Fast Large-Scale Model-Based Iterative Tomography via Exploiting Mathematical Structure, Hierarchical Optimization, Smart Initialization, and Distributed GPU Computing

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.