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

Abstract

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 ≃0.7σCMB, where σCMB 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.

Digital deblurring of CMB maps: Performance and efficient implementation

“…The region analysed is almost identical to the one in Baccigalupi et al (2000): it is a squared patch (340 × 340 pixels) with side of about 20…”

“…For example, available prior information about the signals can be used in a regularised inversion via Wiener filtering and maximum entropy methods, either on small sky patches (Hobson et al 1998) or on the whole sky (Bouchet & Gispert 1999;Stolyarov et al 2002). It has been shown that under certain independence assumption on the signals, the map-operating algorithms based on Independent Component Analysis (ICA) techniques can be applied on sky patches (Baccigalupi et al 2000) as well as on the whole sky (Maino et al 2002).…”

“…Second, a better understanding of sky emissions, from foregrounds in particular, is achieved if multifrequency sky maps are compared on a common resolution. Third, some map-based component separation algorithms, such as ICA (Baccigalupi et al 2000;Maino et al 2002) require input maps with similar level of degradation. Furthermore, although the aim of satellite missions such as Planck and MAP is to obtain full sky maps of the CMB, the strength of the CMB over other backgrounds or contaminating sources will vary over the sky.…”

“…Our first application to a realistic map is presented in Sect. 6, where we consider a region in the sky (already addressed by Baccigalupi et al 2000) in which the CMB emission largely dominates over foregrounds. We will assume observational conditions, frequencies, angular resolution and noise level corresponding to the Low Frequency Instrument (LFI) of the PLANCK satellite.…”

Mining Pixels: The Extraction and Classification of Astronomical Sources

“…ICA is more computationally intensive than PCA, and obviously has a lower compression efficiency in terms of residual rms error, but it provides a better separation of mixed components (e.g. Baccigalupi et al 2000 [3] or Bijaoui, this conference). Contrarily to Principal Components, Individual Components are sensitive to localized, oriented, and bandpass-selective features when trained with "natural" image data (Bell & Sejnowski [6]), a property shared with the spatial receptive fields of simple cells in mammalian cortex.…”