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

Jianwei ZHENG; Xinjie ZHOU; Honghui XU; Mengjie QING; Cong BAI

doi:10.3788/gzxb20225102.0210003

Journals >Acta Photonica Sinica >Volume 51 >Issue 2 >Page 0210003 > Article

Acta Photonica Sinica
Vol. 51, Issue 2, 0210003 (2022)

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

Jianwei ZHENG, Xinjie ZHOU, Honghui XU, Mengjie QING, and Cong BAI^*

Author Affiliations

School of Computer Science and Technology，Zhejiang University of Technology，Hangzhou 310023，China

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DOI: 10.3788/gzxb20225102.0210003 Cite this Article

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 Copy Citation Text

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Comparison of l0-norm，l1-norm and log function

Fig. 1. Comparison of l₀-norm，l₁-norm and log function

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Fig. 2. Flowchart of the proposed method.

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Fig. 3. Three data sets were used in the experiment

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Fig. 4. Effect of different parameters R and

η

on MSPNR results

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

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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 2. Solution of LRTRLogTNN model via ADMM algorithm

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

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

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

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Methods	NSSR	CSTF	UTV	LTMR	LRTRLogTNN
Running time/s	25.81	120.47	169.60	34.90	672.56

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

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