3,410 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&
Statistical single channel source separation
PhD ThesisSingle channel source separation (SCSS) principally is one of the challenging fields
in signal processing and has various significant applications. Unlike conventional
SCSS methods which were based on linear instantaneous model, this research sets out
to investigate the separation of single channel in two types of mixture which is
nonlinear instantaneous mixture and linear convolutive mixture. For the nonlinear
SCSS in instantaneous mixture, this research proposes a novel solution based on a
two-stage process that consists of a Gaussianization transform which efficiently
compensates for the nonlinear distortion follow by a maximum likelihood estimator to
perform source separation. For linear SCSS in convolutive mixture, this research
proposes new methods based on nonnegative matrix factorization which decomposes a
mixture into two-dimensional convolution factor matrices that represent the spectral
basis and temporal code. The proposed factorization considers the convolutive mixing
in the decomposition by introducing frequency constrained parameters in the model.
The method aims to separate the mixture into its constituent spectral-temporal source
components while alleviating the effect of convolutive mixing. In addition, family of
Itakura-Saito divergence has been developed as a cost function which brings the
beneficial property of scale-invariant. Two new statistical techniques are proposed,
namely, Expectation-Maximisation (EM) based algorithm framework which
maximizes the log-likelihood of a mixed signals, and the maximum a posteriori
approach which maximises the joint probability of a mixed signal using multiplicative
update rules. To further improve this research work, a novel method that incorporates
adaptive sparseness into the solution has been proposed to resolve the ambiguity and
hence, improve the algorithm performance. The theoretical foundation of the proposed
solutions has been rigorously developed and discussed in details. Results have
concretely shown the effectiveness of all the proposed algorithms presented in this
thesis in separating the mixed signals in single channel and have outperformed others
available methods.Universiti Teknikal Malaysia Melaka(UTeM),
Ministry of Higher Education of Malaysi
Blind Multilinear Identification
We discuss a technique that allows blind recovery of signals or blind
identification of mixtures in instances where such recovery or identification
were previously thought to be impossible: (i) closely located or highly
correlated sources in antenna array processing, (ii) highly correlated
spreading codes in CDMA radio communication, (iii) nearly dependent spectra in
fluorescent spectroscopy. This has important implications --- in the case of
antenna array processing, it allows for joint localization and extraction of
multiple sources from the measurement of a noisy mixture recorded on multiple
sensors in an entirely deterministic manner. In the case of CDMA, it allows the
possibility of having a number of users larger than the spreading gain. In the
case of fluorescent spectroscopy, it allows for detection of nearly identical
chemical constituents. The proposed technique involves the solution of a
bounded coherence low-rank multilinear approximation problem. We show that
bounded coherence allows us to establish existence and uniqueness of the
recovered solution. We will provide some statistical motivation for the
approximation problem and discuss greedy approximation bounds. To provide the
theoretical underpinnings for this technique, we develop a corresponding theory
of sparse separable decompositions of functions, including notions of rank and
nuclear norm that specialize to the usual ones for matrices and operators but
apply to also hypermatrices and tensors.Comment: 20 pages, to appear in IEEE Transactions on Information Theor
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