Oriented total variation l1/2 regularization

• TV l1/2 regularization tends to smooth the detail and noise rather than the structure.
• OTV, which relies on the directional derivatives, keeps the edges sharp in image regularization.
• OTV l1/2 regularization can effectively remove the additive noise in images.
• TV l1/2 regularization can effectively remove the coding artifact in video coding.

Total Variation (TV) is a widely used image restoration/decomposition model. It is observed that the classical TV l1 and TV l2 regularization, on the one hand, do not favor higher-gradient structures over lower-gradient details as expected for structure preserving image processing, and on the other hand, tend to reduce the horizontal and vertical gradients, and thus inevitably blur the oblique edges in images. In this paper, we address these two problems by defining Oriented Total Variation l1/2 (OTV l1/2). It is theoretically and experimentally demonstrated that applying l1/2 regularization to the directional derivatives of images leads to superior structure preservation. OTV l1/2 regularization can be applied to image denoising and video compression, and the experimental results verify that OTV l1/2 outperforms other similar models.