A Monte Carlo comparison between template-based and Wiener-filter CMB dipole estimators

We review and compare two different cosmic microwave background (CMB) dipole estimators discussed in the literature and assess their performances through Monte Carlo simulations. The first method amounts to simple template regression with partial sky data, while the second method is an optimal Wiener filter (or Gibbs sampling) implementation. The main difference between the two methods is that the latter approach takes into account correlations with higher-order CMB temperature fluctuations that arise from nonorthogonal spherical harmonics on an incomplete sky, which for recent CMB data sets (such as Planck) is the dominant source of uncertainty. For an accepted sky fraction of 81% and an angular CMB power spectrum corresponding to the best-fit Planck 2018 ΛCDM model, we find that the uncertainty on the recovered dipole amplitude is about six times smaller for the Wiener filter approach than for the template approach, corresponding to 0.5 and 3 μK, respectively. Similar relative differences are found for the corresponding directional parameters and other sky fractions. We note that the Wiener filter algorithm is generally applicable to any dipole estimation problem on an incomplete sky, as long as a statistical and computationally tractable model is available for the unmasked higher-order fluctuations. The methodology described in this paper forms the numerical basis for the most recent determination of the CMB solar dipole from Planck, as summarized by Planck Collaboration Int. LVII (2020).

Influence of Mismarking Fiducial Locations on EEG Source Estimation

Mismarking locations of the fiducials can have a significant influence on the digitized electrode locations and cortical source estimation using high-density EEG. Under-standing and quantifying how uncertainties in the fiducial locations affect the locations of cortical sources is important for interpreting EEG analyses. We systematically shifted fiducial locations to investigate the relationship between variations of fiducial locations and the corresponding estimations of the source locations. We quantified the uncertainty of the dipole locations using the enclosing volume of the dipole locations and the maximum width of the dipole cluster. Shifting fiducial locations 1.5 cm increased the uncertainty of the dipole locations to span a volume >1 cm3 and about 2.5 cm wide. Results suggest that the fiducials need to be digitized accurately within at least 0.5 cm of the absolute actual fiducial location to limit the uncertainty of a dipole location to <1 cm. Additionally, we used random fiducial shift combinations to estimate the effects of combinations of the fiducial shifts on dipole location estimation. This analysis showed that dipole locations were within the bounds of our dipole estimation uncertainty volumes. Based on the outcomes, we suggest marking fiducials carefully before placement of the cap and to use a digitization method with an accuracy of <0.5 cm.

Highly Automated Dipole EStimation (HADES)

Automatic estimation of current dipoles from biomagnetic data is still a problematic task. This is due not only to the ill-posedness of the inverse problem but also to two intrinsic difficulties introduced by the dipolar model: the unknown number of sources and the nonlinear relationship between the source locations and the data. Recently, we have developed a new Bayesian approach, particle filtering, based on dynamical tracking of the dipole constellation. Contrary to many dipole-based methods, particle filtering does not assume stationarity of the source configuration: the number of dipoles and their positions are estimated and updated dynamically during the course of the MEG sequence. We have now developed a Matlab-based graphical user interface, which allows nonexpert users to do automatic dipole estimation from MEG data with particle filtering. In the present paper, we describe the main features of the software and show the analysis of both a synthetic data set and an experimental dataset.