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

arXiv: https://arxiv.org/abs/2304.03483 · HTML: https://mlsanity.com/paper/2304.03483/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 140 references that are in the map.
- First posted on arXiv 7 Apr 2023.

## Builds on (most cited first, 30 of 35)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- [A Deep Cascade of Convolutional Neural Networks for Dynamic MR Image Reconstruction](https://mlsanity.com/paper/1704.02422/) (2017)
- [FILM: Frame Interpolation for Large Motion](https://mlsanity.com/paper/2202.04901/) (2022)
- [Gradient Step Denoiser for convergent Plug-and-Play](https://mlsanity.com/paper/2110.03220/) (2021)
- [Convolutional Recurrent Neural Networks for Dynamic MR Image Reconstruction](https://mlsanity.com/paper/1712.01751/) (2017)
- [Regularization by Denoising: Clarifications and New Interpretations](https://mlsanity.com/paper/1806.02296/) (2018)
- [Global Convergence of ADMM in Nonconvex Nonsmooth Optimization](https://mlsanity.com/paper/1511.06324/) (2015)
- [Plug-and-Play Methods for Integrating Physical and Learned Models in Computational Imaging](https://mlsanity.com/paper/2203.17061/) (2022)
- [DeepRED: Deep Image Prior Powered by RED](https://mlsanity.com/paper/1903.10176/) (2019)
- [Time-Dependent Deep Image Prior for Dynamic MRI](https://mlsanity.com/paper/1910.01684/) (2019)
- [Plug-and-Play Unplugged: Optimization Free Reconstruction using Consensus Equilibrium](https://mlsanity.com/paper/1705.08983/) (2017)
- [Generalized Low Rank Models](https://mlsanity.com/paper/1410.0342/) (2014)
- [Regularization by Denoising via Fixed-Point Projection (RED-PRO)](https://mlsanity.com/paper/2008.00226/) (2020)
- [prDeep: Robust Phase Retrieval with a Flexible Deep Network](https://mlsanity.com/paper/1803.00212/) (2018)
- [Provable Convergence of Plug-and-Play Priors with MMSE denoisers](https://mlsanity.com/paper/2005.07685/) (2020)
- [Block Coordinate Regularization by Denoising](https://mlsanity.com/paper/1905.05113/) (2019)
- [DIMENSION: Dynamic MR Imaging with Both K-space and Spatial Prior Knowledge Obtained via Multi-Supervised Network Training](https://mlsanity.com/paper/1810.00302/) (2018)
- [A Cone-Beam X-Ray CT Data Collection designed for Machine Learning](https://mlsanity.com/paper/1905.04787/) (2019)
- [Spatial-Temporal Transformer for Video Snapshot Compressive Imaging](https://mlsanity.com/paper/2209.01578/) (2022)
- [Real-time Cardiovascular MR with Spatio-temporal Artifact Suppression using Deep Learning - Proof of Concept in Congenital Heart Disease](https://mlsanity.com/paper/1803.05192/) (2018)
- [Dynamic imaging using a deep generative SToRM (Gen-SToRM) model](https://mlsanity.com/paper/2102.00034/) (2021)
- [LAPNet: Non-rigid Registration derived in k-space for Magnetic Resonance Imaging](https://mlsanity.com/paper/2107.09060/) (2021)
- [Multi-Slice Fusion for Sparse-View and Limited-Angle 4D CT Reconstruction](https://mlsanity.com/paper/2008.01567/) (2020)
- [Deep Manifold Learning for Dynamic MR Imaging](https://mlsanity.com/paper/2104.01102/) (2021)
- [PnP-ReG: Learned Regularizing Gradient for Plug-and-Play Gradient Descent](https://mlsanity.com/paper/2204.13940/) (2022)
- [Deformation corrected compressed sensing (DC-CS): a novel framework for accelerated dynamic MRI](https://mlsanity.com/paper/1405.7718/) (2014)
- [Low-rank and Adaptive Sparse Signal (LASSI) Models for Highly Accelerated Dynamic Imaging](https://mlsanity.com/paper/1611.04069/) (2016)

## Built on by (most cited first, 2 of 2)

- [RSR-NF: Neural Field Regularization by Static Restoration Priors for Dynamic Imaging](https://mlsanity.com/paper/2503.10015/) (2025)
- [DYRECT Computed Tomography: DYnamic Reconstruction of Events on a Continuous Timescale](https://mlsanity.com/paper/2412.00065/) (2024)

## Abstract (arXiv)

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.