skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: A novel CMB component separation method: hierarchical generalized morphological component analysis

Abstract

We present a novel technique for cosmic microwave background (CMB) foreground subtraction based on the framework of blind source separation. Inspired by previous work incorporating local variation to generalized morphological component analysis (GMCA), we introduce hierarchical GMCA (HGMCA), a Bayesian hierarchical graphical model for source separation. We test our method on Nside = 256 simulated sky maps that include dust, synchrotron, free–free, and anomalous microwave emission, and show that HGMCA reduces foreground contamination by $$25{{\ \rm per\ cent}}$$ over GMCA in both the regions included and excluded by the Planck UT78 mask, decreases the error in the measurement of the CMB temperature power spectrum to the 0.02–0.03 percent level at ℓ > 200 (and $$\lt 0.26{{\ \rm per\ cent}}$$ for all ℓ), and reduces correlation to all the foregrounds. We find equivalent or improved performance when compared to state-of-the-art internal linear combination type algorithms on these simulations, suggesting that HGMCA may be a competitive alternative to foreground separation techniques previously applied to observed CMB data. Additionally, we show that our performance does not suffer when we perturb model parameters or alter the CMB realization, which suggests that our algorithm generalizes well beyond our simplified simulations. Finally, our results open a new avenue for constructing CMB maps through Bayesian hierarchical analysis.

Authors:
ORCiD logo [1];  [2];  [3];  [3]
  1. Department of Physics, Harvard University, Cambridge, MA 02138, USA, Department of Physics, Stanford University, Stanford, CA 94305, USA
  2. Department of Mathematics, Harvard University, Cambridge, MA 02138, USA, Department of Computer Science and Engineering, University of California San Diego, San Diego, CA 92092, USA
  3. Department of Physics, Harvard University, Cambridge, MA 02138, USA
Publication Date:
Research Org.:
Harvard Univ., Cambridge, MA (United States)
Sponsoring Org.:
USDOE; National Science Foundation (NSF)
OSTI Identifier:
1632766
Alternate Identifier(s):
OSTI ID: 1657201
Grant/Contract Number:  
SC0020223; AST-1813694
Resource Type:
Published Article
Journal Name:
Monthly Notices of the Royal Astronomical Society
Additional Journal Information:
Journal Name: Monthly Notices of the Royal Astronomical Society Journal Volume: 494 Journal Issue: 1; Journal ID: ISSN 0035-8711
Publisher:
Royal Astronomical Society
Country of Publication:
United Kingdom
Language:
English
Subject:
79 ASTRONOMY AND ASTROPHYSICS; methods: data analysis; cosmic background radiation

Citation Formats

Wagner-Carena, Sebastian, Hopkins, Max, Diaz Rivero, Ana, and Dvorkin, Cora. A novel CMB component separation method: hierarchical generalized morphological component analysis. United Kingdom: N. p., 2020. Web. doi:10.1093/mnras/staa744.
Wagner-Carena, Sebastian, Hopkins, Max, Diaz Rivero, Ana, & Dvorkin, Cora. A novel CMB component separation method: hierarchical generalized morphological component analysis. United Kingdom. doi:https://doi.org/10.1093/mnras/staa744
Wagner-Carena, Sebastian, Hopkins, Max, Diaz Rivero, Ana, and Dvorkin, Cora. Thu . "A novel CMB component separation method: hierarchical generalized morphological component analysis". United Kingdom. doi:https://doi.org/10.1093/mnras/staa744.
@article{osti_1632766,
title = {A novel CMB component separation method: hierarchical generalized morphological component analysis},
author = {Wagner-Carena, Sebastian and Hopkins, Max and Diaz Rivero, Ana and Dvorkin, Cora},
abstractNote = {We present a novel technique for cosmic microwave background (CMB) foreground subtraction based on the framework of blind source separation. Inspired by previous work incorporating local variation to generalized morphological component analysis (GMCA), we introduce hierarchical GMCA (HGMCA), a Bayesian hierarchical graphical model for source separation. We test our method on Nside = 256 simulated sky maps that include dust, synchrotron, free–free, and anomalous microwave emission, and show that HGMCA reduces foreground contamination by $25{{\ \rm per\ cent}}$ over GMCA in both the regions included and excluded by the Planck UT78 mask, decreases the error in the measurement of the CMB temperature power spectrum to the 0.02–0.03 percent level at ℓ > 200 (and $\lt 0.26{{\ \rm per\ cent}}$ for all ℓ), and reduces correlation to all the foregrounds. We find equivalent or improved performance when compared to state-of-the-art internal linear combination type algorithms on these simulations, suggesting that HGMCA may be a competitive alternative to foreground separation techniques previously applied to observed CMB data. Additionally, we show that our performance does not suffer when we perturb model parameters or alter the CMB realization, which suggests that our algorithm generalizes well beyond our simplified simulations. Finally, our results open a new avenue for constructing CMB maps through Bayesian hierarchical analysis.},
doi = {10.1093/mnras/staa744},
journal = {Monthly Notices of the Royal Astronomical Society},
number = 1,
volume = 494,
place = {United Kingdom},
year = {2020},
month = {3}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: https://doi.org/10.1093/mnras/staa744

