An Optimization Method for Hyperspectral
Endmember Extraction Based on K-SVD
Xiaoxiao Feng, Luxiao He, Ya Zhang, and Yun Tang
Abstract
Mixed pixels are common in hyperspectral imagery (
HSI
). Due
to the complexity of the ground object distribution, some end-
member extraction methods cannot obtain good results and
the processes are complex. Therefore, this paper proposes an
optimization method for
HSI
endmember extraction, which
improves the accuracy of the results based on K-singular
value decomposition (
K-SVD
). The proposed method comprises
three core steps. (1) Based on the contribution value of initial
endmembers, partially observed data selected according to
the appropriate confidence participate in the calculation. (2)
Construction of the error model to eliminate the background
noise. (3) Using the
K-SVD
to perform column-by-column itera-
tion on the endmembers to achieve the overall optimality. Ex-
periments with three real images are applied, demonstrating
the proposed method can improve the overall endmember ac-
curacy by 15.1%–55.7% compared with the original methods.
Introduction
Owing to the limited light energy of the camera, spatial reso-
lution and spectral resolution are not compatible. Hyperspec-
tral sensors generally have low spatial resolution and very
high spectral resolution. The separable number of features
increase with the spectral resolution, while the spatial scale
of a single feature reduces correspondingly. Therefore, a
pixel in hyperspectral imagery (
HSI
) is often a mixture of
multiple spectral spectra, and this kind of pixel mixed with
a variety of pure features is called mixed pixel (Keshava and
Mustard 2002). The observed spectral signature at each pixel
is actually a spectral mixture of several pure materials (i.e.,
endmembers) (Sun
et al.
2017). Mixed p
affect the accuracy of feature recognition
but also hinder the further applications
remote sensing (Addink, De Jong, and Pebesma 2007; Xu and
Gong 2007; Zhang and Qiu 2012). Spectral unmixing is an ef-
fective way to solve the mixed pixel problem, which includes
endmember extraction and abundance reconstruction. End-
member extraction is a process to extract pure spectra in
HSI
(Shao and Zhang 2014; Sun
et al.
2017).
There are two kinds of combination models of endmem-
bers and their corresponding abundance: linear and nonlinear
models, and the linear mixture model (
LMM
) has been widely
used in the past few decades to solve spectral unmixing prob-
lems. On the premise that the abundance of the components
satisfies the nonnegative and sum-to-one constraints, the
geometrical-based methods assume that all the pixels in the
HSI
are distributed in simplex and the vertices of the simplex
are the corresponding endmembers. There are many typical
geometrical-based methods that use the fact that the observed
spectral vectors will be contained in a simplex after affine
transformation, where the endmembers are located in the ver-
texes. N-finder algorithm (
N-FINDR
) (Winter 1999) determines
the endmembers by finding the vertices of the largest volume
of the simplex. Vertex Component Analysis (
VCA
) (Nascimen-
to and Dias 2005) is modeled by a convex, and the orthogonal
subspace projection is repeated to obtain endmembers.
Although some geometrical-based methods are not based
on the pure pixel premise, they obtain not ideal results with
noisy observations, such as the Minimum Volume Simplex
Analysis (
MVSA
) (Li and Bioucas-Dias 2008). Because the
MVSA
states that the vertices of the minimum-volume simplex
enclosing the
HSI
pixels will yield high fidelity estimates of
endmember signatures associated with the
HSI
data (Sun
et
al.
2017), many scholars have proposed various statistical-
based methods, which have achieved better accuracy. Spectral
unmixing can be considered as a Blind Source Separation
problem (Yang
et al.
2011), where the mixed pixels, end-
members, and abundances in the spectral unmixing can be
considered as the observed signals, mixing matrix, and source
signals, respectively. Minimum Volume Constrained-Non-
negative Matrix Factorization (
MVCNMF
) (Miao and Qi 2007)
incorporates a volume constraint into Nonnegative Matrix
Factorization (
NMF
) and indicates that there may be two pos-
sibilities for a compliant simplex: one is circumscribed to the
data and has the smallest volume, and the other is tangential
to the data and has the largest volume. Abundance Separation
and Smoothness constraint
NMF
(
ASSNMF
) (Liu
et al.
2011)
fully considers the spatial information of
HSI
, which adds the
abundance separation and smoothness
bjective function, and combines
NMF
ixing. The sparse unmixing algorithm
via splitting and augmented Lagrangian (Bioucas-Dias and
Figueiredo 2010) is a semisupervised approach, in which
mixed pixels are expressed in form of linear combinations of
a known endmember large spectral library. Spatial group spar-
sity regularized
NMF
(
SGSNMF
) (Wang
et al.
2017) incorporates
a spatial group sparsity regularizer into the
NMF
-based unmix-
ing process. Recently, there were many methods showing
promising performance of sparsity in hyperspectral unmixing
(Lu, Wu, and Yuan 2014; Zhong
et al.
2016).
Recently, many optimized endmember extraction methods
have been proposed. Li
et al.
(2017) proposed a novel end-
member extraction algorithm based on evolutionary multiob-
jective optimization. In this method, endmember extraction is
modelled as a multiobjective optimization problem, and is op-
timizing two objective functions: one is root-mean-square er-
ror between the original image and its remixed image, and the
other is the number of endmembers. (Xu, Du, and Fan 2019)
Xiaoxiao Feng, Luxiao He, and Ya Zhang are with the State
Key Laboratory of Information Engineering in Surveying,
Mapping, and Remote Sensing, Wuhan University, No.129
Luoyu Road, Hubei 430079, Wuhan, China (fengxx2018@
whu.edu.cn).
Yun Tang is with the School of Remote Sensing and
Information Engineering, Wuhan University, No.129 Luoyu
Road, Hubei 430079, Wuhan, China.
Photogrammetric Engineering & Remote Sensing
Vol. 85, No. 12, December 2019, pp. 879–887.
0099-1112/19/879–887
© 2019 American Society for Photogrammetry
and Remote Sensing
doi: 10.14358/PERS.85.12.879
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
December 2019
879
