276 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
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
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
A convex model for non-negative matrix factorization and dimensionality reduction on physical space
A collaborative convex framework for factoring a data matrix into a
non-negative product , with a sparse coefficient matrix , is proposed.
We restrict the columns of the dictionary matrix to coincide with certain
columns of the data matrix , thereby guaranteeing a physically meaningful
dictionary and dimensionality reduction. We use regularization
to select the dictionary from the data and show this leads to an exact convex
relaxation of in the case of distinct noise free data. We also show how
to relax the restriction-to- constraint by initializing an alternating
minimization approach with the solution of the convex model, obtaining a
dictionary close to but not necessarily in . We focus on applications of the
proposed framework to hyperspectral endmember and abundances identification and
also show an application to blind source separation of NMR data.Comment: 14 pages, 9 figures. EE and JX were supported by NSF grants
{DMS-0911277}, {PRISM-0948247}, MM by the German Academic Exchange Service
(DAAD), SO and MM by NSF grants {DMS-0835863}, {DMS-0914561}, {DMS-0914856}
and ONR grant {N00014-08-1119}, and GS was supported by NSF, NGA, ONR, ARO,
DARPA, and {NSSEFF.
- …