Sampling sparse signals on the sphere: Algorithms and applications

Ivan Dokmanić, Yue M. Lu

Research output: Contribution to journalReview article

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 languageEnglish (US)
Article number7265080
Pages (from-to)189-202
Number of pages14
JournalIEEE Transactions on Signal Processing
Volume64
Issue number1
DOIs
StatePublished - Jan 1 2016
Externally publishedYes

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

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