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Journal of ZheJiang University (Engineering Science)  2022, Vol. 56 Issue (7): 1276-1284    DOI: 10.3785/j.issn.1008-973X.2022.07.002
    
Anomaly detection algorithm based on FrFT transform and total variation regularization
Fei SUN1(),Xiao-run LI1,*(),Liao-ying ZHAO2,Shao-qi YU1
1. College of Electrical Engineering, Zhejiang University, Hangzhou 310027, China
2. College of Computer Science, Hangzhou Dianzi University, Hangzhou 310018, China
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Abstract  

A hyperspectral anomaly detection algorithm based on fractional Fourier transform (FrFT) and total variation regularization constraint was proposed aiming at the challenge of insufficient utilization of spatial information and contamination of background dictionary in low-rank and sparse representation based hyperspectral anomaly detection algorithms. The high-dimensional image data was mapped to multiple subspaces through the clustering algorithm. A pure background dictionary was obtained by constructing the FrFT-RX operator in order to enhance the discrimination between anomalies and background. A total variation regularization constraint was introduced into the low-rank and sparse representation model in order to describe the spatial features of background and anomalies in the intermediate domain after FrFT transformation. The optimal solution of the model was obtained by using the alternating direction method of multipliers. The anomaly detection results were obtained. The experimental results on three real hyperspectral datasets demonstrate that the proposed algorithm has a higher detection rate and a lower false alarm rate compared with the other five anomaly detection algorithms.



Key wordshyperspectral image      anomaly detection      low-rank and sparse representation      fractional Fourier transform (FrFT)      total variation regularization     
Received: 20 July 2021      Published: 26 July 2022
CLC:  TP 391  
Fund:  国家自然科学基金资助项目(61671408);教育部联合基金资助项目(6141A02022362)
Corresponding Authors: Xiao-run LI     E-mail: 21910147@zju.edu.cn;lxr@zju.edu.cn
Cite this article:

Fei SUN,Xiao-run LI,Liao-ying ZHAO,Shao-qi YU. Anomaly detection algorithm based on FrFT transform and total variation regularization. Journal of ZheJiang University (Engineering Science), 2022, 56(7): 1276-1284.

URL:

https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2022.07.002     OR     https://www.zjujournals.com/eng/Y2022/V56/I7/1276


基于FrFT变换和全变分正则化的异常检测算法

针对低秩稀疏表示的高光谱异常检测算法中背景字典易被污染、空间信息利用不足的问题,提出基于分数阶傅里叶变换(FrFT)和全变分正则化约束的高光谱图像异常检测算法. 通过聚类算法,将图像高维数据映射至多个子空间;构造FrFT-RX算子,增大背景和异常的可分性,得到较纯净的背景字典. 为了表示FrFT变换后中间域内背景与异常的空间特征,在低秩稀疏表示模型中引入全变分正则化项约束. 采用交替方向乘子法对模型进行优化求解,得到异常检测的结果. 在3个真实高光谱数据上开展目标检测实验,实验结果表明,与其他5种异常检测算法相比,本文算法具有更高的检测率和较低的虚警率.


关键词: 高光谱影像,  异常检测,  低秩稀疏表示,  分数阶傅里叶变换(FrFT),  全变分正则化 
Fig.1 Flowchart of anomaly detection algorithm based on FrFT transform and total variation regularization
Fig.2 Comparison chart of FrFT effect
Fig.3 Urban hyperspectral dataset
Fig.4 Pavia hyperspectral dataset
Fig.5 Hyperion hyperspectral dataset
Fig.6 Influence of different $ p $ on AUC
Fig.7 Influence of different parameter on AUC
Fig.8 Anomaly detection results of various detection algorithms in Urban dataset
Fig.9 Anomaly detection results of various detection algorithms in Pavia dataset
Fig.10 Anomaly detection results of various detection algorithms in Hyperion dataset
数据集 AUC
GRX RPCA FRFE LSMAD LRASR 提出方法
Urban 0.9757 0.9798 0.9977 0.9955 0.9968 0.9992
Pavia 0.9907 0.9933 0.9775 0.9935 0.9966 0.9990
Hyperion 0.9741 0.9768 0.9828 0.9921 0.9880 0.9977
Tab.1 AUC of different methods in three datasets
Fig.11 ROC curves of three datasets
数据集 Pf, η
GRX RPCA FRFE LSMAD LRASR 本文方法
Urban 0.0490 0.0219 0.0306 0.024 2 0.060 2 0.015 1
Pavia 0.0232 0.0061 0.0625 0.005 0 0.064 7 0.010 2
Hyperion 0.0402 0.0189 0.0141 0.010 7 0.066 1 0.012 3
Tab.2  $ {(P}_{\mathrm{f}},\eta ) $ of different methods in three datasets
数据集 Pd, η
GRX RPCA FRFE LSMAD LRASR 本文方法
Urban 0.2949 0.2609 0.4432 0.3672 0.5072 0.5423
Pavia 0.1632 0.1081 0.1302 0.1292 0.2634 0.2937
Hyperion 0.1817 0.1408 0.1090 0.1828 0.3139 0.3305
Tab.3  ${({P}}_{{\rm{d}}},\eta )$ of different methods in three datasets
s
数据集 tr
GRX RPCA FRFE LSMAD LRASR 本文方法
Urban 0.0627 3.6739 18.3643 9.3211 37.0203 148.9941
Pavia 0.0699 4.5899 17.6630 15.9884 150.7036 298.8545
Hyperion 0.0623 2.7474 16.4124 9.5605 37.5466 153.2101
Tab.4 Detection time of different methods in three datasets
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