Cauchy Nonnegative Matrix Factorization for Hyperspectral Unmixing Based on Graph Laplacian Regularization

Shanxue Chen; Shaohua Xu

doi:10.3788/LOP232437

Laser & Optoelectronics Progress, Volume. 61, Issue 14, 1428004(2024)

Cauchy Nonnegative Matrix Factorization for Hyperspectral Unmixing Based on Graph Laplacian Regularization

Shanxue Chen¹ and Shaohua Xu^2、*

¹Engineering Research Center of Mobile Communications of the Ministry of Education, School of Communication and Information Engineering, Chongqing University of Posts and Telecommunications, Chongqing 400065, China

²Chongqing Key Laboratory of Mobile Communications Technology, School of Communication and Information Engineering, Chongqing University of Posts and Telecommunications, Chongqing 400065, China

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Figures & Tables(19)

Fig. 1. Comparison of different loss function models

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Fig. 2. Distribution of pixel and abundance in local neighborhood

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Fig. 3. Flow of CNMF-GLR algorithm

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Fig. 4. Spectra of 4 ground objects in the Jasper Ridge dataset

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Fig. 5. Comparison of average D_SAD and E_RMSE in different neighborhoods

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Fig. 6. Average D_SAD and E_RMSE of CNMF-GLR under different $λ_{1}$ and $λ_{2}$ values

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Fig. 7. RGB display on the real data set

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Fig. 8. Comparison between end element spectra extracted by CNMF-GLR and reference spectra

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Fig. 9. Abundance image comparison of different algorithms in the Jasper Ridge dataset

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Fig. 10. Comparison between end element spectra extracted by CNMF-GLR and reference spectra

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Fig. 11. Abundance image comparison of different algorithms in Urban dataset

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Table 1. Comparison of average D_SAD of various algorithms under the influence of Gaussian white noise

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Table 1. Comparison of average D_SAD of various algorithms under the influence of Gaussian white noise

SNR /dB	MVCNMF /arb.units	CauchyNM-F /arb.units	L21NMF-SSR /arb.units	DSGLSU /arb.units	SSCNMF /arb.units	CNMF-GLR /arb.units
10	0.35536	0.30956	0.22786	0.24786	0.22897	0.20864
15	0.22466	0.20687	0.17657	0.19756	0.18864	0.17056
20	0.15284	0.13786	0.09764	0.10258	0.10189	0.09540
25	0.07867	0.07246	0.04556	0.07045	0.05874	0.04626
30	0.01897	0.03765	0.00761	0.01087	0.00996	0.00789

Table 2. E_RMSE comparison of various algorithms under the influence of Gaussian white noise

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Table 2. E_RMSE comparison of various algorithms under the influence of Gaussian white noise

SNR /dB	MVCNMF /arb.units	CauchyNM-F /arb.units	L21NMF-SSR/arb.units	DSGLSU/arb.units	SSCNMF / arb.units	CNMF-GLR / arb.units
10	0.087496	0.071213	0.069864	0.082456	0.070896	0.066233
15	0.057897	0.061012	0.047892	0.048964	0.052168	0.047223
20	0.048887	0.053396	0.034687	0.041268	0.039864	0.032899
25	0.028794	0.036765	0.013786	0.020489	0.018964	0.014896
30	0.012560	0.011587	0.006987	0.009645	0.008650	0.007231

Table 3. Comparison of average D_SAD of various algorithms under the influence of salt and pepper noise

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Table 3. Comparison of average D_SAD of various algorithms under the influence of salt and pepper noise

Grade/ arb.units	MVCNMF/ arb.units	CauchyNM-F/ arb.units	L₂₁NMF-SSR/ arb.units	DSGLSU/ arb.units	SSCNMF/ arb.units	CNMF-GLR/ arb.units
0.02	0.15814	0.12948	0.09764	0.10246	0.08979	0.08245
0.04	0.17687	0.13687	0.10788	0.13765	0.09864	0.08978
0.06	0.18094	0.15255	0.11868	0.15867	0.11736	0.09877
0.08	0.19924	0.16786	0.13254	0.17486	0.12387	0.11187
0.1	0.23948	0.16356	0.14786	0.18765	0.12278	0.11089

Table 4. E_RMSE comparison of various algorithms under the influence of salt and pepper noise

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Table 4. E_RMSE comparison of various algorithms under the influence of salt and pepper noise

Grade /arb.units	MVCNMF /arb.units	CauchyNM-F /arb.units	L₂₁NMF-SSR /arb.units	DSGLSU /arb.units	SSCNMF / arb.units	CNMF-GLR / arb.units
0.02	0.092149	0.068497	0.056798	0.078465	0.061286	0.039765
0.04	0.146836	0.087658	0.062488	0.098654	0.062186	0.057865
0.06	0.220817	0.113244	0.128247	0.143284	0.087657	0.064692
0.08	0.301487	0.154658	0.133684	0.167687	0.092468	0.070258
0.1	0.387996	0.155765	0.138994	0.193245	0.102865	0.079864

Table 5. Comparison of D_SAD values of different algorithms in the Jasper Ridge dataset

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Table 5. Comparison of D_SAD values of different algorithms in the Jasper Ridge dataset

