The hyperspectral-image (HSI) noise-reduction step is a very significant preprocessing phase of data-quality enhancement. It has been attracting immense research attention in the remote sensing and image processing domains. Many methods have been developed for HSI restoration, the goal of which is to remove noise from the whole HSI cube simultaneously without considering the spectral–spatial similarity. When a noise-removal algorithm is used globally to the entire data set, it would not eliminate all levels of noise, effectively. Furthermore, most of the existing methods remove independent and identically distributed (i.i.d.) Gaussian noise. The real scenarios are much more complicated than this assumption. The complexity created by natural noise that has a non-i.i.d. structure leads to inefficient methods containing underestimation and invalid performance. In this article, we calculated the spatial–spectral similarity criteria by defining a set of clustering-based latent variables (CLVs) in a Bayesian framework to improve the robustness. These criteria can be extracted using the clustering operators. Then, by applying the CLV to the variational Bayesian model, we investigated a new low-rank matrix factorization denoising approach based on the proposed clustering-based latent variable (CLV-LRMF) to remove noise with the non-i.i.d. mixture of Gaussian structures. Finally, we switched to the GPU for MATLAB implementation to reduce the runtime. The experimental results show that the performance has been improved by applying the proposed CLV and demonstrate the effectiveness of the proposed CLV-LRMF over other state-of-the-art methods.

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