Linear Hyperspectral Unmixing Using l0-norm Approximations and Nonnegative Matrix Factorization

186 Pages·2016·3.44 MB·English

Linear Hyperspectral Unmixing Using
-norm Approximations and
(cid:96)
0
Nonnegative Matrix Factorization
by
Yaser Esmaeili Salehani
A thesis submitted to the
Department of Electrical and Computer Engineering
in conformity with the requirements for
the degree of Doctor of Philosophy
Queen’s University
Kingston, Ontario, Canada
October 2016
Copyright c Yaser Esmaeili Salehani, 2016
(cid:13)
Abstract
Spectral unmixing (SU) is a technique to characterize mixed pixels of the hyper-
spectral images measured by remote sensors. Most of the existing spectral unmixing
algorithms are developed using the linear mixing models. Since the number of end-
members/materials present at each mixed pixel is normally scanty compared with
the number of total endmembers (the dimension of spectral library), the problem
becomes sparse. This thesis introduces sparse hyperspectral unmixing methods for
the linear mixing model through two different scenarios. In the first scenario, the
library of spectral signatures is assumed to be known and the main problem is to find
the minimum number of endmembers under a reasonable small approximation error.
Mathematically, the corresponding problem is called the (cid:96) -norm problem which is
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NP-hard problem. Our main study for the first part of thesis is to find more ac-
curate and reliable approximations of (cid:96) -norm term and propose sparse unmixing
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methods via such approximations. The resulting methods are shown considerable
improvements to reconstruct the fractional abundances of endmembers in compari-
son with state-of-the-art methods such as having lower reconstruction errors. In the
second part of the thesis, the first scenario (i.e., dictionary-aided semiblind unmixing
scheme) will be generalized as the blind unmixing scenario that the library of spectral
signatures is also estimated. We apply the nonnegative matrix factorization (NMF)
i
method for proposing new unmixing methods due to its noticeable supports such as
considering the nonnegativity constraints of two decomposed matrices. Furthermore,
we introduce new cost functions through some statistical and physical features of
spectral signatures of materials (SSoM) and hyperspectral pixels such as the collab-
orative property of hyperspectral pixels and the mathematical representation of the
concentrated energy of SSoM for the first few subbands. Finally, we introduce sparse
unmixing methods for the blind scenario and evaluate the efficiency of the proposed
methods via simulations over synthetic and real hyperspectral data sets. The results
illustrate considerable enhancements to estimate the spectral library of materials and
their fractional abundances such as smaller values of spectral angle distance (SAD)
and abundance angle distance (AAD) as well.
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Co-Authorship
List of publications as a result of the contributions of this thesis:
Y. Esmaeili Salehani, S. Gazor, I-M. Kim, S. Yousefi, “(cid:96) -norm Sparse Hy-
0
•
perspectral Unmixing using Arctan Smoothing”, Journal of Remote Sensing,
MDPI, Feb. 2016.
Y. Esmaeili Salehani, S. Gazor, “Collaborative Unmixng Hyperspectral Im-
•
agery via Nonnegative Matrix Factorization”, In International Conference on
Image and Signal Processing (ICISP) (pp. 118-126), Springer, May 2016, Que-
bec, Canada.
Y. Esmaeili Salehani, S. Gazor, I.-M. Kim, S. Yousefi, “Sparse Hyperspec-
•
tral unmixing via Arctan approximation of L0 norm”, IEEE International Geo-
science and Remote Sensing Symposium (IGARSS), Quebec City, Canada, July
2014, IEEE, pp. 2930-2933.
Y. Esmaeili Salehani, S. Gazor, S. Yousefi, I.-M. Kim, “Sparse Hyperspectral
•
unmixing with Adaptive LASSO”, 27th Biennial Symposium on Communica-
tions (QBSC 2014), Kingston, Canada, June 2014, IEEE, pp. 159-163.
