Hyperspectral unmixing with shared endmember variability in homogeneous region

Blocks	10	50	211	601	1157	2499
mSAD	0.419 9	0.230 1	0.086 1	0.060 3	0.064 5	0.082 2
aRMSE	0.209 2	0.157 5	0.081 7	0.092 3	0.096 9	0.112 6
yRMSE	0.107 5	0.046 6	0.019 1	0.011 9	0.010 2	0.008 6
Time/s	7.746 7	16.876 7	18.817 1	43.747 2	96.265 9	203.360 8

Table 1. [in Chinese]

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Table 1. [in Chinese]

算法1：SEVU算法

输入：

$Y \in R^{L \times N}, Y_{s l i c} \in R^{L \times q} b y S L I C, A^{(0)} \in R^{K \times N} b y F C L S,$

$A_{s l i c} \in R^{K \times q} b y S L I C, M^{(0)} \in R^{L \times K} b y V C A, α, β$ $γ, η, q, d M^{(0)} = [d M_{1} | \dots | d M_{q}], \forall d M_{i} \in R^{L \times K} = 0_{L \times K},$

$S^{(0)} = [S_{1} | \dots | S_{q}], \forall S_{i} \in R^{K \times K} = I_{K}$

输出：

$A \in R^{K \times N}, M \in R^{L \times K}, S_{s l i c} = [S_{1} | \dots | S_{q}], \forall S_{i} \in R^{K \times K},$

$d M_{s l i c} = [d M_{1} | \dots | d M_{q}], \forall d M_{i} \in R^{L \times K}$

1. $i \leftarrow 1$ ，如果没达到停止条件执行（2-6）：

2. 从 $n = 1,2, \dots, q$ 使用公式（16）~公式（20）依次求解 $a_{n}$ ， $W_{n}^{(A)}$ ， $T_{n}^{(A)}$ ， $V_{n}^{(A)}$ 和 $G_{n}^{(A)}$ ；

3. 从 $l = 1,2, \dots, L$ 使用公式（23）~公式（25）依次求解 ${\tilde{m}}_{l}$ ， $W_{l}^{(M)}$ 和 $V_{l}^{(M)}$ ；

4. 从 $n = 1,2, \dots, q$ 使用公式（27）公式（29）依次求解 $d M_{n}$ ， $W_{n}^{(d M)}$ 和 $V_{n}^{(d M)}$ ；

5. 从 $n = 1,2, \dots, q$ 使用公式（31）求解 $S_{n}$ ，使用公式（32），公式（33）依次求解 $W_{n}^{(S)}$ 和 $V_{n}^{(S)}$ ；

6. $i = i + 1$ 。

7. 利用上述步骤求得的 $A_{s l i c}, M, d M_{s l i c}, S_{s l i c}$ ，在每一个超像素中，将求得的变异端元作为端元使用FCLS逐像元求解丰度 $A$ 。

Table 2. Evaluation results of each algorithm for mSAD （Synthetic dataset SNR_30 dB）
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Table 2. Evaluation results of each algorithm for mSAD （Synthetic dataset SNR_30 dB）
Algorithm Proposed PLMM ELMM GLMM
Vegetation 0.062 8 0.081 6 0.101 3 0.105 2
Soil 0.033 6 0.039 1 0.053 7 0.054 2
Water 0.160 1 0.189 1 0.524 3 0.264 2
mSAD 0.085 5 0.103 3 0.226 4 0.135 2

Table 3. Evaluation results of each algorithm for aRMSE and yRMSE （Synthetic dataset SNR_30 dB）
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Table 3. Evaluation results of each algorithm for aRMSE and yRMSE （Synthetic dataset SNR_30 dB）
Algorithm Proposed FCLS SCLSU PLMM ELMM GLMM ALMM
aRMSE 0.056 2 0.060 9 0.074 7 0.058 8 0.061 4 0.059 5 0.063 8
yRMSE 0.012 9 0.014 7 0.011 6 0.007 2 0.003 8 0.000 3 0.000 1

Table 4. Evaluation results of each algorithm for mSAD （Jasper Ridge）

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Table 4. Evaluation results of each algorithm for mSAD （Jasper Ridge）

Algorithm	Proposed	VCA	PLMM	ELMM	GLMM
Tree	0.088 5	0.148 1	0.144 7	0.148 0	0.148 0
Water	0.075 7	0.258 2	0.069 7	0.222 6	0.178 8
Soil	0.046 0	0.116 6	0.106 2	0.117 3	0.118 4
Road	0.031 0	0.090 1	0.049 9	0.089 9	0.089 1
mSAD	0.060 3	0.153 3	0.092 6	0.144 4	0.133 6

