MAPCUMBA: A fast iterative multi-grid map-making algorithm for CMB experiments

The data analysis of current Cosmic Microwave Background (CMB) experiments like BOOMERanG or MAXIMA poses severe challenges which already stretch the limits of current (super-) computer capabilities, if brute force methods are used. In this paper we present a practical solution for the optimal map making problem which can be used directly for next generation CMB experiments like ARCHEOPS and TopHat, and can probably be extended relatively easily to the full PLANCK case. This solution is based on an iterative multi-grid Jacobi algorithm which is both fast and memory sparing. Indeed, if there areNtod data points along the one dimensional timeline to analyse, the number of operations is of O(Ntod lnNtod) and the memory requirement is O(Ntod). Timing and accuracy issues have been analysed on simulated ARCHEOPS and TopHat data, and we discuss as well the issue of the joint evaluation of the signal and noise statistical properties.

[1]  A. Melchiorri,et al.  A flat Universe from high-resolution maps of the cosmic microwave background radiation , 2000, Nature.

[2]  Julian Borrill.  MADCAP - The Microwave Anisotropy Dataset Computational Analysis Package , 1999 .

[3]  William H. Press,et al.  Numerical recipes in C (2nd ed.): the art of scientific computing , 1992 .

[4]  Don Foster,et al.  TACI and BCMA are receptors for a TNF homologue implicated in B-cell autoimmune disease , 2000, Nature.

[5]  O. Lahav,et al.  Wiener Reconstruction of The Large Scale Structure , 1994, astro-ph/9410080.

[6]  Andrew H. Jaffe,et al.  Simultaneous Estimation of Noise and Signal in Cosmic Microwave Background Experiments , 1999, astro-ph/9909250.

[7]  Joseph Silk,et al.  The Wiener-Filtered COBE DMR Data and Predictions for the Tenerife Experiment , 1995 .

[8]  Julian Borrill.  The challenge of data analysis for future CMB observations , 1999 .

[9]  A. Banday,et al.  Mining the sky : proceedings of the MPA/ESO/MPE workshop held at Garching, Germany, July 31-August 4, 2000 , 2001 .

[10]  Max Tegmark,et al.  A method for subtracting foregrounds from multifrequency CMB sky maps , 1996 .

[11]  M. Janssen,et al.  Mapping the Sky with the COBE Differential Microwave Radiometers , 1992 .

[12]  E. Hivon,et al.  Iterative map-making for scanning experiments , 2000, astro-ph/0006052.

[13]  L. Knox,et al.  Determination of inflationary observables by cosmic microwave background anisotropy experiments. , 1995, Physical review. D, Particles and fields.