Introducing Mexican needlets for CMB analysis: Issues for practical applications and comparison with standard needlets

Understand

Over the last few years, needlets have a emerged as a useful tool for the analysis of Cosmic Microwave Background (CMB) data.

• Our aim in this paper is first to introduce in the CMB literature a different form of needlets, known as Mexican needlets, first discussed in the mathematical literature by Geller and Mayeli (2009a,b).
• We then proceed with an extensive study of the properties of both standard and Mexican needlets; these properties depend on some parameters which can be tuned in order to optimize the performance for a given application.
• Our second aim in this paper is then to give practical advice on how to adjust these parameters in order to achieve the best properties for a given problem in CMB data analysis.