Blind spectral unmixing by local maximization of non-Gaussianity

We approach the estimation of material percentages per pixel (endmember fractional abundances) in hyperspectral remote-sensed images as a blind source separation problem. This task is commonly known as spectral unmixing. Classical techniques require the knowledge of the existing materials and their spectra, which is an unrealistic situation in most cases. In contrast to recently presented blind techniques based on independent component analysis, we implement here a dependent component analysis strategy, namely the MaxNG (maximum non-Gaussianity) algorithm, which is capable to separate even strongly dependent signals. We prove that, when the abundances verify a separability condition, they can be extracted by searching the local maxima of non-Gaussianity. We also provide enough theoretical as well as experimental facts that indicate that this condition holds true for endmember abundances. In addition, we discuss the implementation of MaxNG in a noisy scenario, we introduce a new technique for the removal of scale ambiguities of estimated sources, and a new fast algorithm for the calculation of a Parzen windows-based NG measure. We compare MaxNG to commonly used independent component analysis algorithms, such as FastICA and JADE. We analyze the efficiency of MaxNG in terms of the number of sensor channels, the number of available samples and other factors, by testing it on synthetically generated as well as real data. Finally, we present some examples of application of our technique to real images captured by the MIVIS airborne imaging spectrometer. Our results show that MaxNG is a good tool for spectral unmixing in a blind scenario.