Combinatorics

Linear subspace

Pattern recognition (psychology)

Noise reduction

Subspace topology

Mathematics

Algorithm

Mathematical optimization

Basis (linear algebra)

Hyperspectral imaging

Rank (graph theory)

Minification

Artificial intelligence

Regularization (linguistics)

Geometry

Computer science

Non-local low-rank tensor approximation has been developed as a state-of-the-art method for hyperspectral image (HSI) denoising. Unfortunately, while their denoising performance benefits little from more spectral bands, the running time of these methods significantly increases. In this paper, we claim that the HSI lies in a global spectral low-rank subspace, and the spectral subspaces of each full band patch groups should lie in this global low-rank subspace. This motivates us to propose a unified spatial-spectral paradigm for HSI denoising. As the new model is hard to optimize, An efficient algorithm motivated by alternating minimization is developed. This is done by first learning a low-dimensional orthogonal basis and the related reduced image from the noisy HSI. Then, the non-local low-rank denoising and iterative regularization are developed to refine the reduced image and orthogonal basis, respectively. Finally, the experiments on synthetic and both real datasets demonstrate the superiority against the stateof-the-art HSI denoising methods.

Non-Local Meets Global: An Integrated Paradigm for Hyperspectral Denoising