Hyperspectral Image Denoising Based on Non-Convex Correlated Total Variation

Hyperspectral image (HSI) quality is generally degraded by diverse noise contamination during acquisition, which adversely impacts subsequent processing performance. Current techniques predominantly rely on nuclear norms and low-rank matrix approximation theory to model the inherent property that HSIs lie in a low-dimensional subspace. Recent research has demonstrated that HSI gradient maps also exhibit low-rank priors. The correlated total variation (CTV), which is defined as the nuclear norm of gradient maps, can simultaneously model low-rank and local smoothness priors, and shows better performance than the standard nuclear norm. However, similar to nuclear norms, CTV may excessively penalize large singular values. To overcome these constraints, this study introduces a non-convex correlated total variation (NCTV), which shows the potential to eliminate mixed noise (including Gaussian, impulse, stripe, and dead-line noise) while preserving critical textures and spatial–spectral details. Numerical experiments on both simulated and real HSI datasets demonstrate that the proposed NCTV method achieves better performance in detail retention compared with the state-of-the-art techniques.