Hyperspectral image denoising based on global and non-local low-rank factorizations

The ever increasing spectral resolution of the hyperspectral images (HSIs) is often obtained at the cost of a decrease in the signal-to-noise of the measurements, thus calling for effective denoising techniques. HSIs from the real world live in low dimensional subspaces and are self-similar. The low dimensionality stems from the high correlation existing among the reflectance vectors and the self-similarity is common to images of the real world. In this paper, we exploit the above two properties. The low dimensionality is a global property, which enables the denoising to be formulated just with respect to the subspace representation coefficients, thus greatly improving the denoising performance and reducing the processing computational complexity. The self-similarity is exploited via low-rank tensor factorization of non-local similar 3D-patches. The proposed factorization hinges on optimal shrinkage/thresholding of SVD singular value of low-rank tensor unfoldings. As a result, the proposed method has no parameters, apart from the noise variance. Its effectiveness is illustrated in a comparison with state-of-the-art competitors.