A Weighted Difference of Anisotropic and Isotropic Total Variation Model for Image Processing
CALIFORNIA UNIV LOS ANGELES DEPT OF MATHEMATICS
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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 difference 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 start-of-the-art methods.