Experimental aspects of the approximate error formula for tomographic reconstruction

Computed tomography (CT) has grown in the past few years as an effective tool for nondestructive testing of various types of components and materials. Most CT scanners for this purpose use the convolution backprojection (CBP) algorithm for reconstructing the density function in a cross section of interest. Natterer has developed Sobolev space theorems which predict the theoretical error in CBP for a given class of certain meathematical functions. Recently, Munshi et al. developed a Sobolev space model for CBP to study the theoretical error which incoroporates a theorem to analyze and synthesize the filter functions (or convolvers) for the CBP algorithm. Reconstructions have been performed (from data collected by an X-ray CT scanner) for a test object comprised of 50 µm adhesive tape and 50 µm aluminum foils. The number of data rays is 512, the number of projections is 400, and the pixel size is 20 µm: Reconstructed images with the standard CBP filters follow the trendpredicted by the theory. These results are currently being used to develop special filters for nondestructive characterization of materials