A Novel Linear Hyperspectral Unmixing Method Based on Collaborative Sparsity and Total Variation
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摘要: 稀疏分解是高光谱图像（Hyperspectral image，HSI）解混中的常用方法，为了克服传统稀疏解混方法只重视挖掘空间相关性而忽视稀疏性精确刻画的缺点，本文提出一种新的基于协同稀疏和全变差（Total variation，TV）相结合的高光谱空谱联合线性解混方法，从而进一步提高解混的精度.该方法基于已知光谱库的高光谱稀疏线性回归模型，利用TV正则项对高光谱邻域像元间的相关性进行约束；同时，协同稀疏性被用来刻画丰度系数的行稀疏性，从而表明协同稀疏先验对空谱联合解混精度的提高至关重要；最后采用交替方向乘子法求解模型.模拟高光谱数据实验结果定量地验证本文方法能够比现有同类方法获得更精确的解混结果，同时真实高光谱数据实验结果定性地验证了本文方法的有效性.Abstract: Sparse decomposition is one of the popular tools for hyperspectral unmixing. In order to overcome the shortcomings of traditional sparse unmixing methods which only pay attention to the spatial correlation and neglect depicting sparsity accurately, we propose a new spatial-spectrally linear hyperspectral unmixing method based on collaborative sparsity and total variation (TV) regularization to further improve the accuracy of unmixing. This method is based on hyperspectral sparse linear regression model with a spectral library given in advance, in which the total variation is utilized to impose a constraint on the correlation between neighboring pixels of hyperspectral image (HSI). Meanwhile, the collaborative sparsity is explored to depict the row-sparse characteristic of the fractional abundances, thus pointing out the fact that the collaborative sparsity prior plays an important role in further accuracy improvement of HSI spatial-spectral unmixing. At last, the proposed model is solved by the alternating direction method of multipliers. Experimental results on simulated hyperspectral data quantitatively validate that the our method outperforms those state-of-the-art algorithms, and the experimental results on real hyperspectral data qualitatively verify the effectiveness of the algorithm.1) 本文责任编委 辛景民
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图 1 基于协同稀疏和TV正则项的高光谱线性解混方法的流程图
Fig. 1 Flowchart of the method based on collaborative sparsity and total variation
图 3 模拟数据图以及其中5个端元的真实丰度图
Fig. 3 Simulated image and five true fractional abundances of endmembers in the simulated dataset
图 4 不同噪声下CLSUnSAL-TV算法得到的关于参数$\lambda$和$\lambda_{\text{TV}}$的SRE函数图
Fig. 4 SRE (dB) as a function of parameters $\lambda$ and $\lambda_{\text{TV}}$ obtained by CLSUnSAL-TV algorithm in different noise levels
图 5 信噪比为40 dB情况下6种算法解混得到的丰度图
Fig. 5 Reconstructed abundances of six methods for simulated dataset when SNR = 40 (dB)
图 6 Cuprite数据的RGB伪彩合成图(波段15、23、117)
Fig. 6 The false color image of AVIRIS Cuprite (band 15、23、117)
图 7 对真实数据使用6种方法解混得到的丰度图
Fig. 7 Reconstructed abundances of six methods for real dataset
表 1 6种方法在最优参数($\lambda, \lambda_{\text{TV}}, \mu$)时对模拟数据集解混得到的SRE (dB), RMSE ($10^{-2}$)以及所需时间$t$ (s)
Table 1 SRE, RMSE ($10^{-2}$), the running time (seconds), and optimal parameters of the six unmixing methods for the simulated dataset
Constraint SNR (dB) NCLS SUnSAL CLSUnSAL NCLS-TV SUnSAL-TV 本文方法 SRE $-$6.605 2.810 5.781 6.325 9.752 9.887 不添加 RMSE 7.39 2.50 1.77 1.67 1.14 1.11 "和为一" 20 $t$ 27.893 15.895 46.083 288.623 344.225 312.128 约束 $\lambda$ 0 0.01 1 0 0.005 0.5 $\lambda_{\text{TV}}$ 0 0 0 0.01 0.01 0.05 $\mu$ 0.01 0.05 0.02 0.05 0.05 0.03 SRE 0.910 6.155 9.501 10.054 14.153 15.095 不添加 RMSE 3.11 1.70 1.16 1.09 0.68 0.61 "和为一" 30 $t$ 12.322 27.303 52.105 110.546 114.569 91.574 约束 $\lambda$ 0 0.01 1 0 0.005 0.5 $\lambda_{\text{TV}}$ 0 0 0 0.01 0.01 0.05 $\mu$ 0.01 0.05 0.02 0.05 0.05 0.03 SRE 5.497 11.150 17.850 18.772 22.003 23.625 不添加 RMSE 1.83 0.96 0.41 0.40 0.27 0.23 "和为一" 40 $t$ 7.2 30.76 17.406 122.905 129.609 97.493 约束 $\lambda$ 0 0.01 0.5 0 0.0005 0.1 $\lambda_{\text{TV}}$ 0 0 0 0.05 0.005 0.005 $\mu$ 0.01 0.05 0.08 0.04 0.04 0.05 SRE 2.339 2.861 5.826 7.033 10.069 10.123 添加 RMSE 2.64 2.50 1.75 1.54 1.08 1.06 "和为一" 20 $t$ 36.146 22.197 58.385 28.750 351.530 320.872 约束 $\lambda$ 0 0.1 1 0 0.0005 0.05 $\lambda_{\text{TV}}$ 0 0 0 0.05 0.1 0.05 $\mu$ 0.01 0.05 0.05 0.05 0.5 0.3 SRE 5.955 6.176 9.680 13.424 14.619 15.272 添加 RMSE 1.74 1.70 1.53 0.74 0.64 0.60 "和为一" 30 $t$ 18.981 31.524 62.153 119.349 125.995 124.671 约束 $\lambda$ 0 0.05 1 0 0.005 0.5 $\lambda_{\text{TV}}$ 0 0 0 0.01 0.01 0.005 $\mu$ 0.01 0.05 0.02 0.8 0.8 0.02 SRE 10.633 11.317 19.010 22.344 22.390 23.998 添加 RMSE 1.01 0.94 0.39 0.26 0.25 0.22 "和为一" 40 $t$ 11.571 35.470 27.047 128.115 140.698 109.489 约束 $\lambda$ 0 0.01 0.5 0 0.0005 0.1 $\lambda_{\text{TV}}$ 0 0 0 0.05 0.005 0.005 $\mu$ 0.01 0.05 0.03 0.05 0.1 0.04 
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