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) |
|---|---|
| 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 |
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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
Cite this
Sampling sparse signals on the sphere : Algorithms and applications. / Dokmanić, Ivan; Lu, Yue M.
In: IEEE Transactions on Signal Processing, Vol. 64, No. 1, 7265080, 01.01.2016, p. 189-202.Research output: Contribution to journal › Review article
}
TY - JOUR
T1 - Sampling sparse signals on the sphere
T2 - Algorithms and applications
AU - Dokmanić, Ivan
AU - Lu, Yue M.
PY - 2016/1/1
Y1 - 2016/1/1
N2 - 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.
AB - 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.
KW - Annihilation filter
KW - diffusion sampling
KW - finite rate of innovavtion
KW - shot noise removal
KW - sound source localization
KW - sparse sampling
KW - sphere
KW - spherical harmonics
UR - http://www.scopus.com/inward/record.url?scp=85009355271&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85009355271&partnerID=8YFLogxK
U2 - 10.1109/TSP.2015.2478751
DO - 10.1109/TSP.2015.2478751
M3 - Review article
AN - SCOPUS:85009355271
VL - 64
SP - 189
EP - 202
JO - IEEE Transactions on Signal Processing
JF - IEEE Transactions on Signal Processing
SN - 1053-587X
IS - 1
M1 - 7265080
ER -