Denoising hyperspectral images (HSIs) is a crucial preprocessing procedure due to the noise originating from intra-imaging mechanisms and environmental factors. Utilizing domain-specific knowledge of HSIs, such as spectral correlation, spatial self-similarity, and spatial-spectral correlation, is essential for deep learning-based denoising. Existing methods are often constrained by running time, space complexity, and computational complexity, employing strategies that explore these priors separately. While the strategies can avoid some redundant information, considering that hyperspectral images are 3-D images with strong spatial continuity and spectral correlation, this kind of strategy inevitably overlooks subtle long-range spatial-spectral information that positively impacts image restoration. This paper proposes a Spatial-Spectral Selective State Space Model-based U-shaped network, termed Spatial-Spectral U-Mamba (SSUMamba), for hyperspectral image denoising. We can obtain complete global spatial-spectral correlation within a module thanks to the linear space complexity in State Space Model (SSM) computations. We introduce an Alternating Scan (SSAS) strategy for HSI data, which helps model the information flow in multiple directions in 3-D HSIs. Experimental results demonstrate that our method outperforms several compared methods. The source code will be available at https://github.com/lronkitty/SSUMamba.

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