4,513 research outputs found
Sparse component separation for accurate CMB map estimation
The Cosmological Microwave Background (CMB) is of premier importance for the
cosmologists to study the birth of our universe. Unfortunately, most CMB
experiments such as COBE, WMAP or Planck do not provide a direct measure of the
cosmological signal; CMB is mixed up with galactic foregrounds and point
sources. For the sake of scientific exploitation, measuring the CMB requires
extracting several different astrophysical components (CMB, Sunyaev-Zel'dovich
clusters, galactic dust) form multi-wavelength observations. Mathematically
speaking, the problem of disentangling the CMB map from the galactic
foregrounds amounts to a component or source separation problem. In the field
of CMB studies, a very large range of source separation methods have been
applied which all differ from each other in the way they model the data and the
criteria they rely on to separate components. Two main difficulties are i) the
instrument's beam varies across frequencies and ii) the emission laws of most
astrophysical components vary across pixels. This paper aims at introducing a
very accurate modeling of CMB data, based on sparsity, accounting for beams
variability across frequencies as well as spatial variations of the components'
spectral characteristics. Based on this new sparse modeling of the data, a
sparsity-based component separation method coined Local-Generalized
Morphological Component Analysis (L-GMCA) is described. Extensive numerical
experiments have been carried out with simulated Planck data. These experiments
show the high efficiency of the proposed component separation methods to
estimate a clean CMB map with a very low foreground contamination, which makes
L-GMCA of prime interest for CMB studies.Comment: submitted to A&
Prototype selection for parameter estimation in complex models
Parameter estimation in astrophysics often requires the use of complex
physical models. In this paper we study the problem of estimating the
parameters that describe star formation history (SFH) in galaxies. Here,
high-dimensional spectral data from galaxies are appropriately modeled as
linear combinations of physical components, called simple stellar populations
(SSPs), plus some nonlinear distortions. Theoretical data for each SSP is
produced for a fixed parameter vector via computer modeling. Though the
parameters that define each SSP are continuous, optimizing the signal model
over a large set of SSPs on a fine parameter grid is computationally infeasible
and inefficient. The goal of this study is to estimate the set of parameters
that describes the SFH of each galaxy. These target parameters, such as the
average ages and chemical compositions of the galaxy's stellar populations, are
derived from the SSP parameters and the component weights in the signal model.
Here, we introduce a principled approach of choosing a small basis of SSP
prototypes for SFH parameter estimation. The basic idea is to quantize the
vector space and effective support of the model components. In addition to
greater computational efficiency, we achieve better estimates of the SFH target
parameters. In simulations, our proposed quantization method obtains a
substantial improvement in estimating the target parameters over the common
method of employing a parameter grid. Sparse coding techniques are not
appropriate for this problem without proper constraints, while constrained
sparse coding methods perform poorly for parameter estimation because their
objective is signal reconstruction, not estimation of the target parameters.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS500 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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
Principal Component Analysis and Radiative Transfer modelling of Spitzer IRS Spectra of Ultra Luminous Infrared Galaxies
The mid-infrared spectra of ultraluminous infrared galaxies (ULIRGs) contain
a variety of spectral features that can be used as diagnostics to characterise
the spectra. However, such diagnostics are biased by our prior prejudices on
the origin of the features. Moreover, by using only part of the spectrum they
do not utilise the full information content of the spectra. Blind statistical
techniques such as principal component analysis (PCA) consider the whole
spectrum, find correlated features and separate them out into distinct
components.
We further investigate the principal components (PCs) of ULIRGs derived in
Wang et al.(2011). We quantitatively show that five PCs is optimal for
describing the IRS spectra. These five components (PC1-PC5) and the mean
spectrum provide a template basis set that reproduces spectra of all z<0.35
ULIRGs within the noise. For comparison, the spectra are also modelled with a
combination of radiative transfer models of both starbursts and the dusty torus
surrounding active galactic nuclei. The five PCs typically provide better fits
than the models. We argue that the radiative transfer models require a colder
dust component and have difficulty in modelling strong PAH features.
Aided by the models we also interpret the physical processes that the
principal components represent. The third principal component is shown to
indicate the nature of the dominant power source, while PC1 is related to the
inclination of the AGN torus.
Finally, we use the 5 PCs to define a new classification scheme using 5D
Gaussian mixtures modelling and trained on widely used optical classifications.
The five PCs, average spectra for the four classifications and the code to
classify objects are made available at: http://www.phys.susx.ac.uk/~pdh21/PCA/Comment: 11 pages, 12 figures, accepted for publication in MNRA
Joint Tensor Factorization and Outlying Slab Suppression with Applications
We consider factoring low-rank tensors in the presence of outlying slabs.
