Probabilis)c image reconstruc)on, foreground removal, and power spectrum inference from radio interferometers

Transcription

1 Probabilis)c image reconstruc)on, foreground removal, and power spectrum inference from radio interferometers Ben Wandelt IAP, ILP, UPMC, CNRS Sorbonne University

2 Theore>cal interest in 21cm cosmology Khatri & Wandelt, "21 cm radia>on: A new probe of fundamental physics," Highlights of Astronomy, 15, , "21- cm Radia>on: A New Probe of Varia>on in the Fine- Structure Constant," Physical Review LeTers, 98, , 2007, astro- ph/ "Cosmic (Super)String Constraints from 21cm Radia>on," Physical Review LeTers, 100, , 2008, arxiv: Epoch of Re- ioniza>on w/ Yi Mao: Mao, Y., D'Aloisio, A., Wandelt, B. D., Zhang, J., and Shapiro, P. R.,"The Linear Perturba>on Theory of Reioniza>on in Posi>on- Space: Cosmological Radia>ve Transfer Along the Light- Cone," ArXiv e- prints, 2014, arxiv: Probing sta>s>cs of ini>al condi>ons beyond CMB (strong involvement in Planck) "Low"- redshif 21cm brightness mapping of large scale structure

3 Recent contribu>ons in data analysis of interferometric data ("radiostats")

4 This talk References: SuTon and Wandelt, astro- ph/ (ApJS 2006) SuTer, Wandelt, Malu, arxiv: (ApJ 2011) SuTer et al., arxiv: (MNRAS 2014) Zhang et al., in prepara>on 2015 Collaborators: Paul M. Su=er, Le Zhang Ted Bunn, Ata Karakci, Jason McEwen, Peter Timbie, Greg Tucker et al.

5 Probabilis)c image reconstruc)on in radio interferometry SuTer et al., arxiv: (MNRAS 2014) SuTon and Wandelt, astro- ph/ (ApJS 2006) SuTer, Wandelt, Malu, arxiv: (ApJ 2011)

6 Interferometers 6

7 signal Data model primary beam uv- plane d = IFAs + n data

8 d = IFAs + n the need for deconvolu>on F d

9 CLEAN is robust minimally parametric data- driven? informa>ve scalable fast 9

10 the community responds Maximum Entropy Mul>- scale Mul>- frequency Compressed Sensing 10

11 signal The Wiener filter B.signal + noise Wiener filtered signal WF = IFA * S IFA 2 S + N need to know signal covariance 11 need to know noise covariance

12 an infinity of guesses no Wiener filter no yes data no

13 WF map + fluctua>ons Gibbs sampling is a both power spectrum inference and non- linear Wiener filter isotropic Gaussian process prior augment missing fluctua>ons from prior WF map construct Wiener- filtered map compute power spectrum Ini>al guess of signal covariance (Su$er, Wandelt, Malu. 2011; Karakci et al. 2013)

14 (Su$er et al. 2013)

15 (Su$er et al. 2013) example: Einstein

16 (Su$er et al. 2013) test images

17 Gibbs performs beter than CLEAN (Su$er et al. 2013)

18 Sampling approach provides an error model

19 Applica>on of this methodology to 21cm data requires Moving from 2D maps to 3D data cubes Include powerful foreground removal Faster opera>on find peak rather than sample Done now running first simula>on tests è Zhang et al in prep: HIEMICA

20 The SMICA Planck map shining example of the power of semi- blind foreground cleaning

21 Assump>ons in "standard" approaches E.g. fit power- law to foreground emission Assumes foregrounds are smooth in a specific way Principal Component Analysis Throws away dominant signal components indiscriminately Assumes foregrounds are the dominant component low- rank sufficiently different from cosmological signal that signal will not be strongly destroyed. No criteria for number of components to be removed Results are then de- biased based on Monte Carlo simula>ons using expected parameters (possibly involving strong assump>ons) This leads to model risk: what if the assump>ons are wrong?

22 Blind foreground cleaning approach Model the observa>ons as d = s+f+n Non- cosmological components f are assumed to be low- rank shares this advantage with PCA. Includes noise model Infers signal at the same >me based on power spectrum diversity between foregrounds and signal; and very different sta>s>cal proper>es (isotropy and homogeneity) Find op>mum separa>on efficiently using specially adapted op>miza>on algorithm Op>mality built- in due to full Bayesian forward model

23 Component power spectra point sources synchrotron Galac>c free- free extragalac>c free- free 21- cm signal

24 Input and recovered components

25 Recovered power spectra compared to PCA analysis

26 Conclusions Probabilis>c approach allows the construc>on of powerful techniques for signal reconstruc>on from interferometric data Semi- blind techniques guard against model error HIEMICA: semi- blind foreground separa>on method Demonstrated high- fidelity map and power spectrum reconstruc>ons Separa>ng foreground that are up to 1000 >mes brighter than the cosmological signal. No noise bias Major improvements on large scales Number of components are selected based on quan>ta>ve criteria Next step: simulate EoR applica>on.

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28 Input components

29 Recovered components

30 Frequency behavior of input and recovered foreground components Mixing matrix Inferred components synchrotron point sources Galac>c free- free extragalac>c free- free Physical templates

31 Simula>on parameters 64 3 grid 30 o x 30 o field Model includes a cosmological signal Synchrotron foreground Galac>c free- free Extra- galac>c point sources Extra- galac>c free- free