A new nonconvex low-rank tensor approximation method with applications to hyperspectral images denoising

Abstract Hyperspectral images (HSIs) are frequently corrupted by mixing noise during their acquisition and transmission. Such complicated noise may reduce the quality of the obtained HSIs and limit the accuracy of the subsequent processing. By using the low-rank prior of the tensor formed by spatial and spectral information and further exploring the intrinsic structure of the underlying HSI from noisy observations, in this paper, we propose a new nonconvex low-rank tensor approximation method including optimization model and efficient iterative algorithm to eliminate multiple types of noise. The proposed mathematical model consists of a nonconvex low-rank regularization term using the γ nuclear norm, which is nonconvex surrogate to Tucker rank, and two data fidelity terms representing sparse and Gaussian noise components, which are regularized by the ℓ 1 -norm and the Frobenius norm, respectively. To solve this model, we propose an efficient augmented Lagrange multiplier algorithm. We also study the convergence and parameter setting of the algorithm. Extensive experimental results show that the proposed method has better denoising performance than the state-of-the-art competing methods for low-rank tensor approximation and noise modeling.