Abstract. We propose a weighted difference of anisotropic and isotropic total variation (TV) as a regularization for image processing tasks, based on the well-known TV model and natural image statistics. Due to the form of our model, it is natural to compute via a difference of convex algorithm (DCA). We draw its connection to the Bregman iteration for convex problems and prove that the iteration generated from our algorithm converges to a stationary point with the objective function values decreasing monotonically. A stopping strategy based on the stable oscillatory pattern of the iteration error from the ground truth is introduced. In numerical experiments on image denoising, image deblurring, and magnetic resonance imaging (MRI) reconstruction, our method improves on the classical TV model consistently and is on par with representative state-of-the-art methods. Key words. anisotropic TV, isotropic TV, weighted difference, difference of convex algorithm, convergence to stationary points, stable oscillatory errors, Bregman and split Bregman iterations AMS subject classifications. 90C90, 65K10, 49N45, 49M20
Lou et al. REF proposed a weighted difference of anisotropic and isotropic total variation model for image restoration.
A Weighted Difference of Anisotropic and Isotropic Total Variation Model for Image Processing
SIAM J. Imaging Sciences
SIAM J. Imaging Sciences
Mathematics Computer Science