Orthogonal Subspace Projection-based Go Decomposition Approach To Hyperspectral Anomaly Detection

Hyperspectral data are acquired by hundreds of contiguous spectral bands with very high spectral resolution.As a result,they can be used to uncover and reveal many unknown subtle material substances.In many practical application hyperspectral imaging has been widely used in ecology,geology,environmental protection,military and so on where the anomalous targets generally provide vital and crucial information in data exploitation.Therefore,anomaly detection has received considerable interest in hyperspectral image processing.In order to design and develop an effective anomaly detector,two major issues need to be addressed,how to deal with background(BKG)and noise.Recently,a method named go decomposition(GoDec)to carry out low rank and sparse decomposition(LRaSMD)is proposed and it can be used to decompose a data space into three component spaces,low rank space L,sparse space S and noise space N.However,two major issues arising in GoDec have not been investigated,the first one is how to determine the rank m of L and the sparsity cardinality k of S,and the second one is how to take advantage of L and S to design anomaly detectors.Focusing on these two issues,the related works are carried out,and the main work can be divided into the following three aspects:(1)To address the first issue,which is how to determine the rank m of L and the sparsity cardinality k of S,a new method to estimating the two parameters is proposed,and a new decomposition is proposed.Firstly,the virtual dimensionality(VD)is employed to determine the rank p of the joint subspace L(10)S,and then minimax-singular value decomposition(MX-SVD)is used to determine the rank of the sparse space S.To further reduce noise effect in S,sparse cardinality(SC)is imposed on S to create an anomaly space(AS)from which anomalies can be detected more effectively.Different from the eigenspace decomposition of GoDec which uses QR decomposition to perform decomposition and singular vectors as basis vectors,OSP-GoDec proposed in the dissertation replaces the bilateral random projection(BRP)with orthogonal subspace projection(OSP)and the OSP decomposition can be achieved.The experimental results show the effectiveness of the proposed method to determine the input parameters of GoDec and the proposed decomposition method OSP-GoDec.(2)To address the second issue,which is how to take advantage of L and S to design anomaly detectors,new anomaly detectors named OSP-GoDec-AD are proposed.Different from RXD and R-AD,based on the results of LRa SMD,the OSP-GoDec-AD detectors are designed to suppresse BKG via inverting the sample covariance/correlation matrix in S or L or L+S and in the meantime detect anomalies in S or L+S.As a results,the OSP-GoDec-AD make full use of the information provided by the low-rank background and the sparse anomalies.Extensive experiments show the effectiveness of OSP-GoDec-AD detectors.(3)As for the issue that it is difficult to find the basis vectors to represent the BKG accurately in using OSP for BKG suppression,new OSP-based anomaly detectors(OSP-AD)and its data sphering version OSPDS-AD are proposed.Instead of finding the basis vectors of the BKG to suppress BKG before anomaly detection,the proposed OSP-AD takes advantage of decomposition results and uses OSP-based target detector to annihilate BKG via OSP in L or L+S,while detects anomalies in S or L+S.To further suppress the interruption of the BKG,the data sphering process is introduced into OSP-AD and the anomaly target subspaces are sphered.The experiments show the effectiveness of the OSP-AD detectors.