This problem is important in practice, because data collected in many
real-world applications, such as speech, fluorescence, and some social network
data, fit this paradigm. Prior work tackles this problem by iteratively
selecting a fixed number of slabs and fitting, a procedure which may not
converge. We formulate this problem from a group-sparsity promoting point of
view, and propose an alternating optimization framework to handle the
corresponding () minimization-based low-rank tensor
factorization problem. The proposed algorithm features a similar per-iteration
complexity as the plain trilinear alternating least squares (TALS) algorithm.
Convergence of the proposed algorithm is also easy to analyze under the
framework of alternating optimization and its variants. In addition,
regularization and constraints can be easily incorporated to make use of
\emph{a priori} information on the latent loading factors. Simulations and real
data experiments on blind speech separation, fluorescence data analysis, and
social network mining are used to showcase the effectiveness of the proposed
algorithm
Functional Regression
Functional data analysis (FDA) involves the analysis of data whose ideal
units of observation are functions defined on some continuous domain, and the
observed data consist of a sample of functions taken from some population,
sampled on a discrete grid. Ramsay and Silverman's 1997 textbook sparked the
development of this field, which has accelerated in the past 10 years to become
one of the fastest growing areas of statistics, fueled by the growing number of
applications yielding this type of data. One unique characteristic of FDA is
the need to combine information both across and within functions, which Ramsay
and Silverman called replication and regularization, respectively. This article
will focus on functional regression, the area of FDA that has received the most
attention in applications and methodological development. First will be an
introduction to basis functions, key building blocks for regularization in
functional regression methods, followed by an overview of functional regression
methods, split into three types: [1] functional predictor regression
(scalar-on-function), [2] functional response regression (function-on-scalar)
and [3] function-on-function regression. For each, the role of replication and
regularization will be discussed and the methodological development described
in a roughly chronological manner, at times deviating from the historical
timeline to group together similar methods. The primary focus is on modeling
and methodology, highlighting the modeling structures that have been developed
and the various regularization approaches employed. At the end is a brief
discussion describing potential areas of future development in this field
Bayesian separation of spectral sources under non-negativity and full additivity constraints
This paper addresses the problem of separating spectral sources which are
linearly mixed with unknown proportions. The main difficulty of the problem is
to ensure the full additivity (sum-to-one) of the mixing coefficients and
non-negativity of sources and mixing coefficients. A Bayesian estimation
approach based on Gamma priors was recently proposed to handle the
non-negativity constraints in a linear mixture model. However, incorporating
the full additivity constraint requires further developments. This paper
studies a new hierarchical Bayesian model appropriate to the non-negativity and
sum-to-one constraints associated to the regressors and regression coefficients
of linear mixtures. The estimation of the unknown parameters of this model is
performed using samples generated using an appropriate Gibbs sampler. The
performance of the proposed algorithm is evaluated through simulation results
conducted on synthetic mixture models. The proposed approach is also applied to
the processing of multicomponent chemical mixtures resulting from Raman
spectroscopy.Comment: v4: minor grammatical changes; Signal Processing, 200
A review of blind source separation in NMR spectroscopy
27 pagesInternational audienceFourier transform is the data processing naturally associated to most NMR experiments. Notable exceptions are Pulse Field Gradient and relaxation analysis, the structure of which is only partially suitable for FT. With the revamp of NMR of complex mixtures, fueled by analytical challenges such as metabolomics, alternative and more apt mathematical methods for data processing have been sought, with the aim of decomposing the NMR signal into simpler bits. Blind source separation is a very broad definition regrouping several classes of mathematical methods for complex signal decomposition that use no hypothesis on the form of the data. Developed outside NMR, these algorithms have been increasingly tested on spectra of mixtures. In this review, we shall provide an historical overview of the application of blind source separation methodologies to NMR, including methods specifically designed for the specificity of this spectroscopy
Structured Sparsity Models for Multiparty Speech Recovery from Reverberant Recordings
We tackle the multi-party speech recovery problem through modeling the
acoustic of the reverberant chambers. Our approach exploits structured sparsity
models to perform room modeling and speech recovery. We propose a scheme for
characterizing the room acoustic from the unknown competing speech sources
relying on localization of the early images of the speakers by sparse
approximation of the spatial spectra of the virtual sources in a free-space
model. The images are then clustered exploiting the low-rank structure of the
spectro-temporal components belonging to each source. This enables us to
identify the early support of the room impulse response function and its unique
map to the room geometry. To further tackle the ambiguity of the reflection
ratios, we propose a novel formulation of the reverberation model and estimate
the absorption coefficients through a convex optimization exploiting joint
sparsity model formulated upon spatio-spectral sparsity of concurrent speech
representation. The acoustic parameters are then incorporated for separating
individual speech signals through either structured sparse recovery or inverse
filtering the acoustic channels. The experiments conducted on real data
recordings demonstrate the effectiveness of the proposed approach for
multi-party speech recovery and recognition.Comment: 31 page
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