TY  - JOUR
AU  - Rodriguez-Alvarez, M. J.
AU  - Sanchez, F.
AU  - Soriano, A.
AU  - Iborra, A.
PY  - 2010
DA  - 2010//
TI  - Sparse Givens resolution of large system of linear equations: Applications to image reconstruction
T2  - Math. Comput. Model.
JO  - Mathematical and Computer Modelling
SP  - 1258
EP  - 1264
VL  - 52
IS  - 7-8
PB  - Pergamon-Elsevier Science Ltd
KW  - Givens rotations
KW  - QR-factorization
KW  - Computed tomography
KW  - Image reconstruction
AB  - 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.
SN  - 0895-7177
UR  - https://doi.org/10.1016/j.mcm.2010.03.016
DO  - 10.1016/j.mcm.2010.03.016
LA  - English
N1  - ISI:000280933700043
ID  - Rodriguez-Alvarez_etal2010
ER  -