# RSR-NF: Neural Field Regularization by Static Restoration Priors for Dynamic Imaging

arXiv: https://arxiv.org/abs/2503.10015 · HTML: https://mlsanity.com/paper/2503.10015/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 83 references that are in the map.
- First posted on arXiv 13 Mar 2025.

## Builds on (most cited first, 30 of 41)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Nerfies: Deformable Neural Radiance Fields](https://mlsanity.com/paper/2011.12948/) (2020)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Neural Scene Flow Fields for Space-Time View Synthesis of Dynamic Scenes](https://mlsanity.com/paper/2011.13084/) (2020)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [Dynamic View Synthesis from Dynamic Monocular Video](https://mlsanity.com/paper/2105.06468/) (2021)
- [Space-time Neural Irradiance Fields for Free-Viewpoint Video](https://mlsanity.com/paper/2011.12950/) (2020)
- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- [Neural Radiance Flow for 4D View Synthesis and Video Processing](https://mlsanity.com/paper/2012.09790/) (2020)
- [Inversion by Direct Iteration: An Alternative to Denoising Diffusion for Image Restoration](https://mlsanity.com/paper/2303.11435/) (2023)
- [NeRP: Implicit Neural Representation Learning with Prior Embedding for Sparsely Sampled Image Reconstruction](https://mlsanity.com/paper/2108.10991/) (2021)
- [Regularization by Denoising: Clarifications and New Interpretations](https://mlsanity.com/paper/1806.02296/) (2018)
- [A Structured Dictionary Perspective on Implicit Neural Representations](https://mlsanity.com/paper/2112.01917/) (2021)
- [Plug-and-Play Methods for Integrating Physical and Learned Models in Computational Imaging](https://mlsanity.com/paper/2203.17061/) (2022)
- [Neural Trajectory Fields for Dynamic Novel View Synthesis](https://mlsanity.com/paper/2105.05994/) (2021)
- [DeepRED: Deep Image Prior Powered by RED](https://mlsanity.com/paper/1903.10176/) (2019)
- [Dynamic CT Reconstruction from Limited Views with Implicit Neural Representations and Parametric Motion Fields](https://mlsanity.com/paper/2104.11745/) (2021)
- [Time-Dependent Deep Image Prior for Dynamic MRI](https://mlsanity.com/paper/1910.01684/) (2019)
- [RARE: Image Reconstruction using Deep Priors Learned without Ground Truth](https://mlsanity.com/paper/1912.05854/) (2019)
- [Recovery of Continuous 3D Refractive Index Maps from Discrete Intensity-Only Measurements using Neural Fields](https://mlsanity.com/paper/2112.00002/) (2021)
- [prDeep: Robust Phase Retrieval with a Flexible Deep Network](https://mlsanity.com/paper/1803.00212/) (2018)
- [Spatiotemporal implicit neural representation for unsupervised dynamic MRI reconstruction](https://mlsanity.com/paper/2301.00127/) (2022)
- [Neural Implicit k-Space for Binning-free Non-Cartesian Cardiac MR Imaging](https://mlsanity.com/paper/2212.08479/) (2022)
- [Block Coordinate Regularization by Denoising](https://mlsanity.com/paper/1905.05113/) (2019)
- [A Cone-Beam X-Ray CT Data Collection designed for Machine Learning](https://mlsanity.com/paper/1905.04787/) (2019)
- [Dynamic imaging using a deep generative SToRM (Gen-SToRM) model](https://mlsanity.com/paper/2102.00034/) (2021)
- [Partition of unity networks: deep hp-approximation](https://mlsanity.com/paper/2101.11256/) (2021)
- [Implicit Neural Networks with Fourier-Feature Inputs for Free-breathing Cardiac MRI Reconstruction](https://mlsanity.com/paper/2305.06822/) (2023)

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

- [Continuous Representation Methods, Theories, and Applications: An Overview and Perspectives](https://mlsanity.com/paper/2505.15222/) (2025)
- [Splannequin: Freezing Monocular Mannequin-Challenge Footage with Dual-Detection Splatting](https://mlsanity.com/paper/2512.05113/) (2025)

## Abstract (arXiv)

Dynamic imaging involves the reconstruction of a spatio-temporal object at all times using its undersampled measurements. In particular, in dynamic computed tomography (dCT), only a single projection at one view angle is available at a time, making the inverse problem very challenging. Moreover, ground-truth dynamic data is usually either unavailable or too scarce to be used for supervised learning techniques. To tackle this problem, we propose RSR-NF, which uses a neural field (NF) to represent the dynamic object and, using the Regularization-by-Denoising (RED) framework, incorporates an additional static deep spatial prior into a variational formulation via a learned restoration operator. We use an ADMM-based algorithm with variable splitting to efficiently optimize the variational objective. We compare RSR-NF to three alternatives: NF with only temporal regularization; a recent method combining a partially-separable low-rank representation with RED using a denoiser pretrained on static data; and a deep-image prior-based model. The first comparison demonstrates the reconstruction improvements achieved by combining the NF representation with static restoration priors, whereas the other two demonstrate the improvement over state-of-the art techniques for dCT.