Reconstruction of real tomographic data using algebraic methods

We propose an algebraic image reconstruction method that can cope with the size and features of datasets produced by actual scanners, such as angular flying focal spot and detector offset. Image reconstruction is performed by minimizing a penalized least squares objective function by means of a preconditioned conjugate gradient (PCG) algorithm. Efficient implementation of the matrix-vector products that represent projection and backprojection operations is crucial to reconstruction speed, as such operations are performed at least once per iteration. For this purpose, we developed an efficient storage scheme for the projection matrix that allowed fast matrix-vector products. These features, along with an appropriate choice of the preconditioning matrix, yielded a numerically efficient method which produces results with better quality than those provided by usual filtered backprojection techniques.