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Register a new userApplication of beam deconvolution technique to power spectrum estimation for CMB measurements
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We present two novel methods for the estimation of the angular power spectrum of cosmic microwave background (CMB) anisotropies. We assume an absolute CMB experiment with arbitrary asymmetric beams and arbitrary sky coverage. The methods differ from earlier ones in that the power spectrum is estimated directly from time-ordered data, without first compressing the data into a sky map, and they take into account the effect of asymmetric beams. In particular, they correct the beam-induced leakage from temperature to polarization. The methods are applicable to a case where part of the sky has been masked out to remove foreground contamination, leaving a pure CMB signal, but incomplete sky coverage. The first method (DQML) is derived as the optimal quadratic estimator, which simultaneously yields an unbiased spectrum estimate and minimizes its variance. We successfully apply it to multipoles up to $ell$=200. The second method is derived as a weak-signal approximation from the first one. It yields an unbiased estimate for the full multipole range, but relaxes the requirement of minimal variance. We validate the methods with simulations for the 70 GHz channel of {tt Planck} surveyor, and demonstrate that we are able to correct the beam effects in the $TT$, $EE$, $BB$, and $TE$ spectra up to multipole $ell$=1500. Together the two methods cover the complete multipole range with no gap in between.
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The cosmic microwave background (CMB) power spectrum is a powerful cosmological probe as it entails almost all the statistical information of the CMB perturbations. Having access to only one sky, the CMB power spectrum measured by our experiments is only a realization of the true underlying angular power spectrum. In this paper we aim to recover the true underlying CMB power spectrum from the one realization that we have without a need to know the cosmological parameters. The sparsity of the CMB power spectrum is first investigated in two dictionaries; Discrete Cosine Transform (DCT) and Wavelet Transform (WT). The CMB power spectrum can be recovered with only a few percentage of the coefficients in both of these dictionaries and hence is very compressible in these dictionaries. We study the performance of these dictionaries in smoothing a set of simulated power spectra. Based on this, we develop a technique that estimates the true underlying CMB power spectrum from data, i.e. without a need to know the cosmological parameters. This smooth estimated spectrum can be used to simulate CMB maps with similar properties to the true CMB simulations with the correct cosmological parameters. This allows us to make Monte Carlo simulations in a given project, without having to know the cosmological parameters. The developed IDL code, TOUSI, for Theoretical pOwer spectrUm using Sparse estImation, will be released with the next version of ISAP.
We present an analysis of the effects of beam deconvolution on noise properties in CMB measurements. The analysis is built around the artDeco beam deconvolver code. We derive a low-resolution noise covariance matrix that describes the residual noise in deconvolution products, both in harmonic and pixel space. The matrix models the residual correlated noise that remains in time-ordered data after destriping, and the effect of deconvolution on it. To validate the results, we generate noise simulations that mimic the data from the Planck LFI instrument. A $chi^2$ test for the full 70 GHz covariance in multipole range $ell=0-50$ yields a mean reduced $chi^2$ of 1.0037. We compare two destriping options, full and independent destriping, when deconvolving subsets of available data. Full destriping leaves substantially less residual noise, but leaves data sets intercorrelated. We derive also a white noise covariance matrix that provides an approximation of the full noise at high multipoles, and study the properties on high-resolution noise in pixel space through simulations.
We present a method for beam deconvolution for cosmic microwave background (CMB) anisotropy measurements. The code takes as input the time-ordered data, along with the corresponding detector pointings and known beam shapes, and produces as output the harmonic a_Tlm, a_Elm, and a_Blm coefficients of the observed sky. From these one can further construct temperature and Q and U polarisation maps. The method is applicable to absolute CMB measurements with wide sky coverage, and is independent of the scanning strategy. We test the code with extensive simulations, mimicking the resolution and data volume of Planck 30GHz and 70GHz channels, but with exaggerated beam asymmetry. We apply it to multipoles up to l=1700 and examine the results in both pixel space and harmonic space. We also test the method also in presence of white noise.
Observations of the Cosmic Microwave Background (CMB) provide increasingly accurate information about the structure of the Universe at the recombination epoch. Most of this information is encoded in the angular power spectrum of the CMB. The aim of this work is to propose a versatile and powerful method for spectral estimation on the sphere which can easily deal with non-stationarity, foregrounds and multiple experiments with various specifications. In this paper, we use needlets (wavelets) on the sphere to construct natural and efficient spectral estimators for partially observed and beamed CMB with non stationary noise. In the case of a single experiment, we compare this method with Pseudo-$C_ell$ methods. The performance of the needlet spectral estimators (NSE) compares very favorably to the best Pseudo--$C_ell$ estimators, over the whole multipole range. On simulations with a simple model (CMB + uncorrelated noise with known variance per pixel + mask), they perform uniformly better. Their distinctive ability to aggregate many different experiments, to control the propagation of errors and to produce a single wide-band error bars is highlighted. The needlet spectral estimator is a powerful, tunable tool which is very well suited to angular power spectrum estimation of spherical data such as incomplete and noisy CMB maps.
We develop a new method for deconvolving the smearing effect of the survey window in the analysis of the galaxy multipole power spectra from a redshift survey. This method is based on the deconvolution theorem, and is compatible with the use of the fast Fourier transform. It is possible to measure the multipole power spectra deconvolved from the window effect efficiently. Applying this method to the luminous red galaxy sample of the Sloan Digital Sky Survey data release 7 as well as mock catalogues, we demonstrate how the method works properly. Using this deconvolution technique, the amplitude of the multipole power spectrum is corrected. Besides, the covariance matrices of the deconvolved power spectra get quite close to the diagonal form. This is also advantageous in the study of the BAO signature.
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