131 research outputs found
Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches
Imaging spectrometers measure electromagnetic energy scattered in their
instantaneous field view in hundreds or thousands of spectral channels with
higher spectral resolution than multispectral cameras. Imaging spectrometers
are therefore often referred to as hyperspectral cameras (HSCs). Higher
spectral resolution enables material identification via spectroscopic analysis,
which facilitates countless applications that require identifying materials in
scenarios unsuitable for classical spectroscopic analysis. Due to low spatial
resolution of HSCs, microscopic material mixing, and multiple scattering,
spectra measured by HSCs are mixtures of spectra of materials in a scene. Thus,
accurate estimation requires unmixing. Pixels are assumed to be mixtures of a
few materials, called endmembers. Unmixing involves estimating all or some of:
the number of endmembers, their spectral signatures, and their abundances at
each pixel. Unmixing is a challenging, ill-posed inverse problem because of
model inaccuracies, observation noise, environmental conditions, endmember
variability, and data set size. Researchers have devised and investigated many
models searching for robust, stable, tractable, and accurate unmixing
algorithms. This paper presents an overview of unmixing methods from the time
of Keshava and Mustard's unmixing tutorial [1] to the present. Mixing models
are first discussed. Signal-subspace, geometrical, statistical, sparsity-based,
and spatial-contextual unmixing algorithms are described. Mathematical problems
and potential solutions are described. Algorithm characteristics are
illustrated experimentally.Comment: This work has been accepted for publication in IEEE Journal of
Selected Topics in Applied Earth Observations and Remote Sensin
An Alternating Direction Algorithm for Matrix Completion with Nonnegative Factors
This paper introduces an algorithm for the nonnegative matrix
factorization-and-completion problem, which aims to find nonnegative low-rank
matrices X and Y so that the product XY approximates a nonnegative data matrix
M whose elements are partially known (to a certain accuracy). This problem
aggregates two existing problems: (i) nonnegative matrix factorization where
all entries of M are given, and (ii) low-rank matrix completion where
nonnegativity is not required. By taking the advantages of both nonnegativity
and low-rankness, one can generally obtain superior results than those of just
using one of the two properties. We propose to solve the non-convex constrained
least-squares problem using an algorithm based on the classic alternating
direction augmented Lagrangian method. Preliminary convergence properties of
the algorithm and numerical simulation results are presented. Compared to a
recent algorithm for nonnegative matrix factorization, the proposed algorithm
produces factorizations of similar quality using only about half of the matrix
entries. On tasks of recovering incomplete grayscale and hyperspectral images,
the proposed algorithm yields overall better qualities than those produced by
two recent matrix-completion algorithms that do not exploit nonnegativity
Dictionary-based Tensor Canonical Polyadic Decomposition
To ensure interpretability of extracted sources in tensor decomposition, we
introduce in this paper a dictionary-based tensor canonical polyadic
decomposition which enforces one factor to belong exactly to a known
dictionary. A new formulation of sparse coding is proposed which enables high
dimensional tensors dictionary-based canonical polyadic decomposition. The
benefits of using a dictionary in tensor decomposition models are explored both
in terms of parameter identifiability and estimation accuracy. Performances of
the proposed algorithms are evaluated on the decomposition of simulated data
and the unmixing of hyperspectral images
Endmember Extraction From Hyperspectral Imagery Based on Probabilistic Tensor Moments
This letter presents a novel hyperspectral endmember extraction approach that integrates a tensor-based decomposition scheme with a probabilistic framework in order to take
advantage of both technologies when uncovering the signatures
of pure spectral constituents in the scene. On the one hand,
statistical unmixing models are generally able to provide accurate
endmember estimates by means of rather complex optimization
algorithms. On the other hand, tensor decomposition techniques
are very effective factorization tools which are often constrained
by the lack of physical interpretation within the remote sensing field. In this context, this letter develops a new hybrid
endmember extraction approach based on the decomposition
of the probabilistic tensor moments of the hyperspectral data.
