In this study, multi-patch collaborative learning is introduced into variational low-rank matrix factorization to suppress mixed noise in hyperspectral images (HSIs). Firstly, based on the spatial consistency and nonlocal self-similarities, the HSI is partitioned into overlapping patches with a full band. The similarity metric with fusing features is exploited to select the most similar patches and construct the corresponding collaborative patches. Secondly, considering that the latent clean

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... holds the low-rank property across the spectra, whereas the noise component does not, variational low-rank matrix factorization is proposed in the Bayesian framework for each collaborative patch. Using Gaussian distribution adaptively adjusted by a gamma distribution, the noise-free data can be learned by exploring low-rank properties of collaborative patches in the spatial/spectral domain. Additionally, the Dirichlet process Gaussian mixture model is utilized to approximate the statistical characteristics of mixed noises, which is constructed by exploiting the Gaussian distribution, the inverse Wishart distribution, and the Dirichlet process. Finally, variational inference is utilized to estimate all variables and solve the proposed model using closed-form equations. Widely used datasets with different settings are adopted to conduct experiments. The quantitative and qualitative results indicate the effectiveness and superiority of the proposed method in reducing mixed noises in HSIs.