Spatial-spectral reweighted sparse multi-layer nonnegative matrix factorization for hyperspectral image unmixing

Fig. 2. Experimental results of different models dealing with synthetic datasets

Fig. 3. First row （a） shows the true abundance and the second row （b） shows the abundance obtained by the model

Fig. 4. Comparison of the estimated endmember curves with the true endmember curves for the synthetic dataset

Fig. 5. Comparison between the abundance obtained by the model and the true abundance

Fig. 6. Comparison of the true endmember curves with the reference endmember curve

Fig. 7. Abundance map obtained by the model （From top to bottom， the first row：Alunite， Pyrope， Muscovite， Andradite .The second row： Dumortierite， Montmorillonite， Sphene， Kaolinite_2 . The third row： Nontronite， Chalcedony， Buddingtonite， Kaolinite_1）

Fig. 8. Comparison of the true endmember curves with the reference endmember curve （From left to right， from top to bottom， the first row of subgraphs are： Alunite， Andradite， Buddingtonite， Dumortierite. The second row of subgraphs are：Kaolinite_1， Kaolinite_2， Muscovite， Montmorillonite.The third row of subgraphs are： Nontronite， Pyrope， Sphene， Chalcedony.）

Table 1. [in Chinese]

Table 1. [in Chinese]

算法1：SSRS-MLNMF算法
输入：高光谱图像数据 $X \in R^{L \times N}$ ，端元数量 $P$ ，参数 $α_{0}, τ, L_{m a x}, T_{m a x}$
输出：端元矩阵 $E \in R^{L \times P}$ 和丰度矩阵 $S \in R^{P \times N}$
初始化： $A, S$ ，计算空间权重和光谱权重并融合得到 $W^{s p a - s p e}$ ，计算高光谱粗略图，并构建去噪权重 $V$ Repeat： 1. $A_{l + 1} \leftarrow A_{l} . * (X_{l} S_{l}^{T}) . / (A_{l} S_{l} S_{l}^{T} + \frac{1}{4} α_{A} {(A_{l})}^{- \frac{3}{4}})$ 2. $\begin{array}{l} S_{l + 1} \leftarrow S_{l} . * (A_{l}^{T} X_{l}) \\ . / (A_{l}^{T} A_{l} S_{l} + \frac{1}{4} α_{S} V ⊙ {(V ⊙ S_{l})}^{- \frac{3}{4}}) \end{array}$
3.更新权重因子： $V^{t + 1} = \frac{1}{{‖S^{t}‖}_{2,1} + ξ}$ 4.更新条件： $k + 1 \leftarrow k$ 停止条件：直到满足停止条件。
结束：返回结果： $A = \prod_{l = 1}^{L} A_{l}, S = S_{L}$

Table 1. mSAD comparison of different algorithms under different noise levels （synthetic dataset）

Table 1. mSAD comparison of different algorithms under different noise levels （synthetic dataset）

SNR/算法	VCA	L1-NMF	MLNMF	DMF	Pro-BM3D	Proposed
SNR=10 dB	0.251 2	0.118 5	0.105 4	0.226 9	0.036 5	0.041 3
SNR=20 dB	0.207 6	0.070 1	0.068 5	0.207 3	0.041 4	0.039 9
SNR=30 dB	0.183 9	0.064 8	0.064 3	0.126 4	0.040 5	0.038 7
SNR=40 dB	0.119 3	0.050 5	0.059 3	0.106 6	0.036 1	0.035 8

Table 2. RMSE comparison of different algorithms under different noise levels （synthetic dataset）

Table 2. RMSE comparison of different algorithms under different noise levels （synthetic dataset）

SNR/算法	VCA	L1-NMF	MLNMF	DMF	Pro-BM3D	Proposed
SNR=10 dB	0.137 9	01 421	0.057 9	0.142 1	0.060 2	0.053 9
SNR=20 dB	0.093 8	0.107 4	0.055 9	0.121 9	0.049 8	0.047 2
SNR=30 dB	0.105 8	0.096 5	0.048 2	0.101 5	0.046 4	0.045 1
SNR=40 dB	0.102 8	0.082 4	0.046 4	0.081 5	0.047 2	0.043 7

Table 3. Optimal structural parameters of the model （synthetic dataset）
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Table 3. Optimal structural parameters of the model （synthetic dataset）
层数每层迭代次数 mSAD
5 1 000 0.076 9
5 800 0.060 2
10 1 000 0.029 1
10 800 0.051 2
15 800 0.048 7
15 500 0.057 1

