3,952 research outputs found
Implementation strategies for hyperspectral unmixing using Bayesian source separation
Bayesian Positive Source Separation (BPSS) is a useful unsupervised approach
for hyperspectral data unmixing, where numerical non-negativity of spectra and
abundances has to be ensured, such in remote sensing. Moreover, it is sensible
to impose a sum-to-one (full additivity) constraint to the estimated source
abundances in each pixel. Even though non-negativity and full additivity are
two necessary properties to get physically interpretable results, the use of
BPSS algorithms has been so far limited by high computation time and large
memory requirements due to the Markov chain Monte Carlo calculations. An
implementation strategy which allows one to apply these algorithms on a full
hyperspectral image, as typical in Earth and Planetary Science, is introduced.
Effects of pixel selection, the impact of such sampling on the relevance of the
estimated component spectra and abundance maps, as well as on the computation
times, are discussed. For that purpose, two different dataset have been used: a
synthetic one and a real hyperspectral image from Mars.Comment: 10 pages, 6 figures, submitted to IEEE Transactions on Geoscience and
Remote Sensing in the special issue on Hyperspectral Image and Signal
Processing (WHISPERS
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
Informed baseline subtraction of proteomic mass spectrometry data aided by a novel sliding window algorithm
Proteomic matrix-assisted laser desorption/ionisation (MALDI) linear
time-of-flight (TOF) mass spectrometry (MS) may be used to produce protein
profiles from biological samples with the aim of discovering biomarkers for
disease. However, the raw protein profiles suffer from several sources of bias
or systematic variation which need to be removed via pre-processing before
meaningful downstream analysis of the data can be undertaken. Baseline
subtraction, an early pre-processing step that removes the non-peptide signal
from the spectra, is complicated by the following: (i) each spectrum has, on
average, wider peaks for peptides with higher mass-to-charge ratios (m/z), and
(ii) the time-consuming and error-prone trial-and-error process for optimising
the baseline subtraction input arguments. With reference to the aforementioned
complications, we present an automated pipeline that includes (i) a novel
`continuous' line segment algorithm that efficiently operates over data with a
transformed m/z-axis to remove the relationship between peptide mass and peak
width, and (ii) an input-free algorithm to estimate peak widths on the
transformed m/z scale. The automated baseline subtraction method was deployed
on six publicly available proteomic MS datasets using six different m/z-axis
transformations. Optimality of the automated baseline subtraction pipeline was
assessed quantitatively using the mean absolute scaled error (MASE) when
compared to a gold-standard baseline subtracted signal. Near-optimal baseline
subtraction was achieved using the automated pipeline. The advantages of the
proposed pipeline include informed and data specific input arguments for
baseline subtraction methods, the avoidance of time-intensive and subjective
piecewise baseline subtraction, and the ability to automate baseline
subtraction completely. Moreover, individual steps can be adopted as
stand-alone routines.Comment: 50 pages, 19 figure
Fast and Robust Recursive Algorithms for Separable Nonnegative Matrix Factorization
In this paper, we study the nonnegative matrix factorization problem under
the separability assumption (that is, there exists a cone spanned by a small
subset of the columns of the input nonnegative data matrix containing all
columns), which is equivalent to the hyperspectral unmixing problem under the
linear mixing model and the pure-pixel assumption. We present a family of fast
recursive algorithms, and prove they are robust under any small perturbations
of the input data matrix. This family generalizes several existing
hyperspectral unmixing algorithms and hence provides for the first time a
theoretical justification of their better practical performance.Comment: 30 pages, 2 figures, 7 tables. Main change: Improvement of the bound
of the main theorem (Th. 3), replacing r with sqrt(r
Minimum Density Hyperplanes
Associating distinct groups of objects (clusters) with contiguous regions of
high probability density (high-density clusters), is central to many
statistical and machine learning approaches to the classification of unlabelled
data. We propose a novel hyperplane classifier for clustering and
semi-supervised classification which is motivated by this objective. The
proposed minimum density hyperplane minimises the integral of the empirical
probability density function along it, thereby avoiding intersection with high
density clusters. We show that the minimum density and the maximum margin
hyperplanes are asymptotically equivalent, thus linking this approach to
maximum margin clustering and semi-supervised support vector classifiers. We
propose a projection pursuit formulation of the associated optimisation problem
which allows us to find minimum density hyperplanes efficiently in practice,
and evaluate its performance on a range of benchmark datasets. The proposed
approach is found to be very competitive with state of the art methods for
clustering and semi-supervised classification
Low Complexity Regularization of Linear Inverse Problems
Inverse problems and regularization theory is a central theme in contemporary
signal processing, where the goal is to reconstruct an unknown signal from
partial indirect, and possibly noisy, measurements of it. A now standard method
for recovering the unknown signal is to solve a convex optimization problem
that enforces some prior knowledge about its structure. This has proved
efficient in many problems routinely encountered in imaging sciences,
statistics and machine learning. This chapter delivers a review of recent
advances in the field where the regularization prior promotes solutions
conforming to some notion of simplicity/low-complexity. These priors encompass
as popular examples sparsity and group sparsity (to capture the compressibility
of natural signals and images), total variation and analysis sparsity (to
promote piecewise regularity), and low-rank (as natural extension of sparsity
to matrix-valued data). Our aim is to provide a unified treatment of all these
regularizations under a single umbrella, namely the theory of partial
smoothness. This framework is very general and accommodates all low-complexity
regularizers just mentioned, as well as many others. Partial smoothness turns
out to be the canonical way to encode low-dimensional models that can be linear
spaces or more general smooth manifolds. This review is intended to serve as a
one stop shop toward the understanding of the theoretical properties of the
so-regularized solutions. It covers a large spectrum including: (i) recovery
guarantees and stability to noise, both in terms of -stability and
model (manifold) identification; (ii) sensitivity analysis to perturbations of
the parameters involved (in particular the observations), with applications to
unbiased risk estimation ; (iii) convergence properties of the forward-backward
proximal splitting scheme, that is particularly well suited to solve the
corresponding large-scale regularized optimization problem
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