Analysis of CMB maps with 2D wavelets

¹ Instituto de Física de Cantabria, Fac. Ciencias, Avda. de los Castros s/n, 39005 Santander, Spain
² Dpto. Física Moderna, Universidad de Cantabria, Avda. de los Castros s/n, 39005 Santander, Spain
³ Dpto. de Electrónica y Computadores, Universidad de Cantabria, Avda. de los Castros s/n, 39005 Santander, Spain
⁴ Dpto. Matemáticas, Universidad de Oviedo, c/ Calvo Sotelo s/n, 33007 Oviedo, Spain
⁵ Astronomy Dept. & Center for Particle Astrophysics, University of California, 601 Campbell Hall, Berkeley, CA 94720, U.S.A.
⁶ Dpto. de Física, Universidad de Oviedo, c/ Calvo Sotelo s/n, 33007 Oviedo, Spain
⁷ Osservatorio Astronomico di Padova, vicolo dell'osservatorio n5, 35122 Padova, Italy

Send offprint request to: L. Cayón

Received: 11 March 1999
Accepted: 26 August 1999

Abstract

We consider the 2D wavelet transform with two scales to study sky maps of temperature anisotropies in the cosmic microwave background radiation (CMB). We apply this technique to simulated maps of small sky patches of size and pixels. The relation to the standard approach, based on the , is established through the introduction of the scalogram. We consider temperature fluctuations derived from standard, open and flat-Λ Cold Dark Matter (CDM) models. We analyze CMB anisotropies maps plus uncorrelated Gaussian noise (uniform and non-uniform) at different levels. We explore in detail the denoising of such maps and compare the results with other techniques already proposed in the literature. Wavelet methods provide a good reconstruction of the image and power spectrum. Moreover, they are faster than previously proposed methods.