SSUMamba: A spatial-spectral selective state space model for hyperspectral image denoising Hyperspectral images (HSIs) are widely used in material recognition, object detection, object tracking, change detection, and environmental protection. However, noise from imaging mechanisms and environmental factors can degrade HSI quality. Denoising is a crucial preprocessing step to enhance image quality and practical utility. Recent advances in deep learning have shown promise in HSI denoising, but traditional methods often struggle with modeling long-range spatial-spectral dependencies. SSUMamba is a novel approach that leverages the state space model (SSM) for efficient long-range dependency modeling. It introduces a memory-efficient spatial-spectral U-Mamba (SSUMamba) for HSI denoising, with the spatial-spectral continuous scan (SSCS) Mamba as the core component. The SSCS Mamba alternates row, column, and band orders to generate sequences and uses bidirectional SSM to exploit long-range spatial-spectral dependencies. 3D convolutions are embedded to enhance local spatial-spectral modeling. Experiments show that SSUMamba achieves superior denoising results with lower memory consumption per batch compared to transformer-based methods. The source code is available at https://github.com/lronkitty/SSUMamba. SSUMamba features a U-shaped architecture and leverages the spatial-spectral continuous scan scheme (SSCS) to exploit long-range spatial-spectral dependencies. It incorporates residual blocks to model local spatial-spectral correlations and enhance texture preservation. The method demonstrates superior denoising potential compared to CNN-based methods and transformer-based methods. The proposed SSUMamba outperforms other methods in denoising performance, structural preservation, and spectral fidelity. It effectively models spatial-spectral correlation and ensures spatial-spectral continuity for HSI sequence generation. The method is evaluated on synthetic and real-world datasets, including the ICVL testing set, Houston 2018 HSI, Pavia City Center HSI, Gaofen-5 Wuhan HSI, and Earth Observing-1 HSI. SSUMamba achieves better performance in denoising, especially in handling mixture noise. It leverages the spatial-spectral continuous scan scheme to capture long-range spatial-spectral correlations and continuity. The method is efficient, with linear complexity and lower memory consumption. The paper concludes that SSUMamba is a promising approach for HSI denoising, with potential applications in other tasks such as HSI superresolution and classification. Future work includes exploring more efficient and robust network designs for faster and higher-performance HSI denoising.SSUMamba: A spatial-spectral selective state space model for hyperspectral image denoising Hyperspectral images (HSIs) are widely used in material recognition, object detection, object tracking, change detection, and environmental protection. However, noise from imaging mechanisms and environmental factors can degrade HSI quality. Denoising is a crucial preprocessing step to enhance image quality and practical utility. Recent advances in deep learning have shown promise in HSI denoising, but traditional methods often struggle with modeling long-range spatial-spectral dependencies. SSUMamba is a novel approach that leverages the state space model (SSM) for efficient long-range dependency modeling. It introduces a memory-efficient spatial-spectral U-Mamba (SSUMamba) for HSI denoising, with the spatial-spectral continuous scan (SSCS) Mamba as the core component. The SSCS Mamba alternates row, column, and band orders to generate sequences and uses bidirectional SSM to exploit long-range spatial-spectral dependencies. 3D convolutions are embedded to enhance local spatial-spectral modeling. Experiments show that SSUMamba achieves superior denoising results with lower memory consumption per batch compared to transformer-based methods. The source code is available at https://github.com/lronkitty/SSUMamba. SSUMamba features a U-shaped architecture and leverages the spatial-spectral continuous scan scheme (SSCS) to exploit long-range spatial-spectral dependencies. It incorporates residual blocks to model local spatial-spectral correlations and enhance texture preservation. The method demonstrates superior denoising potential compared to CNN-based methods and transformer-based methods. The proposed SSUMamba outperforms other methods in denoising performance, structural preservation, and spectral fidelity. It effectively models spatial-spectral correlation and ensures spatial-spectral continuity for HSI sequence generation. The method is evaluated on synthetic and real-world datasets, including the ICVL testing set, Houston 2018 HSI, Pavia City Center HSI, Gaofen-5 Wuhan HSI, and Earth Observing-1 HSI. SSUMamba achieves better performance in denoising, especially in handling mixture noise. It leverages the spatial-spectral continuous scan scheme to capture long-range spatial-spectral correlations and continuity. The method is efficient, with linear complexity and lower memory consumption. The paper concludes that SSUMamba is a promising approach for HSI denoising, with potential applications in other tasks such as HSI superresolution and classification. Future work includes exploring more efficient and robust network designs for faster and higher-performance HSI denoising.