Hyperspectral Image Denoising Based on Global and Nonlocal Low-Rank Factorizations

The ever-increasing spectral resolution of hyperspectral images (HSIs) is often obtained at the cost of a decrease in the signal-to-noise ratio of the measurements, thus calling for effective denoising techniques. HSIs from the real world lie in low-dimensional subspaces and are self-similar. The low dimensionality stems from the high correlation existing among the reflectance vectors, and self-similarity is common in real-world images. In this article, we exploit the above two properties. The low dimensionality is a global property that enables the denoising to be formulated just with respect to the subspace representation coefficients, thus greatly improving the denoising performance and reducing the computational complexity during processing. The self-similarity is exploited via a low-rank tensor factorization of nonlocal similar 3-D patches. The proposed factorization hinges on the optimal shrinkage/thresholding of the singular value decomposition (SVD) singular values of low-rank tensor unfoldings. As a result, the proposed method is user friendly and insensitive to its parameters. Its effectiveness is illustrated in a comparison with state-of-the-art competitors. A MATLAB demo of this work is available at <uri>https://github.com/LinaZhuang</uri> for the sake of reproducibility.