Hyperspectral remote sensing exploits the fact that all substances scatter electromagnetic energy, at specific wavelengths, in distinctive patterns related to their molecular composition. Hyperspectral sensors have been developed to sample the scattered portion of the electromagnetic spectrum that extends from the visible region through the near-infrared and mid-infrared, in hundreds of narrow contiguous bands. The number and variety of potential civilian and military applications for hyperspectral remote sensing is enormous.

     One of the most challenging task underlying many hyperspectral imagery applications is the spectral unmixing, which decompose a mixed pixel into a collection of reflectance spectra, called endmember signatures, and a set corresponding abundance fractions.

     Due to the spatial resolution of the hyperspectral sensors, a single pixel in a image is as a mixture of the substances present in the corresponding resolution cell. Depending on the substance distribution at each pixel, the observed mixture is either linear or non-linear. Linear mixing model assumes that substances are surface distributed in the scene and the incident solar radiation is scattered by surface through a single bounce. Non-linear model assumes that substances are volume distributed in the scene and the incident solar radiation is scattered by the scene through multiple bounces. Linear spectral unmixing is one of the most important approaches for the analysis of hyperspectral data. It considers that a mixed pixel is a linear combination of endmembers signatures weighted by correspondent abundance fractions.

     Under the linear mixing model, and assuming that the number of substances and their reflectance spectrum are known, hyperspectral unmixing is a simple linear problem, which can be addressed, for example, under the maximum likelihood setup. In practice this knowledge is very difficult, if not impossible, to obtain. Hyperspectral unmixing falls, therefore, into the class of blind source separation problems.

     Independent Component Analysis has recently been proposed as a tool to blindly unmix hyperspectral data. ICA is based on the assumption of mutually independent sources, which is not the case of hyperspectral data, since the sum of abundance fractions is constant, implying statistical dependence among them. This dependence compromises ICA applicability to hyperspectral images. Nevertheless, some endmembers may be approximately unmixed.

     Herein, we have a matlab demo about ICA performance on Hyperspectral data.   ( matlab demo code)   (cuprite data)

     Vertex Component Analysis (VCA) is a new unsupervised unmixing algorithm which exploits geometric concepts and it works both with unprojected and with projected data. The algorithm iteratively projects data onto a direction orthogonal to the subspace spanned by the endmembers already determined. The new endmember signature corresponds to the extreme of the projection. The algorithm iterates until all endmembers are exhausted (see Figure 1).

     This new algorithm competes with the state-of-the-art methods with a computational complexity between one and two orders of magnitude lower than the best available method (See figures 2 and 3).

     Matlab demo code for VCA algorithm   ( matlab demo code)   (cuprite data)

                                 Figure 1

                                 Figure 2                                                                                                    Figure 3