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 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 the 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值恢复每个时间点的时变二维或三维物体。特别在动态断层扫描中，每个时刻可能仅能获取单个视角下的单张投影，这使得该问题严重病态。本研究首次提出RED-PSM方法，融合两种强大技术解决这一挑战性成像问题。第一种是部分可分离模型，该方法通过引入时空对象的低秩先验实现高效建模；第二种是近年提出的去噪正则化（RED）框架，该框架可灵活利用前沿图像去噪算法的卓越性能解决各类逆问题。我们构建了基于RED的部分可分离目标函数，并结合变量分裂与ADMM算法提出计算高效且可扩展的优化方案。理论分析证明，该目标函数收敛于满足一阶最优性条件的驻点。通过基于投影域的特定初始化策略可加速收敛。通过与近期基于深度先验的TD-DIP方法对比，我们验证了采用学习型图像去噪器的RED-PSM在性能与计算效率上的提升。尽管研究重点聚焦动态断层扫描，我们也展示了RED-PSM在心脏动态MRI场景中的性能优势。