# NETT: Solving Inverse Problems with Deep Neural Networks

@article{Li2018NETTSI, title={NETT: Solving Inverse Problems with Deep Neural Networks}, author={Housen Li and Johannes Schwab and Stephan Antholzer and Markus Haltmeier}, journal={ArXiv}, year={2018}, volume={abs/1803.00092} }

Recovering a function or high-dimensional parameter vector from indirect measurements is a central task in various scientific areas. Several methods for solving such inverse problems are well developed and well understood. Recently, novel algorithms using deep learning and neural networks for inverse problems appeared. While still in their infancy, these techniques show astonishing performance for applications like low-dose CT or various sparse data problems. However, there are few theoretical… Expand

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#### References

SHOWING 1-10 OF 95 REFERENCES

Solving ill-posed inverse problems using iterative deep neural networks

- Computer Science, Mathematics
- ArXiv
- 2017

The method builds on ideas from classical regularization theory and recent advances in deep learning to perform learning while making use of prior information about the inverse problem encoded in the forward operator, noise model and a regularizing functional to results in a gradient-like iterative scheme. Expand

One Network to Solve Them All — Solving Linear Inverse Problems Using Deep Projection Models

- Computer Science, Mathematics
- 2017 IEEE International Conference on Computer Vision (ICCV)
- 2017

This work proposes a general framework to train a single deep neural network that solves arbitrary linear inverse problems and demonstrates superior performance over traditional methods using wavelet sparsity prior while achieving performance comparable to specially-trained networks on tasks including compressive sensing and pixel-wise inpainting. Expand

MoDL: Model-Based Deep Learning Architecture for Inverse Problems

- Computer Science, Medicine
- IEEE Transactions on Medical Imaging
- 2019

This work introduces a model-based image reconstruction framework with a convolution neural network (CNN)-based regularization prior, and proposes to enforce data-consistency by using numerical optimization blocks, such as conjugate gradients algorithm within the network. Expand

Adversarial Regularizers in Inverse Problems

- Computer Science, Mathematics
- NeurIPS
- 2018

This work proposes a new framework for applying data-driven approaches to inverse problems, using a neural network as a regularization functional, that can be applied even if only unsupervised training data is available. Expand

Deep Convolutional Neural Network for Inverse Problems in Imaging

- Computer Science, Mathematics
- IEEE Transactions on Image Processing
- 2017

The proposed network outperforms total variation-regularized iterative reconstruction for the more realistic phantoms and requires less than a second to reconstruct a <inline-formula> <tex-math notation="LaTeX">$512\times 512$ </tex- math></inline- formula> image on the GPU. Expand

Deep learning for photoacoustic tomography from sparse data

- Computer Science, Medicine
- Inverse problems in science and engineering
- 2019

A direct and highly efficient reconstruction algorithm based on deep learning is developed for the sparse data problem in photoacoustic tomography (PAT), which reconstructs images with a quality comparable to state of the art iterative approaches for PAT from sparse data. Expand

Sparse synthesis regularization with deep neural networks

- Mathematics, Computer Science
- 2019 13th International conference on Sampling Theory and Applications (SampTA)
- 2019

An encoder-decoder network is trained by including an ℓ1-penalty and it is demonstrated that the trained decoder network allows sparse signal reconstruction using thresholded encoded coefficients without losing much quality of the original image. Expand

Input Convex Neural Networks

- Computer Science, Mathematics
- ICML
- 2017

This paper presents the input convex neural network architecture. These are scalar-valued (potentially deep) neural networks with constraints on the network parameters such that the output of the… Expand

NETT regularization for compressed sensing photoacoustic tomography

- Mathematics, Computer Science
- BiOS
- 2019

The deep learning method of [H. Li, J. Schwab, S. Antholzer, and M. Haltmeier] is applied for the first time to the CS-PAT problem, and a network architecture and training strategy for the NETT is proposed that is expected to be useful for other inverse problems as well. Expand

A U-Nets Cascade for Sparse View Computed Tomography

- Computer Science
- MLMIR@MICCAI
- 2018

A new convolutional neural network architecture for image reconstruction in sparse view computed tomography using a cascade of U-nets and data consistency layers yields superior visual results and better preserves the overall image structure as well as fine diagnostic details, e.g. the coronary arteries. Expand