Exploration of Differentiability in a Proton Computed Tomography Simulation Framework
Abstract
Objective. Algorithmic differentiation (AD) can be a useful technique to numerically optimize design and algorithmic parameters by, and quantify uncertainties in, computer simulations. However, the effectiveness of AD depends on how "well-linearizable" the software is. In this study, we assess how promising derivative information of a typical proton computed tomography (pCT) scan computer simulation is for the aforementioned applications. Approach. This study is mainly based on numerical experiments, in which we repeatedly evaluate three representative computational steps with perturbed input values. We support our observations with a review of the algorithmic steps and arithmetic operations performed by the software, using debugging techniques. Main results. The model-based iterative reconstruction (MBIR) subprocedure (at the end of the software pipeline) and the Monte Carlo (MC) simulation (at the beginning) were piecewise differentiable. Jumps in the MBIR function arose from the discrete computation of the set of voxels intersected by a proton path. Jumps in the MC function likely arose from changes in the control flow that affect the amount of consumed random numbers. The tracking algorithm solves an inherently non-differentiable problem. Significance. The MC and MBIR codes are ready for the integration of AD, and further research on surrogate models for the tracking subprocedure is necessary.
Cite
@article{arxiv.2202.05551,
title = {Exploration of Differentiability in a Proton Computed Tomography Simulation Framework},
author = {Max Aehle and Johan Alme and Gergely Gábor Barnaföldi and Johannes Blühdorn and Tea Bodova and Vyacheslav Borshchov and Anthony van den Brink and Viljar Eikeland and Gregory Feofilov and Christoph Garth and Nicolas R. Gauger and Ola Grøttvik and Håvard Helstrup and Sergey Igolkin and Ralf Keidel and Chinorat Kobdaj and Tobias Kortus and Lisa Kusch and Viktor Leonhardt and Shruti Mehendale and Raju Ningappa Mulawade and Odd Harald Odland and George O'Neill and Gábor Papp and Thomas Peitzmann and Helge Egil Seime Pettersen and Pierluigi Piersimoni and Rohit Pochampalli and Maksym Protsenko and Max Rauch and Attiq Ur Rehman and Matthias Richter and Dieter Röhrich and Max Sagebaum and Joshua Santana and Alexander Schilling and Joao Seco and Arnon Songmoolnak and Ákos Sudár and Ganesh Tambave and Ihor Tymchuk and Kjetil Ullaland and Monika Varga-Kofarago and Lennart Volz and Boris Wagner and Steffen Wendzel and Alexander Wiebel and RenZheng Xiao and Shiming Yang and Sebastian Zillien},
journal= {arXiv preprint arXiv:2202.05551},
year = {2023}
}
Comments
27 pages, 11 figures