Polarized wavelets and curvelets on the sphere

The statistics of the temperature anisotropies in the primordial cosmic microwave background radiation field provide a wealth of information for cosmology and for estimating cosmological parameters. An even more acute inference should stem from the study of maps of the polarization state of the CMB radiation. Measuring the extremely weak CMB polarization signal requires very sensitive instruments. The full-sky maps of both temperature and polarization anisotropies of the CMB to be delivered by the upcoming Planck Surveyor satellite experiment are hence being awaited with excitement. Multiscale methods, such as isotropic wavelets, steerable wavelets, or curvelets, have been proposed in the past to analyze the CMB temperature map. In this paper, we contribute to enlarging the set of available transforms for polarized data on the sphere. We describe a set of new multiscale decompositions for polarized data on the sphere, including decimated and undecimated Q-U or E-B wavelet transforms and Q-U or E-B curvelets. The proposed transforms are invertible and so allow for applications in data restoration and denoising.Comment: Accepted. Full paper will figures available at http://jstarck.free.fr/aa08_pola.pd

Magnon Broadening Effects in Double Layered Manganite La_1.2 Sr_1.8 Mn_2 O_7

Magnon linewidth of La_1.2 Sr_1.8 Mn_2 O_7 near the Brillouin zone boundary is investigated from both theoretical and experimental points of view. Abrupt magnon broadening is ascribed to a strong magnon-phonon coupling. Magnon broadening observed in cubic perovskite manganites is also discussed.Comment: 4 pages + 1 jpeg figur

Sparsity and morphological diversity for hyperspectral data analysis

Recently morphological diversity and sparsity have emerged as new and effective sources of diversity for Blind Source Separation. Based on these new concepts, novelmethods such as Generalized Morphological Component Analysis have been put forward. The latter takes advantage of the very sparse representation of structured data in large overcomplete dictionaries, to separate sources based on their morphology. Building on GMCA, the purpose of this contribution is to describe a new algorithm for hyperspectral data processing. Large-scale hyperspectral data refers to collected data that exhibit sparse spectral signatures in addition to sparse spatial morphologies, in specified dictionaries of spectral and spatial waveforms. Numerical experiments are reported which demonstrate the validity of the proposed extension for solving source separation problems involving hyperspectral data

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

SZ and CMB reconstruction using Generalized Morphological Component Analysis

In the last decade, the study of cosmic microwave background (CMB) data has become one of the most powerful tools to study and understand the Universe. More precisely, measuring the CMB power spectrum leads to the estimation of most cosmological parameters. Nevertheless, accessing such precious physical information requires extracting several different astrophysical components from the data. Recovering those astrophysical sources (CMB, Sunyaev-Zel'dovich clusters, galactic dust) thus amounts to a component separation problem which has already led to an intense activity in the field of CMB studies. In this paper, we introduce a new sparsity-based component separation method coined Generalized Morphological Component Analysis (GMCA). The GMCA approach is formulated in a Bayesian maximum a posteriori (MAP) framework. Numerical results show that this new source recovery technique performs well compared to state-of-the-art component separation methods already applied to CMB data.Comment: 11 pages - Statistical Methodology - Special Issue on Astrostatistics - in pres

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

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

Sparsity constraints for hyperspectral data analysis: linear mixture model and beyond

The recent development of multi-channel sensors has motivated interest in devising new methods for the coherent processing of multivariate data. An extensive work has already been dedicated to multivariate data processing ranging from blind source separation (BSS) to multi/hyper-spectral data restoration. Previous work has emphasized on the fundamental role played by sparsity and morphological diversity to enhance multichannel signal processing. GMCA is a recent algorithm for multichannel data analysis which was used successfully in a variety of applications including multichannel sparse decomposition, blind source separation (BSS), color image restoration and inpainting. Inspired by GMCA, a recently introduced algorithm coined HypGMCA is described for BSS applications in hyperspectral data processing. It assumes the collected data is a linear instantaneous mixture of components exhibiting sparse spectral signatures as well as sparse spatial morphologies, each in specified dictionaries of spectral and spatial waveforms. We report on numerical experiments with synthetic data and application to real observations which demonstrate the validity of the proposed method

