Tensor singular spectral analysis for 3D feature extraction in hyperspectral images.

Due to the cubic structure of a hyperspectral image (HSI), how to characterize its spectral and spatial properties in three dimensions is challenging. Conventional spectral-spatial methods usually extract spectral and spatial information separately, ignoring their intrinsic correlations. Recently, some 3D feature extraction methods are developed for the extraction of spectral and spatial features simultaneously, although they rely on local spatial-spectral regions and thus ignore the global spectral similarity and spatial consistency. Meanwhile, some of these methods contain huge model parameters which require a large number of training samples. In this paper, a novel Tensor Singular Spectral Analysis (TensorSSA) method is proposed to extract global and low-rank features of HSI. In TensorSSA, an adaptive embedding operation is first proposed to construct a trajectory tensor corresponding to the entire HSI, which takes full advantage of the spatial similarity and improves the adequate representation of the global low-rank properties of the HSI. Moreover, the obtained trajectory tensor, which contains the global and local spatial and spectral information of the HSI, is decomposed by the Tensor singular value decomposition (t-SVD) to explore its low-rank intrinsic features. Finally, the efficacy of the extracted features is evaluated using the accuracy of image classification with a support vector machine (SVM) classifier. Experimental results on three publicly available datasets have fully demonstrated the superiority of the proposed TensorSSA over a few state-of-the-art 2D/3D feature extraction and deep learning algorithms, even with a limited number of training samples

Observation of Dirac Cone Warping and Chirality Effects in Silicene

We performed low temperature scanning tunneling microscopy (STM) and spectroscopy (STS) studies on the electronic properties of (√3 × √3)R30° phase of silicene on Ag(111) surface. We found the existence of Dirac Fermion chirality through the observation of −1.5 and −1.0 power law decay of quasiparticle interference (QPI) patterns. Moreover, in contrast to the trigonal warping of Dirac cone in graphene, we found that the Dirac cone of silicene is hexagonally warped, which is further confirmed by density functional calculations and explained by the unique superstructure of silicene. Our results demonstrate that the (√3 × √3)R30° phase is an ideal system to investigate the unique Dirac Fermion properties of silicene