# Image Reconstruction: From Sparsity to Data-adaptive Methods and Machine Learning

arXiv: https://arxiv.org/abs/1904.02816 · HTML: https://mlsanity.com/paper/1904.02816/

## Key facts

- Cited by 60 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Apr 2019.

## Built on by (most cited first, 30 of 60)

- [Transformers in Medical Imaging: A Survey](https://mlsanity.com/paper/2201.09873/) (2022)
- [SNIPS: Solving Noisy Inverse Problems Stochastically](https://mlsanity.com/paper/2105.14951/) (2021)
- [Solving Inverse Problems with Latent Diffusion Models via Hard Data Consistency](https://mlsanity.com/paper/2307.08123/) (2023)
- [Multi-institutional Collaborations for Improving Deep Learning-based Magnetic Resonance Image Reconstruction Using Federated Learning](https://mlsanity.com/paper/2103.02148/) (2021)
- [Flow Priors for Linear Inverse Problems via Iterative Corrupted Trajectory Matching](https://mlsanity.com/paper/2405.18816/) (2024)
- [Imaging with Equivariant Deep Learning](https://mlsanity.com/paper/2209.01725/) (2022)
- [SITCOM: Step-wise Triple-Consistent Diffusion Sampling for Inverse Problems](https://mlsanity.com/paper/2410.04479/) (2024)
- [Content-aware Scalable Deep Compressed Sensing](https://mlsanity.com/paper/2207.09313/) (2022)
- [Sparse-view Cone Beam CT Reconstruction using Data-consistent Supervised and Adversarial Learning from Scarce Training Data](https://mlsanity.com/paper/2201.09318/) (2022)
- [A review and experimental evaluation of deep learning methods for MRI reconstruction](https://mlsanity.com/paper/2109.08618/) (2021)
- [CoSIGN: Few-Step Guidance of ConSIstency Model to Solve General INverse Problems](https://mlsanity.com/paper/2407.12676/) (2024)
- [A Geometry-Informed Deep Learning Framework for Ultra-Sparse 3D Tomographic Image Reconstruction](https://mlsanity.com/paper/2105.11692/) (2021)
- [CS4ML: A general framework for active learning with arbitrary data based on Christoffel functions](https://mlsanity.com/paper/2306.00945/) (2023)
- [Analysis of Deep Image Prior and Exploiting Self-Guidance for Image Reconstruction](https://mlsanity.com/paper/2402.04097/) (2024)
- [PiRD: Physics-informed Residual Diffusion for Flow Field Reconstruction](https://mlsanity.com/paper/2404.08412/) (2024)
- [Regularization-Agnostic Compressed Sensing MRI Reconstruction with Hypernetworks](https://mlsanity.com/paper/2101.02194/) (2021)
- [2DeteCT -- A large 2D expandable, trainable, experimental Computed Tomography dataset for machine learning](https://mlsanity.com/paper/2306.05907/) (2023)
- [Deep Physics-Guided Unrolling Generalization for Compressed Sensing](https://mlsanity.com/paper/2307.08950/) (2023)
- [High-Precision Inversion of Dynamic Radiography Using Hydrodynamic Features](https://mlsanity.com/paper/2112.01627/) (2021)
- [K-band: Self-supervised MRI Reconstruction via Stochastic Gradient Descent over K-space Subsets](https://mlsanity.com/paper/2308.02958/) (2023)
- [Patient-Level Anatomy Meets Scanning-Level Physics: Personalized Federated Low-Dose CT Denoising Empowered by Large Language Model](https://mlsanity.com/paper/2503.00908/) (2025)
- [Model-based Reconstruction with Learning: From Unsupervised to Supervised and Beyond](https://mlsanity.com/paper/2103.14528/) (2021)
- [Deep Auto-encoder with Neural Response](https://mlsanity.com/paper/2111.15309/) (2021)
- [NESTANets: Stable, accurate and efficient neural networks for analysis-sparse inverse problems](https://mlsanity.com/paper/2203.00804/) (2022)
- [Subtle Data Crimes: Naively training machine learning algorithms could lead to overly-optimistic results](https://mlsanity.com/paper/2109.08237/) (2021)
- [Learning Sparsity-Promoting Regularizers using Bilevel Optimization](https://mlsanity.com/paper/2207.08939/) (2022)
- [SC-VAE: Sparse Coding-based Variational Autoencoder with Learned ISTA](https://mlsanity.com/paper/2303.16666/) (2023)
- [Robust Physics-based Deep MRI Reconstruction Via Diffusion Purification](https://mlsanity.com/paper/2309.05794/) (2023)
- [Reconstructing Richtmyer-Meshkov instabilities from noisy radiographs using low dimensional features and attention-based neural networks](https://mlsanity.com/paper/2408.00985/) (2024)
- [Balanced conic rectified flow](https://mlsanity.com/paper/2510.25229/) (2025)

## Abstract (arXiv)

The field of medical image reconstruction has seen roughly four types of methods. The first type tended to be analytical methods, such as filtered back-projection (FBP) for X-ray computed tomography (CT) and the inverse Fourier transform for magnetic resonance imaging (MRI), based on simple mathematical models for the imaging systems. These methods are typically fast, but have suboptimal properties such as poor resolution-noise trade-off for CT. A second type is iterative reconstruction methods based on more complete models for the imaging system physics and, where appropriate, models for the sensor statistics. These iterative methods improved image quality by reducing noise and artifacts. The FDA-approved methods among these have been based on relatively simple regularization models. A third type of methods has been designed to accommodate modified data acquisition methods, such as reduced sampling in MRI and CT to reduce scan time or radiation dose. These methods typically involve mathematical image models involving assumptions such as sparsity or low-rank. A fourth type of methods replaces mathematically designed models of signals and systems with data-driven or adaptive models inspired by the field of machine learning. This paper focuses on the two most recent trends in medical image reconstruction: methods based on sparsity or low-rank models, and data-driven methods based on machine learning techniques.