Identifiability of the Simplex Volume Minimization Criterion for Blind Hyperspectral Unmixing: The No Pure-Pixel Case

Signal, image and data processing for hyperspectral imaging has recently received enormous attention in remote sensing [1, 2], having numerous applications such as environmental monitoring, land mapping and classification, and object detection. Such developments are made possible by exploiting the unique features of hyperspectral images, most notably, their high spectral resolutions. In this scope, blind hyperspectral unmixing (HU) is one of the topics that has aroused much interest not only from remote sensing [3], but also from other communities recently [4-7]. Simply speaking, the problem of blind HU is to solve a problem reminiscent of blind source separation in signal processing, and the desired outcome is to unambiguously separate the endmember spectral signatures and their corresponding abundance maps from the observed hyperspectal scene, with no or little 1 prior information of the mixing system. Being given little information to solve the problem, blind HU is a challenging--but also fundamentally intriguing--problem with many possibilities. Readers are referred to some recent articles for overview of blind HU [3,4], and here we shall not review the numerous possible ways to perform blind HU.