Map-making methods for cosmic microwave background experiments

The map-making step of cosmic microwave background (CMB) data analysis involves linear inversion problems that cannot be performed by a brute-force approach for the large time-lines of today. In this paper we present optimal vector-only map-making methods, which are an iterative COBE method, a Wiener direct filter and a Wiener iterative method. We apply these methods on diverse simulated data, and we show that they produce very well restored maps, by removing nearly completely the correlated noise that appears as intense stripes on the simply pixel-averaged maps. The COBE iterative method can be applied to any signals, assuming the stationarity of the noise in the time-line. The Wiener methods assume both the stationarity of the noise and the sky, which is the case for CMB-only data. We apply the methods to Galactic signals too, and test them on balloon-borne experiment strategies and on a satellite whole-sky survey.     

Wavelet analysis and the detection of non-Gaussianity in the cosmic microwave background

We investigate the use of wavelet transforms in detecting and characterizing non-Gaussian structure in maps of the cosmic microwave background (CMB). We apply the method to simulated maps of the KaiserStebbins effect resulting from cosmic strings, on to which Gaussian signals of varying amplitudes are superposed. We find that the method significantly outperforms standard techniques based on measuring the moments of the pixel temperature distribution. We also compare the results with those obtained using techniques based on Minkowski functionals, and we again find the wavelet method to be superior. In particular, using the wavelet technique, we find that it is possible to detect non-Gaussianity even in the presence of a superposed Gaussian signal with 3 times the rms amplitude of the original cosmic string map. We also find that the wavelet technique is useful in characterizing the angular scales at which the non-Gaussian signal occurs.     

Wavelet domain Bayesian denoising of string signal in the cosmic microwave background

An algorithm is proposed for denoising the signal induced by cosmic strings in the cosmic microwave background. A Bayesian approach is taken, based on modelling the string signal in the wavelet domain with generalized Gaussian distributions. Good performance of the algorithm is demonstrated by simulated experiments at arcminute resolution under noise conditions including primary and secondary cosmic microwave background anisotropies, as well as instrumental noise.     

Maximum likelihood algorithm for parametric component separation in cosmic microwave background experiments

We discuss an approach to the component separation of microwave, multifrequency sky maps as those typically produced from cosmic microwave background (CMB) anisotropy data sets. The algorithm is based on the two-step, parametric, likelihood-based technique recently elaborated on by Eriksen et al., where the foreground spectral parameters are estimated prior to the actual separation of the components. In contrast with the previous approaches, we accomplish the former task with help of an analytically derived likelihood function for the spectral parameters, which, we show, yields estimates equal to the maximum likelihood values of the full multidimensional data problem. We then use these estimates to perform the second step via the standard, generalized-least-squares-like procedure. We demonstrate that the proposed approach is equivalent to a direct maximization of the full data likelihood, which is recast in a computationally tractable form. We use the corresponding curvature matrices to characterize statistical properties of the recovered parameters. We incorporate in the formalism some of the essential features of the CMB data sets, such as inhomogeneous pixel domain noise, unknown map offsets as well as calibration errors and study their consequences for the separation. We find that the calibration is likely to have a dominant effect on the precision of the spectral parameter determination for a realistic CMB experiment. We apply the algorithm to simulated data and discuss the results. Our focus is on partial sky, total intensity and polarization, CMB experiments such as planned balloon-borne and ground-based efforts, however, the techniques presented here should be also applicable to the full-sky data as for instance, those produced by the Wilkinson Microwave Anisotropy Probe ( WMAP ) satellite and anticipated from the Planck mission.     

Neural networks and the separation of cosmic microwave background and astrophysical signals in sky maps

