Virtual Dimensionality of Hyperspectral Data: Use of Multiple Hypothesis Testing for Controlling Type-I Error

Estimating the number of materials present in a scene is the fundamental step in many hyperspectral remote sensing applications. The virtual dimensionality (VD) estimates the number of spectrally distinct materials in the hyperspectral data. The VD is generally considered as the number of signal sources under binary hypothesis, based on the Neyman-Pearson detection criteria. We observe that the hypothesis testing procedure used in many approaches is prone to inflated Type-I (false positive) error. This is due to carrying out the binary hypothesis test individually on each band image, i.e., more than 200 images in hyperspectral data. In this article, we propose multiple hypothesis testing to control the expected proportion of falsely rejected null hypotheses, i.e., false discovery rate (FDR), and in turn, improve the probability of better performance in estimating the VD. To this end, we employ Benjamini and Hochberg procedure that controls the FDR. We provide multiple hypothesis testing-based algorithms to estimate VD wherein the hypothesis can be formulated according to eigenanalysis, the target specified by statistical approach, and by geometric analysis. The efficacies of the proposed algorithms are evaluated by estimating the number of endmembers for the spectral unmixing application. We conduct experiments on four synthetic hyperspectral data sets at different noise levels as well as on two well-known real hyperspectral datasets. Time complexity and execution time are discussed to study the algorithmic aspects while sensitivity analyses of parameters are carried out for better performance analysis of the proposed approach. We found that the use of multiple hypothesis testing improves estimation of number of endmembers in hyperspectral data.