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&

Sunyaev-Zel'dovich clusters reconstruction in multiband bolometer camera surveys

We present a new method for the reconstruction of Sunyaev-Zel'dovich (SZ) galaxy clusters in future SZ-survey experiments using multiband bolometer cameras such as Olimpo, APEX, or Planck. Our goal is to optimise SZ-Cluster extraction from our observed noisy maps. We wish to emphasize that none of the algorithms used in the detection chain is tuned on prior knowledge on the SZ -Cluster signal, or other astrophysical sources (Optical Spectrum, Noise Covariance Matrix, or covariance of SZ Cluster wavelet coefficients). First, a blind separation of the different astrophysical components which contribute to the observations is conducted using an Independent Component Analysis (ICA) method. Then, a recent non linear filtering technique in the wavelet domain, based on multiscale entropy and the False Discovery Rate (FDR) method, is used to detect and reconstruct the galaxy clusters. Finally, we use the Source Extractor software to identify the detected clusters. The proposed method was applied on realistic simulations of observations. As for global detection efficiency, this new method is impressive as it provides comparable results to Pierpaoli et al. method being however a blind algorithm. Preprint with full resolution figures is available at the URL: w10-dapnia.saclay.cea.fr/Phocea/Vie_des_labos/Ast/ast_visu.php?id_ast=728Comment: Submitted to A&A. 32 Pages, text onl

Sparsity and adaptivity for the blind separation of partially correlated sources

Blind source separation (BSS) is a very popular technique to analyze multichannel data. In this context, the data are modeled as the linear combination of sources to be retrieved. For that purpose, standard BSS methods all rely on some discrimination principle, whether it is statistical independence or morphological diversity, to distinguish between the sources. However, dealing with real-world data reveals that such assumptions are rarely valid in practice: the signals of interest are more likely partially correlated, which generally hampers the performances of standard BSS methods. In this article, we introduce a novel sparsity-enforcing BSS method coined Adaptive Morphological Component Analysis (AMCA), which is designed to retrieve sparse and partially correlated sources. More precisely, it makes profit of an adaptive re-weighting scheme to favor/penalize samples based on their level of correlation. Extensive numerical experiments have been carried out which show that the proposed method is robust to the partial correlation of sources while standard BSS techniques fail. The AMCA algorithm is evaluated in the field of astrophysics for the separation of physical components from microwave data.Comment: submitted to IEEE Transactions on signal processin

Techniques for noise removal from EEG, EOG and air flow signals in sleep patients

Noise is present in the wide variety of signals obtained from sleep patients. This noise comes from a number of sources, from presence of extraneous signals to adjustments in signal amplification and shot noise in the circuits used for data collection. The noise needs to be removed in order to maximize the information gained about the patient using both manual and automatic analysis of the signals. Here we evaluate a number of new techniques for removal of that noise, and the associated problem of separating the original signal sources.Comment: 9 pages, 3 figure

Neural networks and separation of Cosmic Microwave Background and astrophysical signals in sky maps

The Independent Component Analysis (ICA) algorithm is implemented as a neural network for separating signals of different origin in astrophysical sky maps. Due to its self-organizing capability, it works without prior assumptions on the signals, neither on their frequency scaling, nor on the signal maps themselves; instead, it learns directly from the input data how to separate the physical components, making use of their statistical independence. To test the capabilities of this approach, we apply the ICA algorithm on sky patches, taken from simulations and observations, at the microwave frequencies, that are going to be deeply explored in a few years on the whole sky, by the Microwave Anisotropy Probe (MAP) and by the {\sc Planck} Surveyor Satellite. The maps are at the frequencies of the Low Frequency Instrument (LFI) aboard the {\sc Planck} satellite (30, 44, 70 and 100 GHz), and contain simulated astrophysical radio sources, Cosmic Microwave Background (CMB) radiation, and Galactic diffuse emissions from thermal dust and synchrotron. We show that the ICA algorithm is able to recover each signal, with precision going from 10% for the Galactic components to percent for CMB; radio sources are almost completely recovered down to a flux limit corresponding to $0.7\sigma_{CMB}$, where $\sigma_{CMB}$ is the rms level of CMB fluctuations. The signal recovering possesses equal quality on all the scales larger then the pixel size. In addition, we show that the frequency scalings of the input signals can be partially inferred from the ICA outputs, at the percent precision for the dominant components, radio sources and CMB.Comment: 15 pages; 6 jpg and 1 ps figures. Final version to be published in MNRA

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

Mathematical tools for identifying the fetal response to physical exercise during pregnancy

In the applied mathematics literature there exist a significant number of tools that can reveal the interaction between mother and fetus during rest and also during and after exercise. These tools are based on techniques from a number of areas such as signal processing, time series analysis, neural networks, heart rate variability as well as dynamical systems and chaos. We will briefly review here some of these methods, concentrating on a method of extracting the fetal heart rate from the mixed maternal-fetal heart rate signal, that is based on phase space reconstructio