MUSIC-CSR: Hyperspectral Unmixing via Multiple Signal Classification and Collaborative Sparse Regression

Spectral unmixing aims at finding the spectrally pure constituent materials (also called endmembers) and their respective fractional abundances in each pixel of a hyperspectral image scene. In recent years, sparse unmixing has been widely used as a reliable spectral unmixing methodology. In this approach, the observed spectral vectors are expressed as linear combinations of spectral signatures assumed to be known a priori and presented in a large collection, termed spectral library or dictionary, usually acquired in laboratory. Sparse unmixing has attracted much attention as it sidesteps two common limitations of classic spectral unmixing approaches, namely, the lack of pure pixels in hyperspectral scenes and the need to estimate the number of endmembers in a given scene, which are very difficult tasks. However, the high mutual coherence of spectral libraries, jointly with their ever-growing dimensionality, strongly limits the operational applicability of sparse unmixing. In this paper, we introduce a two-step algorithm aimed at mitigating the aforementioned limitations. The algorithm exploits the usual low dimensionality of the hyperspectral data sets. The first step, which is similar to the multiple signal classification array signal processing algorithm, identifies a subset of the library elements, which contains the endmember signatures. Because this subset has cardinality much smaller than the initial number of library elements, the sparse regression we are led to is much more well conditioned than the initial one using the complete library. The second step applies collaborative sparse regression, which is a form of structured sparse regression, exploiting the fact that only a few spectral signatures in the library are active. The effectiveness of the proposed approach, termed MUSIC-CSR, is extensively validated using both simulated and real hyperspectral data sets.

I. Introduction

SPECTRAL unmixing is an important technique for hyperspectral data exploitation [1]. It decomposes the (possibly mixed) pixel spectra measured by an imaging spectrometer into a collection of pure constituent spectra (called endmembers) and their corresponding fractional abundances, which quantify the proportion of each pure material in the pixel [2]. Mixed pixels appear due to the relatively low spatial resolution of the sensor flying at high altitudes, or because the materials form intimate mixtures [3]. In a linear spectral unmixing scenario, the mixed pixels can be expressed as a linear combination of the endmember signatures present in the scene weighted by their respective fractional abundances. The exploitation of this model, in spite of its simplicity, has fostered a large amount of research leading to a plethora of endmember extraction and abundance estimation algorithms developed with (and without) the assumption that pure pixels¹

A pure pixel contains just one endmember.

can be found in the original hyperspectral image. A detailed review of techniques developed for spectral unmixing in recent years is available at [4].