Locally Supported Orthogonal Wavelet Bases on the Sphere via Stereographic Projection

Figure 4

(a) An example of kernel of spherical harmonics: localized, but not locally supported; (b) the initial data set, in spherical coordinates (𝜃,𝜑); (c) Its approximation at level 6 using a spherical harmonics kernel; (d) approximation at first level using the spherical wavelet associated to the Daubechies wavelet db2.

(a)

(b)

(c)

(d)