Optimal short scan convolution reconstruction for fan beam CT

The problem of using a divergent fan beam convolution reconstruction algorithm in conjunction with a minimal complete (180 degrees plus the fan angle) data set is reviewed. It is shown that by proper weighting of the initial data set, image quality essentially equivalent to the quality of reconstructions from 360 degrees data sets is obtained. The constraints on the weights are that the sum of the two weights corresponding to the same line-integral must equal one, in regions of no data the weights must equal zero, and the weights themselves as well as the gradient of the weights must be continuous over the full 360 degrees. After weighting the initial data with weights that satisfy these constraints, image reconstruction can be conveniently achieved by using the standard (hardwired if available) convolver and backprojector of the specific scanner.