Robust iterative methods: Convergence and applications to proton computed tomography

Abstract

Robust methods, such as Tikhonov regularization and Bounded data uncertainty, have been used extensively in relatively small problems involving dense matrices for many decades, but have not been used in large-scale iterative methods for image reconstruction in particle imaging until recently. In this case, robust methods may allow more accurate reconstruction of images in the presence of errors of both the energy measurement of the protons and ions but also in the estimated path taken by the proton or ion through the object. Robust systems may also be used when entire blocks of data are missing, or in low-dose reconstructions using a very small number of particles without substantial loss of image quality. In this contribution, we demonstrate that robust methods show great promise in proton/ion (particle) computed tomography (pCT), and, for the first time, that they can be proven to converge. Thus, the convergence of robust methods as well as benefits for reconstruction in uncertain systems is shown to constitute the main advantage for pCT reconstruction.