IEEE JOURNAL OF SELECTED TOPICS IN APPLIED EARTH OBSERVATIONS AND REMOTE SENSING, VOL. 8, NO. 6, JUNE 2015 2665
Equivalent-Sparse Unmixing Through Spatial and
Spectral Constrained Endmember Selection
From an Image-Derived Spectral Library
Shaohui Mei, Member, IEEE,QianDu,Senior Member, IEEE, and Mingyi He, Member, IEEE
Abstract—Spectral variation, which is inevitably present in
hyperspectral data due to nonuniformity and inconsistency of illu-
mination, may result in considerable difficulty in spectral unmix-
ing. In this paper, a field endmember library is constructed to
accommodate spectral variation by representing each endmem-
ber class by a batch of image-derived spectra. In order to perform
unmixing by such a field endmember library, a novel spatial and
spectral endmember selection (SSES) algorithm is designed to
search for a spatial and spectral constrained endmember sub-
set per pixel for abundance estimation (AE). The net effect is to
achieve sparse unmixing equivalently, considering the fact t hat
only a few endmembers in the large library have nonzero abun-
dances. Thus, the resulting algorithm is called spatial and spectral
constrained sparse unmixing (SSCSU). Experimental results using
both synthetic and real hyperspectral images demonstrate that the
proposed SSCSU algorithm not only improves the performance of
traditional AE algorithms by considering spectral variation, but
also outperforms the existing sparse unmixing approaches.
Index Terms—Hyperspectral image, in-field spectral variation,
mixed pixel, sparse unmixing, spectral unmixing.
I. INTRODUCTION
H
YPERSPECTRAL optical imaging, which records a
detailed spectrum of the reflected solar energy in each
spatial position of an image, has become a promising technique
to discriminate different materials according to their spectral
fingerprint. However, due to the rough spatial resolution [1],
most of the pixels acquired by hyperspectral remote sensors are
composed of several ground materials, which are well known
as mixed pixels or mixtures. The widely presence of mixtures
influences the performance of image classification and target
recognition [2]. Therefore, spectral unmixing, which extracts
fractional abundance of pure materials (known as endmember)
within a pixel, has been developed to solve such mixed-pixel
problems [3].
Manuscript received August 21, 2014; revised December 28, 2014; accepted
January 19, 2015. Date of publication March 10, 2015; date of current
version July 30, 2015. This work was supported in part by the National
Natural Science Foundation of China (61201324, 61171154, 61420106007)
and Natural Science Foundation of Shaanxi Province (2013JQ801).
S. Mei and M. He are with the School of Electronics and Information,
Northwestern Polytechnical University, Xi’an 710129, China.
Q. Du is with the Department of Electrical and Computer Engineering,
Geosystems Research Institute, Mississippi State University, Starkville, MS
39762 USA.
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/JSTARS.2015.2403254
Generally, spectral unmixing techniques involve two steps:
1) to identify the spectrally unique signatures of pure ground
materials which is known as endmember extraction (EE); 2) to
express individual image pixels in terms of linear/nonlinear
combinations of endmembers which is known as abundance
estimation (AE). In the past decades, a large number of algo-
rithms has been proposed for these two steps, such as N-FINDR
algorithm [4], vertex component analysis (VCA) [5], simplex
growing algorithm (SGA) [6], automated morphological end-
member extraction (AMEE) algorithm [7], [8], and spatial
purity-based endmember extraction (SPEE) algorithm [ 9], [10]
for EE; gradient descent maximum entropy (GDME) algorithm
[11], fully constrained least square (FCLS) algorithm [12],
and multichannel hopfield neural network (MHNN) [2], [13]
for AE. In addition, unsupervised unmixing algorithms, which
usually perform EE and AE simultaneously, have also widely
been researched, such as nonnegative matrix factorization based
algorithms [14]–[17], convex optimization based algorithms
[18]–[20], to name a few.
Since the solar illumination lacks uniformity and consis-
tency over large areas, even homogeneous ground objects often
present different spectral signatures, which can be considered
as within-class spectral variation. As shown in Fig. 1, in the
AVIRIS image over Indian Pines area, although pixels of “Loc
1,” “Loc 2,” “Loc 3,” and “Loc 4” are of the same class called
“Soybeans-min,” their corresponding spectra are obviously dif-
ferent. Therefore, if only one spectrum is selected as represen-
tative of an endmember for unmixing, estimated abundances
may not be accurate. Generally, two approaches can be uti-
lized to accommodate within-class spectral variation: 1) model
each endmember class by a probability density function (pdf);
2) construct an endmember library where each endmember
class is represented by a batch of spectra. In the stochastic mix-
ing model (SMM), a pdf per endmember class is used to model
the spectral variation statistically. The expectation maximiza-
tion (EM) algorithm [ 21], [22] and Bayesian self-organizing
map [23], [24] can be utilized to estimate parameters in end-
member distribution and their corresponding fractional abun-
dance. However, it is difficult to know the true pdf of endmem-
bers in an image, although it is often assumed to be Gaussian. In
addition, inaccurate estimation of parameters in pdf also affects
the unmixing results. Therefore, in this paper, we focus on the
construction of an improved endmember library.
A s pectral library usually contains hundreds or thousands
of spectra. However, the number of endmembers present in
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