Hyperspectral Image Denoising Based on Hyper-Laplacian Total Variation in Spectral Gradient Domain

This article introduces a novel hyperspectral image (HSI) denoising method based on Hyper-Laplacian Total Variation in Spectral Gradient (HLTVSG). Our research identifies that compared to the original HSI, the spectral gradient of HSIs exhibits both a lower rank and a more favorable structure for total variation (TV) regularization due to its lower image entropy. To capitalize on the low-rank property of HSIs, we employ a subspace representation approach within the spectral gradient domain. Beyond low rankness, HSIs also possess abundant spatial information, which is often regularized by using TV. Traditional TV inherently assumes that the $\ell _{1}$ -norm of spatial gradient follows the Laplacian distribution. However, our analysis reveals that the spatial gradient of the subspace representation coefficients obeys a hyper-Laplacian distribution. Therefore, we introduce the hyper-Laplacian TV (HLTV) to better constrain the spatial local smoothness (LSS) of the representation coefficients. In addition, to eliminate the sparse noise and the stripe noise, an $\ell _{1}$ -norm and low-rank constraint are also employed. Finally, an augmented Lagrange multiplier (ALM) algorithm is utilized to solve the proposed model. Extensive experimental results on simulation and real datasets indicate that the proposed method outperforms many state-of-the-art methods both visually and quantitatively.