Hyperspectral unmixing: geometrical, statistical, and sparse regression-based approaches

Abstract

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.

Two Linear Unmixing Algorithms to Recognize Targets Using Supervised Classification and Orthogonal Rotation in Airborne Hyperspectral Images

“…Up-to-date overview on hyperspectral unmixing is given in [4,5]. The challenges related to target detection, which is the main focus of this paper, are described in the survey papers [6,7].…”

HyperMix: A new tool for quantitative evaluation of end member identification and spectral unmixing techniques

“…During the past years, many algorithms and models have been developed for endmember identification and abundance estimation in remotely sensed hyperspectral images [5,6], thus making spectral unmixing a hot topic in the hyperspectral imaging literature. However, the codes and implementations of these algorithms have not been available in open source format as of yet, and there is no clearly standardized data set for benchmarking the accuracy of spectral unmixing techniques.…”

Context dependent spectral unmixing.

“…It states that every pixel's spectral signature is a convex combination of endmembers in the scene. This has been shown to hold in cases where the endmembers are mixed by the spatial resolution of the imaging sensor [1,36]. If the convex geometry holds, the endmembers are the spectra found at the corners of a convex region enclosing all the spectra in the hyperspectral scene.…”

“…The proportion p t of the target s t in pixel x can be estimated as [76]: 36) where P b ⊥ is the same as in equation (2.34). The numerator in (2.36) has been proposed as a detection statistic under the Orthogonal Subspace Projection (OSP) name [76]:…”

“…Despite its simplicity, the linear mixing model has proved to be an acceptable approximation of the light scattering mechanisms in many real scenarios. Furthermore, in contrast to nonlinear mixing, the linear mixing model is the basis of a plethora of unmixing algorithms [1,30,[36][37][38][39][40][41][42][43][44][45][46][47][48]. …”