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Author  |
Rodriguez-Alvarez, M.J.; Sanchez, F.; Soriano, A.; Iborra, A. |
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Title |
Sparse Givens resolution of large system of linear equations: Applications to image reconstruction |
Type |
Journal Article |
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Year |
2010 |
Publication |
Mathematical and Computer Modelling |
Abbreviated Journal |
Math. Comput. Model. |
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Volume |
52 |
Issue |
7-8 |
Pages |
1258-1264 |
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Keywords |
Givens rotations; QR-factorization; Computed tomography; Image reconstruction |
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Abstract |
In medicine, computed tomographic images are reconstructed from a large number of measurements of X-ray transmission through the patient (projection data). The mathematical model used to describe a computed tomography device is a large system of linear equations of the form AX = B. In this paper we propose the QR decomposition as a direct method to solve the linear system. QR decomposition can be a large computational procedure. However, once it has been calculated for a specific system, matrices Q and R are stored and used for any acquired projection on that system. Implementation of the QR decomposition in order to take more advantage of the sparsity of the system matrix is discussed. |
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Address |
[Rodriguez-Alvarez, Maria-Jose; Iborra, Amadeo] Univ Politecn Valencia, Inst Matemat Multidisciplinar, E-46022 Valencia, Spain, Email: mjrodri@imm.upv.es |
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Corporate Author |
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Publisher |
Pergamon-Elsevier Science Ltd |
Place of Publication |
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Language |
English |
Summary Language |
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Original Title |
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Series Editor |
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Series Title |
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Abbreviated Series Title |
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Series Volume |
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Series Issue |
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Edition |
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ISSN |
0895-7177 |
ISBN |
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Conference |
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Notes |
ISI:000280933700043 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
no |
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Call Number |
IFIC @ elepoucu @ |
Serial |
395 |
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Author |
Rodriguez-Alvarez, M.J.; Sanchez, F.; Soriano, A.; Iborra, A.; Mora, C. |
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Title |
Exploiting symmetries for weight matrix design in CT imaging |
Type |
Journal Article |
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Year |
2011 |
Publication |
Mathematical and Computer Modelling |
Abbreviated Journal |
Math. Comput. Model. |
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Volume |
54 |
Issue |
7-8 |
Pages |
1655-1664 |
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Keywords |
Computerized tomography imaging; Polar grid; System matrix; Rotation symmetries; ART |
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Abstract |
In this paper we propose several methods of constructing the system matrix (SM) of a Computed Tomography (CT) scanner with two objectives: (1) to construct SMs in the shortest possible time and store them in an ordinary PC without losing quality, (2) to analyze the possible applications of the proposed method to 3D, taking into account SMs' sizes, computing time and reconstructed image quality. In order to build the SM, we propose two new field of view (FOV) pixellation schemes, based on a polar coordinate system (polar grid) by taking advantage of the polar rotation symmetries of CT devices. Comparisons between the SMs proposed are performed using two phantom and a real CT-simulator images. Global error, contrast, noise and homogeneity of the reconstructed images are discussed. |
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Address |
[Rodriguez-Alvarez, MJ; Iborra, A; Mora, C] Univ Politecn Valencia, Inst Matemat Multidisciplinar, Valencia 46022, Spain, Email: mjrodri@imm.upv.es |
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Corporate Author |
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Thesis |
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| |
Publisher |
Pergamon-Elsevier Science Ltd |
Place of Publication |
|
Editor |
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| |
Language |
English |
Summary Language |
|
Original Title |
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Series Editor |
|
Series Title |
|
Abbreviated Series Title |
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Series Volume |
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Series Issue |
|
Edition |
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ISSN |
0895-7177 |
ISBN |
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Medium |
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Area |
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Expedition |
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Conference |
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Notes |
WOS:000293269200007 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
no |
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Call Number |
IFIC @ elepoucu @ |
Serial |
708 |
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| Permanent link to this record |
