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Register a new userBlind separation of noisy Gaussian stationary sources. Application to cosmic microwave background imaging
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Added by
Jacques Delabrouille
Publication date
2002
fields
Physics
and research's language is
English
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We present a new source separation method which maximizes the likelihood of a model of noisy mixtures of stationary, possibly Gaussian, independent components. The method has been devised to address the problem of imaging CMB anisotropies. It works in the spectral domain where, thanks to two simple approximations, the likelihood assumes a simple form which is easy to handle (low dimensional sufficient statistics) and to maximize (via the EM algorithm).
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The data from Cosmic Microwave Background (CMB) experiments are becoming more complex with each new experiment. A consistent way of analysing these data sets is required so that direct comparison is possible between the various experimental results. This thesis presents several techniques that can be used to analyse CMB data.
We discuss the potential of a next generation space-borne CMB experiment for studies of extragalactic sources with reference to COrE+, a project submitted to ESA in response to the M4 call. We consider three possible options for the telescope size: 1m, 1.5m and 2m (although the last option is probably impractical, given the M4 boundary conditions). The proposed instrument will be far more sensitive than Planck and will have a diffraction-limited angular resolution. These properties imply that even the 1m telescope option will perform substantially better than Planck for studies of extragalactic sources. The source detection limits as a function of frequency have been estimated by means of realistic simulations. The most significant improvements over Planck results are presented for each option. COrE+ will provide much larger samples of truly local star-forming galaxies, making possible analyses of the properties of galaxies (luminosity functions, dust mass functions, star formation rate functions, dust temperature distributions, etc.) across the Hubble sequence. Even more interestingly, COrE+ will detect, at |b|> 30 deg, thousands of strongly gravitationally lensed galaxies. Such large samples are of extraordinary astrophysical and cosmological value in many fields. Moreover, COrE+ high frequency maps will be optimally suited to pick up proto-clusters of dusty galaxies, i.e. to investigate the evolution of large scale structure at larger redshifts than can be reached by other means. Thanks to its high sensitivity COrE+ will also yield a spectacular advance in the blind detection of extragalactic sources in polarization. This will open a new window for studies of radio source polarization and of the global properties of magnetic fields in star forming galaxies and of their relationships with SFRs.
A maximum entropy method (MEM) is presented for separating the emission due to different foreground components from simulated satellite observations of the cosmic microwave background radiation (CMBR). In particular, the method is applied to simulated observations by the proposed Planck Surveyor satellite. The simulations, performed by Bouchet and Gispert (1998), include emission from the CMBR, the kinetic and thermal Sunyaev-Zeldovich (SZ) effects from galaxy clusters, as well as Galactic dust, free-free and synchrotron emission. We find that the MEM technique performs well and produces faithful reconstructions of the main input components. The method is also compared with traditional Wiener filtering and is shown to produce consistently better results, particularly in the recovery of the thermal SZ effect.
Regional data analysis is concerned with the analysis and modeling of measurements that are spatially separated by specifically accounting for typical features of such data. Namely, measurements in close proximity tend to be more similar than the ones further separated. This might hold also true for cross-dependencies when multivariate spatial data is considered. Often, scientists are interested in linear transformations of such data which are easy to interpret and might be used as dimension reduction. Recently, for that purpose spatial blind source separation (SBSS) was introduced which assumes that the observed data are formed by a linear mixture of uncorrelated, weakly stationary random fields. However, in practical applications, it is well-known that when the spatial domain increases in size the weak stationarity assumptions can be violated in the sense that the second order dependency is varying over the domain which leads to non-stationary analysis. In our work we extend the SBSS model to adjust for these stationarity violations, present three novel estimators and establish the identifiability and affine equivariance property of the unmixing matrix functionals defining these estimators. In an extensive simulation study, we investigate the performance of our estimators and also show their use in the analysis of a geochemical dataset which is derived from the GEMAS geochemical mapping project.
We discuss the potential of a next generation space-borne Cosmic Microwave Background (CMB) experiment for studies of extragalactic sources. Our analysis has particular bearing on the definition of the future space project, CORE, that has been submitted in response to ESAs call for a Medium-size mission opportunity as the successor of the Planck satellite. Even though the effective telescope size will be somewhat smaller than that of Planck, CORE will have a considerably better angular resolution at its highest frequencies, since, in contrast with Planck, it will be diffraction limited at all frequencies. The improved resolution implies a considerable decrease of the source confusion, i.e. substantially fainter detection limits. In particular, CORE will detect thousands of strongly lensed high-z galaxies distributed over the full sky. The extreme brightness of these galaxies will make it possible to study them, via follow-up observations, in extraordinary detail. Also, the CORE resolution matches the typical sizes of high-z galaxy proto-clusters much better than the Planck resolution, resulting in a much higher detection efficiency; these objects will be caught in an evolutionary phase beyond the reach of surveys in other wavebands. Furthermore, CORE will provide unique information on the evolution of the star formation in virialized groups and clusters of galaxies up to the highest possible redshifts. Finally, thanks to its very high sensitivity, CORE will detect the polarized emission of thousands of radio sources and, for the first time, of dusty galaxies, at mm and sub-mm wavelengths, respectively.
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