A preprocessor for geotomographic imaging of irregular geometric scans

Abstract

An algorithm that acts as a preprocessor to the straight ray algebraic reconstruction technique (ART) algorithm, for the purpose of dealing with nonrectangular scanning geometries, is described. The mathematics of ART in its elementary form is reviewed, showing how the discretization of the rectangular scanning space defines quantities in the projection matrix of the algorithm. A triangular discretization approach for the scanning space that allows nonrectangular or twisted plane geometries to be addressed is proposed, and the effect of this approach on the projection matrix is discussed. An algorithm for determining the projection matrix under these discretization conditions is described, followed by some commentary on its computer implementation. The performance of this preprocessor algorithm, working with standard ART, in reconstructing various synthetic images is demonstrated. >