目的 高光谱图像由于其成像机理、设备误差和成像环境等因素导致采集到的数据存在噪声。传统稀疏表示方法需要把高光谱图像划分为一系列的重叠局部图像块进行表示，通过对重叠图像块去噪结果进行平均，实现整体图像去噪。这种局部—整体去噪方法不可避免地会破坏高光谱图像空间关系，产生较差的去噪效果和视觉瑕疵。本文利用卷积算子的平移不变性，采用卷积稀疏编码（convolutional sparse coding，CSC）对高光谱图像进行整体表示，保留不同图像块之间的空间关系，提升高光谱图像去噪性能。方法 将每个波段去噪看做单任务，采用卷积稀疏编码描述单波段的局部空间结构关系。通过共享稀疏编码系数，实现不同波段之间的全局光谱关联关系建模，形成多任务卷积稀疏编码模型。多任务卷积稀疏编码模型一方面可以实现高光谱图像的空间—光谱关系联合建模；另一方面，对高光谱图像进行整体处理，有效地利用图像块之间的关系，因此具有很强的去噪能力。借鉴深度学习强大的表征能力，将多任务卷积稀疏编码模型的算法迭代过程通过深度展开（deep unfolding）方式转化为端到端可学习深度神经网络，即多任务卷积稀疏编码网络（multitask convolutional sparse coding network，MTCSC-Net），进一步提升模型去噪能力和运行效率。结果 在ICVL和CAVE（Columbia Imaging and Vision Laboratory）数据集上进行了仿真实验，在Urban数据集上进行了真实数据实验，并与8种方法进行比较，表明了本文算法的有效性。与传统基于图像块的稀疏去噪算法相比，在CAVE数据集上本文算法的峰值信噪比（peak signal-to-noise ratio，PSNR）提升1.38 dB；在ICVL数据集上提升0.64 dB。结论 提出的多任务卷积稀疏编码网络能有效利用高光谱图像的空间—光谱关联信息，具有更强的去噪能力。

Objective Hyperspectral images（HSIs）are contaminated by noises due to the imaging mechanism，equipment errors，and imaging environment. Because of the diverse sensitivity of sensors at different wavelengths，the noise intensities among bands are always dissimilar，that is，spectrally non-independent and identically distributed noises exist. Noise interference greatly limits the interpretation and application of HSIs. Therefore，HSI denoising is an indispensable preprocessing step to improve the utility of HSIs. Sparse-representation（SR）-based methods assume clean HSIs are structural and can be linearly represented by a few atoms in the dictionary，while structureless random noise cannot be represented. However，most SR-based methods follow the pipeline to break the compete HSIs into many overlapped，small local patches，sparsely representing each small patch independently，and average overlapped pixels between each patch to recover HSIs globally. Such a“local-global”denoising mechanism ignores dependencies between overlapping patches，producing lower denoising effectiveness and visual defects. Differently，convolutional sparse coding（CSC）employs convolution kernels as atoms and can represent the image without patch division thanks to the shift-invariant property of the convolution operators. In this way，the spatial relationships between different patches are naturally retained. Inspired by this， this paper introduces a multitask convolutional sparse coding network（MTCSC-Net）for HIS denoising. Method In this paper，the denoising problem of an individual band is regarded as a single task and the CSC model is used to describe the local spatial structure correlation within each band. The denoising of all the bands is regarded as a multitask problem. All the bands are connected by sharing the sparse coding coefficients to depict the global spectral correlation between different bands，forming a multitask convolutional sparse coding（MTCSC）model. The MTCSC model can realize joint spatialspectral relationship modeling of HSIs. Moreover，the MTCSC model takes the HSIs as whole and can naturally remain the spatial relationship between pixels；thus，it has a strong denoising ability. Drawing on the powerful learning ability of deep learning，this paper transforms the iterative optimization of the MTCSC model into an end-to-end learnable deep neural network by the deep unfolding technique，that is，MTCSC-Net，to improve the model denoising ability and efficiency further. Result In this paper，our method is evaluated on the ICVL and CAVE datasets. In both experiments，different levels of Gaussian noises are added to clean HSI to produce noise-clean pairs. Besides the synthetic experiment，MTCSC-Net is tested on the real-world HYDICE Urban Dataset（Urban）dataset. Eight methods are selected for comparison to prove the effectiveness of the proposed denoising method. Experimental results show peak signal-to-noise ratio（PSNR）is improved by 1. 38 dB on the CAVE dataset and 0. 64 dB on the ICVL dataset，compared with the traditional patch-based SR method. The visual results show MTCSC-Net can produce cleaner spatial images and more accurate spectral reflectance with a better match with the reference ones. Conclusion The MTCSC-Net proposed in this paper can effectively utilize the spatialspectral correlation information of HSIs and has a strong denoising ability.