Hyperspectral Image Denoising Based on Tensor Nuclear Norm Framelet Representation and Total Variation

During hyperspectral data acquisition, noise contamination inevitably degrades image quality and affects the accuracy of subsequent applications. To address this issue, this study proposes a hyperspectral image denoising model based on a tensor kernel norm framework combined with total variation regularization. First, the proposed model employs a tensor kernel norm framework tailored for highly correlated third-order tensors. In this framework, each tensor tube exhibits sparsity, and the sum of matrix ranks corresponding to the frontal slices of the transformed tensor is minimized, thereby fully capturing the low-rank characteristics of hyperspectral images. Second, a weighted spatial–spectral total variation term, expressed using the l_{2, 1} norm, is incorporated to enhance sparsity while preserving local smoothness in the spatial– spectral domain. Finally, these two components are effectively integrated to jointly exploit the low-rank properties of hyperspectral images and the sparse smoothness of the spatial–spectral domain, thereby achieving removal of high-intensity Gaussian noise and strip noise. Both simulation and real-data experiments demonstrate that, compared with five classical denoising algorithms, the proposed model achieves superior denoising performance. The restored images exhibit improved clarity, better detail preservation, and well-maintained structural contours without excessive smoothing.