365 research outputs found
Generalized linear mixing model accounting for endmember variability
Endmember variability is an important factor for accurately unveiling vital
information relating the pure materials and their distribution in hyperspectral
images. Recently, the extended linear mixing model (ELMM) has been proposed as
a modification of the linear mixing model (LMM) to consider endmember
variability effects resulting mainly from illumination changes. In this paper,
we further generalize the ELMM leading to a new model (GLMM) to account for
more complex spectral distortions where different wavelength intervals can be
affected unevenly. We also extend the existing methodology to jointly estimate
the variability and the abundances for the GLMM. Simulations with real and
synthetic data show that the unmixing process can benefit from the extra
flexibility introduced by the GLMM
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
A convex formulation for hyperspectral image superresolution via subspace-based regularization
Hyperspectral remote sensing images (HSIs) usually have high spectral
resolution and low spatial resolution. Conversely, multispectral images (MSIs)
usually have low spectral and high spatial resolutions. The problem of
inferring images which combine the high spectral and high spatial resolutions
of HSIs and MSIs, respectively, is a data fusion problem that has been the
focus of recent active research due to the increasing availability of HSIs and
MSIs retrieved from the same geographical area.
We formulate this problem as the minimization of a convex objective function
containing two quadratic data-fitting terms and an edge-preserving regularizer.
The data-fitting terms account for blur, different resolutions, and additive
noise. The regularizer, a form of vector Total Variation, promotes
piecewise-smooth solutions with discontinuities aligned across the
hyperspectral bands.
The downsampling operator accounting for the different spatial resolutions,
the non-quadratic and non-smooth nature of the regularizer, and the very large
size of the HSI to be estimated lead to a hard optimization problem. We deal
with these difficulties by exploiting the fact that HSIs generally "live" in a
low-dimensional subspace and by tailoring the Split Augmented Lagrangian
Shrinkage Algorithm (SALSA), which is an instance of the Alternating Direction
Method of Multipliers (ADMM), to this optimization problem, by means of a
convenient variable splitting. The spatial blur and the spectral linear
operators linked, respectively, with the HSI and MSI acquisition processes are
also estimated, and we obtain an effective algorithm that outperforms the
state-of-the-art, as illustrated in a series of experiments with simulated and
real-life data.Comment: IEEE Trans. Geosci. Remote Sens., to be publishe
Robust retrieval of material chemical states in X-ray microspectroscopy
X-ray microspectroscopic techniques are essential for studying morphological
and chemical changes in materials, providing high-resolution structural and
spectroscopic information. However, its practical data analysis for reliably
retrieving the chemical states remains a major obstacle to accelerating the
fundamental understanding of materials in many research fields. In this work,
we propose a novel data formulation model for X-ray microspectroscopy and
develop a dedicated unmixing framework to solve this problem, which is robust
to noise and spectral variability. Moreover, this framework is not limited to
the analysis of two-state material chemistry, making it an effective
alternative to conventional and widely-used methods. In addition, an
alternative directional multiplier method with provable convergence is applied
to obtain the solution efficiently. Our framework can accurately identify and
characterize chemical states in complex and heterogeneous samples, even under
challenging conditions such as low signal-to-noise ratios and overlapping
spectral features. Extensive experimental results on simulated and real
datasets demonstrate its effectiveness and reliability.Comment: 12 page
False Discovery and Its Control in Low Rank Estimation
Models specified by low-rank matrices are ubiquitous in contemporary
applications. In many of these problem domains, the row/column space structure
of a low-rank matrix carries information about some underlying phenomenon, and
it is of interest in inferential settings to evaluate the extent to which the
row/column spaces of an estimated low-rank matrix signify discoveries about the
phenomenon. However, in contrast to variable selection, we lack a formal
framework to assess true/false discoveries in low-rank estimation; in
particular, the key source of difficulty is that the standard notion of a
discovery is a discrete one that is ill-suited to the smooth structure
underlying low-rank matrices. We address this challenge via a geometric
reformulation of the concept of a discovery, which then enables a natural
definition in the low-rank case. We describe and analyze a generalization of
the Stability Selection method of Meinshausen and B\"uhlmann to control for
false discoveries in low-rank estimation, and we demonstrate its utility
compared to previous approaches via numerical experiments
The Linearized Inverse Problem in Multifrequency Electrical Impedance Tomography
This paper provides an analysis of the linearized inverse problem in
multifrequency electrical impedance tomography. We consider an isotropic
conductivity distribution with a finite number of unknown inclusions with
different frequency dependence, as is often seen in biological tissues. We
discuss reconstruction methods for both fully known and partially known
spectral profiles, and demonstrate in the latter case the successful employment
of difference imaging. We also study the reconstruction with an imperfectly
known boundary, and show that the multifrequency approach can eliminate
modeling errors and recover almost all inclusions. In addition, we develop an
efficient group sparse recovery algorithm for the robust solution of related
linear inverse problems. Several numerical simulations are presented to
illustrate and validate the approach.Comment: 25 pp, 11 figure
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