Save / Share:

Works referenced in this record:

Linear Inversion of Band-Limited Reflection Seismograms
journal, October 1986

  • Santosa, Fadil; Symes, William W.
  • SIAM Journal on Scientific and Statistical Computing, Vol. 7, Issue 4
  • DOI: 10.1137/0907087

Planck 2015 results : X. Diffuse component separation: Foreground maps
journal, September 2016


Spin-SILC: CMB polarization component separation with spin wavelets
journal, August 2016

  • Rogers, Keir K.; Peiris, Hiranya V.; Leistedt, Boris
  • Monthly Notices of the Royal Astronomical Society, Vol. 463, Issue 3
  • DOI: 10.1093/mnras/stw2128

Planck 2015 results : XII. Full focal plane simulations
journal, September 2016


HEALPix: A Framework for High‐Resolution Discretization and Fast Analysis of Data Distributed on the Sphere
journal, April 2005

  • Gorski, K. M.; Hivon, E.; Banday, A. J.
  • The Astrophysical Journal, Vol. 622, Issue 2
  • DOI: 10.1086/427976

Sparse component separation for accurate cosmic microwave background estimation
journal, January 2013


S2LET: A code to perform fast wavelet analysis on the sphere
journal, October 2013


Planck 2013 results. XVI. Cosmological parameters
journal, October 2014


Exact reconstruction with directional wavelets on the sphere
journal, August 2008


A needlet internal linear combination analysis of WMAP 7-year data: estimation of CMB temperature map and power spectrum: A NILC analysis of WMAP 7-year data
journal, November 2011


Second-Generation Curvelets on the Sphere
journal, January 2017

  • Chan, Jennifer Y. H.; Leistedt, Boris; Kitching, Thomas D.
  • IEEE Transactions on Signal Processing, Vol. 65, Issue 1
  • DOI: 10.1109/TSP.2016.2600506

A full sky, low foreground, high resolution CMB map from WMAP
journal, November 2008


Localisation of directional scale-discretised wavelets on the sphere
journal, January 2018

  • McEwen, Jason D.; Durastanti, Claudio; Wiaux, Yves
  • Applied and Computational Harmonic Analysis, Vol. 44, Issue 1
  • DOI: 10.1016/j.acha.2016.03.009

Planck 2013 results. XIX. The integrated Sachs-Wolfe effect
journal, October 2014


Planck 2015 results : XI. CMB power spectra, likelihoods, and robustness of parameters
journal, September 2016


Foreground separation methods for satellite observations of the cosmic microwave background
journal, October 1998


Component separation methods for the PLANCK mission
journal, October 2008


Wavelets on the 2-Sphere: A Group-Theoretical Approach
journal, November 1999

  • Antoine, J. -P; Vandergheynst, P.
  • Applied and Computational Harmonic Analysis, Vol. 7, Issue 3
  • DOI: 10.1006/acha.1999.0272

Planck 2015 results : XIII. Cosmological parameters
journal, September 2016


Planck 2013 results. I. Overview of products and scientific results
journal, October 2014


FIVE-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE ( WMAP ) OBSERVATIONS: BAYESIAN ESTIMATION OF COSMIC MICROWAVE BACKGROUND POLARIZATION MAPS
journal, August 2009


A needlet ILC analysis of WMAP 9-year polarization data: CMB polarization power spectra
journal, August 2013

  • Basak, S.; Delabrouille, J.
  • Monthly Notices of the Royal Astronomical Society, Vol. 435, Issue 1
  • DOI: 10.1093/mnras/stt1158

Joint Planck and WMAP CMB map reconstruction
journal, March 2014


Wavelet-Bayesian inference of cosmic strings embedded in the cosmic microwave background
journal, September 2017

  • McEwen, J. D.; Feeney, S. M.; Peiris, H. V.
  • Monthly Notices of the Royal Astronomical Society, Vol. 472, Issue 4
  • DOI: 10.1093/mnras/stx2268

A Novel Sampling Theorem on the Rotation Group
journal, December 2015

  • McEwen, Jason D.; Buttner, Martin; Leistedt, Boris
  • IEEE Signal Processing Letters, Vol. 22, Issue 12
  • DOI: 10.1109/LSP.2015.2490676

