TNNG: Total Nuclear Norms of Gradients for Hyperspectral Image Prior

Abstract

We introduce a novel regularization function for hyperspectral image (HSI), which is based on the nuclear norms of gradient images. Unlike conventional low-rank priors, we achieve a gradient-based low-rank approximation by minimizing the sum of nuclear norms associated with rotated planes in the gradient of a HSI. Our method explicitly and simultaneously exploits the correlation in the spectral domain as well as the spatial domain. Our method exploits the low-rankness of a global region to enhance the dimensionality reduction by the prior. Since our method considers the low-rankness in the gradient domain, it more sensitively detects anomalous variations. Our method achieves high-fidelity image recovery using a single regularization function without the explicit use of any sparsity-inducing priors such as ℓ0, ℓ1 and total variation (TV) norms. We also apply this regularization to a gradient-based robust principal component analysis and show its superiority in HSI decomposition. To demonstrate, the proposed regularization is validated on a variety of HSI reconstruction/decomposition problems with performance comparisons to state-of-the-art methods its superior performance.