A Tensor Subspace Representation-Based Method for Hyperspectral Image Denoising

In hyperspectral image (HSI) denoising, subspace-based denoising methods can reduce the computational complexity of the denoising algorithm. However, the existing matrix subspaces, which are generated by the unfolding matrix of the HSI tensor, cannot completely represent a tensor since the unfolding operation will destroy the tensor structure. To overcome this, we design a novel basis tensor that is directly learned from the original tensor and present a tensor subspace representation (TenSR), which is a more authentic representation for delivering the intrinsic structure of the tensor than a matrix subspace representation. Equipped with the TenSR, we then propose a TenSR-based HSI denoising (TenSRDe) model, which simultaneously considers the low-tubal rankness of the HSI tensor and the nonlocal self-similarity of the coefficient tensor. Moreover, we develop an efficient proximal alternating minimization (PAM) algorithm to solve the proposed nonconvex model and theoretically prove that the algorithm globally converges to a critical point. Experiments implemented on simulated and real data sets substantiate the denoising effect and efficiency of the proposed method.