Hyperspectral Anomaly Detection Based On Tensor Representation

As a three-dimensional image,hyperspectral image can simultaneously capture spatial information of the imaging area and spectral information of ground objects.Each pixel in the image reflects nearly continuous spectral curve of materials and can be used to distinguish tiny differences among ground objects.As one of the most important research hotspots in hyperspectral image processing,anomaly detection aims to detect pixels whose spectral signatures are different from local or global background.The anomaly detection is performed without any prior spectral signatures about the background and anomaly,which makes it challenging but more valuable due to matching with the practical application.Most traditional anomaly detection algorithms focus on redundant spectral information,and the three-dimensional image is unfolded into a matrix,which destroys the structural information of the image.In this dissertation,the tensor representation is utilized to model the three-dimensional hyperspectral images to take full advantage of the spatial-spectral information for hyperspectral anomaly detection.The main research work is arranged as follows:(1)Hyperspectral anomaly detection with tensor average rank and piecewise smoothness constraints is proposed.Traditional methods based on low rank representation cannot take full advantage of the spatial information of hyperspectral images,which degrades the performance of detectors.To solve this problem,an anomaly detection method based on dictionary representation and tensor representation is proposed.The hyperspectral image is divided into a background tensor and an anomaly tensor,and the background tensor is represented as the mode-3 product of a background dictionary and a coefficient tensor.By the dictionary representation,the coefficient tensor retains the spatial information and spectral information of the background and has global low-rank structure.The tensor nuclear norm based on the tensor singular value decomposition is exploited to characterize the global low-rank structure.The total variation regularization is incorporated due to the piecewise smoothness of the background.In addition,a robust background dictionary is constructed based on local clustering.Both spatial and spectral distances are considered in this dictionary construction method.A spatialspectral distance is defined and utilized to cluster the pixels in local region,which avoids different types of background pixels existing in the same category.The subspace of each local clustering is derived by the singular value decomposition.Each pixel is projected into the corresponding subspace,and the pixel with the smallest residual is considered as the most representative background pixel of the local clustering,and hence selected as a dictionary atom.Experimental results on several real hyperspectral datasets show the superiority of the proposed method.(2)Spatial invariant tensor self-representation model for hyperspectral anomaly detection is proposed.In traditional representation-based anomaly detection methods,the atom in a dictionary is utilized to represent pixels within the same band,which cannot directly exploit the spectral correlation and spatial correlation of the hyperspectral image.To solve this problem,the background tensor is represented by virtue of the tensor self-representation model.The hyperspectral image is divided into a background tensor,an anomaly tensor,and a noise tensor.The background tensor is expressed as the tensor product of the data itself and a coefficient tensor.With this representation,each lateral slice of the coefficient tensor integrates the spatial information of a direction and spectral information.The lateral slices are restricted to lie in a low-dimensional subspace to depict the spatial-spectral correlation of the background.Considering that hyperspectral images have two spatial directions,two different representative tensors integrating different spatial-spectral information are restricted to lie in the same lowdimensional subspace to achieve a more balanced and informative model.In addition,the group sparsity is characterized by minimizing the l2.1.1 norm of the anomaly tensor to promote the separation of the background and anomaly.Extensive experiments on several real datasets demonstrate the great ability of the proposed method in suppressing background and detecting anomaly.(3)Hyperspectral anomaly detection based on adaptive low-rank transformed tensor is proposed.Most tensor-transform-based methods have high computational complexity due to the redundancy of hyperspectral images.And the predefined orthogonal matrices cannot fully depict the data-specific information.To solve this problem,an adaptive low-dimensional matrix is proposed to transform the data.Considering the strong spectral correlation of hyperspectral images and to reduce the computational complexity of the transform,the background tensor is expressed as the product of a lowdimensional transformed tensor and a low-dimensional matrix.By the low-dimensional matrix,the spectral information of the hyperspectral image is incorporated into each frontal slice of the transformed tensor.Meanwhile,the frontal slice of the transformed tensor retains the spatial information of the image,and the spatial-spectral correlation of the image is depicted by minimizing the sum of the nuclear norm of all frontal slices.To better incorporate spatial information and spectral information into the transformed tensor,a data-depend matrix is adaptively derived by an iteration procedure.Besides,the group sparsity of anomalous pixels is depicted by imposing l2.1.1 norm on the anomaly tensor.All regularization terms and a fidelity term are integrated into a non-convex problem,and the proximal alternating minimization algorithm is utilized to solve it.Finally,the sequence generated by the optimization algorithm is proven to converge to a critical point.Experimental results conducted on several real datasets demonstrate the superiority of the proposed method compared with several state-of-the-art anomaly detection algorithms.