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 A X = B . In this paper we propose the Q R decomposition as a direct method to solve the linear system. Q R 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 Q R decomposition in order to take more advantage of the sparsity of the system matrix is discussed.