Dynamic imaging addresses the recovery of a time-varying 2D or 3D object at each time instant using its undersampled measurements. In particular, in the case of dynamic tomography, only a single projection at a single view angle may be available at a time, making the problem severely ill-posed. In this work, we propose an approach, RED-PSM, which combines for the first time two powerful techniques to address this challenging imaging problem. The first, are partially separable models, which have been used to efficiently introduce a low-rank prior for the spatio-temporal object. The second is the recent \textit{Regularization by Denoising (RED)}, which provides a flexible framework to exploit the impressive performance of state-of-the-art image denoising algorithms, for various inverse problems. We propose a partially separable objective with RED and a computationally efficient and scalable optimization scheme with variable splitting and ADMM. Theoretical analysis proves the convergence of our objective to a value corresponding to a stationary point satisfying the first-order optimality conditions. Convergence is accelerated by a particular projection-domain-based initialization. We demonstrate the performance and computational improvements of our proposed RED-PSM with a learned image denoiser by comparing it to a recent deep-prior-based method known as TD-DIP. Although the main focus is on dynamic tomography, we also show performance advantages of RED-PSM in a cardiac dynamic MRI setting.

翻译：动态成像旨在利用欠采样测量数据，恢复每个时间点的时变二维或三维物体。特别是在动态断层扫描中，单个时间点可能仅能获取单一视角下的单个投影，导致该问题严重病态。本文提出一种名为RED-PSM的方法，首次将两种强大技术相结合以解决这一成像难题：其一是部分可分离模型，该模型通过引入时空对象的低秩先验实现高效建模；其二是近年提出的去噪正则化（RED，Regularization by Denoising）框架，该框架可灵活利用先进图像去噪算法的卓越性能解决各类逆问题。我们提出了基于RED的部分可分离目标函数，并结合变量分裂与交替方向乘子法（ADMM），构建了计算高效且可扩展的优化方案。理论分析证明，该目标函数可收敛至满足一阶最优性条件的驻点值，且通过基于投影域的初始化加速收敛。通过将学习型图像去噪器与近期基于深度先验的方法TD-DIP进行对比，我们展示了所提RED-PSM在性能与计算效率上的提升。尽管本文主要聚焦于动态断层扫描，但我们亦证明了RED-PSM在心脏动态磁共振成像场景中的性能优势。