Digital deblurring of CMB maps II. Asymmetric point spread function

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.