目的 基于非负矩阵分解的高光谱图像无监督解混算法普遍存在着目标函数对噪声敏感、在低信噪比条件下端元提取和丰度估计性能不佳的缺点。因此，提出一种基于稳健非负矩阵分解的高光谱图像混合像元分解算法。方法 首先在传统基于非负矩阵分解的解混算法基础上，对目标函数加以改进，用更加稳健的L₁范数作为重建误差项，提高算法对噪声的适应能力，得到新的无监督解混目标函数。针对新目标函数的非凸特性，利用梯度下降法对端元矩阵和丰度矩阵交替迭代求解，进而完成优化求解，得到端元和丰度估计值。结果 分别利用模拟和真实高光谱数据，对算法性能进行定性和定量分析。在模拟数据集中，将本文算法与具有代表性的5种无监督解混算法进行比较，相比于对比算法中最优者，本文算法在典型信噪比20 dB下，光谱角距离（spectral angle distance，SAD）增大了10.5%，信号重构误差（signal to reconstruction error，SRE）减小了9.3%；在真实数据集中，利用光谱库中的地物光谱特征验证本文算法端元提取质量，并利用真实地物分布定性分析丰度估计结果。结论 提出的基于稳健非负矩阵分解的高光谱无监督解混算法，在低信噪比条件下，能够获得较好的端元提取和丰度估计精度，解混效果更好。

Objective During hyperspectral remote sensing imaging, each captured pixel in the image always has mixed spectrum of several pure constituent spectra due to the low spatial resolution of hyperspectral cameras and the diversity of spectral signatures in nature scenes. The mixed pixels limit the application of hyperspectral images (HSI), such as target detection, classification, and change detection, to a great extent. In many real-world applications, subpixel level accuracy is often required to improve the performance. Thus, the unmixing is very essential in the HSI analysis. In most scenarios, the spectral signatures in HSI, also termed endmembers, are unknown in advance. Therefore, the unmixing has to be performed in an unsupervised way, usually involving two steps, namely, endmember extraction and abundance coefficient estimation. In this study, we assume that the generation of mixed pixels in HSI is based on a linear mixing model. Moreover, the observed HSI, endmembers in the image, and the corresponding abundances are all non-negative, according to their physical meaning. In recent years, non-negative matrix factorization (NMF) based approaches has received extensive attention and become a research hotspot because of making full use of the HSI sparsity. However, existing non-negative matrix factorization-based approaches are not robust enough for noisy HSI data. The main reason is that a least square loss function, which is sensitive to noise and prone to large deviations, is always used for endmember extraction in these approaches. To overcome the drawbacks of NMF-based approaches, we can improve the robustness of the unmixing approaches by choosing a new loss function, which is robust. In this study, we utilize more robust L₁ loss function for NMF when performing the endmember extraction and proposed a novel unsupervised hyperspectral unmixing method based on robust NMF. Method To perform the unsupervised hyperspectral unmixing, with the endmembers unknown, both endmember extraction and the corresponding abundance fraction estimation are needed to be solved. The hyperspectral unmixing problem can be modeled as a NMF due to the similarity of underlying mathematical models. In real scenes, hyperspectral image data often contains noise and missing values, and objective functions used for endmember extraction in existing NMF-based approaches are sensitive to noise and prone to large deviations. Therefore, we use the L₁ norm on the reconstruction error term instead of the common L₂ norm to construct a new objective function. However, the new objective function is nonconvex. We can obtain the global optimal solution of one variable when the other is fixed. In addition, considering the nonsmooth L₁ norm term, to solve the optimization problem in the proposed unmixing approach is challenging. Thus, we propose an efficient multiplicative updating algorithm with the theory of the iterative reweighted least squares. In this way, each iteration can guarantee positive result. Finally, we can obtain the extracted endmembers and estimated abundances when iterative convergences. Result To verify the effectiveness and competitiveness of the proposed unsupervised unmixing, synthetic and real-world dataset are used in the experiments. The performance of the proposed approach is comprehensively evaluated with visual observations and quantitative measures. For quantitative comparison, three categories of evaluation indexes are used in this study. The indexes to measure the quality of the endmember extraction are the spectral angle distance (SAD) and the spectral information divergence (SID). Similarly, the performance discriminators to evaluate the accuracy of the abundance estimation are the abundance angle distance (AAD) and the abundance information divergence (AID). Moreover, the metrics to evaluate the performance of the reconstruction of spectral mixtures are the root mean square error (RMSE) and the signal to reconstruction error (SRE).With the synthetic dataset, we compare the proposed method with five representative methods. Among them, vertex component analysis (VCA) is a classic geometrical-based method and also the initialization of the proposed method. Minimum volume constrained nonnegative matrix factorization (MVCNMF), robust collaborative NMF (RCoNMF), and total variation regularized reweighted sparse NMF (TVWSNMF) are NMF-based approaches, and an untied denoising autoencoder with sparsity for spectral unmixing (uDAS) is deep learning-based approach. The experimental results showed that, when signal-to-noise ratio (SNR) is 20 dB, the SAD (less is better) of the proposed algorithm decreased by 41.3%, 43%, 65.6%, 10.5%, and 58.0% compared with the VCA, MVCNMF, RCoNMF, TVWSNMF, and uDAS; the SID (less is better) decreased by 68.9%, 83.6%, 95.5%, 62.2%, and 97.0%; the AAD (less is better) decreased by 28.5%, 12.5%, 45.8%, 8.4%, and 42.5%; the AID (less is better) decreased by 38.1%, 28.7%, 51.1%, 17.2%, and 49.7%; the RMSE (less is better) decreased by 48.3%, 31.2%, 68.9%, 33.5%, and 67.8%; and SRE (dB) (higher is better) increased by 23.7%, 14.5%, 60.0%, 9.3%, and 47.3%, respectively. With the real world data set, the ability of the proposed approach to extract endmembers can be evaluated using the corresponding USGS(United States Geological Survey) library signatures. Moreover, given that the ground truth abundance maps are unknown exactly, the abundance estimation results can only be evaluated qualitatively. The experimental results demonstrated that the extracted endmembers achieved a good match with the ground truth signatures. In addition, the proposed approach achieved piecewise smooth abundance maps with high spatial consistency. Conclusion In this study, we proposed a novel NMF-based unmixing approach to perform the unsupervised hyperspectral unmixing in noisy environments. Different from the current NMF-based unmixing approaches, robust L₁ norm is used as the reconstruction error term in the objective function to improve the accuracy of the endmember extraction and abundance estimation. Compared with the state-of-the-art approaches, experimental results of synthetic data set and real world data set illustrate that the proposed approach performs well under different noise conditions, especially in low SNR.