64 research outputs found
Correntropy Maximization via ADMM - Application to Robust Hyperspectral Unmixing
In hyperspectral images, some spectral bands suffer from low signal-to-noise
ratio due to noisy acquisition and atmospheric effects, thus requiring robust
techniques for the unmixing problem. This paper presents a robust supervised
spectral unmixing approach for hyperspectral images. The robustness is achieved
by writing the unmixing problem as the maximization of the correntropy
criterion subject to the most commonly used constraints. Two unmixing problems
are derived: the first problem considers the fully-constrained unmixing, with
both the non-negativity and sum-to-one constraints, while the second one deals
with the non-negativity and the sparsity-promoting of the abundances. The
corresponding optimization problems are solved efficiently using an alternating
direction method of multipliers (ADMM) approach. Experiments on synthetic and
real hyperspectral images validate the performance of the proposed algorithms
for different scenarios, demonstrating that the correntropy-based unmixing is
robust to outlier bands.Comment: 23 page
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
Nonlinear unmixing of hyperspectral images: Models and algorithms
When considering the problem of unmixing hyperspectral images, most of the literature in the geoscience and image processing areas relies on the widely used linear mixing model (LMM). However, the LMM may be not valid, and other nonlinear models need to be considered, for instance, when there are multiscattering effects or intimate interactions. Consequently, over the last few years, several significant contributions have been proposed to overcome the limitations inherent in the LMM. In this article, we present an overview of recent advances in nonlinear unmixing modeling
Non-convex regularization in remote sensing
In this paper, we study the effect of different regularizers and their
implications in high dimensional image classification and sparse linear
unmixing. Although kernelization or sparse methods are globally accepted
solutions for processing data in high dimensions, we present here a study on
the impact of the form of regularization used and its parametrization. We
consider regularization via traditional squared (2) and sparsity-promoting (1)
norms, as well as more unconventional nonconvex regularizers (p and Log Sum
Penalty). We compare their properties and advantages on several classification
and linear unmixing tasks and provide advices on the choice of the best
regularizer for the problem at hand. Finally, we also provide a fully
functional toolbox for the community.Comment: 11 pages, 11 figure
Bayesian Nonparametric Unmixing of Hyperspectral Images
Hyperspectral imaging is an important tool in remote sensing, allowing for
accurate analysis of vast areas. Due to a low spatial resolution, a pixel of a
hyperspectral image rarely represents a single material, but rather a mixture
of different spectra. HSU aims at estimating the pure spectra present in the
scene of interest, referred to as endmembers, and their fractions in each
pixel, referred to as abundances. Today, many HSU algorithms have been
proposed, based either on a geometrical or statistical model. While most
methods assume that the number of endmembers present in the scene is known,
there is only little work about estimating this number from the observed data.
In this work, we propose a Bayesian nonparametric framework that jointly
estimates the number of endmembers, the endmembers itself, and their
abundances, by making use of the Indian Buffet Process as a prior for the
endmembers. Simulation results and experiments on real data demonstrate the
effectiveness of the proposed algorithm, yielding results comparable with
state-of-the-art methods while being able to reliably infer the number of
endmembers. In scenarios with strong noise, where other algorithms provide only
poor results, the proposed approach tends to overestimate the number of
endmembers slightly. The additional endmembers, however, often simply represent
noisy replicas of present endmembers and could easily be merged in a
post-processing step
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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