Concentration Uncertainty Principles for Signals on the Unit Sphere

Abstract

The uncertainty principle is an important and powerful tool, with many applications in signal processing. This paper presents two concentration uncertainty principles for signals on the sphere which relate the localization of the concentration of a signal in spatial and spectral domains, as an analogue of the general Donoho and Stark uncertainty principles in time-frequency analysis. Using the spherical and spectral truncation operators, we derive the L1-norm and L2-norm uncertainty principles which respectively relate the signal concentration in spatial and spectral domains as absolute value and the energy of a signal. We also analyze the sharpness of the bound imposed by the derived L2-norm uncertainty principle. The proposed uncertainty measures can be applied to signal processing problems on the sphere. Show more