Removal of Mixed Noise in Hyperspectral Images Based on Subspace Representation and Nonlocal Low-Rank Tensor Decomposition

Abstract

Hyperspectral images (HSIs) contain abundant spectral and spatial structural information, but they are inevitably contaminated by a variety of noises during data reception and transmission, leading to image quality degradation and subsequent application hindrance. Hence, removing mixed noise from hyperspectral images is an important step in improving the performance of subsequent image processing. It is a well-established fact that the data information of hyperspectral images can be effectively represented by a global spectral low-rank subspace due to the high redundancy and correlation (RAC) in the spatial and spectral domains. Taking advantage of this property, a new algorithm based on subspace representation and nonlocal low-rank tensor decomposition is proposed to filter the mixed noise of hyperspectral images. The algorithm first obtains the subspace representation of the hyperspectral image by utilizing the spectral low-rank property and obtains the orthogonal basis and representation coefficient image (RCI). Then, the representation coefficient image is grouped and denoised using tensor decomposition and wavelet decomposition, respectively, according to the spatial nonlocal self-similarity. Afterward, the orthogonal basis and denoised representation coefficient image are optimized using the alternating direction method of multipliers (ADMM). Finally, iterative regularization is used to update the image to obtain the final denoised hyperspectral image. Experiments on both simulated and real datasets demonstrate that the algorithm proposed in this paper is superior to related mainstream methods in both quantitative metrics and intuitive vision. Because it is denoising for image subspace, the time complexity is greatly reduced and is lower than related denoising algorithms in terms of computational cost.