A comparative study between matched and mis-matched projection/back projection pairs used with ASIRT reconstruction method

For algebraic reconstruction techniques both forward and back projection operators are needed. The ability to perform accurate reconstruction relies fundamentally on the forward projection and back projection methods which are usually, the transpose of each other. Even though the mis-matched pairs may introduce additional errors during the iterative process, the usefulness of mis-matched projector/back projector pairs has been proved in image reconstruction. This work investigates the performance of matched and mis-matched reconstruction pairs using popular forward projectors and their transposes when used in reconstruction tasks with additive simultaneous iterative reconstruction techniques (ASIRT) in a parallel beam approach. Simulated noiseless phantoms are used to compare the performance of the investigated pairs in terms of the root mean squared errors (RMSE) which are calculated between reconstructed slices and the reference in different regions. Results show that mis-matched projection/back projection pairs can promise more accuracy of reconstructed images than matched ones. The forward projection operator performance seems independent of the choice of the back projection operator and vice versa.