Unmatched projector/backprojector pairs in an iterative reconstruction algorithm

Abstract

Computational burden is a major concern when an iterative algorithm is used to reconstruct a three-dimensional (3-D) image with attenuation, detector response, and scatter corrections. Most of the computation time is spent executing the projector and backprojector of an iterative algorithm. Usually, the projector and the backprojector are transposed operators of each other. The projector should model the imaging geometry and physics as accurately as possible. Some researchers have used backprojectors that are computationally less expensive than the projectors to reduce computation time. This paper points out that valid backprojectors should satisfy a condition that the projector/backprojector matrix must not contain negative eigenvalues. This paper also investigates the effects when unmatched projector/backprojector pairs are used.

PET iterative reconstruction incorporating an efficient positron range correction method

“…The effect of including positron blurring in both forward and backward projection operations is investigated in [23], where it is shown that the use of positron blurring during backprojection has a smoothing effect on the reconstructed image leading to a delayed convergence, requiring a large number of iterations to reach a comparable detail level. Furthermore in [24] it is shown that MLEM algorithms demonstrate first a short convergent trend but then deviates from the desired solution, independent from the projector/backprojector pair matching. The authors concluded that the concrete choice for the backprojector may not be a very critical factor in a practical image reconstruction problem.…”

Easy implementation of advanced tomography algorithms using the ASTRA toolbox with Spot operators

“…(4) and (5). However, it was shown that an unmatched forward and backprojector can even improve convergence rates of reconstruction algorithms [19,37].…”

Study of CT-based positron range correction in high resolution 3D PET imaging

“…Indeed, positron range blurring is only taken into account in the projection operation. This approach has been used in several works [14,15] where it is shown that good reconstructed images can be attained with full modeling of blurring effects during the projection step, whereas a simplified modeling is employed into the backprojector.…”