Spectral weighted sparse unmixing of hyperspectral images based on framelet transform

Chenguang XU; Hongyu XU; Chunyan YU; Chengzhi DENG

doi:10.37188/OPE.20233109.1404

Optics and Precision Engineering, Volume. 31, Issue 9, 1404(2023)

Spectral weighted sparse unmixing of hyperspectral images based on framelet transform

Chenguang XU, Hongyu XU, Chunyan YU, and Chengzhi DENG^*

Jiangxi Province Key Laboratory of Water Information Cooperative Sensing and Intelligent Processing，Nanchang Institute of Technology， Nanchang330099， China

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Figures & Tables(10)

$True fractional abundances of endmembers in DC1$

Fig. 1. True fractional abundances of endmembers in DC1

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$True fractional abundances of endmembers in DC2$

Fig. 2. True fractional abundances of endmembers in DC2

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Fig. 3. Estimated abundance and difference maps of DC1 after unmixing by five methods under 40 dB

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Fig. 4. Estimated abundance and difference maps of DC2 after unmixing by five methods under 40 dB

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Fig. 5. True and best estimated abundance of DC1 and DC2 after unmixing by five methods under SNR=20 dB

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Fig. 6. Map of different minerals in Cuprite mining district in Nevada

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Fig. 7. Abundance map of cuprite data after unmixing with five methods

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Table 1. Pseudo-code of SFSU

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Table 1. Pseudo-code of SFSU

1. Input： spectrum library $S$ and observed data $Y$ .

2. Initialize： $k = 0$ ， $t = 0$ ， $α > 0$ ， $λ > 0$ ， $μ > 0$ ， $U^{0} = {(S^{T} S + 2 I)}^{- 1} (S^{T} Y)$ ， $V_{1}^{0} = S U^{0}$ ， $V_{2}^{0} = W U^{0}$ ， $V_{3}^{0} = U^{0}$ ， $D_{1}^{0} = 0$ ， $D_{2}^{0} = 0$ ， $D_{3}^{0} = 0$ 。

3. Repeat until the stop condition is reached

（1） Update $Κ$ with formula （15），

（2） Repeat until the stop condition is reached

（a） Update variables $U_{}^{t + 1},$ $V_{1}^{t + 1},$ $V_{2}^{t + 1},$ $V_{3}^{t + 1}$ with formulas （19）-（22） respectively.

（b） Update Lagrangian operators：

$D_{1}^{t + 1} = D_{1}^{t} - (S U^{t + 1} - V_{1}^{t + 1}) .$

$D_{2}^{t + 1} = D_{2}^{t} - (W U^{t + 1} - V_{2}^{t + 1}) .$

$D_{3}^{t + 1} = D_{3}^{t} - (U^{t + 1} - V_{3}^{t + 1}) .$

（c） Update inner iteration times： $t = t + 1 .$

（d） variable replacement：

$U_{}^{k + 1} = U_{}^{t + 1}$ ， $D_{}^{k + 1} = D_{}^{t + 1}$ .

（3） Update outer iteration times： $k = k + 1 .$

4. Output： $X$ .

Table 2. Results of DC1 after unmixing under different SNRs

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Table 2. Results of DC1 after unmixing under different SNRs

Algorithms	SNR=20				SNR=30				SNR=40
Algorithms	$S R E / d B$	$p_{s}$	$λ$	$α$	$S R E / d B$	$p_{s}$	$λ$	$α$	$S R E / d B$	$p_{s}$	$λ$	$α$
SUnSAL	2.844 5	0.178 5	0.5	-	6.117 1	0.808 5	0.05	-	11.149 8	0.999 6	0.01	-
CLSUnSAL	5.911	0.927 5	20	-	7.515 0	0.967 8	1.5	-	14.853 7	1	0.5	-
RWCLSUnSAL	0.965 8	0.089 1	0.007	-	5.104 9	0.581 9	0.001	-	8.901 9	0.981 7	0.000 2	-
FSU	8.530 6	0.972 4	0.05	0.005	11.103 4	0.993 1	0.01	0.05	18.273 1	0.999 1	0.02	0.1
SFSU	11.018 6	0.988 6	0.05	0.001	20.871 7	1	0.05	0.01	26.979 0	1	0.07	0.08

Table 3. Results of DC2 after unmixing under different SNRs

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Table 3. Results of DC2 after unmixing under different SNRs

Algorithms	SNR=20				SNR=30				SNR=40
Algorithms	$S R E / d B$	$p_{s}$	$λ$	$α$	$S R E / d B$	$p_{s}$	$λ$	$α$	$S R E / d B$	$p_{s}$	$λ$	$α$
SUnSAL	4.216 7	0.559 7	0.2	-	8.475 8	0.798 3	0.02	-	14.271 2	0.990 2	0.005	-
CLSUnSAL	3.414 8	0.468 6	2.2	-	6.619 8	0.735 8	0.33	-	11.446 8	0.971 5	0.02	-
RWCLSUnSAL	3.683 2	0.533 5	0.03	-	8.185 3	0.812 7	0.01	-	14.868 4	0.973 90	0.000 1	-
FSU	7.447 3	0.744 1	0.05	0.005	12.627 5	0.967 4	0.01	0.05	16.341 2	0.999 6	0.001	0.1
SFSU	8.369 5	0.842 5	0.2	0.006	16.044 6	0.963 2	0.007	0.01	29.523 7	1	0.007	0.1

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Chenguang XU, Hongyu XU, Chunyan YU, Chengzhi DENG. Spectral weighted sparse unmixing of hyperspectral images based on framelet transform[J]. Optics and Precision Engineering, 2023, 31(9): 1404

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Paper Information

Category: Information Sciences

Received: May. 18, 2022

Accepted: --

Published Online: Jun. 6, 2023

The Author Email: Chengzhi DENG (dengcz@nit.edu.cn)

DOI:10.37188/OPE.20233109.1404

Topics

laser devices and laser physics

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