A Greedy Algorithm for a Sparse Scalet Decomposition

International audienceSparse decompositions were mainly developed to optimize the signal or the image compression. The sparsity was first obtained by a coefficient thresholding. The matching pursuit (MP) algorithms were implemented to extract the optimal patterns from a given dictionary. They carried out a new insight on the sparse representations. In this communication, this way is followed. It takes into account the goal to obtain a sparse multiscale decomposition with the different constraints: i/ to get a sparse representation with patterns looking like to Gaussian functions, ii/ to be able to decompose into patterns with only positive amplitudes, iii/ to get a representation from a translated and dilated pattern, iv/ to constrain the representation by a threshold, v/ to separate the sparse signal from a smooth baseline. Different greedy algorithms were built from the use of redundant wavelet transforms (pyramidal and `a trous ones), for 1D signals and 2D images. Experimentations on astronomical images allow one a gain of about two in sparsity compared to a classical DWT thresholding. A fine denoising is obtained. The results do not display any wavy artifacts. This decomposition is an efficient tool for astronomical image analysis

A new family of non--linear filters for background subtraction of wide--field surveys

In this paper the definitions and the properties of a newle dedicated set of high-frequency filters based on smoothing-and-clipping are briefly described. New applications for reduction of wide--field 2048x2048 CCD spectral and direct images of a new deep survey KISS (KPNO International Spectral Survey) are also presented. The developed software is available both as a C subroutine and as an installed MIDAS environment command.Comment: 8 pages with 2 Postscript figures. The text with full figures obtainable from this http URL http://193.125.89.73/~akn/cont_with_figures.ps.g

Automated derivation of stellar atmospheric parameters and chemical abundances: the MATISSE algorithm

We present an automated procedure for the derivation of atmospheric parameters (Teff, log g, [M/H]) and individual chemical abundances from stellar spectra. The MATrix Inversion for Spectral SythEsis (MATISSE) algorithm determines a basis, B_\theta(\lambda), allowing to derive a particular stellar parameter \theta by projection of an observed spectrum. The B_\theta(\lambda) function is determined from an optimal linear combination of theoretical spectra and it relates, in a quantitative way, the variations in the spectrum flux with variations in \theta. An application of this method to the GAIA/RVS spectral range is described, together with its performances for different types of stars of various metallicities. Blind tests with synthetic spectra of randomly selected parameters and observed input spectra are also presented. The method gives rapid, accurate and stable results and it can be efficiently applied to the study of stellar populations through the analysis of large spectral data sets, including moderate to low signal to noise spectra

A multiscale regularized restoration algorithm for XMM-Newton data

We introduce a new multiscale restoration algorithm for images with few photons counts and its use for denoising XMM data. We use a thresholding of the wavelet space so as to remove the noise contribution at each scale while preserving the multiscale information of the signal. Contrary to other algorithms the signal restoration process is the same whatever the signal to noise ratio is. Thresholds according to a Poisson noise process are indeed computed analytically at each scale thanks to the use of the unnormalized Haar wavelet transform. Promising preliminary results are obtained on X-ray data for Abell 2163 with the computation of a temperature map.Comment: To appear in the Proceedings of `Galaxy Clusters and the High Redshift Universe Observed in X-rays', XXIth Moriond Astrophysics Meeting (March 2001), Eds. Doris Neumann et a

Introduction to the Restoration of Astrophysical Images by Multiscale Transforms and Bayesian Methods

This book is a collection of 19 articles which reflect the courses given at the Collège de France/Summer school “Reconstruction d'images − Applications astrophysiques“ held in Nice and Fréjus, France, from June 18 to 22, 2012. The articles presented in this volume address emerging concepts and methods that are useful in the complex process of improving our knowledge of the celestial objects, including Earth

