  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.
