Recovery of Sparse Positive Signals on the Sphere from Low Resolution Measurements

Abstract

This letter considers the problem of recovering a positive stream of Diracs on a sphere from its projection onto the space of low-degree spherical harmonics, namely, from its low-resolution version. We suggest recovering the Diracs via a tractable convex optimization problem. The resulting recovery error is proportional to the noise level and depends on the density of the Diracs. We validate the theory by numerical experiments.

References in corpus (2)

• Super-resolution on the Sphere using Convex Optimization
• Continuous wavelet transforms on $n$-dimensional spheres

Cited by in corpus (1)

• Slepian Spatial-Spectral Concentration Problem on the Sphere: Analytical Formulation for Limited Colatitude-Longitude Spatial Region