Non-local extension of total variation regularization for image restoration

Total-variation (TV) regularization is widely adopted in image restoration problems to exploit the feature that natural images are smooth with small gradient values at most regions. Basic TV method assumes identical zero-mean Laplacian distribution for the gradients at all pixels. However, for real-world images, the statistics of gradients may not be stationary, and the zero-mean assumption of gradients may not be valid either for a specific pixel. This paper presents a non-local extension of TV regularization for image restoration, called Non-Local Gradient Sparsity Regularization (NGSR). The NGSR model employs a separate gradient value distribution for each pixel. To figure out the distribution parameters, the NGSR method exploits a set of patches which are similar to the patch centered at current pixel and estimates the distribution parameter adaptively. Experimental results demonstrate that the proposed NGSR outperforms traditional TV remarkably for image restoration.