Patrick Simon Argelander-Institute for Astronomy, Bonn, Germany

Wiener filter of 3-D lensing data
Combine all “source redshift bins” into one vector
(
) (
)
γ ≡ γ (1) ,γ (2) , . . . =P γκ Q (1) , Q (2) , . . . δ m ≡ P γκ Qδ m
Need to find solution for δ m for given cosmic shear:
ɛ =P γκ Q δ m + n
Minimum variance solution for δ
δ mv
m
= SQ t P † γκ
[
N −1 P γκ QSQ t P † γκ + α1 ] −1
N −1 ɛ
S ≡〈δ m δ t m〉
signal covariance
N ≡〈nn † 〉 noise covariance
α=1: full Wiener filtering (less noise, biased)
α=0: no prior (plenty noise, unbiased)