During the process of signal sampling and digital imaging, hyperspectral images (HSI) inevitably suffer from the contamination of mixed noises. The fidelity and efficiency of subsequent applications are considerably reduced along with this degradation. Recently, as a formidable implement for image processing, low-rank regularization has been widely extended to the restoration of HSI. Meanwhile, further exploration of the non-local self-similarity of low-rank images are proven useful in

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... g the spatial redundancy of HSI. Better preservation of spatial-spectral features is achieved under both low-rank and non-local regularizations. However, existing methods generally regularize the original space of HSI, the exploration of the intrinsic properties in subspace, which leads to better denoising performance, is relatively rare. To address these challenges, a joint method of subspace low-rank learning and non-local 4-d transform filtering, named SLRL4D, is put forward for HSI restoration. Technically, the original HSI is projected into a low-dimensional subspace. Then, both spectral and spatial correlations are explored simultaneously by imposing low-rank learning and non-local 4-d transform filtering on the subspace. The alternating direction method of multipliers-based algorithm is designed to solve the formulated convex signal-noise isolation problem. Finally, experiments on multiple datasets are conducted to illustrate the accuracy and efficiency of SLRL4D.