研究目的

To propose a sampling scheme that can perfectly reconstruct a collection of spikes on the sphere from samples of their lowpass-filtered observations, improving over previously known FRI sampling schemes on the sphere by a factor of four.

研究成果

The paper presents a new sampling theorem for sparse signals on the sphere, showing how to reconstruct sparse collections of spikes from their lowpass-filtered observations. The algorithm uses the available spectrum more efficiently than existing schemes, reducing the number of samples required. The versatility of the algorithm is demonstrated through applications in sampling diffusion processes, shot noise removal, and sound source localization.

研究不足

The algorithm does not require any separation between the Diracs in the noiseless setting, but a theoretical analysis of the stability in the presence of noise is not yet available. The number of Diracs is assumed to be known up to a range.