Hyperspectral Image Super Resolution via Nonconvex Low-rank Constraint of Tensor Ring Factors

Fig. 5. The first line gives the visual comparison of the reconstruction results at the 21th band of the Curpriter Mine dataset，and the second line shows the related error images

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Fig. 6. The PSNR values of five methods in different bands of three data sets are compared

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Fig. 7. The first line gives the visual comparison of the reconstruction results at the 80th band of the Washington DC mall dataset，and the second line shows the related error image

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Fig. 8. The first line gives the visualization comparison of reconstruction results at band 63 of Pavia City Center dataset，and the second line is the related error image

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Table 1. The closed form solution for Eq.（12）

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Table 1. The closed form solution for Eq.（12）

Input：

H_{1}

，

H_{2}

，

H_{3}

，

B

，

S

1：Eigen-decomposition of $B$ ： $B = F K F^{H}$

2： $\bar{K} = K (l_{d} \otimes l_{n})$

3：Eigen-decomposition of $H$ ： $H_{1} = Q_{1} Λ Q_{1}^{- 1}$

4： $O = Q_{1}^{- 1} H_{3} F$

5：for $i = 1$ to $L$ do：

6： $o_{l} = λ_{l}^{- 1} o_{l} - λ_{l}^{- 1} o_{l} \bar{K} (λ_{l} d I_{n} + \sum_{t = 1}^{d} K_{t}^{2}) {\bar{K}}^{H}$

7：end for

8：set $A_{(3)} = Q_{1} \bar{A} F^{H}$

Output： $A_{(3)}$

Table 2. Solution of LRTRLogTNN model via ADMM algorithm

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Table 2. Solution of LRTRLogTNN model via ADMM algorithm

Input：HR-MSI

X

；LR-HSI

Y

；tradeoff parameter

λ

，

η

，Randomly sampled

G^{n}, n = 1, \dots, N

，TR Rank

R

，maximum iteration

T

Output：HR-HSI $Z$

Initialization： $λ = 1$ ， $η = 0.7$ ， $R = 11$ ， $T = 30$ ， $μ_{1} = μ_{2} = 0.001$ ， $i t e r = 0$ ；

Learn the orthogonal basis matrix $D$ from $X_{(3)}$ via SVD；

While not converged do：

iter=iter+1；

Update $A_{(3)}$ via table 1；

For $n = 1, \dots, N$ ，Update $G^{(n)}$ via（20）；

Update $J$ via（22）；

For $n = 1, \dots, N$ ，Update $M_{i}^{(n)}$ via（25）；

end

Output： $Z = A \times_{3} D$

Table 3. Quantitative evaluation results of all test methods in Cuprite Mine data set

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Table 3. Quantitative evaluation results of all test methods in Cuprite Mine data set

Methods	Quantitative metrics
Methods	MPSNR	MSSIM	UIQI	CC	SAM	ERGAS	DD	RMSE
Best values	$+ \infty$	1	1	1	0	0	0	0
NSSR	37.961 0	0.964 2	0.981 3	0.990 2	1.673 7	0.973 5	2.574 5	0.015 0
CSTF	39.520 7	0.975 2	0.987 4	0.993 1	1.584 7	0.804 9	2.168 1	0.012 4
UTV	41.365 1	0.980 0	0.968 9	0.994 2	1.453 8	0.765 8	1.864 6	0.011 5
LTMR	42.745 3	0.975 2	0.993 0	0.995 9	1.198 0	0.603 4	1.528 6	0.009 6
LRTRLogTNN	43.176 3	0.987 9	0.993 6	0.996 3	1.143 6	0.603 4	1.449 1	0.009 0

Table 4. Quantitative evaluation index results of testing methods in Washington DC Mall data set

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Table 4. Quantitative evaluation index results of testing methods in Washington DC Mall data set

Qethods	Quantitative metrics
Qethods	MPSNR	MSSIM	UIQI	CC	SAM	ERGAS	DD	RMSE
Best values	$+ \infty$	1	1	1	0	0	0	0
NSSR	38.879 7	0.976 6	0.991 0	0.993 8	3.778 9	1.717 2	2.495 7	0.018 2
CSTF	39.419 1	0.979 8	0.994 3	0.995 9	4.029 3	1.542 1	2.463 7	0.013 9
UTV	38.973	0.975 3	0.993 9	0.995 7	4.457 1	1.691 3	2.722 1	0.014 4
LTMR	41.133 7	0.986 5	0.995 8	0.997 0	3.108 9	1.253 8	1.920 9	0.011 9
LRTRLogTNN	41.87	0.988 5	0.996 4	0.997 5	2.699 5	1.138 3	1.673 3	0.010 9

Table 5. Quantitative evaluation index results of testing methods in Pavia City Center data set

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Table 5. Quantitative evaluation index results of testing methods in Pavia City Center data set

Methods	Quantitative metrics
Methods	MPSNR	MSSIM	UIQI	CC	SAM	ERGAS	DD	RMSE
Best values	$+ \infty$	1	1	1	0	0	0	0
NSSR	44.672 0	0.993 3	0.996 5	0.997 1	2.411 7	0.934 3	1.109 7	0.007 4
CSTF	45.910 5	0.995 1	0.998 1	0.998 2	2.396 5	0.796 9	0.987 2	0.005 5
UTV	46.694 7	0.995 8	0.998 4	0.998 6	2.262 4	0.709 7	0.893 9	0.004 9
LTMR	47.618 1	0.996 8	0.998 7	0.998 9	1.910 7	0.633 1	0.751 2	0.004 2
LRTRLogTNN	48.276 3	0.998 9	0.998 9	0.999 1	1.784 5	0.557 6	0.698 1	0.003 8

Table 6. Comparison results of running time by applying five test methods on Pavia City Center data set
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Table 6. Comparison results of running time by applying five test methods on Pavia City Center data set
Methods NSSR CSTF UTV LTMR LRTRLogTNN
Running time/s 25.81 120.47 169.60 34.90 672.56

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Jianwei ZHENG, Xinjie ZHOU, Honghui XU, Mengjie QING, Cong BAI. Hyperspectral Image Super Resolution via Nonconvex Low-rank Constraint of Tensor Ring Factors[J]. Acta Photonica Sinica, 2022, 51(2): 0210003

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Paper Information

Category:

Received: Jun. 25, 2021

Accepted: Sep. 6, 2021

Published Online: May. 19, 2022

The Author Email: BAI Cong (congbai@zjut.edu.cn)

DOI:10.3788/gzxb20225102.0210003

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. The closed form solution for Eq.（12）

Table 1. The closed form solution for Eq.（12）

Table 2. Solution of LRTRLogTNN model via ADMM algorithm

Table 2. Solution of LRTRLogTNN model via ADMM algorithm

Table 3. Quantitative evaluation results of all test methods in Cuprite Mine data set

Table 3. Quantitative evaluation results of all test methods in Cuprite Mine data set

Table 4. Quantitative evaluation index results of testing methods in Washington DC Mall data set

Table 4. Quantitative evaluation index results of testing methods in Washington DC Mall data set

Table 5. Quantitative evaluation index results of testing methods in Pavia City Center data set

Table 5. Quantitative evaluation index results of testing methods in Pavia City Center data set

Table 6. Comparison results of running time by applying five test methods on Pavia City Center data set

Table 6. Comparison results of running time by applying five test methods on Pavia City Center data set