MvSSIM: A quality assessment index for hyperspectral images

Quality assessment indexes play a fundamental role in the analysis of hyperspectral image (HSI) cubes. To assess the quality of an HSI cube, the structural similarity (SSIM) index has been widely applied in a band-by-band manner, as SSIM was originally designed for 2D images, and then the mean SSIM (MeanSSIM) index over all bands is adopted. MeanSSIM fails to accommodate the spectral structure which is a unique characteristic of HSI. Hence in this paper, we propose a new and simple multivariate SSIM (MvSSIM) index for HSI, by treating the pixel spectrum as a multivariate random vector. MvSSIM maintains SSIM's ability to assess the spatial structural similarity via correlation between two images of the same band; and adds an ability to assess the spectral structural similarity via covariance among different bands. MvSSIM is well founded on multivariate statistics and can be easily implemented through simple sample statistics involving mean vectors, covariance matrices and cross-covariance matrices. Experiments show that MvSSIM is a proper quality assessment index for distorted HSIs with different kinds of degradations.