Compressive sensing with un-trained neural networks: Gradient descent finds the smoothest approximation

By Reinhard Heckel, M. Soltanolkotabi. 2020

93 citations recorded by the source corpus.

Un-trained convolutional neural networks have emerged as highly successful tools for image recovery and restoration. They are capable of solving standard inverse problems such as denoising and compressive sensing with excellent results by simply fitting a neural network model to measurements from a single image or signal without the need for any additional training data. For some applications, this critically requires additional regularization in the form of early stopping the optimization. For signal recovery from a few measurements, however, un-trained convolutional networks have an intriguing self-regularizing property: Even though the network can perfectly fit any image, the network recovers a natural image from few measurements when trained with gradient descent until convergence. In this paper, we provide numerical evidence for this property and study it theoretically. We show that---without any further regularization---an un-trained convolutional neural network can approximately reconstruct signals and images that are sufficiently structured, from a near minimal number of random measurements.

Subfields: Biomedical Engineering, Computational Mechanics, Computer Vision and Pattern Recognition, Optimization & Training

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Biomedical Engineering

1. A. Dimakis
2. Ravi Ramamoorthi
3. Ben Mildenhall
4. Wenlin Gong
5. Shensheng Han
6. Ren Ng
7. Mingliang Chen
8. Jonathan T. Barron

In Computational Mechanics

1. Jonathan T. Barron
2. Ben Mildenhall
3. Pratul P. Srinivasan
4. A. Dimakis
5. Giannis Daras
6. Matthew Tancik
7. Ajil Jalal
8. Eric Price

In Computer Vision and Pattern Recognition

1. Jonathan T. Barron
2. Pratul P. Srinivasan
3. Ben Mildenhall
4. Andreas Geiger
5. Matthew Tancik
6. Luc Van Gool
7. Jitendra Malik
8. Chen Change Loy

In Optimization & Training

1. Giannis Daras
2. Chenglong Wang
3. A. Dimakis
4. Ravi Ramamoorthi
5. Ajil Jalal
6. Fei Wang
7. Yu Zhang
8. Guohai Situ

Citations in the corpus

• Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains (2020, background): “For a conventional MLP, the eigenvalues of the NTK decay rapidly [4, 5, 14].”
• Far-field super-resolution ghost imaging with a deep neural network constraint (2022, methodology): “A similar concept has also been used for computational imaging, such as phase retrieval 34,35 , CS 36,37 , and diffraction tomography 38 .”
• Robust Compressed Sensing MRI with Deep Generative Priors (2021, background): “[37] Reinhard Heckel and Mahdi Soltanolkotabi.”