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

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

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

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

Blind Source Separation: the Sparsity Revolution

International audienceOver the last few years, the development of multi-channel sensors motivated interest in methods for the coherent processing of multivariate data. Some specific issues have already been addressed as testified by the wide literature on the so-called blind source separation (BSS) problem. In this context, as clearly emphasized by previous work, it is fundamental that the sources to be retrieved present some quantitatively measurable diversity. Recently, sparsity and morphological diversity have emerged as a novel and effective source of diversity for BSS. We give here some essential insights into the use of sparsity in source separation and we outline the essential role of morphological diversity as being a source of diversity or contrast between the sources. This paper overviews a sparsity-based BSS method coined Generalized Morphological Component Analysis (GMCA) that takes advantages of both morphological diversity and sparsity, using recent sparse overcomplete or redundant signal representations. GMCA is a fast and efficient blind source separation method. In remote sensing applications, the specificity of hyperspectral data should be accounted for. We extend the proposed GMCA framework to deal with hyperspectral data. In a general framework, GMCA provides a basis for multivariate data analysis in the scope of a wide range of classical multivariate data restorate. Numerical results are given in color image denoising and inpainting. Finally, GMCA is applied to the simulated ESA/Planck data. It is shown to give effective astrophysical component separation

High expression of gabarapl1 is associated with a better outcome for patients with lymph node-positive breast cancer

International audienceBACKGROUND: This study evaluates the relation of the early oestrogen-regulated gene gabarapl1 to cellular growth and its prognostic significance in breast adenocarcinoma. METHODS: First, the relation between GABARAPL1 expression and MCF-7 growth rate was analysed. Thereafter, by performing macroarray and reverse transcriptase quantitative-polymerase chain reaction (RT-qPCR) experiments, gabarapl1 expression was quantified in several histological breast tumour types and in a retrospective cohort of 265 breast cancers. RESULTS: GABARAPL1 overexpression inhibited MCF-7 growth rate and gabarapl1 expression was downregulated in breast tumours. Gabarapl1 mRNA levels were found to be significantly lower in tumours presenting a high histological grade, with a lymph node-positive (pN+) and oestrogen and/or progesterone receptor-negative status. In univariate analysis, high gabarapl1 levels were associated with a lower risk of metastasis in all patients (hazard ratio (HR) 4.96), as well as in pN+ patients (HR 14.96). In multivariate analysis, gabarapl1 expression remained significant in all patients (HR 3.63), as well as in pN+ patients (HR 5.65). In univariate or multivariate analysis, gabarapl1 expression did not disclose any difference in metastasis risk in lymph node-negative patients. CONCLUSIONS: Our data show for the first time that the level of gabarapl1 mRNA expression in breast tumours is a good indicator of the risk of recurrence, specifically in pN+ patients

Planck 2013 results. XXII. Constraints on inflation

We analyse the implications of the Planck data for cosmic inflation. The Planck nominal mission temperature anisotropy measurements, combined with the WMAP large-angle polarization, constrain the scalar spectral index to be ns = 0:9603 _ 0:0073, ruling out exact scale invariance at over 5_: Planck establishes an upper bound on the tensor-to-scalar ratio of r < 0:11 (95% CL). The Planck data thus shrink the space of allowed standard inflationary models, preferring potentials with V00 < 0. Exponential potential models, the simplest hybrid inflationary models, and monomial potential models of degree n _ 2 do not provide a good fit to the data. Planck does not find statistically significant running of the scalar spectral index, obtaining dns=dln k = 0:0134 _ 0:0090. We verify these conclusions through a numerical analysis, which makes no slowroll approximation, and carry out a Bayesian parameter estimation and model-selection analysis for a number of inflationary models including monomial, natural, and hilltop potentials. For each model, we present the Planck constraints on the parameters of the potential and explore several possibilities for the post-inflationary entropy generation epoch, thus obtaining nontrivial data-driven constraints. We also present a direct reconstruction of the observable range of the inflaton potential. Unless a quartic term is allowed in the potential, we find results consistent with second-order slow-roll predictions. We also investigate whether the primordial power spectrum contains any features. We find that models with a parameterized oscillatory feature improve the fit by __2 e_ _ 10; however, Bayesian evidence does not prefer these models. We constrain several single-field inflation models with generalized Lagrangians by combining power spectrum data with Planck bounds on fNL. Planck constrains with unprecedented accuracy the amplitude and possible correlation (with the adiabatic mode) of non-decaying isocurvature fluctuations. The fractional primordial contributions of cold dark matter (CDM) isocurvature modes of the types expected in the curvaton and axion scenarios have upper bounds of 0.25% and 3.9% (95% CL), respectively. In models with arbitrarily correlated CDM or neutrino isocurvature modes, an anticorrelated isocurvature component can improve the _2 e_ by approximately 4 as a result of slightly lowering the theoretical prediction for the ` <_ 40 multipoles relative to the higher multipoles. Nonetheless, the data are consistent with adiabatic initial conditions

Planck 2013 results. XIII. Galactic CO emission

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Planck intermediate results XIII : Constraints on peculiar velocities

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Planck 2013 results. XXVII. Doppler boosting of the CMB : Eppur si muove

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