Introduction

The processing of signals whose domain is the 2-sphere or unit sphere1 has been an ongoing area of research in the past few decades and is becoming increasingly more active. Such signals are widely used in geodesy and planetary studies (Simons et al., 1997; Wieczorek and Simons, 2005; Simons et al., 2006; Audet, 2011). In many cases of interest flat Euclidean modeling of planetary and heavenly data does not work. Planetary curvature should be taken into account especially for small heavenly bodies such as the Earth, Venus, Mars, and the Moon (Wieczorek, 2007). Other applications, for the processing of signals on the 2-sphere, include the study of cosmic microwave background in cosmology (Wiaux et al., 2005; Starck et al., 2006; Spergel et al., 2007), 3D beamforming/sensing (Simons et al., 2006; Górski et al., 2005; Armitage and Wandelt, 2004; Ng, 2005; Wandelt and Górski, 2001; Rafaely, 2004; Wiaux et al., 2006), computer graphics and computer vision (Brechbühler et al., 1995; Schröder and Sweldens, 2000; Han et al., 2007), electromagnetic inverse problems (Colton and Kress, 1998), brain cortical surface analysis in medical imaging (Yu et al., 2007; Yeo et al., 2008), and channel modeling for wireless communication systems (Pollock et al., 2003; Abhayapala et al., 2003). This type of processing exhibits important differences from the processing of signals on Euclidean domains—such as time-based signals whose domain is the real line R, or 2D or 3D signals and images, whose domain is multi-dimensional, but still Euclidean.