Flexible-bandwidth Needlets

TL;DR

This paper introduces a flexible construction of spherical needlets that allows for variable support in the harmonic domain, enhancing adaptability for analyzing isotropic random fields with improved localization and uncorrelation properties.

Contribution

It presents a generalized needlet framework with variable harmonic support, extending the standard constructions and analyzing its properties for isotropic random fields.

Findings

Enhanced localization in high-frequency regimes

Broader assumptions for uncorrelation properties

Flexible harmonic support improves analysis capabilities

Abstract

We investigate here a generalized construction of spherical wavelets/needlets which admits extra-flexibility in the harmonic domain, i.e., it allows the corresponding support in multipole (frequency) space to vary in more general forms than in the standard constructions. We study the analytic properties of this system and we investigate its behaviour when applied to isotropic random fields: more precisely, we establish asymptotic localization and uncorrelation properties (in the high-frequency sense) under broader assumptions than typically considered in the literature.