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) |
|---|---|
| Pages (from-to) | 1-23 |
| Number of pages | 23 |
| Journal | SIAM Journal on Scientific Computing |
| Volume | 28 |
| Issue number | 1 |
| DOIs | |
| State | Published - 2006 |
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Keywords
- Fenchel duality
- Generalized newton-type methods
- Image restoration
- Total bounded variation
ASJC Scopus subject areas
- Applied Mathematics
- Computational Mathematics
Cite this
An infeasible primal-dual algorithm for total bounded variation-based inf-convolution-type image restoration. / Hintermüller, M.; Stadler, Georg.
In: SIAM Journal on Scientific Computing, Vol. 28, No. 1, 2006, p. 1-23.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - An infeasible primal-dual algorithm for total bounded variation-based inf-convolution-type image restoration
AU - Hintermüller, M.
AU - Stadler, Georg
PY - 2006
Y1 - 2006
N2 - 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.
AB - 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.
KW - Fenchel duality
KW - Generalized newton-type methods
KW - Image restoration
KW - Total bounded variation
UR - http://www.scopus.com/inward/record.url?scp=77950679349&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=77950679349&partnerID=8YFLogxK
U2 - 10.1137/040613263
DO - 10.1137/040613263
M3 - Article
AN - SCOPUS:77950679349
VL - 28
SP - 1
EP - 23
JO - SIAM Journal of Scientific Computing
JF - SIAM Journal of Scientific Computing
SN - 1064-8275
IS - 1
ER -