A study of errors due to reconstruction filters in computed tomography

In the summation convolution backprojection method of image reconstruction in computed tomography, the final image accuracy depends on the convolution filter used. Filters are designed to attenuate high spatial frequencies when noisy projection data are used. This paper explores the differences between the images reconstructed using a range of filters, and compares the results with the case of the ramp filter that provides the “best” image for ideal, noise-free, projection data. It is shown that systematic errors between these images and the best image exist, and that these errors are related to the second differential of the reconstruction filter with respect to spatial frequency. This error determination may be used to correct computed tomography images that have been reconstructed using inappropriate filters, and this theory is tested using noise-free projection data from two computer simulated images. It is shown that the corrected images are far closer to the original images.