An application of differential geometry to image restoration

Ponente(s): Thomas Batard Gautret

In this talk, we present a new variational model for color image restoration, called High Order DIP-VBTV, which combines two priors: a deep image prior (DIP), which assumes that the restored image can be generated through a neural network, and a high order vector bundle total variation (VBTV), which generalizes the vectorial total variation (VTV) on vector bundles. VBTV is determined by a geometric quadruplet: a Riemannian metric and a covariant derivative on the base manifold, as well as a covariant derivative and a metric on the vector bundle. Whereas the VTV prior encourages the restored images to be piecewise constant, the VBTV prior encourages them to be piecewise parallel with respect to a covariant derivative. For well-chosen geometric quadruplets, we show that the minimization of the high order VBTV encourages the solutions of the restoration model to share some visual content with the clean image. Then, we show in experiments that the high order DIP-VBTV benefits from this property by outperforming DIP-VTV on various tasks like denoising, deblurring and super-resolution.