Table 5. Evaluation results of each algorithm for aRMSE and yRMSE （Jasper Ridge）
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Table 5. Evaluation results of each algorithm for aRMSE and yRMSE （Jasper Ridge）
Algorithm Proposed FCLS SCLSU PLMM ELMM GLMM ALMM
aRMSE 0.092 3 0.123 7 0.110 1 0.116 5 0.126 1 0.124 8 0.115 7
yRMSE 0.011 9 0.011 7 0.010 4 0.006 8 0.003 1 0.000 2 0.000 1

Table 6. Evaluation results of each algorithm for yRMSE （Cuprite）
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Table 6. Evaluation results of each algorithm for yRMSE （Cuprite）
Algorithm Proposed FCLS SCLSU PLMM ELMM GLMM ALMM
yRMSE 0.006 4 0.014 5 0.014 0 0.003 4 0.004 2 0.000 1 0.000 3

Table 7. Evaluation results of each algorithm for mSAD （Cuprite）

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Table 7. Evaluation results of each algorithm for mSAD （Cuprite）

Algorithm	Proposed	VCA	PLMM	ELMM	GLMM
Alunite	0.127 6	0.129 3	0.184 7	0.129 6	0.129 8
Andradite	0.077 4	0.081 5	0.144 2	0.058 8	0.066 1
Buddingtonite	0.118 3	0.114 9	0.113 8	0.114 9	0.114 8
Dumortierite	0.077 6	0.064 1	0.078 0	0.064 2	0.064 2
Kaolinite1	0.067 1	0.083 9	0.122 0	0.081 0	0.079 5
Kaolinite2	0.049 2	0.069 4	0.068 8	0.069 9	0.070 4
Muscovite	0.152 4	0.083 0	0.196 1	0.083 5	0.083 7
Montmorillonite	0.048 6	0.049 8	0.078 7	0.052 1	0.052 4
Nontronite	0.097 4	0.073 4	0.094 8	0.073 3	0.073 4
Pyrope	0.053 2	0.209 5	0.228 9	0.209 6	0.209 4
Sphene	0.254 5	0.300 1	0.050 2	0.300 2	0.300 1
Chalcedony	0.080 5	0.144 4	0.061 8	0.144 5	0.144 7
mSAD	0.100 3	0.117 0	0.118 7	0.115 1	0.115 7

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Ning WANG, Wenxing BAO, Kewen QU, Wei FENG. Hyperspectral unmixing with shared endmember variability in homogeneous region[J]. Optics and Precision Engineering, 2024, 32(4): 578

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Paper Information

Category:

Received: Aug. 5, 2023

Accepted: --

Published Online: Apr. 2, 2024

The Author Email: BAO Wenxing (bwx71@163.com), QU Kewen (kewen.qu@nmu.edu.cn)

DOI:10.37188/OPE.20243204.0578

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Effect of number of superpixel blocks on mSAD， aRMSE， yRMSE

Table 1. Effect of number of superpixel blocks on mSAD， aRMSE， yRMSE

Table 1. [in Chinese]

Table 1. [in Chinese]

Table 2. Evaluation results of each algorithm for mSAD （Synthetic dataset SNR_30 dB）

Table 2. Evaluation results of each algorithm for mSAD （Synthetic dataset SNR_30 dB）

Table 3. Evaluation results of each algorithm for aRMSE and yRMSE （Synthetic dataset SNR_30 dB）

Table 3. Evaluation results of each algorithm for aRMSE and yRMSE （Synthetic dataset SNR_30 dB）

Table 4. Evaluation results of each algorithm for mSAD （Jasper Ridge）

Table 4. Evaluation results of each algorithm for mSAD （Jasper Ridge）

Table 5. Evaluation results of each algorithm for aRMSE and yRMSE （Jasper Ridge）

Table 5. Evaluation results of each algorithm for aRMSE and yRMSE （Jasper Ridge）

Table 6. Evaluation results of each algorithm for yRMSE （Cuprite）

Table 6. Evaluation results of each algorithm for yRMSE （Cuprite）

Table 7. Evaluation results of each algorithm for mSAD （Cuprite）

Table 7. Evaluation results of each algorithm for mSAD （Cuprite）

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