Projection algorithms with correction

We present in this paper two versions of a general correction procedure applied to a classical iterative method, which gives us the possibility, under certain assumptions, to obtain an extension of it to inconsistent linear least-squares problems. We prove that some well known extended projection type algorithms from image reconstruction in computerized tomography fit into one or the other of these general versions and are derived as particular cases of them. We also present some numerical experiments on two phantoms widely used in image reconstruction literature. The experiments show the importance of this correction procedure, reflected in the quality of reconstructed images. 2000 MS Classification: 65F10, 65F20