ABSTRACT
Signals are inherently defined on the sphere in a large number of applications found in various branches of science and engineering, including, but not limited to, geophysics, planetary science, medical imaging, cosmology, and acoustics. Slepian basis or Slepian functions are band-limited in spherical harmonic domain, orthogonal over the whole sphere and region, and serve as complete basis for the representation of band-limited signals on the sphere. Exploiting these characteristics, Slepian functions on the sphere have been used for localized spectral and spatial analyses, signal estimation from incomplete measurements, and sparse and efficient representations of spherical signals in a wide range of applications found in geophysics, cosmology and planetary studies, optics, and computer graphics, to name a few. This chapter presents an illustration to show that the use of Slepian basis enables sparse representation of a spatially concentrated band-limited signal.
