| Publication type: |
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Article in peer-reviewed journal |
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| Subject: |
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Mathematics/Analysis of PDEs
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| Title: |
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A variational approach to the inversion of truncated Fourier operators |
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| Author(s): |
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Nathael Alibaud ( ) 1, Pierre Maréchal 2, Yaowaluk Saesor 3 |
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| Laboratory: |
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| Abstract: |
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Truncated Fourier operators play an important role in many inverse problems of signal and image science. A variational approach to the regularization of their pseudo-inverses is considered. A particular regularization parameter, which can be interpreted in terms of resolution level, appears to play the essential role. This paper presents results on the behavior of the regularized solution as this parameter tends to zero. Notably, reasonably mild conditions are shown to ensure strong convergence of the regularized solution to the pseudo-inverse of the data. |
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| Fulltext language: |
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English |
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| Production date: |
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2008-09-10 |
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| Journal: |
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| Inverse Problems (Inverse Probl.) |
| Publisher |
Institute of Physics: Hybrid Open Access |
| ISSN |
0266-5611 (eISSN : 1361-6420) |
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| Audience: |
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international |
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| Publication date: |
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2009-02-13 |
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| Volume: |
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5 |
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| Issue: |
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4 |
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| Page, identifiant, ...: |
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045002 |
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| Classification: |
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PACS: 02.30.Nw, 84.40.Ua, 07.05.Pj, 02.30.Zz, 07.50.Qx, 02.30.Tb; 2000 MSC: 47A52, 68U10, 94A08 |
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| Comment: |
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20 pages |
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