RED-PSM：用于动态成像的分解低秩模型去噪正则化
RED-PSM: Regularization by Denoising of Factorized Low Rank Models for Dynamic Imaging
AI总结：
本文提出 RED-PSM，将部分可分低秩模型与去噪正则化结合，并通过变量分裂和 ADMM 求解，显著提升动态断层成像及心脏动态 MRI 的重建性能。
摘要：
动态成像旨在利用欠采样测量恢复每个时刻随时间变化的二维或三维物体。特别是在动态断层成像中，某一时刻可能仅有单一视角下的单幅投影可用，导致该问题具有严重的不适定性。我们提出了 RED-PSM 方法，首次结合两种强大技术来应对这一具有挑战性的成像问题。第一种技术是非参数化分解低秩模型，也称为部分可分模型（PSM），已被用于为时空对象高效引入低秩先验。第二种技术是近期提出的去噪正则化（RED），它为在各类逆问题中利用最先进图像去噪算法的出色性能提供了灵活框架。我们提出了结合 RED 的部分可分目标函数，以及采用变量分裂和 ADMM 的计算高效且可扩展的优化方案。理论分析证明，我们的目标函数会收敛到与满足一阶最优性条件的驻点相对应的值。一种特定的基于投影域的初始化方法可加速收敛。通过将所提出的采用学习型图像去噪器的 RED-PSM 与近期名为 TD-DIP 的深度先验方法进行比较，我们展示了其性能和计算效率提升。尽管主要关注动态断层成像，我们还展示了 RED-PSM 在心脏动态 MRI 场景中的性能优势。
英文摘要：
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. We propose an approach, RED-PSM, which combines for the first time two powerful techniques to address this challenging imaging problem. The first, are non-parametric factorized low rank models, also known as partially separable models (PSMs), 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 performance advantages of RED-PSM in a cardiac dynamic MRI setting.
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