DIP-VBTV: A Color Image Restoration Model Combining a Deep Image Prior and a Vector Bundle Total Variation
Thomas Batard, Gloria Haro, Coloma Ballester · SIAM Journal on Imaging Sciences · 2021
In this paper, we introduce a new variational model for color image restoration, called 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 vector bundle total variation (VBTV), which generalizes the vectorial total variation (VTV) on vector bundles. VBTV is determined by a geometric triplet: a Riemannian metric on the base manifold, 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 triplets, we show that the minimization of VBTV encourages the solutions of the restoration model to share some visual content with the clean image. Then, we show in experiments that DIP-VBTV benefits from this property by outperforming DIP-VTV and state-of-the-art unsupervised methods. It demonstrates the relevance of combining DIP and VBTV priors.