# A Review of Convolutional Neural Networks for Inverse Problems in Imaging

arXiv: https://arxiv.org/abs/1710.04011 · HTML: https://mlsanity.com/paper/1710.04011/

## Key facts

- Cited by 81 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Oct 2017.

## Built on by (most cited first, 30 of 81)

- [SNIPS: Solving Noisy Inverse Problems Stochastically](https://mlsanity.com/paper/2105.14951/) (2021)
- [Can stable and accurate neural networks be computed? -- On the barriers of deep learning and Smale's 18th problem](https://mlsanity.com/paper/2101.08286/) (2021)
- [On Measuring and Controlling the Spectral Bias of the Deep Image Prior](https://mlsanity.com/paper/2107.01125/) (2021)
- [Two-layer neural networks with values in a Banach space](https://mlsanity.com/paper/2105.02095/) (2021)
- [What's in a Prior? Learned Proximal Networks for Inverse Problems](https://mlsanity.com/paper/2310.14344/) (2023)
- [Recovery Analysis for Plug-and-Play Priors using the Restricted Eigenvalue Condition](https://mlsanity.com/paper/2106.03668/) (2021)
- [Online Deep Equilibrium Learning for Regularization by Denoising](https://mlsanity.com/paper/2205.13051/) (2022)
- [Theoretical Perspectives on Deep Learning Methods in Inverse Problems](https://mlsanity.com/paper/2206.14373/) (2022)
- [Learning Regularization Parameters of Inverse Problems via Deep Neural Networks](https://mlsanity.com/paper/2104.06594/) (2021)
- [SGD-Net: Efficient Model-Based Deep Learning with Theoretical Guarantees](https://mlsanity.com/paper/2101.09379/) (2021)
- [An Optimization-Based Meta-Learning Model for MRI Reconstruction with Diverse Dataset](https://mlsanity.com/paper/2110.00715/) (2021)
- [Real-Time Topology Optimization in 3D via Deep Transfer Learning](https://mlsanity.com/paper/2102.07657/) (2021)
- [Untrained networks for compressive lensless photography](https://mlsanity.com/paper/2103.07609/) (2021)
- [Prior Mismatch and Adaptation in PnP-ADMM with a Nonconvex Convergence Analysis](https://mlsanity.com/paper/2310.00133/) (2023)
- [Scaling Up Bayesian Uncertainty Quantification for Inverse Problems using Deep Neural Networks](https://mlsanity.com/paper/2101.03906/) (2021)
- [Blind Inversion using Latent Diffusion Priors](https://mlsanity.com/paper/2407.01027/) (2024)
- [Deformation-Compensated Learning for Image Reconstruction without Ground Truth](https://mlsanity.com/paper/2107.05533/) (2021)
- [Image-to-Image MLP-mixer for Image Reconstruction](https://mlsanity.com/paper/2202.02018/) (2022)
- [PtychoDV: Vision Transformer-Based Deep Unrolling Network for Ptychographic Image Reconstruction](https://mlsanity.com/paper/2310.07504/) (2023)
- [Deep Model-Based Architectures for Inverse Problems under Mismatched Priors](https://mlsanity.com/paper/2207.13200/) (2022)
- [Block Coordinate Plug-and-Play Methods for Blind Inverse Problems](https://mlsanity.com/paper/2305.12672/) (2023)
- [Plug-and-Play Posterior Sampling under Mismatched Measurement and Prior Models](https://mlsanity.com/paper/2310.03546/) (2023)
- [Reconstructing High-resolution Turbulent Flows Using Physics-Guided Neural Networks](https://mlsanity.com/paper/2109.03327/) (2021)
- [All-optical image denoising using a diffractive visual processor](https://mlsanity.com/paper/2309.09215/) (2023)
- [Glimpse: Generalized Locality for Scalable and Robust CT](https://mlsanity.com/paper/2401.00816/) (2024)
- [NESTANets: Stable, accurate and efficient neural networks for analysis-sparse inverse problems](https://mlsanity.com/paper/2203.00804/) (2022)
- [CoRRECT: A Deep Unfolding Framework for Motion-Corrected Quantitative R2* Mapping](https://mlsanity.com/paper/2210.06330/) (2022)
- [Robustness of Deep Equilibrium Architectures to Changes in the Measurement Model](https://mlsanity.com/paper/2211.00531/) (2022)
- [A Direct Sampling-Based Deep Learning Approach for Inverse Medium Scattering Problems](https://mlsanity.com/paper/2305.00250/) (2023)
- [Learning of Sea Surface Height Interpolation from Multi-variate Simulated Satellite Observations](https://mlsanity.com/paper/2310.07626/) (2023)

## Abstract (arXiv)

In this survey paper, we review recent uses of convolution neural networks (CNNs) to solve inverse problems in imaging. It has recently become feasible to train deep CNNs on large databases of images, and they have shown outstanding performance on object classification and segmentation tasks. Motivated by these successes, researchers have begun to apply CNNs to the resolution of inverse problems such as denoising, deconvolution, super-resolution, and medical image reconstruction, and they have started to report improvements over state-of-the-art methods, including sparsity-based techniques such as compressed sensing. Here, we review the recent experimental work in these areas, with a focus on the critical design decisions: Where does the training data come from? What is the architecture of the CNN? and How is the learning problem formulated and solved? We also bring together a few key theoretical papers that offer perspective on why CNNs are appropriate for inverse problems and point to some next steps in the field.