Discrete Wavelet Frames on the sphere

In this paper we exploit the Continuous Wavelet Transform (CWT) on the sphere introduced in [1, 2] to build the associated Discrete Wavelet Frames. We first explore half-continuous frames, i.e, frames where the position remains a continuous variable, and then move on to a fully discrete theory. This forces us to introduce the notion of controlled frames [5], which reflects the particular nature of the underlying theory, particularly the apparent conflict between dilation and the compacity of the S2 manifold. We conclude with some numerical illustrations and future work.