Hyperspectral image recovery employing a multidimensional nonlocal total variation model

•A multidimensional nonlocal TV is proposed to utilize highly correlated bands.•A spectrally adaptive parameter is designed for different noise-intensity bands.•The framework of split Bregman iteration is adopted effectively in the model.•The model also works well on mixed-problem with noise and dead pixels.

Hyperspectral images (HSIs) have a high spectral resolution and ground-object recognition ability, but inevitably suffer from various factors in the imaging procedure, such as atmospheric effects, secondary illumination, and the physical limitations, which have a direct bearing on the visual quality of the images and the accuracy of the subsequent processing. HSI restoration is therefore a crucial task for improving the precision of the subsequent products. Currently, patch-based schemes have offered promising results for the preservation of detailed information and the removal of additive noise. In HSIs, the information in the spectral dimension is more redundant than the information in the spatial dimension. We therefore propose a multidimensional hyperspectral nonlocal model, in which both the correlation of the spectral bands and the similarity of the spatial structure are considered. In the model, a multidimensional nonlocal total variation constraint is applied to preserve edge sharpness. Experiments with both synthetic and real hyperspectral data illustrate that the proposed method can obtain promising results in HSI restoration.