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- Publisher Website: 10.1088/0266-5611/32/11/115011
- Scopus: eid_2-s2.0-85009231192
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Article: Linearized primal-dual methods for linear inverse problems with total variation regularization and finite element discretization
Title | Linearized primal-dual methods for linear inverse problems with total variation regularization and finite element discretization |
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Authors | |
Keywords | total variation convergence rate saddle-point problem primal-dual method numerical optimization linear inverse problem finite element |
Issue Date | 2016 |
Citation | Inverse Problems, 2016, v. 32, n. 11 How to Cite? |
Abstract | © 2016 IOP Publishing Ltd. Linear inverse problems with total variation regularization can be reformulated as saddle-point problems; the primal and dual variables of such a saddle-point reformulation can be discretized in piecewise affine and constant finite element spaces, respectively. Thus, the well-developed primal-dual approach (a.k.a. the inexact Uzawa method) is conceptually applicable to such a regularized and discretized model. When the primal-dual approach is applied, the resulting subproblems may be highly nontrivial and it is necessary to discuss how to tackle them and thus make the primal-dual approach implementable. In this paper, we suggest linearizing the data-fidelity quadratic term of the hard subproblems so as to obtain easier ones. A linearized primal-dual method is thus proposed. Inspired by the fact that the linearized primal-dual method can be explained as an application of the proximal point algorithm, a relaxed version of the linearized primal-dual method, which can often accelerate the convergence numerically with the same order of computation, is also proposed. The global convergence and worst-case convergence rate measured by the iteration complexity are established for the new algorithms. Their efficiency is verified by some numerical results. |
Persistent Identifier | http://hdl.handle.net/10722/251195 |
ISSN | 2023 Impact Factor: 2.0 2023 SCImago Journal Rankings: 1.185 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Tian, Wenyi | - |
dc.contributor.author | Yuan, Xiaoming | - |
dc.date.accessioned | 2018-02-01T01:54:52Z | - |
dc.date.available | 2018-02-01T01:54:52Z | - |
dc.date.issued | 2016 | - |
dc.identifier.citation | Inverse Problems, 2016, v. 32, n. 11 | - |
dc.identifier.issn | 0266-5611 | - |
dc.identifier.uri | http://hdl.handle.net/10722/251195 | - |
dc.description.abstract | © 2016 IOP Publishing Ltd. Linear inverse problems with total variation regularization can be reformulated as saddle-point problems; the primal and dual variables of such a saddle-point reformulation can be discretized in piecewise affine and constant finite element spaces, respectively. Thus, the well-developed primal-dual approach (a.k.a. the inexact Uzawa method) is conceptually applicable to such a regularized and discretized model. When the primal-dual approach is applied, the resulting subproblems may be highly nontrivial and it is necessary to discuss how to tackle them and thus make the primal-dual approach implementable. In this paper, we suggest linearizing the data-fidelity quadratic term of the hard subproblems so as to obtain easier ones. A linearized primal-dual method is thus proposed. Inspired by the fact that the linearized primal-dual method can be explained as an application of the proximal point algorithm, a relaxed version of the linearized primal-dual method, which can often accelerate the convergence numerically with the same order of computation, is also proposed. The global convergence and worst-case convergence rate measured by the iteration complexity are established for the new algorithms. Their efficiency is verified by some numerical results. | - |
dc.language | eng | - |
dc.relation.ispartof | Inverse Problems | - |
dc.subject | total variation | - |
dc.subject | convergence rate | - |
dc.subject | saddle-point problem | - |
dc.subject | primal-dual method | - |
dc.subject | numerical optimization | - |
dc.subject | linear inverse problem | - |
dc.subject | finite element | - |
dc.title | Linearized primal-dual methods for linear inverse problems with total variation regularization and finite element discretization | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1088/0266-5611/32/11/115011 | - |
dc.identifier.scopus | eid_2-s2.0-85009231192 | - |
dc.identifier.volume | 32 | - |
dc.identifier.issue | 11 | - |
dc.identifier.spage | null | - |
dc.identifier.epage | null | - |
dc.identifier.eissn | 1361-6420 | - |
dc.identifier.isi | WOS:000392494200001 | - |
dc.identifier.issnl | 0266-5611 | - |