Separation of Correlated Astrophysical Sources Using Multiple-Lag Data Covariance Matrices
journal, September 2005

  • Bedini, L.; Herranz, D.; Salerno, E.
  • EURASIP Journal on Advances in Signal Processing, Vol. 2005, Issue 15
  • DOI: 10.1155/ASP.2005.2400

High resolution foreground cleaned CMB map from WMAP
journal, December 2003

  • Tegmark, Max; de Oliveira-Costa, Angélica; Hamilton, Andrew J. S.
  • Physical Review D, Vol. 68, Issue 12
  • DOI: 10.1103/PhysRevD.68.123523

Multidetector multicomponent spectral matching and applications for cosmic microwave background data analysis
journal, December 2003


Cosmic microwave background power spectrum estimation and map reconstruction with the expectation-maximization algorithm
journal, November 2003


Power Spectrum Estimation from High‐Resolution Maps by Gibbs Sampling
journal, December 2004

  • Eriksen, H. K.; O’Dwyer, I. J.; Jewell, J. B.
  • The Astrophysical Journal Supplement Series, Vol. 155, Issue 2
  • DOI: 10.1086/425219

Power Spectrum of Primordial Inhomogeneity Determined from the FOUR-Year [ITAL]COBE[/ITAL] DMR Sky Maps
journal, June 1996

  • Górski, K. M.; Banday, A. J.; Bennett, C. L.
  • The Astrophysical Journal, Vol. 464, Issue 1
  • DOI: 10.1086/310077

A Multi-Level Solver for Gaussian Constrained Cosmic Microwave Background Realizations
journal, January 2014

  • Seljebotn, D. S.; Mardal, K. -A.; Jewell, J. B.
  • The Astrophysical Journal Supplement Series, Vol. 210, Issue 2
  • DOI: 10.1088/0067-0049/210/2/24

Asymptotics for spherical needlets
journal, June 2009

  • Baldi, P.; Kerkyacharian, G.; Marinucci, D.
  • The Annals of Statistics, Vol. 37, Issue 3
  • DOI: 10.1214/08-AOS601

Localized Tight Frames on Spheres
journal, January 2006

  • Narcowich, F. J.; Petrushev, P.; Ward, J. D.
  • SIAM Journal on Mathematical Analysis, Vol. 38, Issue 2
  • DOI: 10.1137/040614359

NINE-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE ( WMAP ) OBSERVATIONS: FINAL MAPS AND RESULTS
journal, September 2013

  • Bennett, C. L.; Larson, D.; Weiland, J. L.
  • The Astrophysical Journal Supplement Series, Vol. 208, Issue 2
  • DOI: 10.1088/0067-0049/208/2/20

SPATIAL VARIATIONS IN THE SPECTRAL INDEX OF POLARIZED SYNCHROTRON EMISSION IN THE 9 yr WMAP SKY MAPS
journal, July 2014


The Python Sky Model: software for simulating the Galactic microwave sky
journal, May 2017

  • Thorne, B.; Dunkley, J.; Alonso, D.
  • Monthly Notices of the Royal Astronomical Society, Vol. 469, Issue 3
  • DOI: 10.1093/mnras/stx949

Blind Component Separation in Wavelet Space: Application to CMB Analysis
journal, September 2005

  • Moudden, Y.; Cardoso, J. -F.; Starck, J. -L.
  • EURASIP Journal on Advances in Signal Processing, Vol. 2005, Issue 15
  • DOI: 10.1155/ASP.2005.2437

Fast and Efficient Template Fitting of Deterministic Anisotropic Cosmological Models Applied to WMAP Data
journal, June 2006

  • Jaffe, T. R.; Banday, A. J.; Eriksen, H. K.
  • The Astrophysical Journal, Vol. 643, Issue 2
  • DOI: 10.1086/501343

Sparse and Non-Negative BSS for Noisy Data
journal, November 2013

  • Rapin, Jeremy; Bobin, Jerome; Larue, Anthony
  • IEEE Transactions on Signal Processing, Vol. 61, Issue 22
  • DOI: 10.1109/TSP.2013.2279358

How Isotropic is the Universe?
journal, September 2016


Independent component analysis: algorithms and applications
journal, June 2000


Template fitting and the large-angle cosmic microwave background anomalies
journal, April 2006


A Novel Sampling Theorem on the Sphere
journal, December 2011


Planck 2013 results. XII. Diffuse component separation
journal, October 2014


SILC: a new Planck internal linear combination CMB temperature map using directional wavelets
journal, May 2016

  • Rogers, Keir K.; Peiris, Hiranya V.; Leistedt, Boris
  • Monthly Notices of the Royal Astronomical Society, Vol. 460, Issue 3
  • DOI: 10.1093/mnras/stw1121