End member	MVCNMF / arb.units	CauchyNM-F / arb.units	L21NMF-SSR / arb.units	DSGLSU / arb.units	SSCNMF / arb.units	CNMF-GLR/ arb.units
Runtime /min	8.76	10.24	12.64	13.25	14.37	13.75
water	0.13989	0.08765	0.06276	0.07265	0.07686	0.03213
vegetation	0.12265	0.12023	0.11082	0.12013	0.11265	0.06025
soil	0.17894	0.17214	0.15786	0.16896	0.15876	0.11611
road	0.16379	0.09065	0.06686	0.09685	0.09241	0.05312
mean	0.15131	0.11766	0.09957	0.11464	0.11017	0.06541

Table 6. Comparison of average E_RMSE values of different algorithms in the Jasper Ridge dataset
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Table 6. Comparison of average E_RMSE values of different algorithms in the Jasper Ridge dataset
MVCNMF /
arb.units
CauchyNM-F /arb.units
L₂₁NMF-SSR /
arb.units
DSGLSU /
arb.units
SSCNMF /
arb.units
CNMF-GLR /
arb.units
0.067262 0.047274 0.031131 0.042862 0.038652 0.019101

Table 7. Comparison of D_SAD values of different algorithms in Urban dataset

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Table 7. Comparison of D_SAD values of different algorithms in Urban dataset

End member	MVCNMF / arb.units	CauchyNM-F /arb.units	L₂₁NMF-SSR / arb.units	DSGLSU / arb.units	SSCNMF / arb.units	CNMF-GLR / arb.units
Runtime /min	12.15	15.76	16.88	16.74	18.24	17.68
asphalt	0.34587	0.30221	0.22047	0.24521	0.10275	0.11346
grass	0.32786	0.31865	0.25738	0.30125	0.05860	0.03061
tree	0.20166	0.21636	0.13104	0.20106	0.03998	0.03284
roof	0.22765	0.20168	0.14107	0.19201	0.14687	0.14558
mean	0.27576	0.25972	0.18749	0.23489	0.08705	0.08062

Table 8. Comparison of average E_RMSE values of different algorithms in Urban dataset
View table
Table 8. Comparison of average E_RMSE values of different algorithms in Urban dataset
MVCNMF /
arb.units
CauchyNM-F /arb.units
L₂₁NMF-SSR /
arb.units
DSGLSU /
arb.units
SSCNMF /
arb.units
CNMF-GLR /
arb.units
0.28365 0.26542 0.132851 0.18652 0.082145 0.064547

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Shanxue Chen, Shaohua Xu. Cauchy Nonnegative Matrix Factorization for Hyperspectral Unmixing Based on Graph Laplacian Regularization[J]. Laser & Optoelectronics Progress, 2024, 61(14): 1428004

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Paper Information

Category: Remote Sensing and Sensors

Received: Nov. 6, 2023

Accepted: Nov. 27, 2023

Published Online: Jul. 8, 2024

The Author Email: Shaohua Xu (535849135@qq.com)

DOI:10.3788/LOP232437

CSTR:32186.14.LOP232437

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Comparison of average DSAD of various algorithms under the influence of Gaussian white noise

Table 1. Comparison of average DSAD of various algorithms under the influence of Gaussian white noise

Table 2. ERMSE comparison of various algorithms under the influence of Gaussian white noise

Table 2. ERMSE comparison of various algorithms under the influence of Gaussian white noise

Table 3. Comparison of average DSAD of various algorithms under the influence of salt and pepper noise

Table 3. Comparison of average DSAD of various algorithms under the influence of salt and pepper noise

Table 4. ERMSE comparison of various algorithms under the influence of salt and pepper noise

Table 4. ERMSE comparison of various algorithms under the influence of salt and pepper noise

Table 5. Comparison of DSAD values of different algorithms in the Jasper Ridge dataset

Table 5. Comparison of DSAD values of different algorithms in the Jasper Ridge dataset

Table 6. Comparison of average ERMSE values of different algorithms in the Jasper Ridge dataset

Table 6. Comparison of average ERMSE values of different algorithms in the Jasper Ridge dataset

Table 7. Comparison of DSAD values of different algorithms in Urban dataset

Table 7. Comparison of DSAD values of different algorithms in Urban dataset

Table 8. Comparison of average ERMSE values of different algorithms in Urban dataset

Table 8. Comparison of average ERMSE values of different algorithms in Urban dataset

Table 1. Comparison of average D_SAD of various algorithms under the influence of Gaussian white noise

Table 1. Comparison of average D_SAD of various algorithms under the influence of Gaussian white noise

Table 2. E_RMSE comparison of various algorithms under the influence of Gaussian white noise

Table 2. E_RMSE comparison of various algorithms under the influence of Gaussian white noise

Table 3. Comparison of average D_SAD of various algorithms under the influence of salt and pepper noise

Table 3. Comparison of average D_SAD of various algorithms under the influence of salt and pepper noise

Table 4. E_RMSE comparison of various algorithms under the influence of salt and pepper noise

Table 4. E_RMSE comparison of various algorithms under the influence of salt and pepper noise

Table 5. Comparison of D_SAD values of different algorithms in the Jasper Ridge dataset

Table 5. Comparison of D_SAD values of different algorithms in the Jasper Ridge dataset

Table 6. Comparison of average E_RMSE values of different algorithms in the Jasper Ridge dataset

Table 6. Comparison of average E_RMSE values of different algorithms in the Jasper Ridge dataset

Table 7. Comparison of D_SAD values of different algorithms in Urban dataset

Table 7. Comparison of D_SAD values of different algorithms in Urban dataset

Table 8. Comparison of average E_RMSE values of different algorithms in Urban dataset

Table 8. Comparison of average E_RMSE values of different algorithms in Urban dataset