Sparse Givens resolution of large system of linear equations: Applications to image reconstruction

  • Authors:

  • MaríA-José RodríGuez-Alvarez;Filomeno SáNchez;Antonio Soriano;Amadeo Iborra

  • Affiliations:

  • Instituto de Matemática Multidisciplinar, Universidad Politécnica de Valencia, Building 8G (2 Floor), Camino de Vera, E-46022 Valencia, Spain;IFIC, Centro mixto CSIC-Univ. de Valencia, Edificio Institutos de Investigación, Paterna, E-46071 Valencia, Spain;IFIC, Centro mixto CSIC-Univ. de Valencia, Edificio Institutos de Investigación, Paterna, E-46071 Valencia, Spain;Instituto de Matemática Multidisciplinar, Universidad Politécnica de Valencia, Building 8G (2 Floor), Camino de Vera, E-46022 Valencia, Spain

  • Venue:
  • Mathematical and Computer Modelling: An International Journal
  • Year:
  • 2010

Quantified Score

Hi-index 0.98

Visualization

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.