A Two-Step Architecture for Detection and Estimation of Sub-Pixel Spectral Signatures in Hyperspectral Data

The objective of this paper is to present a two-step hyperspectral data processing that concerns a joint application of multiple sub-pixel detection and estimation of spectral signatures. Specifically, in the first step, the endmembers are identified by the detection strategy and, in the second one, the estimated abundances are refined using the unmixing method. Due to the low spatial resolution of most hyperspectral sensors, targets occupy only a fraction of the pixel, therefore, the reflectance spectra of different sub-pixel targets of interest, including the background spectrum, are mixed together. To solve this issue a generalized replacement model accounting for multiple sub-pixel targets is adopted. The detection problem is formulated as a binary hypothesis test where the alternative accounts for a linear combination of endmembers with the possibility to detect and identify one or more targets from a wide spectral library of plausible targets. Then, the detection architectures based upon the generalized likelihood ratio test are devised. The spectral signature estimation algorithm, fed by the output of the detection one, is based on the compressive sensing paradigm. In this case, the sparse nature of the measurements is brought to light and the endemembers' concentrations are estimated using an a priori wide spectral library realizing an unsupervised unmixing of the observations. The entire processing architecture herein presented is experimentally assessed using a hyperspectral satellite dataset for the retrieval of the vertical column concentrations of atmospheric trace gases in the ultraviolet region.