Tikhonov Regularization in Image Reconstruction with Kaczmarz Extended Algorithm

In a previous paper we proposed a simple and natural extension of Kaczmarz’s projection algorithm (KE, for short) to inconsistent least-squares problems arising in ART image reconstruction in computerized tomography. In the present one we describe two versions of this extension for a Tikhonov regularization of the original inconsistent least-squares problem. The first version deals directly with an (augmented) equivalent formulation of the Tikhonov regularization problem, whereas the second one uses the gradient of the Tikhonov regularized functional. For both new versions of the KE algorithm we present some theoretical considerations together with numerical experiments and comparisons with the initial KE method.