Convergence of wavelet series and applications to computerized tomography

Abstract

In computerized tomography, an image must be recovered from datagiven by the Radon transform of the image. This data is usually in the form ofsampled values of the transform. In this paper we have proved some convergenceresults in generalized Sobolev space using the sampling properties of the prolatespheroidal wavelets which are superior to other wavelets. Our generalized Sobolevspace generalized the various spaces such as Schwartz space, Hormander space[5] andspace studied by Pathak[10].