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。稀疏表示假设干净高光谱图像具有很强的结构信息，可以由字典中少数基原子线性表示，而无结构的随机噪声不能够被表示，从而实现高光谱图像去噪。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)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 本文把每个波段去噪看作单任务，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，本文把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 本文在ICVL和CAVE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，并且和8种方法进行了比较，证明了本文去噪算法的有效性。算法与传统基于图像块的稀疏去噪算法比，在CAVE数据集上PSNR提升1.38 dB; 在ICVL数据集上提升0.64dB。结论 本文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 often affected by various types of noise due to imaging mechanisms, equipment errors, and environmental factors, and more. Because of the different sensitivity of sensors at different wavelengths, the noise intensities among bands are always different, meaning that there are spectrally non-independent and identically distributed (non-i.i.d.) noises. The 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 that clean HSIs possess structural properties 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 a pipeline that divides the complete HSIs into numerous overlapped and small local patches, sparsely represents each patch independently, and averages the overlapped pixels between each patch to recover HSIs globally. This "local-global" denoising mechanism ignores dependencies between overlapping patches, leading to lower denoising effectiveness and visual defects. In contrast, convolutional sparse coding (CSC) employs convolution kernels as atoms and can represent the image without patch division due to the shift-invariant property of convolution operators. This retains the spatial relationships between different patches naturally. Inspired by this, this paper proposes a multitask convolutional sparse coding network for HSI denoising. Method The proposed method considers the denoising problem of an individual band as a single task and uses the CSC model to describe the local spatial structure correlation within each band. The denoising of all bands is regarded as a multitask problem, and all 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. This model allows for joint spatial-spectral relationship modeling of HSIs and naturally retains the spatial relationship between pixels, resulting in strong denoising ability. Using the deep unfolding technique, this paper transforms the iterative optimization of the MTCSC model into an end-to-end learnable deep neural network, i.e., multitask convolutional sparse coding network (MTCSC-Net), to further improve the model"s denoising ability and efficiency. Result The proposed method is evaluated on the ICVL and CAVE datasets, with different levels of Gaussian noise added to produce noise-clean pairs. Additionally, MTCSC-Net is tested on the real-world HYDICE Urban Dataset. Eight methods are selected for comparison to prove the effectiveness of the proposed denoising method. Experimental results show that the PSNR is improved by 1.38 dB on the CAVE dataset and 0.64 dB on the ICVL dataset, compared to traditional patch-based SR methods. Visual results show that MTCSC-Net produces cleaner spatial images and more accurate spectral reflectance, with a better match to the reference ones. Conclusion The proposed multitask convolutional sparse coding network can effectively utilize the spatial-spectral correlation information of HSIs and has stronger denoising ability, making it a promising method for HSI denoising.