基于FrFT变换和全变分正则化的异常检测算法  

Anomaly detection algorithm based on FrFT transform and total variation regularization

作　　者：孙菲 厉小润[1] 赵辽英[2] 余绍奇 SUN Fei;LI Xiao-run;ZHAO Liao-ying;YU Shao-qi(College of Electrical Engineering,Zhejiang University,Hangzhou 310027,China;College of Computer Science,Hangzhou Dianzi University,Hangzhou 310018,China)

机构地区：[1]浙江大学电气工程学院,浙江杭州310027 [2]杭州电子科技大学计算机学院,浙江杭州310018

出　　处：《浙江大学学报（工学版）》2022年第7期1276-1284,共9页Journal of Zhejiang University：Engineering Science

基　　金：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).

摘　　要：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.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.

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 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]