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In this second paper in a series dedicated to developing efficient numericaltechniques for the deblurring Cosmic Microwave Background (CMB) maps, weconsider the case of asymmetric point spread functions (PSF). Althoughconceptually this problem is not different from the symmetric case, there areimportant differences from the computational point of view because it is nolonger possible to use some of the efficient numerical techniques that workwith symmetric PSFs. We present procedures that permit the use of efficienttechniques even when this condition is not met. In particular, two methods areconsidered: a procedure based on a Kronecker approximation technique that canbe implemented with the numerical methods used with symmetric PSFs but that hasthe limitation of requiring only mildly asymmetric PSFs. The second is avariant of the classic Tikhonov technique that works even with very asymmetricPSFs but that requires discarding the edges of the maps. We provide details forefficient implementations of the algorithms. Their performance is tested onsimulated CMB maps.Comment: 9 pages, 13 Figure

Digital deblurring of CMB maps