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

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=BAX=B. In this paper we propose the QRQR decomposition as a direct method to solve the linear system. QRQR decomposition can be a large computational procedure. However, once it has been calculated for a specific system, matrices QQ and RR are stored and used for any acquired projection on that system. Implementation of the QRQR decomposition in order to take more advantage of the sparsity of the system matrix is discussed.