Y. Esmaeili Salehani, S. Gazor, “Sparse Data Reconstruction via Adaptive
•
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(cid:96) -norm and Multilayer NMF”, accepted for publication in the 7th IEEE Annu-
p
al Information Technology, Electronics and Mobile Communication Conference
(IEEE IEMCON 2016), Vancouver, Canada, October 2016.
Y. Esmaeili Salehani, S. Gazor , “Smooth and Sparse Regularization for
•
NMF Hyperspectral Unmixing”, under 1st revision.
Y. Esmaeili Salehani, S. Gazor,“Sparse Hyperspectral Unmixing via Varying
•
(cid:96) -norm Approximation of (cid:96) -norm”, under 2nd revision.
p 0
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Acknowledgments
I would like to appreciate everyone who made this dissertation possible.
First, I would like to thank my supervisors and specifically Professor Saeed Gazor
for his guidance and support in all academical stages paved the way for me. I thank
him for his patience, knowledge and time to have wonderful discussion and ideas
throughout this work. I am also grateful to my PhD committee members, Profes-
sor Soosan Beheshti, Professor Xiang Li, Professor Aboelmagd Noureldin, Professor
Thomas Dean and Professor Tucker Carrington to read my thesis, to attend my de-
fence and to give excellence comments and observations. Also, I would like to thank
my course instructors, Professor Fady Alajaji for the Information theory course and
Professor Ali Ghrayeb for both Coding theory and MIMO communication courses,
valuable and great discussions in the classes and afterwards.
I would like to say a special thank you to my wife for her patience and uncon-
ditional supports for all the time. She helped me to concentrate on completing this
dissertation and supported me faithfully during my endeavors. Nothing I can say can
do justice to how I feel about your support as always, Mona.
I also wish to express my appreciation for my parents and Shahnaz. Without
their belief in my goals, their kindness and affection during my life, I would not be
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able to enter the field of scientific research. I would like to thank my mother-in-
law and father-in-law for their support and kindness throughout my PhD study as
well. Moreover, I would like to thank my sister, brothers and brother-in-law for their
all supports for this journey. Finally, I wish to thank my colleagues and friends at
Queen’s University.
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To:
Danesh and V-D. I
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List of Abbreviations
AAD Abundance Angle Distance
ADMM Alternating Direction Method of Multipliers
ANC Abundance Nonnegativity Constraint
ASC Abundance Sum-to-one Constraint
AWGN Additive White Gaussian Noise
AVIRIS Airbone Visible/Infrared Imaging Spectrometer
BCG Basic Conjugate Gradient
BP Basis Pursuit
BPDN Basis Pursuit Denoising
CBP Constrained Basis Pursuit
CBPDN Constrained Basis Pursuit Denoising
CDF Cumulative Distribution Function
CHL Collaborative Hierarchical LASSO
CHSR Collaborative Hierarchical Sparse Regression
CLS Constrained Least Squares
CSR Constrained Sparse Regression
DCT Discrete Cosine Transform
EEA Endmember Extraction Algorithm
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EM Expectation-Maximization
GLNMF Graph Regularized (cid:96) -Nonnegative Matrix Factorization
1/2
GSUnSAL Group Sparse Unmixing via variable Splitting Augmented Lagrangian
HSI Hyperspectral Image
IRLS Iteratively Reweighted Least Squares
JPL Jet Propulsion Laboratory
KKT Karush-Kuhn-Tucker
LARS Least Angle Regression
LASSO Least Absolute Selection and Shrinkage Operator
LMM Linear Mixing Model
MC Mutual Coherence
MLNMF MultiLayer Nonnegative Matrix Factorization
MSE Mean Square Error
NCCHL Non-negative Constrained Collaborative Hierarchical LASSO
NCHL Non-negative Constrained Hierarchical LASSO
NCLS Nonnegative Constrained Least Squares
NMF Nonnegative Matrix Factorization
OMP Orthogonal Matching Pursuit
PNMM Postnonlinear Mixing Model
PoS Probability of Success
PPNM Polynomial Postnonlinear Model
PPI Pixel Purity Index
RSNR Reconstruction Signal to Noise Ratio
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