Weighted t-Schatten-p Norm Minimization for Real Color Image Denoising

Abstract

In this paper, to fully exploit the spatial and spectral correlation information, we present a new real color image denoising scheme using tensor Schatten-p norm (t-Schatten-p norm) minimization based on t-SVD to recover the underlying low-rank tensor. Similar to matrix Schatten-p norm, using non-convex t-Schatten-p (0 <; p <; 1) norm minimization could obtain better results than the tensor nuclear norm minimization which is a convex relaxation of the nonconvex tensor tubal rank. To avoid over-shrink the tensor tubal rank components, a flexible weighted t-Schatten-p norm model is proposed with weights assigned to different elements of tensor singular tubes. We adopt the generalized iterated shrinkage algorithm to solve the minimization problem efficiently. Extensive experiments on one synthetic and two realistic datasets demonstrate the effectiveness of our proposed method to remove noise both quantitatively and qualitatively.

Keywords

• p norm%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> Weighted 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
• low-rank
• non-local patch group tensor