RED-PSM: Regularization by Denoising of Factorized Low Rank Models for Dynamic Imaging

• URL: http://arxiv.org/abs/2304.03483v4
• Date: Tue, 7 May 2024 18:14:23 GMT
• Title: RED-PSM: Regularization by Denoising of Factorized Low Rank Models for Dynamic Imaging
• Authors: Berk Iskender, Marc L. Klasky, Yoram Bresler,
• Abstract summary: In dynamic tomography, only a single projection at a single view angle may be available at a time. We propose an approach, RED-PSM, which combines for the first time two powerful techniques to address this challenging imaging problem.
• Score: 6.527016551650136
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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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