| Publisher | Springer US |
| Publisher Date | 2008-09-24 |
| Publisher Place | Boston |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | Primal-dual algorithm Image deblurring Image processing Semi-smooth Newton’s method Numeric Computing Total variation Theory of Computation Mathematics Image segmentation Optimization and variational techniques Methods of quasi-Newton type Algebra Bilateral constraints Calculus of Variations and Optimal Control; Optimization Image processing (compression, reconstruction, etc.) |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Computational Mathematics |
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