  For image denoising problems, the structure tensor total variation
(STV)-based models show good performances when compared with other competing
regularization approaches. However, the STV regularizer does not couple the
local information of the image and may not maintain the image details.
Therefore, we employ the anisotropic weighted matrix introduced in the
anisotropic total variation (ATV) model to improve the STV model. By applying
the weighted matrix to the discrete gradient of the patch-based Jacobian
operator in STV, our proposed weighted STV (WSTV) model can effectively capture
local information from images and maintain their details during the denoising
process. The optimization problem in the model is solved by a fast first-order
gradient projection algorithm with a complexity result of $O(1 / i^2)$. For
images with different Gaussian noise levels, the experimental results
demonstrate that the WSTV model can effectively improve the quality of restored
images compared to other TV and STV-based models.
