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.

翻译：基于模型的迭代重建（MBIR）之所以重要，是因为滤波反投影（FBP）等直接方法在稀疏角度断层成像中（尤其是针对时变样本）会引入显著的噪声和伪影。尽管MBIR通过先验引导的优化能够产生高质量的重建结果，但其计算成本传统上限制了其更广泛的应用。在先前的工作中，我们通过使用非均匀快速傅里叶变换（NUFFT）来表达Radon变换及其伴随算子，从而降低了相对于传统基于投影方法的计算复杂度，解决了这一限制。我们还通过采用多GPU系统进行并行处理进一步加速了计算。在本工作中，我们通过引入四种主要策略来进一步加速傅里叶域框架：（1）重新表述MBIR正演算子与伴随算子，利用其多层Toeplitz结构实现高效的傅里叶域计算；（2）改进初始化策略，使用经过标准斜坡滤波器滤波的反投影数据作为初始估计；（3）采用分层多分辨率重建方法，先在粗网格上求解问题，再通过Lanczos插值逐步过渡到更细的网格；（4）使用MPI实现分布式内存计算，在大型高性能计算（HPC）系统上实现近乎线性的扩展性。这些创新共同显著减少了迭代次数，提高了并行效率，并使高质量MBIR重建在大规模断层成像中变得实用。这些进展为近实时MBIR在诸如原位、操作中及时变实验等应用领域打开了大门。