Digital Deblurring of CMB Maps II:
Asymmetric Point Spread Function
R. Vio, J. Nagy, L. Tenorio, P. Andreani, C. Baccigalupi
and W. Wamsteker
In this second paper in a series dedicated to developing efficient
numerical techniques for the deblurring Cosmic Microwave Background
(CMB) maps, we consider the case of asymmetric point spread functions
(PSF). Although conceptually this problem is not different from the
symmetric case, there are important differences from the computational
point of view because it is no longer possible to use some of the
efficient numerical techniques that work with symmetric PSFs. We
present procedures that permit the use of efficient techniques even
when this condition is not met. In particular, two methods are cons
idered: a procedure based on a Kronecker approximation technique that
can be implemented with the numerical methods used with symmetric PSFs
but that has the limitation of requiring only mildly asymmetric
PSFs. The second is a variant of the classic Tikhonov technique that
works eve n with very asymmetric PSFs but that requires discarding the
edges of the maps. We provide details for efficient implementations of
the algorithms. Their performance is tested on simulated CMB maps.