File Download
There are no files associated with this item.
Links for fulltext
(May Require Subscription)
- Publisher Website: 10.1137/030600862
- Scopus: eid_2-s2.0-33646596282
- WOS: WOS:000234471700011
- Find via
Supplementary
- Citations:
- Appears in Collections:
Article: Analysis of half-quadratic minimization methods for signal and image recovery
Title | Analysis of half-quadratic minimization methods for signal and image recovery |
---|---|
Authors | |
Keywords | Preconditioning Optimization Convergence analysis Variational methods Signal and image restoration Maximum a posteriori estimation Inverse problems Half-quadratic regularization |
Issue Date | 2006 |
Citation | SIAM Journal on Scientific Computing, 2006, v. 27, n. 3, p. 937-966 How to Cite? |
Abstract | We address the minimization of regularized convex cost functions which are customarily used for edge-preserving restoration and reconstruction of signals and images. In order to accelerate computation, the multiplicative and the additive half-quadratic reformulation of the original cost-function have been pioneered in Geman and Reynolds [IEEE Trans. Pattern Anal. Machine Intelligence, 14 (1992), pp. 367-383] and Geman and Yang [IEEE Trans. Image Process., 4 (1995), pp. 932-946]. The alternate minimization of the resultant (augmented) cost-functions has a simple explicit form. The goal of this paper is to provide a systematic analysis of the convergence rate achieved by these methods. For the multiplicative and additive half-quadratic regularizations, we determine their upper bounds for their root-convergence factors. The bound for the multiplicative form is seen to be always smaller than the bound for the additive form. Experiments show that the number of iterations required for convergence for the multiplicative form is always less than that for the additive form. However, the computational cost of each iteration is much higher for the multiplicative form than for the additive form. The global assessment is that minimization using the additive form of half-quadratic regularization is faster than using the multiplicative form. When the additive form is applicable, it is hence recommended. Extensive experiments demonstrate that in our MATLAB implementation, both methods are substantially faster (in terms of computational times) than the standard MATLAB OPTIMIZATION TOOLBOX routines used in our comparison study. © 2005 Society for Industrial and Applied Mathematics. |
Persistent Identifier | http://hdl.handle.net/10722/276793 |
ISSN | 2023 Impact Factor: 3.0 2023 SCImago Journal Rankings: 1.803 |
ISI Accession Number ID |
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Nikolova, Mila | - |
dc.contributor.author | Ng, Michael K. | - |
dc.date.accessioned | 2019-09-18T08:34:40Z | - |
dc.date.available | 2019-09-18T08:34:40Z | - |
dc.date.issued | 2006 | - |
dc.identifier.citation | SIAM Journal on Scientific Computing, 2006, v. 27, n. 3, p. 937-966 | - |
dc.identifier.issn | 1064-8275 | - |
dc.identifier.uri | http://hdl.handle.net/10722/276793 | - |
dc.description.abstract | We address the minimization of regularized convex cost functions which are customarily used for edge-preserving restoration and reconstruction of signals and images. In order to accelerate computation, the multiplicative and the additive half-quadratic reformulation of the original cost-function have been pioneered in Geman and Reynolds [IEEE Trans. Pattern Anal. Machine Intelligence, 14 (1992), pp. 367-383] and Geman and Yang [IEEE Trans. Image Process., 4 (1995), pp. 932-946]. The alternate minimization of the resultant (augmented) cost-functions has a simple explicit form. The goal of this paper is to provide a systematic analysis of the convergence rate achieved by these methods. For the multiplicative and additive half-quadratic regularizations, we determine their upper bounds for their root-convergence factors. The bound for the multiplicative form is seen to be always smaller than the bound for the additive form. Experiments show that the number of iterations required for convergence for the multiplicative form is always less than that for the additive form. However, the computational cost of each iteration is much higher for the multiplicative form than for the additive form. The global assessment is that minimization using the additive form of half-quadratic regularization is faster than using the multiplicative form. When the additive form is applicable, it is hence recommended. Extensive experiments demonstrate that in our MATLAB implementation, both methods are substantially faster (in terms of computational times) than the standard MATLAB OPTIMIZATION TOOLBOX routines used in our comparison study. © 2005 Society for Industrial and Applied Mathematics. | - |
dc.language | eng | - |
dc.relation.ispartof | SIAM Journal on Scientific Computing | - |
dc.subject | Preconditioning | - |
dc.subject | Optimization | - |
dc.subject | Convergence analysis | - |
dc.subject | Variational methods | - |
dc.subject | Signal and image restoration | - |
dc.subject | Maximum a posteriori estimation | - |
dc.subject | Inverse problems | - |
dc.subject | Half-quadratic regularization | - |
dc.title | Analysis of half-quadratic minimization methods for signal and image recovery | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1137/030600862 | - |
dc.identifier.scopus | eid_2-s2.0-33646596282 | - |
dc.identifier.volume | 27 | - |
dc.identifier.issue | 3 | - |
dc.identifier.spage | 937 | - |
dc.identifier.epage | 966 | - |
dc.identifier.isi | WOS:000234471700011 | - |
dc.identifier.issnl | 1064-8275 | - |