Effects of random measurements on the performance of target detection in hyperspectral imagery

Hyperspectral pixels are acquired in hundreds of narrow and continuous spectral bands, and the hyperspectral data cubes typically contain hundreds of megabytes. Analysis and processing of the high-dimensional hyperspectral data are computationally expensive and memory inefficient. However, there is a large amount of redundancy between neighboring spectral bands and the hyperspectral pixels lie in a much lower dimensional subspace. Therefore, numerous techniques can be applied to reduce the dimensionality while maintaining the structure of the data. This would lead to a significant reduction of the complexity of the imaging system, as well as an improvement of the computational efficiency of the detection algorithms. In this paper, we explore the use of several dimensionality reduction techniques that can be easily integrated into the imaging sensors. We also investigate their effect on the performance of classical target detection techniques for hyperspectral images, including spectral matched filters (SMF), matched subspace detectors (MSD), support vector machines (SVM), and RX anomaly detection algorithm. Specifically, each N-dimensional spectral pixel is embedded to an M-dimensional measurement space with M « N by a linear transformation (e.g., random measurement matrices, uniform downsampling, PCA). The SMF, MSD, SVM, and RX detectors are then applied to the M-dimensional measurement vectors to detect the targets of interests and their detection performances are compared to those obtained from the entire N-dimensional spectrum by the receiver operating characteristics curves. Through extensive experiments on several HSI datasets, we demonstrate that only 1/5 to 1/3 measurements (i.e., the compression ratio M/N is 1/5 ~ 1/3 ) are necessary to achieve detection performance comparable to that obtained by exploiting the full N-dimensional pixels.