Digital deblurring of CMB maps

II. Asymmetric point spread function

¹ Chip Computers Consulting s.r.l., Viale Don L. Sturzo 82, S.Liberale di Marcon, 30020 Venice, Italy ESA-VILSPA, Apartado 50727, 28080 Madrid, Spain e-mail: robertovio@tin.it
² Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30322, USA e-mail: nagy@mathcs.emory.edu
³ Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden CO 80401, USA e-mail: ltenorio@Mines.EDU
⁴ Osservatorio Astronomico di Padova, vicolo dell'Osservatorio 5, 35122 Padua, Italy e-mail: andreani@pd.astro.it
⁵ SISSA/ISAS, Via Beirut 4, 34014 Trieste, Italy e-mail: bacci@sissa.it
⁶ ESA-VILSPA, Apartado 50727, 28080 Madrid, Spain e-mail: willem.wamsteker@esa.int

Corresponding author: R. Vio, robertovio@tin.it

Received: 11 March 2003
Accepted: 11 July 2003

Abstract

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.