Log In Sign Up

Regularizing linear inverse problems with convolutional neural networks

by   Reinhard Heckel, et al.

Deep convolutional neural networks trained on large datsets have emerged as an intriguing alternative for compressing images and solving inverse problems such as denoising and compressive sensing. However, it has only recently been realized that even without training, convolutional networks can function as concise image models, and thus regularize inverse problems. In this paper, we provide further evidence for this finding by studying variations of convolutional neural networks that map few weight parameters to an image. The networks we consider only consist of convolutional operations, with either fixed or parameterized filters followed by ReLU non-linearities. We demonstrate that with both fixed and parameterized convolutional filters those networks enable representing images with few coefficients. What is more, the underparameterization enables regularization of inverse problems, in particular recovering an image from few observations. We show that, similar to standard compressive sensing guarantees, on the order of the number of model parameters many measurements suffice for recovering an image from compressive measurements. Finally, we demonstrate that signal recovery with a un-trained convolutional network outperforms standard l1 and total variation minimization for magnetic resonance imaging (MRI).


page 8

page 11


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

Un-trained convolutional neural networks have emerged as highly successf...

Invertible generative models for inverse problems: mitigating representation error and dataset bias

Trained generative models have shown remarkable performance as priors fo...

Denoising and Regularization via Exploiting the Structural Bias of Convolutional Generators

Convolutional Neural Networks (CNNs) have emerged as highly successful t...

Convolutional Neural Networks Analyzed via Inverse Problem Theory and Sparse Representations

Inverse problems in imaging such as denoising, deblurring, superresoluti...

Solving Inverse Problems With Deep Neural Networks – Robustness Included?

In the past five years, deep learning methods have become state-of-the-a...

Deep Decoder: Concise Image Representations from Untrained Non-convolutional Networks

Deep neural networks, in particular convolutional neural networks, have ...

One-dimensional Deep Image Prior for Time Series Inverse Problems

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