Curvelet transform on the sphere

Abstract

Spherical maps occur in a range of applications for instance in geophysics or in astrophysics with the study of the cosmic microwave background (CMB) radiation field, where observations are over the whole sky. Analyzing these images requires specific tools. This paper describes a new multiscale decomposition for data on the sphere, namely the curvelet transform on the sphere. The curvelet transform, in its first step, requires the use of an isotropic wavelet transform. Therefore, our new curvelet transform also includes a new wavelet transform on the sphere which has properties similar to those of the a trous isotropic wavelet transform.