DeepAI

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

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.

• 38 publications
• 43 publications
07/06/2019

### Regularizing linear inverse problems with convolutional neural networks

Deep convolutional neural networks trained on large datsets have emerged...
10/31/2019

### Denoising and Regularization via Exploiting the Structural Bias of Convolutional Generators

Convolutional Neural Networks (CNNs) have emerged as highly successful t...
04/18/2019

### One-dimensional Deep Image Prior for Time Series Inverse Problems

We extend the Deep Image Prior (DIP) framework to one-dimensional signal...
05/24/2017

### Towards Understanding the Invertibility of Convolutional Neural Networks

Several recent works have empirically observed that Convolutional Neural...
07/11/2017

### DeepCodec: Adaptive Sensing and Recovery via Deep Convolutional Neural Networks

In this paper we develop a novel computational sensing framework for sen...
12/21/2021

### More is Less: Inducing Sparsity via Overparameterization

In deep learning it is common to overparameterize the neural networks, t...
07/22/2019

### Channel Normalization in Convolutional Neural Network avoids Vanishing Gradients

Normalization layers are widely used in deep neural networks to stabiliz...