Exploration of methods for estimation of number of endmembers in hyperspectral imagery

An endmember is an idealized, pure signature for a class and provides crucial information for hyperspectral image analysis. Recently, endmember extraction has received considerable attention in hyperspectral imaging due to significantly improved spectral resolution where the likelihood of a hyperspectral image pixel uncovered by a hyperspectral image sensor as an endmember is substantially increased. Many algorithms have been proposed for this purpose. One great challenge in endmember extraction is the determination of number of endmembers, p required for an endmember extraction algorithm (EEA) to generate. Unfortunately, this issue has been overlooked and avoided by making an empirical assumption without justification. However, it has been shown that an appropriate selection of p is critical to success in extracting desired endmembers from image data. This paper explores methods available in the literature that can be used to estimate the value, p. These include the commonly used eigenvalue-based energy method, An Information criterion (AIC), Minimum Description Length (MDL), Gershgorin radii-based method, Signal Subspace Estimation (SSE) and Neyman-Pearson detection method in detection theory. In order to evaluate the effectiveness of these methods, two sets of experiments are conducted for performance analysis. The first set consists of synthetic image-based simulations which allow us to evaluate their performance with a priori knowledge, while the second set comprising of real hyperspectral image experiments which demonstrate utility of these methods in real applications.