Real-time Causal Progressive Hyperspectral Anomaly Detection Based On Cholesky Decomposition

Hyperspectral data,with very high spectral resolution,are abundant of spectral and radiometric information collected from observed objects,such as crops,minerals,and cultural relics,etc.The high-spectral-dimension of hyperspectral data usually brings about the issue of expensive computation.It is difficult for a hyperspectral image processing algorithm to perform in real time in applications such as fire point detection,crop pest and disease detection,etc.To accelerate hyperspectral image processing,especially online real time hyperspectral anomaly detection,we proposed two real time hyperspectral anomaly detectors.More specifically,the first one is the real time causal sample-wise anomaly detector for whisk-broom imaging spectrometers,and the second one is the real time causal line-wise anomaly detector for push-broom imaging spectrometers.The quantitative computational performance of the proposed detectors are evaluated in terms of the computational complexity(i.e.,computer floating point operations).Also we gave a quantitative comparative study of different real time detectors in terms of computational complexity to prove the superior computing ability of the detectors developed in this study.In this study,a real hyperspectral dataset acquired by the ground-based Field Imgaing Spectrometer System(FISS)and a synthetic hyperspectral dataset simulated by the airborne hyperspectral images,SpecTIR Avon,were used for experiments on real time causal sample/line-wise anomaly detection.We detailed the analysis of the detection performance of the proposed detectors.Main contributions and conclusions are as follows:(1)The background statistical matrix(i.e.,sample correlation matrix or covariance matrix)was proved to be symmetric positive definite.Thus,Cholesky decomposition of the background statistical matrix along with linear system solving can be used to accelerate the detection process.It is unnecessary to invert the high dimensional matrix with high computational complexity.As a result,the numerical stabilities can be remained.(2)We proposed a real time causal sample-wise anomaly detector based on Cholesky rank-one modification of the sliding background statistical matrix.The Cholesky factor of the background statistical matrix can be updated within a short time period,which could significantly speed up the sample-wise process.In addition,the updating of the Cholesky factor(i.e.,a lower triangular matrix)contributes to data compression in the real time sample-wise process,which further helps online implementation of our proposed real time detector.(3)We developed a real time causal line-wise anomaly detector based on Cholesky decomposition of the sliding background statistical matrix.Unlike Cholesky rank-one modification in sample-wise process,Cholesky decomposition is operated each time a new data line comes in since the number of pixels in a data line has a great impact on the computational performance of processing the entire data line.(4)We designed the sliding background for real time anomaly detection.That is,old background information is deleted from the background when adding new information in the real time process.Considering that an online real time detector usually scan across a large area which covers various ground objects,using all acquired samples for background estimation would result in over background suppression and thus lower down the detection probability.Experimental results showed that the sliding background has the advantage of picking up weak anomalies in the real time process.It is worth noting that the computational complexity of real time sample-wise process using sliding background is a little higher,but not very significant,than that using global background due to the additional process to delete old information.However,the computing time of real time line-wise process remained approximately unchanged even if the deletion process is involved.It is mainly because the number of pixels in a data line has a greater impact on computational performance than the deletion process does.(5)A quantitative comparative study of the computational complexity of different real time sample/line-wise detectors were provided in terms of the computer floating point operations.We analyzed the impact of the technical parameters of imaging spectrometers(i.e.,number of spectral bands and number of pixels in a data line)on the computational performance.This study contributes to finding the most efficient real time anomaly detector for a specified imaging spectrometer.(6)We could acquire better visual inspection of background suppression in the real time sample/line-wise anomaly detection process.Since anomaly detection relies on the contrast between anomalies and the background,the sample/line-varying background can prevent weak anomalies from being suppressed by later detected strong anomalies.Meanwhile,3D-ROC analysis is a comprehensive evaluation of the detection performance of a real time detector in terms of detection probability,false alarm,and background suppression.