%0 Journal Article
%T Sparse Givens resolution of large system of linear equations: Applications to image reconstruction
%A Rodriguez-Alvarez, M. J.
%A Sanchez, F.
%A Soriano, A.
%A Iborra, A.
%J Mathematical and Computer Modelling
%D 2010
%V 52
%N 7-8
%I Pergamon-Elsevier Science Ltd
%@ 0895-7177
%G English
%F Rodriguez-Alvarez_etal2010
%O ISI:000280933700043
%O exported from refbase (https://references.ific.uv.es/refbase/show.php?record=395), last updated on Thu, 01 Nov 2012 20:00:23 +0000
%X 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.
%K Givens rotations
%K QR-factorization
%K Computed tomography
%K Image reconstruction
%R 10.1016/j.mcm.2010.03.016
%U https://doi.org/10.1016/j.mcm.2010.03.016
%P 1258-1264