Hybrid Low-Rank Tensor CP and Tucker Decomposition with Total Variation Regularization for HSI Noise Removal

Abstract

The acquired hyperspectral images (HSIs) are affected by a mixture of several types of noise, which often suffer from information missing. Corrupted HSIs limit the precision of the subsequent processing. In this paper, the weighted Total Variation-regularized Hybrid Model of CP and Tucker (WTV-HMCT) is proposed to accurately identify the intrinsic structures of the clean HSIs. By jointly minimizing CP rank and Tucker rank in the low-rank tensor approximation, WTV-HMCT fully exploits the high-dimensional structure correlations of HSI. To ensure the piecewise smoothness of the recovered image, the hybrid low-rank tensor decomposition approach integrates the weighted spatial spectral total variation regularization for the separation of the noise-free HSI and mixed noise. By the Alternating Direction Method of Multipliers (ADMM), the optimization model is transformed into two subproblems. Finally, an efficient proximal alternating minimization algorithm is developed to optimize the proposed hybrid low-rank tensor decomposition efficiently. The experimental results show that the proposed model effectively handles Gauss noise, striping noise, and mixed noise and that it outperforms the most advanced methods in terms of evaluation metrics and visual evaluation.