Riemannian Loss for Image Restoration
Jing Mu, Xinfeng Zhang, Shuyuan Zhu, Ruiqin Xiong · 2019
Deep neural networks are widely used for image restoration, however the loss criteration is usually set as ℓ2. ℓ2penalizes larger errors, which is unstable for outliers. To avoid the disadvantages, ℓ1is utilized as a more robust and well behaved loss. This paper proposes a novel loss function for restoration networks, which measures geodesic distance in Riemannian manifold and exploits the outstanding properties of ℓ1. Different from ℓ1and ℓ2loss which reflects pixel distance, our loss in Riemannian reflects the structure distance of image. The proposed loss not only preserves the robutness of ℓ1loss, but also reflects the image contrasts. Experimental results on image super resolution and compressed sensing show that our proposed loss function achieves more accurate reconstructions, according to both the objective and perceptual qualities.