DC-Programming versus ℓ0-Superiorization for Discrete Tomography
In this paper we focus on the reconstruction of sparse solutions to underdetermined systems of linear equations with variable bounds. The problem is motivated by sparse and gradient-sparse reconstruction in binary and discrete tomography from limited data. To address the ℓ0-minimization problem we c...
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| Format: | Article |
| Language: | English |
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Sciendo
2018-07-01
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| Series: | Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica |
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| Online Access: | https://doi.org/10.2478/auom-2018-0021 |
| _version_ | 1811272396693307392 |
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| author | Gibali Aviv Petra Stefania |
| author_facet | Gibali Aviv Petra Stefania |
| author_sort | Gibali Aviv |
| collection | DOAJ |
| description | In this paper we focus on the reconstruction of sparse solutions to underdetermined systems of linear equations with variable bounds. The problem is motivated by sparse and gradient-sparse reconstruction in binary and discrete tomography from limited data. To address the ℓ0-minimization problem we consider two approaches: DC-programming and ℓ0-superiorization. We show that ℓ0-minimization over bounded polyhedra can be equivalently formulated as a DC program. Unfortunately, standard DC algorithms based on convex programming often get trapped in local minima. On the other hand, ℓ0-superiorization yields comparable results at significantly lower costs. |
| first_indexed | 2024-04-12T22:39:35Z |
| format | Article |
| id | doaj.art-93f2760c64054201ac5e73ebab1fc6ca |
| institution | Directory Open Access Journal |
| issn | 1844-0835 |
| language | English |
| last_indexed | 2024-04-12T22:39:35Z |
| publishDate | 2018-07-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica |
| spelling | doaj.art-93f2760c64054201ac5e73ebab1fc6ca2022-12-22T03:13:47ZengSciendoAnalele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica1844-08352018-07-0126210513310.2478/auom-2018-0021DC-Programming versus ℓ0-Superiorization for Discrete TomographyGibali Aviv0Petra Stefania1Department of Mathematics, ORT Braude College,Karmiel, IsraelMathematical Imaging Group, Heidelberg University,Heidelberg, GermanyIn this paper we focus on the reconstruction of sparse solutions to underdetermined systems of linear equations with variable bounds. The problem is motivated by sparse and gradient-sparse reconstruction in binary and discrete tomography from limited data. To address the ℓ0-minimization problem we consider two approaches: DC-programming and ℓ0-superiorization. We show that ℓ0-minimization over bounded polyhedra can be equivalently formulated as a DC program. Unfortunately, standard DC algorithms based on convex programming often get trapped in local minima. On the other hand, ℓ0-superiorization yields comparable results at significantly lower costs.https://doi.org/10.2478/auom-2018-0021dc-programmingsparse regularizationsuperiorizationdiscrete tomographysplit convex feasibility problem |
| spellingShingle | Gibali Aviv Petra Stefania DC-Programming versus ℓ0-Superiorization for Discrete Tomography Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica dc-programming sparse regularization superiorization discrete tomography split convex feasibility problem |
| title | DC-Programming versus ℓ0-Superiorization for Discrete Tomography |
| title_full | DC-Programming versus ℓ0-Superiorization for Discrete Tomography |
| title_fullStr | DC-Programming versus ℓ0-Superiorization for Discrete Tomography |
| title_full_unstemmed | DC-Programming versus ℓ0-Superiorization for Discrete Tomography |
| title_short | DC-Programming versus ℓ0-Superiorization for Discrete Tomography |
| title_sort | dc programming versus l0 superiorization for discrete tomography |
| topic | dc-programming sparse regularization superiorization discrete tomography split convex feasibility problem |
| url | https://doi.org/10.2478/auom-2018-0021 |
| work_keys_str_mv | AT gibaliaviv dcprogrammingversusl0superiorizationfordiscretetomography AT petrastefania dcprogrammingversusl0superiorizationfordiscretetomography |