Nonlocal Gradient Sparsity Regularization for Image Restoration

Total variation (TV) regularization is widely used in image restoration to exploit the local smoothness of image content. Essentially, the TV model assumes a zero-mean Laplacian distribution for the gradient at all pixels. However, real-world images are nonstationary in general, and the zero-mean assumption of pixel gradient might be invalid, especially for regions with strong edges or rich textures. This paper introduces a nonlocal (NL) extension of TV regularization, which models the sparsity of the image gradient with pixelwise content-adaptive distributions, reflecting the nonstationary nature of image statistics. Taking advantage of the NL similarity of natural images, the proposed approach estimates the image gradient statistics at a particular pixel from a group of nonlocally searched patches, which are similar to the patch located at the current pixel. The gradient data in these NL similar patches are regarded as the samples of the gradient distribution to be learned. In this way, more accurate estimation of gradient is achieved. Experimental results demonstrate that the proposed method outperforms the conventional TV and several other anchors remarkably and produces better objective and subjective image qualities.