# ADMM-Net: A Deep Learning Approach for Compressive Sensing MRI

arXiv: https://arxiv.org/abs/1705.06869 · HTML: https://mlsanity.com/paper/1705.06869/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 May 2017.

## Built on by (most cited first, 28 of 28)

- [ReconFormer: Accelerated MRI Reconstruction Using Recurrent Transformer](https://mlsanity.com/paper/2201.09376/) (2022)
- [AI-based Reconstruction for Fast MRI -- A Systematic Review and Meta-analysis](https://mlsanity.com/paper/2112.12744/) (2021)
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- [High-Resolution Pelvic MRI Reconstruction Using a Generative Adversarial Network with Attention and Cyclic Loss](https://mlsanity.com/paper/2107.09989/) (2021)
- [ADMM-DAD net: a deep unfolding network for analysis compressed sensing](https://mlsanity.com/paper/2110.06986/) (2021)
- [Jointly Modeling Inter- & Intra-Modality Dependencies for Multi-modal Learning](https://mlsanity.com/paper/2405.17613/) (2024)
- [MEPNet: A Model-Driven Equivariant Proximal Network for Joint Sparse-View Reconstruction and Metal Artifact Reduction in CT Images](https://mlsanity.com/paper/2306.14274/) (2023)
- [Optimization-Derived Learning with Essential Convergence Analysis of Training and Hyper-training](https://mlsanity.com/paper/2206.07875/) (2022)
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- [Robust Physics-based Deep MRI Reconstruction Via Diffusion Purification](https://mlsanity.com/paper/2309.05794/) (2023)
- [Assessment of Data Consistency through Cascades of Independently Recurrent Inference Machines for fast and robust accelerated MRI reconstruction](https://mlsanity.com/paper/2111.15498/) (2021)
- [CSI Feedback with Model-Driven Deep Learning of Massive MIMO Systems](https://mlsanity.com/paper/2112.06405/) (2021)
- [Adaptive Local Neighborhood-based Neural Networks for MR Image Reconstruction from Undersampled Data](https://mlsanity.com/paper/2206.00775/) (2022)
- [Low-rank Tensor Assisted K-space Generative Model for Parallel Imaging Reconstruction](https://mlsanity.com/paper/2212.05503/) (2022)
- [Learned Interferometric Imaging for the SPIDER Instrument](https://mlsanity.com/paper/2301.10260/) (2023)
- [Continuous K-space Recovery Network with Image Guidance for Fast MRI Reconstruction](https://mlsanity.com/paper/2411.11282/) (2024)
- [Deep Learning Techniques for Compressive Sensing-Based Reconstruction and Inference -- A Ubiquitous Systems Perspective](https://mlsanity.com/paper/2105.13191/) (2021)
- [Neural networks with trainable matrix activation functions](https://mlsanity.com/paper/2109.09948/) (2021)
- [Hand Gestures Recognition in Videos Taken with Lensless Camera](https://mlsanity.com/paper/2210.08233/) (2022)
- [Outlier Detection Using Generative Models with Theoretical Performance Guarantees](https://mlsanity.com/paper/2310.09999/) (2023)
- [Reference-Free Image Quality Metric for Degradation and Reconstruction Artifacts](https://mlsanity.com/paper/2405.02208/) (2024)
- [TC-KANRecon: High-Quality and Accelerated MRI Reconstruction via Adaptive KAN Mechanisms and Intelligent Feature Scaling](https://mlsanity.com/paper/2408.05705/) (2024)
- [Dual-domain Multi-path Self-supervised Diffusion Model for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2503.18836/) (2025)
- [Provenance-Driven Reliable Semantic Medical Image Vector Reconstruction via Lightweight Blockchain-Verified Latent Fingerprints](https://mlsanity.com/paper/2512.00999/) (2025)
- [A Study of the Limits of Collaborative DCT-Based Image Denoising via Interpretable Neural Networks](https://mlsanity.com/paper/2609.29334/) (2026)

## Abstract (arXiv)

Compressive sensing (CS) is an effective approach for fast Magnetic Resonance Imaging (MRI). It aims at reconstructing MR images from a small number of under-sampled data in k-space, and accelerating the data acquisition in MRI. To improve the current MRI system in reconstruction accuracy and speed, in this paper, we propose two novel deep architectures, dubbed ADMM-Nets in basic and generalized versions. ADMM-Nets are defined over data flow graphs, which are derived from the iterative procedures in Alternating Direction Method of Multipliers (ADMM) algorithm for optimizing a general CS-based MRI model. They take the sampled k-space data as inputs and output reconstructed MR images. Moreover, we extend our network to cope with complex-valued MR images. In the training phase, all parameters of the nets, e.g., transforms, shrinkage functions, etc., are discriminatively trained end-to-end. In the testing phase, they have computational overhead similar to ADMM algorithm but use optimized parameters learned from the data for CS-based reconstruction task. We investigate different configurations in network structures and conduct extensive experiments on MR image reconstruction under different sampling rates. Due to the combination of the advantages in model-based approach and deep learning approach, the ADMM-Nets achieve state-of-the-art reconstruction accuracies with fast computational speed.