Locating Multiple Multi-scale Electromagnetic Scatterers by A Single Far-field Measurement

Two inverse scattering schemes were recently developed in \cite{LiLiuShangSun} for locating multiple electromagnetic (EM) scatterers, respectively, of small size and regular size compared to the detecting EM wavelength. Both schemes make use of a single far-field measurement. The scheme of locating regular-size scatterers requires the {\it a priori} knowledge of the possible shapes, orientations and sizes of the underlying scatterer components. In this paper, we extend that imaging scheme to a much more practical setting by relaxing the requirement on the orientations and sizes. We also develop an imaging scheme of locating multiple multi-scale EM scatterers, which may include at the same time, both components of regular size and small size. For the second scheme, a novel local re-sampling technique is developed. Furthermore, more robust and accurate reconstruction can be achieved for the second scheme if an additional far-field measurement is used. Rigorous mathematical justifications are provided and numerical results are presented to demonstrate the effectiveness and the promising features of the proposed imaging schemes.Comment: Any comments are welcom

Locality and Structure Regularized Low Rank Representation for Hyperspectral Image Classification

Hyperspectral image (HSI) classification, which aims to assign an accurate label for hyperspectral pixels, has drawn great interest in recent years. Although low rank representation (LRR) has been used to classify HSI, its ability to segment each class from the whole HSI data has not been exploited fully yet. LRR has a good capacity to capture the underlying lowdimensional subspaces embedded in original data. However, there are still two drawbacks for LRR. First, LRR does not consider the local geometric structure within data, which makes the local correlation among neighboring data easily ignored. Second, the representation obtained by solving LRR is not discriminative enough to separate different data. In this paper, a novel locality and structure regularized low rank representation (LSLRR) model is proposed for HSI classification. To overcome the above limitations, we present locality constraint criterion (LCC) and structure preserving strategy (SPS) to improve the classical LRR. Specifically, we introduce a new distance metric, which combines both spatial and spectral features, to explore the local similarity of pixels. Thus, the global and local structures of HSI data can be exploited sufficiently. Besides, we propose a structure constraint to make the representation have a near block-diagonal structure. This helps to determine the final classification labels directly. Extensive experiments have been conducted on three popular HSI datasets. And the experimental results demonstrate that the proposed LSLRR outperforms other state-of-the-art methods.Comment: 14 pages, 7 figures, TGRS201

Optimal Clustering Framework for Hyperspectral Band Selection

Band selection, by choosing a set of representative bands in hyperspectral image (HSI), is an effective method to reduce the redundant information without compromising the original contents. Recently, various unsupervised band selection methods have been proposed, but most of them are based on approximation algorithms which can only obtain suboptimal solutions toward a specific objective function. This paper focuses on clustering-based band selection, and proposes a new framework to solve the above dilemma, claiming the following contributions: 1) An optimal clustering framework (OCF), which can obtain the optimal clustering result for a particular form of objective function under a reasonable constraint. 2) A rank on clusters strategy (RCS), which provides an effective criterion to select bands on existing clustering structure. 3) An automatic method to determine the number of the required bands, which can better evaluate the distinctive information produced by certain number of bands. In experiments, the proposed algorithm is compared to some state-of-the-art competitors. According to the experimental results, the proposed algorithm is robust and significantly outperform the other methods on various data sets