A CLASS OF PRIORS FOR COLOR IMAGE RESTORATION PARAMETRIZED BY LIE GROUPS ACTING ON PIXEL VALUES
Thomas Batard · HAL (Le Centre pour la Communication Scientifique Directe) · 2022
In a recent paper [T.Batard, G. Haro and C. Ballester, SIAM J. Imag. Sci., 2021 ], a new prior for image restoration has been introduced. It first relies on the observation that an image and a degraded version of it can share some visual content, then on the conjecture that an image restoration model can benefit from the use of an image prior encoding this invariance property. The proposed prior considers the restored image as a parallel section of a connection (also called covariant derivative), this latter arising as a solution of a variational problem associated to the Lie group R + * × SO(2) acting on image pixels. In this paper, we propose a twofold generalization of this result. First, we consider other Lie groups acting on image pixels, yielding new optimal connections. Then, we derive a family of α-connections from the optimal connections. The corresponding parallel sections describe new invariance properties which we use as priors encoded as penalty terms in variational models for image restoration. Experiments conducted on color image deblurring show that the proposed generalization of the work of Batard et al. outperforms the original approach.