# Time-Embedded Algorithm Unrolling for Computational MRI

arXiv: https://arxiv.org/abs/2510.16321 · HTML: https://mlsanity.com/paper/2510.16321/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 72 references that are in the map.
- First posted on arXiv 18 Oct 2025.

## Builds on (most cited first, 30 of 39)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [The Perception-Distortion Tradeoff](https://mlsanity.com/paper/1711.06077/) (2017)
- [fastMRI: An Open Dataset and Benchmarks for Accelerated MRI](https://mlsanity.com/paper/1811.08839/) (2018)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [MoDL: Model Based Deep Learning Architecture for Inverse Problems](https://mlsanity.com/paper/1712.02862/) (2017)
- [Learning a Variational Network for Reconstruction of Accelerated MRI Data](https://mlsanity.com/paper/1704.00447/) (2017)
- [Robust Compressed Sensing MRI with Deep Generative Priors](https://mlsanity.com/paper/2108.01368/) (2021)
- [Learned Primal-dual Reconstruction](https://mlsanity.com/paper/1707.06474/) (2017)
- [A Deep Cascade of Convolutional Neural Networks for Dynamic MR Image Reconstruction](https://mlsanity.com/paper/1704.02422/) (2017)
- [Decomposed Diffusion Sampler for Accelerating Large-Scale Inverse Problems](https://mlsanity.com/paper/2303.05754/) (2023)
- [Deep learning for undersampled MRI reconstruction](https://mlsanity.com/paper/1709.02576/) (2017)
- [Deep Learning Methods for Parallel Magnetic Resonance Image Reconstruction](https://mlsanity.com/paper/1904.01112/) (2019)
- [AMP-Net: Denoising based Deep Unfolding for Compressive Image Sensing](https://mlsanity.com/paper/2004.10078/) (2020)
- [Learned D-AMP: Principled Neural Network based Compressive Image Recovery](https://mlsanity.com/paper/1704.06625/) (2017)
- [Advancing machine learning for MR image reconstruction with an open competition: Overview of the 2019 fastMRI challenge](https://mlsanity.com/paper/2001.02518/) (2020)
- [Zero-Shot Self-Supervised Learning for MRI Reconstruction](https://mlsanity.com/paper/2102.07737/) (2021)
- [Physics-Driven Deep Learning for Computational Magnetic Resonance Imaging](https://mlsanity.com/paper/2203.12215/) (2022)
- [Neural Proximal Gradient Descent for Compressive Imaging](https://mlsanity.com/paper/1806.03963/) (2018)
- [VS-Net: Variable splitting network for accelerated parallel MRI reconstruction](https://mlsanity.com/paper/1907.10033/) (2019)
- [U-Nets as Belief Propagation: Efficient Classification, Denoising, and Diffusion in Generative Hierarchical Models](https://mlsanity.com/paper/2404.18444/) (2024)

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

- [UMPIRE-Net: Unrolled Magnitude-Phase Regularization Network for Accelerated MRI](https://mlsanity.com/paper/2608.14422/) (2026)
- [Harnessing Magnitude-Only and Complex Measurements for Improved Dynamic MRI Reconstruction with Learned Priors](https://mlsanity.com/paper/2608.18036/) (2026)

## Abstract (arXiv)

Algorithm unrolling methods have proven powerful for solving the regularized least squares problem in computational magnetic resonance imaging (MRI). These approaches unfold an iterative algorithm with a fixed number of iterations, typically alternating between a neural network-based proximal operator for regularization, a data fidelity operation and auxiliary updates with learnable parameters. While the connection to optimization methods dictate that the proximal operator network should be shared across unrolls, this can introduce artifacts or blurring. Heuristically, practitioners have shown that using distinct networks may be beneficial, but this significantly increases the number of learnable parameters, making it challenging to prevent overfitting. To address these shortcomings, by taking inspirations from proximal operators with varying thresholds in approximate message passing (AMP) and the success of time-embedding in diffusion models, we propose a time-embedded algorithm unrolling scheme for inverse problems. Specifically, we introduce a novel perspective on the iteration-dependent proximal operation in vector AMP (VAMP) and the subsequent Onsager correction in the context of algorithm unrolling, framing them as a time-embedded neural network. Similarly, the scalar weights in the data fidelity operation and its associated Onsager correction are cast as time-dependent learnable parameters. Our extensive experiments on the fastMRI dataset, spanning various acceleration rates and datasets, demonstrate that our method effectively reduces aliasing artifacts and mitigates noise amplification, achieving state-of-the-art performance. Furthermore, we show that our time-embedding strategy extends to existing algorithm unrolling approaches, enhancing reconstruction quality without increasing the computational complexity significantly.