RED-PSM: Regularization by Denoising of Partially Separable Models for Dynamic Imaging

Dynamic imaging involves the recovery of a time-varying 2D or 3D object at each time instant using its undersampled measurements. In particular in 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 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. Our objective is proved to converge 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. Although the emphasis is on dynamic tomography, we also demonstrate the performance advantages of RED-PSM in a dynamic cardiac MRI setting.