13,512 research outputs found
Improving the performance of translation wavelet transform using BMICA
Research has shown Wavelet Transform to be one of the best methods for denoising biosignals. Translation-Invariant
form of this method has been found to be the best performance. In this paper however we utilize this method and merger with our newly created Independent Component Analysis method – BMICA. Different EEG signals are used to verify the method within the MATLAB environment. Results are then compared with those of the actual Translation-Invariant algorithm and evaluated using the performance measures Mean Square Error (MSE), Peak Signal to Noise Ratio (PSNR), Signal to Distortion Ratio (SDR), and Signal to Interference Ratio (SIR). Experiments revealed that the BMICA Translation-Invariant Wavelet Transform out performed in all four measures. This indicates that it performed superior to the basic Translation- Invariant Wavelet Transform algorithm producing cleaner EEG signals which can influence diagnosis as well as clinical studies of the brain
Image Decomposition and Separation Using Sparse Representations: An Overview
This paper gives essential insights into the use of sparsity and morphological diversity in image decomposition and source separation by reviewing our recent work in this field. The idea to morphologically decompose a signal into its building blocks is an important problem in signal processing and has far-reaching applications in science and technology. Starck , proposed a novel decomposition method—morphological component analysis (MCA)—based on sparse representation of signals. MCA assumes that each (monochannel) signal is the linear mixture of several layers, the so-called morphological components, that are morphologically distinct, e.g., sines and bumps. The success of this method relies on two tenets: sparsity and morphological diversity. That is, each morphological component is sparsely represented in a specific transform domain, and the latter is highly inefficient in representing the other content in the mixture. Once such transforms are identified, MCA is an iterative thresholding algorithm that is capable of decoupling the signal content. Sparsity and morphological diversity have also been used as a novel and effective source of diversity for blind source separation (BSS), hence extending the MCA to multichannel data. Building on these ingredients, we will provide an overview the generalized MCA introduced by the authors in and as a fast and efficient BSS method. We will illustrate the application of these algorithms on several real examples. We conclude our tour by briefly describing our software toolboxes made available for download on the Internet for sparse signal and image decomposition and separation
Component separation methods for the Planck mission
The Planck satellite will map the full sky at nine frequencies from 30 to 857
GHz. The CMB intensity and polarization that are its prime targets are
contaminated by foreground emission. The goal of this paper is to compare
proposed methods for separating CMB from foregrounds based on their different
spectral and spatial characteristics, and to separate the foregrounds into
components of different physical origin. A component separation challenge has
been organized, based on a set of realistically complex simulations of sky
emission. Several methods including those based on internal template
subtraction, maximum entropy method, parametric method, spatial and harmonic
cross correlation methods, and independent component analysis have been tested.
Different methods proved to be effective in cleaning the CMB maps from
foreground contamination, in reconstructing maps of diffuse Galactic emissions,
and in detecting point sources and thermal Sunyaev-Zeldovich signals. The power
spectrum of the residuals is, on the largest scales, four orders of magnitude
lower than that of the input Galaxy power spectrum at the foreground minimum.
The CMB power spectrum was accurately recovered up to the sixth acoustic peak.
The point source detection limit reaches 100 mJy, and about 2300 clusters are
detected via the thermal SZ effect on two thirds of the sky. We have found that
no single method performs best for all scientific objectives. We foresee that
the final component separation pipeline for Planck will involve a combination
of methods and iterations between processing steps targeted at different
objectives such as diffuse component separation, spectral estimation and
compact source extraction.Comment: Matches version accepted by A&A. A version with high resolution
figures is available at http://people.sissa.it/~leach/compsepcomp.pd
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&
Compact source detection in multi-channel microwave surveys: from SZ clusters to polarized sources
In this paper we describe the state-of-the art status of multi-frequency
detection techniques for compact sources in microwave astronomy. From the
simplest cases where the spectral behaviour is well-known (i.e. thermal SZ
clusters) to the more complex cases where there is little a priori information
(i.e. polarized radio sources) we will review the main advances and the most
recent results in the detection problem.Comment: 13 pages, 4 figures. Accepted for publication in the Special Issue
"Astrophysical Foregrounds in Microwave Surveys" of the journal Advances in
Astronom
Wavelets, ridgelets and curvelets on the sphere
We present in this paper new multiscale transforms on the sphere, namely the
isotropic undecimated wavelet transform, the pyramidal wavelet transform, the
ridgelet transform and the curvelet transform. All of these transforms can be
inverted i.e. we can exactly reconstruct the original data from its
coefficients in either representation. Several applications are described. We
show how these transforms can be used in denoising and especially in a Combined
Filtering Method, which uses both the wavelet and the curvelet transforms, thus
benefiting from the advantages of both transforms. An application to component
separation from multichannel data mapped to the sphere is also described in
which we take advantage of moving to a wavelet representation.Comment: Accepted for publication in A&A. Manuscript with all figures can be
downloaded at http://jstarck.free.fr/aa_sphere05.pd
Compressive Source Separation: Theory and Methods for Hyperspectral Imaging
With the development of numbers of high resolution data acquisition systems
and the global requirement to lower the energy consumption, the development of
efficient sensing techniques becomes critical. Recently, Compressed Sampling
(CS) techniques, which exploit the sparsity of signals, have allowed to
reconstruct signal and images with less measurements than the traditional
Nyquist sensing approach. However, multichannel signals like Hyperspectral
images (HSI) have additional structures, like inter-channel correlations, that
are not taken into account in the classical CS scheme. In this paper we exploit
the linear mixture of sources model, that is the assumption that the
multichannel signal is composed of a linear combination of sources, each of
them having its own spectral signature, and propose new sampling schemes
exploiting this model to considerably decrease the number of measurements
needed for the acquisition and source separation. Moreover, we give theoretical
lower bounds on the number of measurements required to perform reconstruction
of both the multichannel signal and its sources. We also proposed optimization
algorithms and extensive experimentation on our target application which is
HSI, and show that our approach recovers HSI with far less measurements and
computational effort than traditional CS approaches.Comment: 32 page
SILC: a new Planck Internal Linear Combination CMB temperature map using directional wavelets
We present new clean maps of the CMB temperature anisotropies (as measured by
Planck) constructed with a novel internal linear combination (ILC) algorithm
using directional, scale-discretised wavelets --- Scale-discretised,
directional wavelet ILC or SILC. Directional wavelets, when convolved with
signals on the sphere, can separate the anisotropic filamentary structures
which are characteristic of both the CMB and foregrounds. Extending previous
component separation methods, which use the frequency, spatial and harmonic
signatures of foregrounds to separate them from the cosmological background
signal, SILC can additionally use morphological information in the foregrounds
and CMB to better localise the cleaning algorithm. We test the method on Planck
data and simulations, demonstrating consistency with existing component
separation algorithms, and discuss how to optimise the use of morphological
information by varying the number of directional wavelets as a function of
spatial scale. We find that combining the use of directional and axisymmetric
wavelets depending on scale could yield higher quality CMB temperature maps.
Our results set the stage for the application of SILC to polarisation
anisotropies through an extension to spin wavelets.Comment: 15 pages, 13 figures. Minor changes to match version published in
MNRAS. Map products available at http://www.silc-cmb.or
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