TSLRLN: Tensor subspace low-rank learning with non-local prior for hyperspectral image mixed denoising

Abstract

Low-rank methods have earned high regard for solving problems of mixed denoising in hyperspectral images (HSI). However, for low-rank matrix/tensor-based denoising methods, high computational complexity and high tuning difficulty often accompany good results. To address this challenge, in this paper, we propose a tensor subspace low-rank learning method with a non-local prior to exploit the low-rankness of both spatial and spectral modes of an HSI tensor. Technically, the original noisy HSI tensor was first projected to a low-dimensional subspace. Then, an orthogonal tensor basis of subspace and a tensor coefficient were alternatively learned. The parameter-free non-local prior was enforced in the tensor subspace instead of in the original HSI tensor. Eventually, the t-linear representation of basis and coefficient tensors achieved the restoration of the latent clean low-rank tensor. The proposed method realizes complete tensor operations for subspace low-rank learning and avoids the correlation loss bought about by tensor flattening. Through comparing with the latest denoising methods by using several quantitative and qualitative indexes, extensive experiments conducted on two simulated and two real datasets have proved that the proposed method not only realizes the high accuracy of mixed denoising, but also remarkably improves the computational efficiency and usability in real applications.