Weighted Order- <i>p</i> Tensor Nuclear Norm Minimization and Its Application to Hyperspectral Image Mixed Denoising
Chengxun He, Qiujie Cao, Yang Xu, Le Sun, Zebin Wu, Zhihui Wei
Abstract
Recently, tensor singular value decomposition (t-SVD) has demonstrated excellent performance in various high-dimensional information processing applications. However, in adapting t-SVD to handle the typical tensor data restoration tasks, such as hyperspectral image (HSI) denoising, the following questions remain inadequately addressed: 1) The existing tensor nuclear norm minimization (TNN) regime treats all tensor singular values alike; thus, it lacks flexibility and dominance in dealing with the sophisticated HSI tensor. 2) The existing t-SVD-based denoising methods can not directly process order- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> > 3) tensors; thus, they fail to comprehensively exploit the high-dimensional structural correlation of the HSI tensor along different modes. To address the above challenges, in this study, we first generalize a novel weighted order- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> TNN minimization regime, which integrates the adaptively reweighting strategy for matrix, third-order, and order- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> tensors in a unified architecture. Subsequently, an efficient subspace low-rank learning model is established, using HSI denoising tasks as an application example to corroborate the superiority of the proposed regime in approximating the high-dimensional low-rank structure of natural tensor data. Extensive experimental results substantiate that our effort surpasses existing state-of-the-art low-rank tensor recovery methods in both restoration accuracy and efficiency. The source code is available at https://github.com/CX-He/WTNN.git.