Dust delensing firstlook
Here I describe a first look at the impact of non-Gaussian dust on delensing. One possible concern is that a coupling between long- and short-scale modes can lead to a bias on delensing. To try to capture this we do the following (other suggestions are welcome):
- For a simulated dust map (Q_dust, U_dust) we compute a reconstructed lensing map using a quadratic estimator, phi_dust ~ E_dust B_dust. The noise is set to 3 uK-arcmin, with [lmin , lmax] = [300,3000] for the reconstruction.
- We then perform lensing to get a B template: We take E_dust (which I Weiner filter assuming the same noise level) and lens it according to phi_dust
- We then compute the cross power spectrum of B_template with B_dust on large scales l < 300 (note these modes were not used in the phi reconstruction).
A very preliminary result is shown here: 
There are as many positive as negative points, so no evidence for a bias is seen.
- check this result (e.g. my lensing operation is formally nonlinear in the map amplitudes; also there are multiple choices for filtering when doing delensing, esp. on a cut sky)
- repeat for other sims -- we have a number of models with varying levels of EE / BB power
- Other checks? Look at excess power (not just correlation with low-ell B_dust)