The AMBRE Project: Stellar Parameterisation of the ESO:UVES archived spectra

The AMBRE Project is a collaboration between the European Southern Observatory (ESO) and the Observatoire de la Cote d'Azur (OCA) that has been established in order to carry out the determination of stellar atmospheric parameters for the archived spectra of four ESO spectrographs. The analysis of the UVES archived spectra for their stellar parameters has been completed in the third phase of the AMBRE Project. From the complete ESO:UVES archive dataset that was received covering the period 2000 to 2010, 51921 spectra for the six standard setups were analysed. The AMBRE analysis pipeline uses the stellar parameterisation algorithm MATISSE to obtain the stellar atmospheric parameters. The synthetic grid is currently constrained to FGKM stars only. Stellar atmospheric parameters are reported for 12,403 of the 51,921 UVES archived spectra analysed in AMBRE:UVES. This equates to ~23.9% of the sample and ~3,708 stars. Effective temperature, surface gravity, metallicity and alpha element to iron ratio abundances are provided for 10,212 spectra (~19.7%), while at least effective temperature is provided for the remaining 2,191 spectra. Radial velocities are reported for 36,881 (~71.0%) of the analysed archive spectra. Typical external errors of sigmaTeff~110dex, sigmalogg~0.18dex, sigma[M/H]~0.13dex, and sigma[alpha/Fe]~0.05dex with some reported variation between giants and dwarfs and between setups are reported. UVES is used to observe an extensive collection of stellar and non-stellar objects all of which have been included in the archived dataset provided to OCA by ESO. The AMBRE analysis extracts those objects which lie within the FGKM parameter space of the AMBRE slow rotating synthetic spectra grid. Thus by homogeneous blind analysis AMBRE has successfully extracted and parameterised the targeted FGK stars (23.9% of the analysed sample) from within the ESO:UVES archive.Comment: 19 pages, 16 figures, 11 table

Parameter Estimation from an Optimal Projection in a Local Environment

The parameter fit from a model grid is limited by our capability to reduce the number of models, taking into account the number of parameters and the non linear variation of the models with the parameters. The Local MultiLinear Regression (LMLR) algorithms allow one to fit linearly the data in a local environment. The MATISSE algorithm, developed in the context of the estimation of stellar parameters from the Gaia RVS spectra, is connected to this class of estimators. A two-steps procedure was introduced. A raw parameter estimation is first done in order to localize the parameter environment. The parameters are then estimated by projection on specific vectors computed for an optimal estimation. The MATISSE method is compared to the estimation using the objective analysis. In this framework, the kernel choice plays an important role. The environment needed for the parameter estimation can result from it. The determination of a first parameter set can be also avoided for this analysis. These procedures based on a local projection can be fruitfully applied to non linear parameter estimation if the number of data sets to be fitted is greater than the number of models

Density estimation with non-parametric methods

One key issue in several astrophysical problems is the evaluation of the density probability function underlying an observational discrete data set. We here review two non-parametric density estimators which recently appeared in the astrophysical literature, namely the adaptive kernel density estimator and the Maximum Penalized Likelihood technique, and describe another method based on the wavelet transform. The efficiency of these estimators is tested by using extensive numerical simulations in the one-dimensional case. The results are in good agreement with theoretical functions and the three methods appear to yield consistent estimates. In order to check these estimators with respect to previous studies, two galaxy redshift samples (the galaxy cluster A3526 and the Corona Borealis region) have been analyzed.Comment: 21 pages, LaTeX2e file with 9 figures and 2 tables (automatically included) - To appear in Astronomy & Astrophysic

The AMBRE Project: Parameterisation of FGK-type stars from the ESO:HARPS archived spectra

The AMBRE project is a collaboration between the European Southern Observatory (ESO) and the Observatoire de la Cote d'Azur (OCA). It has been established to determine the stellar atmospheric parameters (effective temperature, surface gravity, global metallicities and abundance of alpha-elements over iron) of the archived spectra of four ESO spectrographs. The analysis of the ESO:HARPS archived spectra is presented. The sample being analysed (AMBRE:HARPS) covers the period from 2003 to 2010 and is comprised of 126688 scientific spectra corresponding to 17218 different stars. For the analysis of the spectral sample, the automated pipeline developed for the analysis of the AMBRE:FEROS archived spectra has been adapted to the characteristics of the HARPS spectra. Within the pipeline, the stellar parameters are determined by the MATISSE algorithm, developed at OCA for the analysis of large samples of stellar spectra in the framework of galactic archaeology. In the present application, MATISSE uses the AMBRE grid of synthetic spectra, which covers FGKM-type stars for a range of gravities and metallicities. We first determined the radial velocity and its associated error for the ~15% of the AMBRE:HARPS spectra, for which this velocity had not been derived by the ESO:HARPS reduction pipeline. The stellar atmospheric parameters and the associated chemical index [alpha/Fe] with their associated errors have then been estimated for all the spectra of the AMBRE:HARPS archived sample. Based on quality criteria, we accepted and delivered the parameterisation of ~71% of the total sample to ESO. These spectra correspond to ~10706 stars; each are observed between one and several hundred times. This automatic parameterisation of the AMBRE:HARPS spectra shows that the large majority of these stars are cool main-sequence dwarfs with metallicities greater than -0.5 dex