一种高精度并行主偏度分析算法及其在遥感图像中的应用

王大虎; 刘畅; 王健; 姚锴; 张振

doi:10.11999/JEIT220960

一种高精度并行主偏度分析算法及其在遥感图像中的应用

doi: 10.11999/JEIT220960

王大虎^{1, 2},
刘畅^{1, 2, ,},
王健^{1, 2},
姚锴^{1, 2},
张振³

1.
中国科学院空天信息创新研究院北京 100190
2.
中国科学院大学电子电气与通信工程学院北京 100094
3.
陆军航空兵学院北京 101123

详细信息

作者简介:
王大虎：男，博士生，研究方向为雷达信号处理、遥感图像处理

刘畅：男，研究员，研究方向为雷达信号处理、雷达图像处理、多任务合成孔径雷达系统

王健：男，博士生，研究方向为立体SAR、雷达信号处理、雷达图像处理

姚锴：男，博士生，研究方向为雷达信号处理、雷达波形设计

张振：男，助理研究员，研究方向为图像处理、无人机系统

通讯作者:
刘畅　cliu@aircas.ac.cn

中图分类号: TN911.7
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- 被引次数: 0
出版历程
- 收稿日期: 2022-07-18
- 修回日期: 2022-11-13
- 录用日期: 2022-12-20
- 网络出版日期: 2022-12-23
- 刊出日期: 2023-10-31

A High Precision Parallel Principal Skewness Analysis Algorithm and Its Application to Remote Sensing Images

WANG Dahu^{1, 2},
LIU Chang^{1, 2
, ,},
WANG Jian^{1, 2},
YAO Kai^{1, 2},
ZHANG Zhen³

1.
Institute of Space Information Innovation, Chinese Academy of Sciences, Beijing 100190, China
2.
School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing 100094, China
3.
Chinese People's Liberation Army Aviation Academy, Beijing 101123, China

摘要

摘要: 主偏度分析(PSA)作为主成分分析(PCA)的一种3阶推广，常用于盲图像分离、SAR图像去噪以及高光谱特征提取等。但现有PSA算法只能得到近似解，这会影响图像后续处理的精度。针对这一问题，该文在现有PSA算法基础上，提出了一种高精度并行主偏度分析(PPSA)算法。PPSA算法充分考虑数据结构，选用协偏度张量的全部切片的特征向量作为迭代的初始值，可以准确地得到实际解。仿真实验以及实际遥感图像实验验证了PPSA算法的有效性与优越性。
- 图像分离 /
- 图像去噪 /
- 主偏度分析 /
- 高精度 /
- 并行 /
- 特征提取
Abstract: Principal Skewness Analysis (PSA), as a third-order extension of Principal Component Analysis (PCA), is often used for blind image separation, SAR image denoising, and hyperspectral feature extraction. However, the existing PSA algorithm can only obtain approximate solutions, which will affect the accuracy of subsequent image processing. In view of this problem, a high-precision Parallel Principal Skewness Analysis (PPSA) algorithm based on the existing PSA algorithm is proposed. The PPSA algorithm considers fully the data structure, and selects the eigenvectors of all slices of the co-skewness tensor as the initial value of the iteration, which can accurately obtain the actual solution. Simulation experiments and actual remote sensing image experiments verify the effectiveness and superiority of the PSA algorithm.
- Image separation /
- Image denoising /
- Principal Skewness Analysis (PSA) /
- High precision /
- Parallel /
- Feature extraction

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图 1 不同初始值，PSA, MPSA算法求解结果

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图 2 不同初始值，NPSA算法求解结果

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图 3 PPSA算法求解结果

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图 4 源图像以及各种算法处理结果

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图 5 原始数据以及各种算法处理结果

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图 6 高光谱Cuprite数据彩色图像

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图 8 PPSA算法对高光谱图像Cuprite的偏度比较

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图 7 4种算法运行时间对比图

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算法1 PPSA算法
输入：输入数据 ${\boldsymbol{R}} \in {{\boldsymbol{R}}^{L \times N} }$
输出：输出变换矩阵 ${\boldsymbol{U}}$ , ${\boldsymbol{Y}} = {{\boldsymbol{U}}^{\rm{T}}}\tilde {\boldsymbol{R}}$
(1) 白化数据，得到 $\tilde {\boldsymbol{R}}$
(2) 根据式(1)计算m阶 $L$ 维张量 ${\boldsymbol{S}}$
(3) 计算张量 ${\boldsymbol{S}}$ 切片的所有特征向量，记为V% main loop: %
(4) ${\text{for }}i = 1:{L^2}{\text{ do}}$
(5) 　　k = 0
(6) 　　 ${\boldsymbol{u}}_i^{(k)} = {\boldsymbol{V}}(:,i)$
(7) 　　while stop conditions are not meet do
(8) 　　　　 ${\boldsymbol{u}}_i^{(k + 1)} = {\boldsymbol{S}}{ \times _1}{\boldsymbol{u}}_i^{(k + 1)}{ \times _3}{\boldsymbol{u}}_i^{(k + 1)}$
(9) 　　　　 ${\boldsymbol{u}}_i^{(k + 1)} = {\boldsymbol{u}}_i^{(k + 1)}/{\left\\| {{\boldsymbol{u}}_i^{(k + 1)} } \right\\|_2}$
(10) 　　end while
(11) 　　 ${{\boldsymbol{U}}_{:i} } = {\boldsymbol{u}}_i^{(k + 1)}$
(12) end for

