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

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