Initially, the input image reflectance values are modeled as a
collection of multinomial distributions provided by a family of
Dirichlet generalized functions. Then, the unmixing process is
effectively conducted by the tensor decomposition of the thirdorder probabilistic tensor moments of the multivariate data.
Our experiments, conducted over four hyperspectral data sets,
reveal that the proposed approach is able to provide efficient and
competitive results when compared to different state-of-the-art
endmember extraction methods
Collaborative sparse regression using spatially correlated supports - Application to hyperspectral unmixing
This paper presents a new Bayesian collaborative sparse regression method for
linear unmixing of hyperspectral images. Our contribution is twofold; first, we
propose a new Bayesian model for structured sparse regression in which the
supports of the sparse abundance vectors are a priori spatially correlated
across pixels (i.e., materials are spatially organised rather than randomly
distributed at a pixel level). This prior information is encoded in the model
through a truncated multivariate Ising Markov random field, which also takes
into consideration the facts that pixels cannot be empty (i.e, there is at
least one material present in each pixel), and that different materials may
exhibit different degrees of spatial regularity. Secondly, we propose an
advanced Markov chain Monte Carlo algorithm to estimate the posterior
probabilities that materials are present or absent in each pixel, and,
conditionally to the maximum marginal a posteriori configuration of the
support, compute the MMSE estimates of the abundance vectors. A remarkable
property of this algorithm is that it self-adjusts the values of the parameters
of the Markov random field, thus relieving practitioners from setting
regularisation parameters by cross-validation. The performance of the proposed
methodology is finally demonstrated through a series of experiments with
synthetic and real data and comparisons with other algorithms from the
literature
Self-Dictionary Sparse Regression for Hyperspectral Unmixing: Greedy Pursuit and Pure Pixel Search are Related
This paper considers a recently emerged hyperspectral unmixing formulation
based on sparse regression of a self-dictionary multiple measurement vector
(SD-MMV) model, wherein the measured hyperspectral pixels are used as the
dictionary. Operating under the pure pixel assumption, this SD-MMV formalism is
special in that it allows simultaneous identification of the endmember spectral
signatures and the number of endmembers. Previous SD-MMV studies mainly focus
on convex relaxations. In this study, we explore the alternative of greedy
pursuit, which generally provides efficient and simple algorithms. In
particular, we design a greedy SD-MMV algorithm using simultaneous orthogonal
matching pursuit. Intriguingly, the proposed greedy algorithm is shown to be
closely related to some existing pure pixel search algorithms, especially, the
successive projection algorithm (SPA). Thus, a link between SD-MMV and pure
pixel search is revealed. We then perform exact recovery analyses, and prove
that the proposed greedy algorithm is robust to noise---including its
identification of the (unknown) number of endmembers---under a sufficiently low
noise level. The identification performance of the proposed greedy algorithm is
demonstrated through both synthetic and real-data experiments
Image Processing and Machine Learning for Hyperspectral Unmixing: An Overview and the HySUPP Python Package
Spectral pixels are often a mixture of the pure spectra of the materials,
called endmembers, due to the low spatial resolution of hyperspectral sensors,
double scattering, and intimate mixtures of materials in the scenes. Unmixing
estimates the fractional abundances of the endmembers within the pixel.
Depending on the prior knowledge of endmembers, linear unmixing can be divided
into three main groups: supervised, semi-supervised, and unsupervised (blind)
linear unmixing. Advances in Image processing and machine learning
substantially affected unmixing. This paper provides an overview of advanced
and conventional unmixing approaches. Additionally, we draw a critical
comparison between advanced and conventional techniques from the three
categories. We compare the performance of the unmixing techniques on three
simulated and two real datasets. The experimental results reveal the advantages
of different unmixing categories for different unmixing scenarios. Moreover, we
provide an open-source Python-based package available at
https://github.com/BehnoodRasti/HySUPP to reproduce the results
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