Sampling spherical finite rate of innovation signals

We propose a sampling scheme that can perfectly reconstruct a collection of spikes on the sphere from samples of their low-pass filtered observations. The proposed algorithm can reconstruct K spikes from (K + √K)² spatial samples, thus improving over previously known FRI sampling schemes on the sphere by a factor of up to four. Further, we show how multiple sound source localization (SSL) by a spherical microphone array can be transformed into a spherical FRI sampling problem. We certify the effectiveness of the proposed algorithm by using it to solve the SSL problem.