We implement an independent component analysis (ICA) algorithm to separate signals of different origin in sky maps at several frequencies. Owing to its self-organizing capability, it works without prior assumptions on either the frequency dependence or the angular power spectrum of the various signals; rather, it learns directly from the input data how to identify the statistically independent components, on the assumption that all but, at most, one of the components have non-Gaussian distributions.
We have applied the ICA algorithm to simulated patches of the sky at the four frequencies (30, 44, 70 and 100 GHz) used by the Low Frequency Instrument of the European Space Agency's Planck satellite. Simulations include the cosmic microwave background (CMB), the synchrotron and thermal dust emissions, and extragalactic radio sources. The effects of the angular response functions of the detectors and of instrumental noise have been ignored in this first exploratory study. The ICA algorithm reconstructs the spatial distribution of each component with rms errors of about 1 per cent for the CMB, and 10 per cent for the much weaker Galactic components. Radio sources are almost completely recovered down to a flux limit corresponding to ≃0.7 σ _CMB, where σ _CMB is the rms level of the CMB fluctuations. The signal recovered has equal quality on all scales larger than the pixel size. In addition, we show that for the strongest components (CMB and radio sources) the frequency scaling is recovered with per cent precision. Thus, algorithms of the type presented here appear to be very promising tools for component separation. On the other hand, we have been dealing here with a highly idealized situation. Work to include instrumental noise, the effect of different resolving powers at different frequencies and a more complete and realistic characterization of astrophysical foregrounds is in progress.     

A novel multifrequency technique for the detection of point sources in cosmic microwave background maps

In this work we address the problem of simultaneous multifrequency detection of extragalactic point sources in the maps of the cosmic microwave background. We apply a new linear filtering technique, the 'matched matrix filters', that incorporates full spatial information, including the cross-correlation among channels, without making any a priori assumption about the spectral behaviour of the sources. A substantial reduction of the background is achieved thanks to the optimal combination of filtered maps. We describe the new technique in detail and apply it to the detection of radio sources and estimation of their parameters in realistic all-sky Planck simulations at 30, 44, 70 and 100 GHz. Then, we compare the results with the single-frequency approach based on the standard matched filter, in terms of reliability, completeness and flux accuracy of the resulting point source catalogues. The new filters outperform the standard matched filters for all these indexes at 30, 44 and 70 GHz, whereas at 100 GHz both kinds of filters have a similar performance. We find a notable increment of the number of true detections for a fixed reliability level. In particular, for a 95 per cent reliability we practically double the number of detections at 30, 44 and 70 GHz.     

Testing isotropy of cosmic microwave background radiation

We introduce new symmetry-based methods to test for isotropy in cosmic microwave background (CMB) radiation. Each angular multipole is factored into unique products of power eigenvectors, related multipoles and singular values that provide two new rotationally invariant measures mode by mode. The power entropy and directional entropy are new tests of randomness that are independent of the usual CMB power. Simulated Galactic plane contamination is readily identified. The ILC– WMAP data maps show seven axes well aligned with one another and the direction Virgo. Parameter free statistics find 12 independent cases of extraordinary axial alignment, low power entropy, or both having 5 per cent probability or lower in an isotropic distribution. Isotropy of the ILC maps is ruled out to confidence levels of better than 99.9 per cent, whether or not coincidences with other puzzles coming from the Virgo axis are included. Our work shows that anisotropy is not confined to the low l region, but extends over a much larger l range.     

Spherical needlets for cosmic microwave background data analysis

We discuss spherical needlets and their properties. Needlets are a form of spherical wavelets which do not rely on any kind of tangent plane approximation and enjoy good localization properties in both pixel and harmonic space; moreover needlet coefficients are asymptotically uncorrelated at any fixed angular distance, which makes their use in statistical procedures very promising. In view of these properties, we believe needlets may turn out to be especially useful in the analysis of cosmic microwave background (CMB) data on the incomplete sky, as well as of other cosmological observations. As a final advantage, we stress that the implementation of needlets is computationally very convenient and may rely completely on standard data analysis packages such as healp ix.     

The discriminating power of wavelets to detect non-Gaussianity in the cosmic microwave background

We investigate the power of wavelets in detecting non-Gaussianity in the cosmic microwave background (CMB). We use a wavelet-based method on small simulated patches of the sky to discriminate between a pure inflationary model and inflationary models that also contain a contribution from cosmic strings. We show the importance of the choice of a good test statistic in order to optimize the discriminating power of the wavelet technique. In particular, we construct the Fisher discriminant function, which combines all the information available in the different wavelet scales. We also compare the performance of different decomposition schemes and wavelet bases. For our case, we find that the Mallat and a ` trous algorithms are superior to the 2D-tensor wavelets. Using this technique, the inflationary and strings models are clearly distinguished even in the presence of a superposed Gaussian component with twice the rms amplitude of the original cosmic string map.