Abstract: Due to the interference of instrumental noise,hyperspectral images (HSI) are often corrupted to some extent by Gaussian noise,which will seriously affect the subsequent performance of image processing.Therefore,image denoising has been considered as an important pre-processing step.Besides,due to the high dimensionality of hyperspectral data,the running efficiency is also a critical factor along with the visual evaluation.For the sake of improving both the efficiency and efficacy,we first project the high-dimensional hyperspectral image into certain spectral subspace,and then learn an orthogonal basis matrix.On that basis,the spatial non-local similarity and the global spectral low rank property of hyperspectral are jointly introduced to denoise the low-dimensional subspaces.Finally,all the restored low-dimensional image can be used along with the orthogonal basis to recover the original HIS data.Among these steps,the non-local denoising process first forms certain amount of tensor cubes by the non-local similarity,and followed by several tensor groups using the block matching method.In general,these groups enjoy strong low-rank essense due to the explicit neighborhood similarity.For better revealing the low-rank property of each tensor group,we propose a weighted and truncated nuclear norm by taking both the advantages of weighted nuclear norm and truncated nuclear norm.Moreover,an improved optimization scheme based on the accelerated proximal gradient is presented for a fast solution.Extensive simulation results show that our denoising scheme outperforms state-of-the-art methods in objective metrics and better preserves visually salient structural features.

Key words: Gaussian noise, Hyperspectral image(HSI), Low-rank regularization, Non-local similarity, Nuclear norm