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 K spikes from (K + √K)2 spatial samples. For large K, 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.
Original language | English (US) |
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Article number | 7265080 |
Pages (from-to) | 189-202 |
Number of pages | 14 |
Journal | IEEE Transactions on Signal Processing |
Volume | 64 |
Issue number | 1 |
DOIs | |
State | Published - Jan 1 2016 |
Externally published | Yes |
Keywords
- Annihilation filter
- diffusion sampling
- finite rate of innovavtion
- shot noise removal
- sound source localization
- sparse sampling
- sphere
- spherical harmonics
ASJC Scopus subject areas
- Signal Processing
- Electrical and Electronic Engineering