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• W1737290388 abstract "We 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 <formula formulatype=inline xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex Notation=TeX>$K$</tex></formula> spikes from <formula formulatype=inline xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex Notation=TeX>$(K+sqrt{K})^2$</tex></formula> spatial samples. For large <formula formulatype=inline xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex Notation=TeX>$K$</tex> </formula> , this sampling requirement improves over previously known FRI sampling schemes on the sphere by a factor of four. We showcase the versatility of the proposed algorithm by applying it to three 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." @default.
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• W1737290388 date "2016-01-01" @default.
• W1737290388 modified "2023-10-03" @default.
• W1737290388 title "Sampling Sparse Signals on the Sphere: Algorithms and Applications" @default.
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• W1737290388 doi "https://doi.org/10.1109/tsp.2015.2478751" @default.
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