Fast Large-Scale Model-Based Iterative Tomography via Exploiting Mathematical Structure, Hierarchical Optimization, Smart Initialization, and Distributed GPU Computing
2026-03-30 • Mathematical Software
Mathematical Software
AI summaryⓘ
The authors improved a method called Model-Based Iterative Reconstruction (MBIR), which produces clearer images from limited data but usually takes a long time to compute. They made the math faster by using special Fourier techniques and running the work on multiple GPUs and computers at once. Their new approach also starts with a better initial guess and gradually refines the image from rough to detailed. These changes help make fast, high-quality imaging possible for experiments that change over time.
Model-Based Iterative ReconstructionRadon transformFiltered Back-ProjectionNon-uniform Fast Fourier TransformGPU parallel computingMulti-resolution reconstructionToeplitz structureMPI (Message Passing Interface)Sparse-angle tomographyHigh-performance computing
Authors
Dinesh Kumar, Jeffrey Donatelli
Abstract
Model-Based Iterative Reconstruction (MBIR) is important because direct methods, such as Filtered Back-Projection (FBP) can introduce significant noise and artifacts in sparse-angle tomography, especially for time-evolving samples. Although MBIR produces high-quality reconstructions through prior-informed optimization, its computational cost has traditionally limited its broader adoption. In previous work, we addressed this limitation by expressing the Radon transform and its adjoint using non-uniform fast Fourier transforms (NUFFTs), reducing computational complexity relative to conventional projection-based methods. We further accelerated computation by employing a multi-GPU system for parallel processing. In this work, we further accelerate our Fourier-domain framework, by introducing four main strategies: (1) a reformulation of the MBIR forward and adjoint operators that exploits their multi-level Toeplitz structure for efficient Fourier-domain computation; (2) an improved initialization strategy that uses back-projected data filtered with a standard ramp filter as the starting estimate; (3) a hierarchical multi-resolution reconstruction approach that first solves the problem on coarse grids and progressively transitions to finer grids using Lanczos interpolation; and (4) a distributed-memory implementation using MPI that enables near-linear scaling on large high-performance computing (HPC) systems. Together, these innovations significantly reduce iteration counts, improve parallel efficiency, and make high-quality MBIR reconstruction practical for large-scale tomographic imaging. These advances open the door to near-real-time MBIR for applications such as in situ, in operando, and time-evolving experiments.