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 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 an optimization scheme with variable splitting and ADMM, and prove 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 TD-DIP.

翻译：动态成像旨在利用欠采样测量值恢复每个时刻随时间变化的二维或三维对象。特别是在动态断层扫描中，每次可能仅能获取单个视角下的单一投影，导致该问题严重病态。本文提出RED-PSM方法，首次结合两种强大技术应对这一成像挑战：其一是部分可分离模型，已用于高效引入时空对象的低秩先验；其二是最新的去噪正则化（RED），为各类逆问题提供灵活框架，充分挖掘先进图像去噪算法的优异性能。我们构建了带RED约束的部分可分离目标函数，并采用变量分裂与ADMM的优化方案，同时证明目标函数可收敛至满足一阶最优条件的驻点对应值。通过基于投影域的特定初始化策略加速收敛。我们通过将学习型图像去噪器与近期深度先验方法TD-DIP进行对比，展示了RED-PSM方法的性能提升与计算效率改进。