Optimization algorithm for hyperspectral image denoising based on tensor decomposition and total variation constraints

Hyperspectral image technology has a wide range of applications in many industries, however, images are often interfered by noise during acquisition and transmission, resulting in difficulties in interpreting the information. To enhance the denoising effect, this study proposes a denoising optimization algorithm that integrates tensor decomposition and anisotropic total variation constraints. This algorithm uses low rank tensor decomposition to capture the global low dimensional structure of hyperspectral data, in order to achieve preliminary separation of noise and signal. It simultaneously introduces anisotropic total variation regularization term, applies direction adaptive gradient smoothing in the spatial dimension to suppress residual noise and maintain edge sharpness, and maintaining inter band continuity in the spectral dimension to avoid step distortion. The simulation experiment results show that under Gaussian noise conditions, the proposed algorithm achieves signal-to-noise ratios of 32.12 dB, 29.84 dB, and 27.41 dB at low, medium, and high noise intensities, respectively, all of which are superior to the comparison methods. In addition, the algorithm maintains a signal-to-noise ratio of 26.32 dB in mixed noise scenarios, reduces spectral angle mapping to 0.061°, and achieves a global relative error index of 9.87, all of which are superior to the comparison methods.