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Abstract:

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.

Registro:

Documento: Artículo
Título:Incomplete oblique projections method for solving regularized least-squares problems in image reconstruction
Autor:Scolnik, H.D.; Echebest, N.E.; Guardarucci, M.T.
Filiación:Departamento de Computación, Fac. de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Argentina
Departamento de Matemática, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, Argentina
Departamento de Ciencias Básicas, Facultad de Ingeniería, Universidad Nacional de La Plata, Argentina
Palabras clave:Computerized tomography; Image reconstruction; Incomplete projections; Least-squares problems; Minimum norm solution; Regularization
Año:2008
Volumen:15
Número:4
Página de inicio:417
Página de fin:438
DOI: http://dx.doi.org/10.1111/j.1475-3995.2008.00643.x
Título revista:International Transactions in Operational Research
Título revista abreviado:Int. Trans. Oper. Res.
ISSN:09696016
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09696016_v15_n4_p417_Scolnik

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Citas:

---------- APA ----------
Scolnik, H.D., Echebest, N.E. & Guardarucci, M.T. (2008) . Incomplete oblique projections method for solving regularized least-squares problems in image reconstruction. International Transactions in Operational Research, 15(4), 417-438.
http://dx.doi.org/10.1111/j.1475-3995.2008.00643.x
---------- CHICAGO ----------
Scolnik, H.D., Echebest, N.E., Guardarucci, M.T. "Incomplete oblique projections method for solving regularized least-squares problems in image reconstruction" . International Transactions in Operational Research 15, no. 4 (2008) : 417-438.
http://dx.doi.org/10.1111/j.1475-3995.2008.00643.x
---------- MLA ----------
Scolnik, H.D., Echebest, N.E., Guardarucci, M.T. "Incomplete oblique projections method for solving regularized least-squares problems in image reconstruction" . International Transactions in Operational Research, vol. 15, no. 4, 2008, pp. 417-438.
http://dx.doi.org/10.1111/j.1475-3995.2008.00643.x
---------- VANCOUVER ----------
Scolnik, H.D., Echebest, N.E., Guardarucci, M.T. Incomplete oblique projections method for solving regularized least-squares problems in image reconstruction. Int. Trans. Oper. Res. 2008;15(4):417-438.
http://dx.doi.org/10.1111/j.1475-3995.2008.00643.x