Table 4. Performance of different algorithms on synthetic dataset

Table 4. Performance of different algorithms on synthetic dataset

	VCA	L1-NMF	MLNMF	DMF	Pro-BM3D	Proposed
Almandine	0.253 4	0.264 9	0.034 4	0.170 4	0.032 0	0.017 1
Ammonio	0.583 7	0.333 6	0.037 3	0.051 8	0.016 3	0.019 0
Antigorite	0.153 7	0.130 8	0.104 8	0.200 2	0.038 3	0.025 8
Axinite	0.639 1	0.122 9	0.123 7	0.176 9	0.046 0	0.061 3
Biotite	0.191 9	0.275 9	0.113 2	0.289 8	0.060 4	0.025 8
Carnallite	0.349 3	0.397 6	0.027 8	0.139 3	0.023 3	0.025 4
mSAD	0.361 9	0.254 2	0.073 5	0.171 4	0.036 1	0.029 1
mRMSE	0.087 8	0.086 7	0.064 1	0.041 5	0.059 6	0.038 1

Table 5. Optimal structural parameters of the model （Jasper Ridge dataset）
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Table 5. Optimal structural parameters of the model （Jasper Ridge dataset）
层数每层迭代次数 mSAD
40 600 0.083 1
40 800 0.088 2
50 600 0.051 6
50 800 0.056 4
60 600 0.066 9
60 800 0.087 3

Table 6. Performance of different algorithms on the Jasper Ridge dataset

Table 6. Performance of different algorithms on the Jasper Ridge dataset

	VCA	L1-NMF	MLNMF	DMF	Pro-BM3D	Proposed
Tree	0.197 9	0.105 6	0.190 3	0.050 7	0.053 2	0.047 1
Water	0.445 5	0.196 4	0.150 0	0.139 1	0.103 5	0.106 8
Dirt	0.279 1	0.362 1	0.238 7	0.206 0	0.025 6	0.030 2
Road	0.265 6	0.402 9	0.196 6	0.116 5	0.031 1	0.022 4
mSAD	0.297 0	0.266 7	0.193 9	0.128 1	0.053 4	0.051 6
mRMSE	0.197 9	0.105 6	0.090 3	0.050 7	0.053 2	0.046 3

Table 7. Optimal structural parameters of the model （Cuprite dataset）
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Table 7. Optimal structural parameters of the model （Cuprite dataset）
层数每层迭代次数 mSAD
15 1 000 0.142 8
15 1 500 0.153 7
20 1 000 0.144 0
20 1 500 0.145 5
25 1 000 0.138 6
25 1 500 0.110 9

Table 8. Performance of different algorithms on the Cuprite dataset

Table 8. Performance of different algorithms on the Cuprite dataset

	VCA	L1NMF	MLNMF	DMF	Pro-BM3D	Proposed
#1 Alunite	1.141 0	0.052 5	0.112 6	1.078	0..1 865	0.177 4
#2 Andradite	0.126 7	0.075 8	0.087 6	0.086 6	0.154 3	0.081 1
#3 Buddingtonite	0.199 8	0.078 1	0.134 5	0.143 7	0.107 6	0.175 5
#4 Dumortierite	0.277 9	0.083 4	0.115 7	0.951 1	0.117 1	0.133 3
#5 Kaolinite_1	0.158 5	0.083 7	0.085 3	0.115 7	0.091 4	0.082 0
#6 Kaolinite_2	0.101 1	0.094 3	0.058 1	0.068 9	0.224 8	0.149 5
#7 Muscovite	0.174 8	0.102 1	1.363 6	1.003 5	0.094 0	0.024 6
#8 Montmorillonite	0.108 5	0.102 3	0.072 4	0.057 9	0.080 0	0.130 2
#9 Nontronite	0.131 2	0.112 1	0.190 6	0.092 8	0.169 8	0.111 4
#10 Pyrope	0.141 2	0.146 2	0.089 6	0.112 9	0.110 8	0.089 3
#11Sphene	0.264 2	0.146 9	0.164 7	0.101 4	0.157 8	0.075 6
#12Chalcedony	0.133 9	0.174 0	0.136	1.017 6	0.161 5	0.101 7
mSAD	0.246 6	0.116 4	0.217 6	0.402 5	0.138 0	0.110 9

Table 9. Sum the time taken by each algorithm to process different datasets