DeepAI AI Chat
Log In Sign Up

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

by   Muhammad Asim, et al.
Northeastern University
Information Technology University

Trained generative models have shown remarkable performance as priors for inverse problems in imaging. For example, Generative Adversarial Network priors permit recovery of test images from 5-10x fewer measurements than sparsity priors. Unfortunately, these models may be unable to represent any particular image because of architectural choices, mode collapse, and bias in the training dataset. In this paper, we demonstrate that invertible neural networks, which have zero representation error by design, can be effective natural signal priors at inverse problems such as denoising, compressive sensing, and inpainting. Given a trained generative model, we study the empirical risk formulation of the desired inverse problem under a regularization that promotes high likelihood images, either directly by penalization or algorithmically by initialization. For compressive sensing, invertible priors can yield higher accuracy than sparsity priors across almost all undersampling ratios. For the same accuracy on test images, they can use 10-20x fewer measurements. We demonstrate that invertible priors can yield better reconstructions than sparsity priors for images that have rare features of variation within the biased training set, including out-of-distribution natural images.


Reducing the Representation Error of GAN Image Priors Using the Deep Decoder

Generative models, such as GANs, learn an explicit low-dimensional repre...

Low Shot Learning with Untrained Neural Networks for Imaging Inverse Problems

Employing deep neural networks as natural image priors to solve inverse ...

Sinogram Enhancement with Generative Adversarial Networks using Shape Priors

Compensating scarce measurements by inferring them from computational mo...

Regularizing linear inverse problems with convolutional neural networks

Deep convolutional neural networks trained on large datsets have emerged...

DAEs for Linear Inverse Problems: Improved Recovery with Provable Guarantees

Generative priors have been shown to provide improved results over spars...

Learning the Night Sky with Deep Generative Priors

Recovering sharper images from blurred observations, referred to as deco...

Generative Flows as a General Purpose Solution for Inverse Problems

Due to the success of generative flows to model data distributions, they...