# Adaptive Selection of Sampling-Reconstruction in Fourier Compressed Sensing

arXiv: https://arxiv.org/abs/2409.11738 · HTML: https://mlsanity.com/paper/2409.11738/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 41 references that are in the map.
- First posted on arXiv 18 Sep 2024.

## Builds on (most cited first, 23 of 23)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [fastMRI: An Open Dataset and Benchmarks for Accelerated MRI](https://mlsanity.com/paper/1811.08839/) (2018)
- [SRDiff: Single Image Super-Resolution with Diffusion Probabilistic Models](https://mlsanity.com/paper/2104.14951/) (2021)
- [SRFlow: Learning the Super-Resolution Space with Normalizing Flow](https://mlsanity.com/paper/2006.14200/) (2020)
- [End-to-End Variational Networks for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2004.06688/) (2020)
- [Reducing Uncertainty in Undersampled MRI Reconstruction with Active Acquisition](https://mlsanity.com/paper/1902.03051/) (2019)
- [Active MR k-space Sampling with Reinforcement Learning](https://mlsanity.com/paper/2007.10469/) (2020)
- [Learning Diverse Image Colorization](https://mlsanity.com/paper/1612.01958/) (2016)
- [Experimental design for MRI by greedy policy search](https://mlsanity.com/paper/2010.16262/) (2020)
- [B-spline Parameterized Joint Optimization of Reconstruction and K-space Trajectories (BJORK) for Accelerated 2D MRI](https://mlsanity.com/paper/2101.11369/) (2021)
- [Extending LOUPE for K-space Under-sampling Pattern Optimization in Multi-coil MRI](https://mlsanity.com/paper/2007.14450/) (2020)
- [On learning adaptive acquisition policies for undersampled multi-coil MRI reconstruction](https://mlsanity.com/paper/2203.16392/) (2022)
- [End-to-End Sequential Sampling and Reconstruction for MRI](https://mlsanity.com/paper/2105.06460/) (2021)
- [Image Restoration by Deep Projected GSURE](https://mlsanity.com/paper/2102.02485/) (2021)
- [FS-NCSR: Increasing Diversity of the Super-Resolution Space via Frequency Separation and Noise-Conditioned Normalizing Flow](https://mlsanity.com/paper/2204.09679/) (2022)
- [On the Robustness of Normalizing Flows for Inverse Problems in Imaging](https://mlsanity.com/paper/2212.04319/) (2022)
- [Fast Bayesian Uncertainty Estimation and Reduction of Batch Normalized Single Image Super-Resolution Network](https://mlsanity.com/paper/1903.09410/) (2019)
- [Learning the sampling density in 2D SPARKLING MRI acquisition for optimized image reconstruction](https://mlsanity.com/paper/2103.03559/) (2021)
- [Learning to sample in Cartesian MRI](https://mlsanity.com/paper/2312.04327/) (2023)

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

- [Predicting before Reconstruction: A generative prior framework for MRI acceleration](https://mlsanity.com/paper/2510.19472/) (2025)
- [Anatomical Token Uncertainty for Transformer-Guided Active MRI Acquisition](https://mlsanity.com/paper/2603.21806/) (2026)

## Abstract (arXiv)

Compressed sensing (CS) has emerged to overcome the inefficiency of Nyquist sampling. However, traditional optimization-based reconstruction is slow and can not yield an exact image in practice. Deep learning-based reconstruction has been a promising alternative to optimization-based reconstruction, outperforming it in accuracy and computation speed. Finding an efficient sampling method with deep learning-based reconstruction, especially for Fourier CS remains a challenge. Existing joint optimization of sampling-reconstruction works (H1) optimize the sampling mask but have low potential as it is not adaptive to each data point. Adaptive sampling (H2) has also disadvantages of difficult optimization and Pareto sub-optimality. Here, we propose a novel adaptive selection of sampling-reconstruction (H1.5) framework that selects the best sampling mask and reconstruction network for each input data. We provide theorems that our method has a higher potential than H1 and effectively solves the Pareto sub-optimality problem in sampling-reconstruction by using separate reconstruction networks for different sampling masks. To select the best sampling mask, we propose to quantify the high-frequency Bayesian uncertainty of the input, using a super-resolution space generation model. Our method outperforms joint optimization of sampling-reconstruction (H1) and adaptive sampling (H2) by achieving significant improvements on several Fourier CS problems.