Dokmanic, IvanLu, Yue M.2015-03-032015-03-032015-03-03201610.1109/Tsp.2015.2478751https://infoscience.epfl.ch/handle/20.500.14299/111822WOS:000366834300014We propose a sampling scheme that can perfectly reconstruct a collection of spikes on the sphere from samples of their lowpass-filtered observations. Central to our algorithm is a generalization of the annihilating filter method, a tool widely used in array signal processing and finite-rate-of-innovation (FRI) sampling. The proposed algorithm can reconstruct $K$ spikes from $(K+\sqrt{K})^2$ spatial samples. This sampling requirement improves over previously known FRI sampling schemes on the sphere by a factor of four for large $K$. We showcase the versatility of the proposed algorithm by applying it to three different problems: 1) sampling diffusion processes induced by localized sources on the sphere, 2) shot noise removal, and 3) sound source localization (SSL) by a spherical microphone array. In particular, we show how SSL can be reformulated as a spherical sparse sampling problem.spheresparse samplingdiffusion samplingsound source localizationannihilation filtershot noise removalspherical harmonicsLCAV-SSPtext::journal::journal article::research article