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表 1 不同初始化方法的比较，选取n个初始值计算100 000次的结果

	随机选取 $n$ 个初始值	随机选取 $n$ 个正交初始值	单个切片的特征向量作为初始值
2	49027	89073	98270
3	12864	53080	98029
4	7450	35373	97222
5	2361	15565	85831
6	836	5171	50430
7	89	281	35851
8	27	129	19981
9	8	29	17004

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表 2 不同初始化方法的比较，选取n × n个初始值计算100 000次的结果

	随机选取 $n \times n$ 个初始值	随机选取 $n \times n$ 正交初始值	全部切片的特征向量作为初始值
2	90833	98184	99997
3	88401	92830	99999
4	88225	90029	99989
5	85646	88451	99994
6	79673	70096	99988
7	79382	69156	99974
8	77576	68546	99991
9	64338	66570	99938

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表 3 FastICA, PSA, MPSA, NPSA, MSDP和PPSA算法评估结果

	指标	FastICA	PSA	MPSA	NPSA	MSDP	PPSA
1	ISI	0.6757	0.0681	0.0551	0.0253	0.0203	0.0203
	TMSE	3.2856×10^–11	2.5547×10^–11	2.5548×10^–11	3.8168×10^–11	1.8645×10^–11	1.8645×10^–11
	$\rho$	0.9544	0.9954	0.9954	0.9992	0.9998	0.9998
		0.9889	0.9992	0.9988	0.99997	0.9992	0.9992
		0.9968	1.0000	1.0000	1.0000	1.0000	1.0000
	PSNR	66.1696	76.6105	77.7449	83.6350	85.9129	85.9129
		70.0325	72.6448	73.7954	74.4358	74.4870	74.4870
		79.2579	90.9901	90.4324	91.1667	91.3285	91.3285
	T(s)	0.0042	0.0011	0.0010	0.0043	2.8594	0.0032
2	ISI	0.4844	0.1442	0.1524	0.0787	0.0745	0.0745
	TMSE	3.2241×10^–11	2.6798×10^–11	2.6337×10^–11	2.5154×10^–11	1.9555×10^–14	1.9555×10^–14
	$\rho$	0.9749	0.9967	0.9967	0.9995	0.9997	0.9997
		0.9900	0.9905	0.9907	0.9920	0.9921	0.9921
		0.9970	0.9999	0.9998	1.0000	1.0000	1.0000
	PSNR	69.1886	74.9389	75.6708	83.4588	83.7674	83.7674
		73.7143	73.1186	74.3531	70.1218	70.6017	70.6017
		76.9175	89.0466	90.4683	94.0776	94.7823	94.7823
	T(s)	0.0052	0.0011	0.0010	0.0042	3.1046	0.0021
3	ISI	0.2965	0.0405	0.0452	0.0041	0.0006	0.0006
	TMSE	2.6603×10^–10	2.6628×10^–10	1.9986×10^–10	3.4050×10^–10	1.7480×10^–10	1.7480×10^–10
	$\rho$	0.9756	0.9966	0.9962	0.9997	1.0000	1.0000
		0.9950	0.9994	0.9995	1.0000	1.0000	1.0000
		0.9969	0.9998	0.9999	1.0000	1.0000	1.0000
	PSNR	69.9228	83.2559	78.8206	91.4669	96.6388	96.6388
		61.8123	61.1492	58.8872	61.2297	64.0212	64.0212
		82.3327	87.5416	90.4749	94.0424	95.1910	95.1910
	T(s)	0.0048	0.0012	0.0009	0.0033	2.9786	0.0022

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表 4 不同算法的平均峰值信噪比和平均绝对误差(计算10次运行的平均结果)

组合	评估指标	FastICA	PSA	NPSA	PPSA	均值滤波	中值滤波
1	PSNR	64.3293	83.6292	83.9879	84.1115	62.0892	60.9464
1	MAE	0.0719	0.0127	0.0120	0.0119	0.1749	0.1957
2	PSNR	61.3562	81.4705	81.8815	81.9711	62.7697	62.3189
2	MAE	0.1631	0.0171	0.0163	0.0161	0.1574	0.1659
3	PSNR	68.6684	78.8200	78.8824	78.9555	64.0314	64.6669
3	MAE	0.0666	0.0245	0.0243	0.0241	0.1306	0.1233
(注释：组合1中 ${E_{{\text{gs}}}}$ =0, $\delta _{{\text{gs}}}^{\text{2}}$ =100, ${E_{{\text{gm}}}}$ =2, $\delta _{{\text{gm}}}^{\text{2}}$ =80；组合2中 ${E_{{\text{gs}}}}$ =0, $\delta _{{\text{gs}}}^{\text{2}}$ =80, ${E_{{\text{gm}}}}$ =2, $\delta _{{\text{gm}}}^{\text{2}}$ =60；组合3中 ${E_{{\text{gs}}}}$ =0, $\delta _{{\text{gs}}}^{\text{2}}$ =60, ${E_{{\text{gm}}}}$ =2, $\delta _{{\text{gm}}}^{\text{2}}$ =40)

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