Spin wave resonances in La_{0.7}Sr_{0.3}MnO_{3} films: measurement of spin wave stiffness and anisotropy field

We studied magnetic field dependent microwave absorption in epitaxial La$_{0.7}$Sr$_{0.3}$MnO$_{3}$ films using an X-band Bruker ESR spectrometer. By analyzing angular and temperature dependence of the ferromagnetic and spin-wave resonances we determine spin-wave stiffness and anisotropy field. The spin-wave stiffness as found from the spectrum of the standing spin-wave resonances in thin films is in fair agreement with the results of inelastic neutron scattering studies on a single crystal of the same composition [Vasiliu-Doloc et al., J. Appl. Phys. \textbf{83}, 7343 (1998)].Comment: 15 pages, 7 figures (now figure captions are included

Le systeme algerien de protection sociale : entre bismarckien et beveridgien

Les systèmes de protection sociale tels qu’ils sont connus aujourd’hui sont issus de l’évolution des systèmes bismarckien et beveridgien. Le premier basé sur le principe d’assurance a vu le jour en Allemagne en 1883, le second basé sur le principe d’assistance a été créé par Beveridge en Grande Bretagne en 1941. Ce dernier était financé principalement par l’impôt et avait comme objectif de couvrir la plus grande partie de la population contre les risques sociaux. Nous proposons dans notre travail de caractériser le système algérien de protection sociale à partir de ces deux types de systèmes. En Algérie, le système de sécurité sociale a été fondé en 1949 sur le principe de l’assurance. L'accès au système était destiné aux travailleurs en contre partie de prélèvements sur leurs salaires. Le système était corporatiste-conservateur (Esping Anderson, 1990) de doctrine bismarckienne. Il a vu plusieurs réformes de l’indépendance à nos jours. Des lois visant à étendre la couverture sociale à une plus large partie de la population ont été introduites dans le système. Pour atteindre cet objectif, les pouvoirs publics ont créé d’autres composantes dans le système de protection sociale à côté du système d’assurance en place depuis 1949. Cela donna un changement de nature du système algérien de protection sociale. Dans ce travail nous allons étudier le système algérien de protection sociale dans sa globalité et essayer de lui accorder selon son architecture institutio- nnelle actuelle un cadre doctrinal cohérent (les prestations résiduelles et la primauté accordée au marché et à la lutte contre la pauvreté ; les assurances sociales et la protection des catégories professionnelles ; les prestations universelles et la recherche de l’égalité). Cette grille de lecture permet d’identifier les traits d’un système national dans son ensemble et dégager les tendances lourdes de son évolution. Celles-ci ne peuvent être dégagées par des analyses sectorielles (maladie, vieillesse …etc.). Par ailleurs, sur le plan économique, le passage de l’économie planifiée à l’économie de marché et la difficulté pour l’Etat d’atteindre le plein emploi ont permis l’apparition de certaines formes d’activités informelles sur le marché du travail. 41,8% de la population occupée ne sont pas affiliés à la sécurité sociale (ONS1, 2014). Cette population ne s’acquitte pas de ses cotisations sociales, mais elle profite de la gratuité des soins d’où la partie universaliste du système algérien de protection sociale. Nous exploiterons les données de la comptabilité nationale pour évaluer les recettes du système de protection sociale en provenance du marché du travail (cotisations des travailleurs) et les recettes en provenance du budget de l’Etat. L’évolution de ces agrégats pourrait constituer un indicateur de la typologie du système algérien de protection sociale.Mots clés : Algérie, Protection sociale, Système Bismarckien, Système Beveridgien, Recettes de la sécurité sociale, Budget social de l’Etat