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- Publisher Website: 10.1007/s10915-018-0888-2
- Scopus: eid_2-s2.0-85057620719
- WOS: WOS:000464896500021
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Article: A Fast Algorithm for Solving Linear Inverse Problems with Uniform Noise Removal
Title | A Fast Algorithm for Solving Linear Inverse Problems with Uniform Noise Removal |
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Authors | |
Keywords | ℓ -Norm ∞ Uniform noise Total variation Linear inverse problems Alternating direction method of multipliers |
Issue Date | 2019 |
Citation | Journal of Scientific Computing, 2019, v. 79, n. 2, p. 1214-1240 How to Cite? |
Abstract | © 2018, Springer Science+Business Media, LLC, part of Springer Nature. In this paper, we develop a fast algorithm for solving an unconstrained optimization model for uniform noise removal which is an important task in inverse problems. The optimization model consists of an ℓ ∞ data fitting term and a total variation regularization term. By utilizing the alternating direction method of multipliers (ADMM) for such optimization model, we demonstrate that one of the ADMM subproblems can be formulated by involving a projection onto ℓ 1 ball which can be solved efficiently by iterations. The convergence of the ADMM method can be established under some mild conditions. In practice, the balance between the ℓ ∞ data fitting term and the total variation regularization term is controlled by a regularization parameter. We present numerical experiments by using the L-curve method of the logarithms of data fitting term and total variation regularization term to select regularization parameters for uniform noise removal. Numerical results for image denoising and deblurring, inverse source, inverse heat conduction problems and second derivative problems have shown the effectiveness of the proposed model. |
Persistent Identifier | http://hdl.handle.net/10722/276623 |
ISSN | 2023 Impact Factor: 2.8 2023 SCImago Journal Rankings: 1.248 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Zhang, Xiongjun | - |
dc.contributor.author | Ng, Michael K. | - |
dc.date.accessioned | 2019-09-18T08:34:10Z | - |
dc.date.available | 2019-09-18T08:34:10Z | - |
dc.date.issued | 2019 | - |
dc.identifier.citation | Journal of Scientific Computing, 2019, v. 79, n. 2, p. 1214-1240 | - |
dc.identifier.issn | 0885-7474 | - |
dc.identifier.uri | http://hdl.handle.net/10722/276623 | - |
dc.description.abstract | © 2018, Springer Science+Business Media, LLC, part of Springer Nature. In this paper, we develop a fast algorithm for solving an unconstrained optimization model for uniform noise removal which is an important task in inverse problems. The optimization model consists of an ℓ ∞ data fitting term and a total variation regularization term. By utilizing the alternating direction method of multipliers (ADMM) for such optimization model, we demonstrate that one of the ADMM subproblems can be formulated by involving a projection onto ℓ 1 ball which can be solved efficiently by iterations. The convergence of the ADMM method can be established under some mild conditions. In practice, the balance between the ℓ ∞ data fitting term and the total variation regularization term is controlled by a regularization parameter. We present numerical experiments by using the L-curve method of the logarithms of data fitting term and total variation regularization term to select regularization parameters for uniform noise removal. Numerical results for image denoising and deblurring, inverse source, inverse heat conduction problems and second derivative problems have shown the effectiveness of the proposed model. | - |
dc.language | eng | - |
dc.relation.ispartof | Journal of Scientific Computing | - |
dc.subject | ℓ -Norm ∞ | - |
dc.subject | Uniform noise | - |
dc.subject | Total variation | - |
dc.subject | Linear inverse problems | - |
dc.subject | Alternating direction method of multipliers | - |
dc.title | A Fast Algorithm for Solving Linear Inverse Problems with Uniform Noise Removal | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1007/s10915-018-0888-2 | - |
dc.identifier.scopus | eid_2-s2.0-85057620719 | - |
dc.identifier.volume | 79 | - |
dc.identifier.issue | 2 | - |
dc.identifier.spage | 1214 | - |
dc.identifier.epage | 1240 | - |
dc.identifier.isi | WOS:000464896500021 | - |
dc.identifier.issnl | 0885-7474 | - |