Exploring the solution space of linear inverse problems with GAN latent geometry
This addresses the need for efficient exploration of solution spaces in inverse problems for applications such as image processing, though it is incremental as it builds on prior GAN-based methods.
The paper tackles the problem of generating multiple feasible reconstructions for linear inverse problems by exploring the latent space of a GAN, achieving solutions an order of magnitude faster than existing methods in tasks like image super-resolution and inpainting.
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.