# Progressive Divide-and-Conquer via Subsampling Decomposition for Accelerated MRI

arXiv: https://arxiv.org/abs/2403.10064 · HTML: https://mlsanity.com/paper/2403.10064/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 46 references that are in the map.
- First posted on arXiv 15 Mar 2024.

## Builds on (most cited first, 21 of 21)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [SwinIR: Image Restoration Using Swin Transformer](https://mlsanity.com/paper/2108.10257/) (2021)
- [MoDL: Model Based Deep Learning Architecture for Inverse Problems](https://mlsanity.com/paper/1712.02862/) (2017)
- [Robust Compressed Sensing MRI with Deep Generative Priors](https://mlsanity.com/paper/2108.01368/) (2021)
- [Deep Unfolding Network for Image Super-Resolution](https://mlsanity.com/paper/2003.10428/) (2020)
- [End-to-End Variational Networks for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2004.06688/) (2020)
- [Deep Generalized Unfolding Networks for Image Restoration](https://mlsanity.com/paper/2204.13348/) (2022)
- [A Deep Cascade of Convolutional Neural Networks for MR Image Reconstruction](https://mlsanity.com/paper/1703.00555/) (2017)
- [DuDoRNet: Learning a Dual-Domain Recurrent Network for Fast MRI Reconstruction with Deep T1 Prior](https://mlsanity.com/paper/2001.03799/) (2020)
- [On hallucinations in tomographic image reconstruction](https://mlsanity.com/paper/2012.00646/) (2020)
- [ReconFormer: Accelerated MRI Reconstruction Using Recurrent Transformer](https://mlsanity.com/paper/2201.09376/) (2022)
- [KiU-Net: Towards Accurate Segmentation of Biomedical Images using Over-complete Representations](https://mlsanity.com/paper/2006.04878/) (2020)
- [Recurrent Variational Network: A Deep Learning Inverse Problem Solver applied to the task of Accelerated MRI Reconstruction](https://mlsanity.com/paper/2111.09639/) (2021)
- [HUMUS-Net: Hybrid unrolled multi-scale network architecture for accelerated MRI reconstruction](https://mlsanity.com/paper/2203.08213/) (2022)
- [Over-and-Under Complete Convolutional RNN for MRI Reconstruction](https://mlsanity.com/paper/2106.08886/) (2021)
- [Model Learning: Primal Dual Networks for Fast MR imaging](https://mlsanity.com/paper/1908.02426/) (2019)
- [Deep J-Sense: Accelerated MRI Reconstruction via Unrolled Alternating Optimization](https://mlsanity.com/paper/2103.02087/) (2021)
- [Fill the K-Space and Refine the Image: Prompting for Dynamic and Multi-Contrast MRI Reconstruction](https://mlsanity.com/paper/2309.13839/) (2023)
- [Unfolded Deep Kernel Estimation for Blind Image Super-resolution](https://mlsanity.com/paper/2203.05568/) (2022)
- [Efficient Blind Compressed Sensing Using Sparsifying Transforms with Convergence Guarantees and Application to MRI](https://mlsanity.com/paper/1501.02923/) (2015)

## Built on by (most cited first, 13 of 13)

- [Single-Image Shadow Removal Using Deep Learning: A Comprehensive Survey](https://mlsanity.com/paper/2407.08865/) (2024)
- [Temporal As a Plugin: Unsupervised Video Denoising with Pre-Trained Image Denoisers](https://mlsanity.com/paper/2409.11256/) (2024)
- [Reconciling Stochastic and Deterministic Strategies for Zero-shot Image Restoration using Diffusion Model in Dual](https://mlsanity.com/paper/2503.01288/) (2025)
- [RF4D:Neural Radar Fields for Novel View Synthesis in Outdoor Dynamic Scenes](https://mlsanity.com/paper/2505.20967/) (2025)
- [Score-based Generative Priors Guided Model-driven Network for MRI Reconstruction](https://mlsanity.com/paper/2405.02958/) (2024)
- [DH-Mamba: Exploring Dual-domain Hierarchical State Space Models for MRI Reconstruction](https://mlsanity.com/paper/2501.08163/) (2025)
- [Digital Staining with Knowledge Distillation: A Unified Framework for Unpaired and Paired-But-Misaligned Data](https://mlsanity.com/paper/2504.09899/) (2025)
- [Efficient Noise Calculation in Deep Learning-based MRI Reconstructions](https://mlsanity.com/paper/2505.02007/) (2025)
- [HierAdaptMR: Cross-Center Cardiac MRI Reconstruction with Hierarchical Feature Adapters](https://mlsanity.com/paper/2508.13026/) (2025)
- [Mamba-Based Modality Disentanglement Network for Multi-Contrast MRI Reconstruction](https://mlsanity.com/paper/2512.19095/) (2025)
- [Revisiting Global Token Mixing in Task-Dependent MRI Restoration: Insights from Minimal Gated CNN Baselines](https://mlsanity.com/paper/2603.01449/) (2026)
- [CogGen: Cognitive-Load-Inspired Fully Unsupervised Deep Generative Modeling for Compressively Sampled MRI Reconstruction](https://mlsanity.com/paper/2603.04438/) (2026)
- [UEPS: Robust and Efficient MRI Reconstruction](https://mlsanity.com/paper/2603.18572/) (2026)

## Abstract (arXiv)

Deep unfolding networks (DUN) have emerged as a popular iterative framework for accelerated magnetic resonance imaging (MRI) reconstruction. However, conventional DUN aims to reconstruct all the missing information within the entire null space in each iteration. Thus it could be challenging when dealing with highly ill-posed degradation, usually leading to unsatisfactory reconstruction. In this work, we propose a Progressive Divide-And-Conquer (PDAC) strategy, aiming to break down the subsampling process in the actual severe degradation and thus perform reconstruction sequentially. Starting from decomposing the original maximum-a-posteriori problem of accelerated MRI, we present a rigorous derivation of the proposed PDAC framework, which could be further unfolded into an end-to-end trainable network. Specifically, each iterative stage in PDAC focuses on recovering a distinct moderate degradation according to the decomposition. Furthermore, as part of the PDAC iteration, such decomposition is adaptively learned as an auxiliary task through a degradation predictor which provides an estimation of the decomposed sampling mask. Following this prediction, the sampling mask is further integrated via a severity conditioning module to ensure awareness of the degradation severity at each stage. Extensive experiments demonstrate that our proposed method achieves superior performance on the publicly available fastMRI and Stanford2D FSE datasets in both multi-coil and single-coil settings.