This paper shows how the cosmic shear power spectra can be directly estimated from a shear map using pseudopower spectrum methods originally developed for the CMB. A key issue is cleanly separating the E and B modes of the shear field that are mixed together by the survey window and stellar masks. These authors achieve impressive results with subpercent errors in the estimated EE and BB power spectra for surveys covering 2000 sq. deg. (in spherical geometry) and 25 sq. deg. (in the flatsky approximation). This is all the more impressive considering that 25% of the area in each case is removed from (simulated) stellar and bad pixel masks.
The authors note that the ~1% residual Bmode power is likely from the socalled "ambiguous" modes that arise from decomposing a spin2 field on a finite region (described in Bunn et al. 2003). As stated in their conclusions, it will be very interesting to see how the methods for removing these ambiguous modes that have already been applied to the CMB work for cosmic shear maps. It's not at all clear to me that the methods of, e.g., Smith & Zaldarriaga (2007) will work because these require specifying a nicely apodized window to cover the masked regions. But the smallscale structure in the stellar masks makes it difficult to devise an apodized mask that still preserves a reasonable signaltonoise ratio.
Another potential practical issue is the computational cost in computing the modemode coupling matrix relating the pseudo and true power spectra. It would be interesting to compare this computational cost with that required for a correlation function analysis. In particular, perhaps it will soon be feasible to undertake a Monte Carlo error analysis for cosmic shear pseudoCls as has been done for the CMB.
[1004.3542] Shear Power Spectrum Reconstruction using PseudoSpectrum Method
Authors:  Chiaki Hikage, Masahiro Takada, Takashi Hamana, David Spergel 
Abstract:  This paper develops a pseudo power spectrum technique for measuring the lensing power spectrum from weak lensing surveys in both the full sky and flat sky limits. The power spectrum approaches have a number of advantages over the traditional correlation function approach. We test the pseudo spectrum method by using numerical simulations with squareshape boundary that include masked regions with complex configuration due to bright stars and saturated spikes. Even when 25% of total area of the survey is masked, the method recovers the Emode power spectrum at a subpercent precision over a wide range of multipoles 100<l<10000, better than the statistical errors expected for a 2000 square degree survey. The residual Bmode spectrum is well suppressed in the amplitudes at less than a percent level relative to the Emode. We also find that the correlated errors of binned power spectra caused by the survey geometry effects are not significant. Our method is applicable to the current and upcoming widefield lensing surveys. 
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