Weighted Nuclear Norms of Transformed Tensors for Nonlocal Hyperspectral Image Denoising

Abstract

Nonlocal low-rank (LR) hyperspectral image (HSI) denoising approaches have gained a lot of attention because of their capacity to fully take advantage of spectral correlation and nonlocal self-similarity (NLSS). Most of the existing LR-tensor-based approaches use tensor singular value decomposition (t-SVD). However, fixed discrete Fourier transform-based t-SVD may compromise the low rank structure. Additionally, these approaches restricts flexibility in dealing with HSI data because it treats the singular values of each frontal slice equally. To overcome these issues, we propose a method using weighted nuclear norms of transformed tensors (WNNTT) for nonlocal HSI denoising. Our approach exploits the low-rankness in both the spectral and NLSS dimensions. We also compare our proposed method with other t-SVD based LR-tensor regularization methods under the same framework. Our experiments show that our WNNTT approach outperforms several state-of-the-art nonlocal t-SVD based methods on open HSI data.