Incomplete oblique projections method for solving regularized least-squares problems in image reconstruction
In this paper we improve on the incomplete oblique projections (IOP) method introduced previously by the authors for solving inconsistent linear systems, when applied to image reconstruction problems. That method uses IOP onto the set of solutions of the augmented system Ax−r=b, and converges to a w...
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2008
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09696016_v15_n4_p417_Scolnik http://hdl.handle.net/20.500.12110/paper_09696016_v15_n4_p417_Scolnik |
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paper:paper_09696016_v15_n4_p417_Scolnik |
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paper:paper_09696016_v15_n4_p417_Scolnik2023-06-08T15:59:01Z Incomplete oblique projections method for solving regularized least-squares problems in image reconstruction Computerized tomography Image reconstruction Incomplete projections Least-squares problems Minimum norm solution Regularization In this paper we improve on the incomplete oblique projections (IOP) method introduced previously by the authors for solving inconsistent linear systems, when applied to image reconstruction problems. That method uses IOP onto the set of solutions of the augmented system Ax−r=b, and converges to a weighted least-squares solution of the system Ax=b. In image reconstruction problems, systems are usually inconsistent and very often rank-deficient because of the underlying discretized model. Here we have considered a regularized least-squares objective function that can be used in many ways such as incorporating blobs or nearest-neighbor interactions among adjacent pixels, aiming at smoothing the image. Thus, the oblique incomplete projections algorithm has been modified for solving this regularized model. The theoretical properties of the new algorithm are analyzed and numerical experiments are presented showing that the new approach improves the quality of the reconstructed images. © 2008 International Federation of Operational Research Societies. 2008 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09696016_v15_n4_p417_Scolnik http://hdl.handle.net/20.500.12110/paper_09696016_v15_n4_p417_Scolnik |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Computerized tomography Image reconstruction Incomplete projections Least-squares problems Minimum norm solution Regularization |
| spellingShingle |
Computerized tomography Image reconstruction Incomplete projections Least-squares problems Minimum norm solution Regularization Incomplete oblique projections method for solving regularized least-squares problems in image reconstruction |
| topic_facet |
Computerized tomography Image reconstruction Incomplete projections Least-squares problems Minimum norm solution Regularization |
| description |
In this paper we improve on the incomplete oblique projections (IOP) method introduced previously by the authors for solving inconsistent linear systems, when applied to image reconstruction problems. That method uses IOP onto the set of solutions of the augmented system Ax−r=b, and converges to a weighted least-squares solution of the system Ax=b. In image reconstruction problems, systems are usually inconsistent and very often rank-deficient because of the underlying discretized model. Here we have considered a regularized least-squares objective function that can be used in many ways such as incorporating blobs or nearest-neighbor interactions among adjacent pixels, aiming at smoothing the image. Thus, the oblique incomplete projections algorithm has been modified for solving this regularized model. The theoretical properties of the new algorithm are analyzed and numerical experiments are presented showing that the new approach improves the quality of the reconstructed images. © 2008 International Federation of Operational Research Societies. |
| title |
Incomplete oblique projections method for solving regularized least-squares problems in image reconstruction |
| title_short |
Incomplete oblique projections method for solving regularized least-squares problems in image reconstruction |
| title_full |
Incomplete oblique projections method for solving regularized least-squares problems in image reconstruction |
| title_fullStr |
Incomplete oblique projections method for solving regularized least-squares problems in image reconstruction |
| title_full_unstemmed |
Incomplete oblique projections method for solving regularized least-squares problems in image reconstruction |
| title_sort |
incomplete oblique projections method for solving regularized least-squares problems in image reconstruction |
| publishDate |
2008 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09696016_v15_n4_p417_Scolnik http://hdl.handle.net/20.500.12110/paper_09696016_v15_n4_p417_Scolnik |
| _version_ |
1768543571456032768 |