Proceedings Article | 23 October 2010
KEYWORDS: Independent component analysis, Algorithm development, Sensors, Signal to noise ratio, Light scattering, Statistical modeling, Reflectivity, Expectation maximization algorithms, Mathematical modeling, Data modeling
Hyperspectral instruments acquire electromagnetic energy scattered within their ground instantaneous field view
in hundreds of spectral channels with high spectral resolution. Very often, however, owing to low spatial resolution
of the scanner or to the presence of intimate mixtures (mixing of the materials at a very small scale) in the scene,
the spectral vectors (collection of signals acquired at different spectral bands from a given pixel) acquired by the
hyperspectral scanners are actually mixtures of the spectral signatures of the materials present in the scene.
Given a set of mixed spectral vectors, spectral mixture analysis (or spectral unmixing) aims at estimating the
number of reference materials, also called endmembers, their spectral signatures, and their fractional abundances.
Spectral unmixing is, thus, a source separation problem where, under a linear mixing model, the sources are the
fractional abundances and the endmember spectral signatures are the columns of the mixing matrix. As such,
the independent component analysis (ICA) framework came naturally to mind to unmix spectral data. However,
the ICA crux assumption of source statistical independence is not satisfied in spectral applications, since the
sources are fractions and, thus, non-negative and sum to one. As a consequence, ICA-based algorithms have
severe limitations in the area of spectral unmixing, and this has fostered new unmixing research directions taking
into account geometric and statistical characteristics of hyperspectral sources.
This paper presents an overview of the principal research directions in hyperspectral unmixing. The presentations
is organized into four main topics: i) mixing models, ii) signal subspace identification, iii) geometrical-based
spectral unmixing, (iv) statistical-based spectral unmixing, and (v) sparse regression-based unmixing. In each
topic, we describe what physical or mathematical problems are involved and summarize state-of-the-art algorithms
to address these problems.
