Exploring the solution space of linear inverse problems with GAN latent geometry

TL;DR

This paper introduces a method to efficiently generate multiple plausible solutions for inverse problems by exploring the latent space of GANs, maintaining measurement consistency while allowing perceptual variation.

Contribution

It presents a novel approach to explore the solution space of inverse problems using GAN latent geometry, enabling faster generation of multiple solutions compared to existing methods.

Findings

Allows generation of multiple solutions fitting measurements and prior

Achieves an order of magnitude faster performance than previous methods

Demonstrates effectiveness on image super-resolution and inpainting

Abstract

Inverse problems consist in reconstructing signals from incomplete sets of measurements and their performance is highly dependent on the quality of the prior knowledge encoded via regularization. While traditional approaches focus on obtaining a unique solution, an emerging trend considers exploring multiple feasibile solutions. In this paper, we propose a method to generate multiple reconstructions that fit both the measurements and a data-driven prior learned by a generative adversarial network. In particular, we show that, starting from an initial solution, it is possible to find directions in the latent space of the generative model that are null to the forward operator, and thus keep consistency with the measurements, while inducing significant perceptual change. Our exploration approach allows to generate multiple solutions to the inverse problem an order of magnitude faster than existing approaches; we show results on image super-resolution and inpainting problems.