A convolution back projection algorithm for local tomography

Abstract

The present work deals with the problem of recovering a local image from localised projections using the concept of approximation identity. It is based on the observation that the Hubert transform of an approximation identity taken from a certain class of compactly supported functions with sufficiently many zero moments has no significant spread of support. The associated algorithm uses data pertaining to the local region along with a small amount of data from its vicinity. The main features of the algorithm are simplicity and similarity with standard filtered back projection (FBP) along with the economic use of data. © Australian Mathematical Society 2005.