Abstract
In this paper, a primal-dual algorithm for total bounded variation (TV)-type image restoration is analyzed and tested. Analytically it turns out that employing a global Lsregularization, with 1 < s ≤ 2, in the dual problem results in a local smoothing of the TVregularization term in the primal problem. The local smoothing can alternatively be obtained as the inflmal convolution of the ℓr-norm, with r-1 + s -1 = 1, and a smooth function. In the case r = s = 2, this results in Gauss-TV-type image restoration. The globalized primal-dual algorithm introduced in this paper works with generalized derivatives, converges locally at a superlinear rate, and is stable with respect to noise in the data. In addition, it utilizes a projection technique which reduces the size of the linear system that has to be solved per iteration. A comprehensive numerical study ends the paper.
Original language | English (US) |
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Pages (from-to) | 1-23 |
Number of pages | 23 |
Journal | SIAM Journal on Scientific Computing |
Volume | 28 |
Issue number | 1 |
DOIs | |
State | Published - 2006 |
Keywords
- Fenchel duality
- Generalized newton-type methods
- Image restoration
- Total bounded variation
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics