Digital Signal Processing Reference
In-Depth Information
10.10 SUMMARY
In this chapter, multiscale transforms on the sphere were presented: the wavelet
transform, the ridgelet transform, and the curvelet transform. The described trans-
forms have many desirable properties such as invertibility. With the wealth of these
multiscale analysis tools and the associated discrete analysis and synthesis trans-
forms on the sphere at hand, several problems with spherical data can be attacked
effectively. Applications to denoising, image decomposition, and inpainting on the
sphere were given. Few applications to challenging data analysis problems in physics
and astrophysics were reported. These tools are expected to be valuable in many
other applications. To disseminate them, a toolbox implementing both the trans-
forms and the denoising, separation, and inpainting algorithms is freely available to
interested users.
