# Fast Directional Continuous Spherical Wavelet Transform Algorithms

@article{McEwen2005FastDC, title={Fast Directional Continuous Spherical Wavelet Transform Algorithms}, author={Jason D. McEwen and Michael P. Hobson and Daniel J. Mortlock and Anthony N. Lasenby}, journal={IEEE Transactions on Signal Processing}, year={2005}, volume={55}, pages={520-529} }

We describe the construction of a spherical wavelet analysis through the inverse stereographic projection of the Euclidean planar wavelet framework, introduced originally by Antoine and Vandergheynst and developed further by Wiaux Fast algorithms for performing the directional continuous wavelet analysis on the unit sphere are presented. The fast directional algorithm, based on the fast spherical convolution algorithm developed by Wandelt and Goacuterski, provides a savings of O(radicNpix) over…

## 64 Citations

### A directional continuous wavelet transform on the sphere

- MathematicsArXiv
- 2006

A new construction of a directional continuous wavelet analysis on the sphere is derived herein. We adopt the harmonic scaling idea for the spherical dilation operator recently proposed by Sanz et…

### Wavelets and wavelet-like transforms on the sphere and their application to geophysical data inversion

- GeologyOptical Engineering + Applications
- 2011

This paper focuses on spherical wavelets developed for geophysical applications on the cubed sphere, and the Slepian "tree", a new construction that combines a quadratic concentration measure with wavelet-like multiresolution.

### On the computation of directional scale-discretized wavelet transforms on the sphere

- Computer ScienceOptics & Photonics - Optical Engineering + Applications
- 2013

This work presents exact and efficient algorithms to compute the scale-discretized wavelet transform of band-limited signals on the sphere and releases a new version of S2DW that is parallelized and contains additional code optimizations.

### Exact reconstruction with directional wavelets on the sphere

- Physics
- 2008

A new formalism is derived for the analysis and exact reconstruction of band-limited signals on the sphere with directional wavelets. It represents an evolution of a previously developed wavelet…

### Directional spin wavelets on the sphere

- Computer ScienceArXiv
- 2015

A directional spin wavelet framework on the sphere is constructed by generalising the scalar scale-discretised wavelet transform to signals of arbitrary spin and is able to probe the directional intensity of spin signals.

### Complex Data Processing: Fast Wavelet Analysis on the Sphere

- Computer Science
- 2007

In the general context of complex data processing, this article reviews a recent practical approach to the continuous wavelet formalism on the sphere. This formalism notably yields a correspondence…

### Fast Directional Spatially Localized Spherical Harmonic Transform

- Computer ScienceIEEE Transactions on Signal Processing
- 2013

Since such typical data-sets on the sphere are of considerable size and the directional SLSHT is intrinsically computationally demanding depending on the band-limits of the signal and window, a fast algorithm for the efficient computation of the transform is developed.

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