Joint Weighted Tensor Schatten <inline-formula> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula>-Norm and Tensor <inline-formula> <tex-math notation="LaTeX">$l_p$ </tex-math></inline-formula>-Norm Minimization for Image Denoising

Abstract

In the traditional non-local similar patch-based denoising algorithms, the image patches are firstly flatted into a vector. The structure information within the image patches is ignored; however, the spatial layout information can be used for improving the denoising performance. To solve this problem, this paper treats the image patches as matrices and proposes a low-rank tensor recovery model for image denoising, and thus it makes full use of spatial information within the image. Meanwhile, the proposed model can realize joint weighted tensor Schatten p-norm and tensor lp-norm minimization, which has two advantages: 1) it can deal with zero mean Gaussian noise, impulse noise, and any other noise that can be approximated by mixing these two kinds of noise and 2) the employed norms require relatively weak incoherence conditions than l1 norm and nuclear norm, and thus they are more robust against outliers and noise. The experimental results show that the proposed algorithm outperforms other state-of-the-art denoising algorithms in both visual perception quality and quantitative measures.

Keywords

• Image denoising
• low-rank tensor recovery
• p-norm%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> tensor Schatten <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">p</italic>-norm