FastICA as a LOFAR-EoR Foreground Cleaning Technique

1. FastICA as a LOFAR-EoR Foreground Cleaning Technique Filipe Abdalla and Emma Woodfield University College London with Saleem Zaroubi, Vibor Jelic, Panos Labropoulos and the LOFAR-EoR working group

2. Problem Outline • 21cm signal dominated both by foregrounds and by noise. • Currently most foreground cleaning methods are parametric, e.g. polynomial. • Non-parametric methods have emerged - Wp smoothing (Harker 09). • Other, powerful techniques have been used on the CMB...

3. Problem Outline • 21cm signal dominated both by foregrounds and by noise. • Currently most foreground cleaning methods are parametric, e.g. polynomial. • Non-parametric methods have emerged - Wp smoothing (Harker 09). • Other, powerful techniques have been used on the CMB... Harker et al.2010

4. Problem Outline • 21cm signal dominated both by foregrounds and by noise. • Currently most foreground cleaning methods are parametric, e.g. polynomial. • Non-parametric methods have emerged - Wp smoothing (Harker 09). • Other, powerful techniques have been used on the CMB... Maino et al. 02

5. Independent Component Analysis and FastICA • x = A s • A is the mixing matrix. If we can find a matrix W such that s = W x we have effectively sorted a mixed signal into its individual components. • “PDF of a mixture of independent components more Gaussian than the PDF of any individual component.” FastICA uses negentropy as a measure of Gaussianity. • Many ICA methods exist (e.g. SMICA, GMCA, MCA), we have started with FastICA as easiest to implement. • FastICA is an independent component analysis algorithm (Hyvärinen A., 1999, IEEE Trans. on Neural Networks, 10,626;Hyvärinen A., Karhunen J., Oja E., 2001, Independent Component Analysis. John Wiley and Sons) • ICA methods are `blind’ and non-parametric. • FastICA recovered the angular PS at the % level and could process all-sky maps in ~ 10 minutes. (Maino02)

6. Data Simulations: 21cm Signal • 10°x10° data cube with 170 slice in frequency, separated by 0.5 Mhz. Frequency range of 115 – 200 MHz (z ~ 11.3 – 6.1) • Box size of 1.8 Gpc over 512 pixels – a resolution of ~3MPc/pixel. • 21cmFAST (Mesinger A., Furlanetto S., Cen R., 2011, MNRAS, 411,955) • Minimum contributing halo temperature of 1e4 K. 21cm map at 150MHz for a 10°x10° observing window. Temperature scale in K.

7. Data Simulations: Foregrounds • Simulations from Jelic V., Zaroubi S., Labropoulos P. et al. 2008, MNRAS, 389, 1319 • Galactic synchrotron radiation, galactic free-free emission • Extragalactic radiation from radio galaxies and clusters Foreground map at 150MHz for a 10°x10° observing window. Temperature scale in K.

8. Data Simulations: Noise • A measurement set of our simulation was filled with a • Gaussian distribution of random numbers and a correlated • noise map created with an imager. • Each map was normalized to the expected rms noise of the LOFAR experiment as set out in Labropoulos et al. • (2009); Jeli´c et al. (2008). • e.g. 52mK at 150MHz for 600 hours of LOFAR observing time. Noise map at 150MHz for a 10°x10° observing window. Temperature scale in K.

9. Data Simulations: Beam Forming Beam forming simulated by convolving with a gaussian PSF normalized to 3 arcmin beam width at 150MHz. Original Adjusted for convolution

10. Results: Residual variance recovery FastICA outputs “residuals” consisting of the reconstructed 21cm signal, noise and fitting errors. FastICA can be carried out in both fourier and real space with no difference between the methods. To estimate the reconstructed 21 variance we remove the noise by hand to check how much signal is mis-fitted.... Simulated residuals Reconstructed residuals

11. Results: 21cm variance recovery Excess variance is recovered, however it underestimates the simulated variance at almost all redshifts. This signal has been misfit – probably as a result of noise leakage into the foregrounds.

12. Simulated 21cm signal - beamformed Simulated 21cm map at 150MHz for a 10°x10° observing window. Signal has been adjusted for beam forming. Temperature scale in K.

13. Reconstructed 21cm signal - beamformed Reconstructed 21cm map at 150MHz for a 10°x10° observing window. Temperature scale in K. Large scale structure recovered but a lot of excess small scale structure – probably as a result of noise leakage into the foregrounds.

14. Results: 21cm Powerspectrum – 169 Mhz We look at the variance as a function of scale using the 2D angular power spectrum. We find the angular power spectrum at each frequency and then average over 5 slices (2.5 MHz). Error Bars:

15. Results: 21cm Powerspectrum – 149 MHz The small scale discrepancy could be an indication that FastICA is not robust to the noise in this method, or it could be a resolution effect.

16. Results: 21cm Powerspectrum – 129 MHz At the lower end of the frequency range the fit degrades significantly.

17. Conclusions • ICA has been a successful method for cleaning CMB data. This is the first attempt at applying the FastICA method to LOFAR-EoR data. • FastICA as foreground cleaning technique would be able to retrieve the EoR signal for a LOFAR set-up, and is especially robust for large scales. • This is not unsurprising as there is more noise at smaller scales and FastICA is not robust to noise. • To do list: • We need to run FastICA on a higher resolution grid to test whether the poor small scale recovery is due to resolution effects or an inherent problem with the noise robustness of FastICA • Other methods have to be tested which can be more robust to noise and potentially recover spectra info, i.e. SMICA...