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:动态成像旨在通过其欠采样测量来恢复每个时间点的时变二维或三维对象。特别是在动态断层扫描的情况下,通常只能在一个方向上获得单个投影,这使得问题非常不适定。在本文中,我们提出了一种方法,RED-PSM,将两种强大的技术首次结合起来,以解决这个具有挑战性的成像问题。首先,使用部分可分模型,为时空对象引入低秩先验,高效地解决问题。其次,使用最近提出的去噪正则化(RED)框架,针对各种反问题利用最先进的图像去噪算法。我们提出了具有 RED 的部分可分目标和变量拆分和 ADMM 的优化方案,并证明了我们的目标收敛到满足一阶最优性条件的静止点对应的值。一种特定的基于投影域的初始化可加速收敛。我们通过将我们的 RED-PSM 与最近的基于深度先验的方法 TD-DIP 进行比较,并通过使用学习的图像去噪器展示了其性能和计算改进。