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

Blind Source Separation Based Analysis of Correlated Harmonic Sources in a Micro Grid Environment

AbstractHarmonics are a persistent problem in power systems starting from the simple to any complex natured power system network. Blind source separation using Independent Component Analysis (ICA) is applied to estimate the harmonic sources with least prior knowledge on the topology of power systems. The limitation of the method is that it assumes that the harmonic sources are statistically independent. However, in simple microgrid system powering a small region, it becomes very likely that the harmonic sources like two housing colonies,etc to have some degree of dependence which makes them correlated to a minimal extent. Under such circumstances, it is observed that the traditional ICA algorithms like FastICA breakdown. In the work, two algorithms suitable for statistical dependence namely the eigBSE(Eigen value based Blind source Extraction) algorithm and the maxNG (maximum non Gaussianity based) algorithm discussed in literature are applied to a simple four bus microgrid model. The separation quality and performance indices of the two algorithms are explored for various correlation coefficient values and it is found that in majority of the cases maxNG algorithm is more precise. More details of the theoretical issues of statistical dependence and the algorithm behaviour needs to be workedout

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

Spin-SILC: CMB polarisation component separation with spin wavelets

We present Spin-SILC, a new foreground component separation method that accurately extracts the cosmic microwave background (CMB) polarisation $E$ and $B$ modes from raw multifrequency Stokes $Q$ and $U$ measurements of the microwave sky. Spin-SILC is an internal linear combination method that uses spin wavelets to analyse the spin-2 polarisation signal $P = Q + iU$. The wavelets are additionally directional (non-axisymmetric). This allows different morphologies of signals to be separated and therefore the cleaning algorithm is localised using an additional domain of information. The advantage of spin wavelets over standard scalar wavelets is to simultaneously and self-consistently probe scales and directions in the polarisation signal $P = Q + iU$ and in the underlying $E$ and $B$ modes, therefore providing the ability to perform component separation and $E$-$B$ decomposition concurrently for the first time. We test Spin-SILC on full-mission Planck simulations and data and show the capacity to correctly recover the underlying cosmological $E$ and $B$ modes. We also demonstrate a strong consistency of our CMB maps with those derived from existing component separation methods. Spin-SILC can be combined with the pseudo- and pure $E$-$B$ spin wavelet estimators presented in a companion paper to reliably extract the cosmological signal in the presence of complicated sky cuts and noise. Therefore, it will provide a computationally-efficient method to accurately extract the CMB $E$ and $B$ modes for future polarisation experiments.Comment: 13 pages, 9 figures. Minor changes to match version published in MNRAS. Map products available at http://www.silc-cmb.org. Companion paper: arXiv:1605.01414 "Wavelet reconstruction of pure E and B modes for CMB polarisation and cosmic shear analyses" (B. Leistedt et al.

SILC: a new Planck Internal Linear Combination CMB temperature map using directional wavelets

We present new clean maps of the CMB temperature anisotropies (as measured by Planck) constructed with a novel internal linear combination (ILC) algorithm using directional, scale-discretised wavelets --- Scale-discretised, directional wavelet ILC or SILC. Directional wavelets, when convolved with signals on the sphere, can separate the anisotropic filamentary structures which are characteristic of both the CMB and foregrounds. Extending previous component separation methods, which use the frequency, spatial and harmonic signatures of foregrounds to separate them from the cosmological background signal, SILC can additionally use morphological information in the foregrounds and CMB to better localise the cleaning algorithm. We test the method on Planck data and simulations, demonstrating consistency with existing component separation algorithms, and discuss how to optimise the use of morphological information by varying the number of directional wavelets as a function of spatial scale. We find that combining the use of directional and axisymmetric wavelets depending on scale could yield higher quality CMB temperature maps. Our results set the stage for the application of SILC to polarisation anisotropies through an extension to spin wavelets.Comment: 15 pages, 13 figures. Minor changes to match version published in MNRAS. Map products available at http://www.silc-cmb.or

Predicting loss in magnetic steels under arbitrary induction waveform and with minor hysteresis loops

We have studied ways of predicting power losses in soft magnetic laminations for generic time dependence of the periodic magnetic polarization J(t). We found that, whatever the frequency and the induction waveform, the loss behavior can be quantitatively assessed within the theoretical framework of the statistical loss model. The prediction requires a limited set of preemptive experimental data, depending on whether or not the arbitrary J(t) waveform is endowed with local slope inversions (i.e., minor hysteresis loops) in its periodic time behavior. In the absence of minor loops, such data reduce, for any peak polarization value Jp, to the loss figures obtained under sinusoidal J(t) at two different frequency values. In the presence of minor loops of semiamplitude Jm, the two-frequency loss experiment should be carried out for both peak polarization values Jp and Jm. Additional knowledge of the quasi-static major loop, to be used for modeling hysteresis loss, does improve the accuracy of the prediction method. A more general approach to loss in soft magnetic laminations is obtained in this way, the only limitation apparently being the onset of skin effect at high frequencie

Analysis of CMB polarization on an incomplete sky

The full sky cosmic microwave background polarization field can be decomposed into 'electric' and 'magnetic' components. Working in harmonic space we construct window functions that allow clean separation of the electric and magnetic modes from observations over only a portion of the sky. Our construction is exact for azimuthally symmetric patches, but should continue to perform well for arbitrary patches. From the window functions we obtain variables that allow for robust estimation of the magnetic component without risk of contamination from the probably much larger electric signal. For isotropic, uncorrelated noise the variables have a very simple diagonal noise correlation, and further analysis using them should be no harder than analysing the temperature field. For an azimuthally-symmetric patch, such as that obtained from survey missions when the galactic region is removed, the exactly-separated variables are fast to compute allowing us to estimate the magnetic signal that could be detected by the Planck satellite in the absence of non-galactic foregrounds. We also discuss the sensitivity of future experiments to tensor modes in the presence of a magnetic signal generated by weak lensing, and give lossless methods for analysing the electric polarization field in the case that the magnetic component is negligible.Comment: 27 pages, 8 figures. New appendix on weak signal detection and revised plots using a better statistic. Other changes to match version accepted by PRD. Sample source code now available at http://cosmologist.info/pola