  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
considered: 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 even 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.
