Recovery of Sparse Positive Signals on the Sphere from Low Resolution Measurements

Tamir Bendory; Yonina C. Eldar

doi:10.1109/LSP.2015.2485281

Recovery of Sparse Positive Signals on the Sphere from Low Resolution Measurements

Tamir Bendory, Yonina C. Eldar

Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

This letter considers the problem of recovering a positive stream of Diracs on a sphere from its projection onto the space of low-degree spherical harmonics, namely, from its low-resolution version. We suggest recovering the Diracs via a tractable convex optimization problem. The resulting recovery error is proportional to the noise level and depends on the density of the Diracs. We validate the theory by numerical experiments.

Original language	English
Article number	7286741
Pages (from-to)	2383-2386
Number of pages	4
Journal	IEEE Signal Processing Letters
Volume	22
Issue number	12
Early online date	10 Oct 2015
DOIs	https://doi.org/10.1109/LSP.2015.2485281
State	Published - Dec 2015

Keywords

Convex optimization
spherical harmonics
super-resolution

All Science Journal Classification (ASJC) codes

Signal Processing
Electrical and Electronic Engineering
Applied Mathematics

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10.1109/LSP.2015.2485281

http://arxiv.org/abs/1508.06262License: Other

Cite this

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title = "Recovery of Sparse Positive Signals on the Sphere from Low Resolution Measurements",

abstract = "This letter considers the problem of recovering a positive stream of Diracs on a sphere from its projection onto the space of low-degree spherical harmonics, namely, from its low-resolution version. We suggest recovering the Diracs via a tractable convex optimization problem. The resulting recovery error is proportional to the noise level and depends on the density of the Diracs. We validate the theory by numerical experiments.",

keywords = "Convex optimization, spherical harmonics, super-resolution",

author = "Tamir Bendory and Eldar, \{Yonina C.\}",

note = "Publisher Copyright: {\textcopyright} 2015 IEEE.",

year = "2015",

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doi = "10.1109/LSP.2015.2485281",

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AU - Bendory, Tamir

AU - Eldar, Yonina C.

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N2 - This letter considers the problem of recovering a positive stream of Diracs on a sphere from its projection onto the space of low-degree spherical harmonics, namely, from its low-resolution version. We suggest recovering the Diracs via a tractable convex optimization problem. The resulting recovery error is proportional to the noise level and depends on the density of the Diracs. We validate the theory by numerical experiments.

AB - This letter considers the problem of recovering a positive stream of Diracs on a sphere from its projection onto the space of low-degree spherical harmonics, namely, from its low-resolution version. We suggest recovering the Diracs via a tractable convex optimization problem. The resulting recovery error is proportional to the noise level and depends on the density of the Diracs. We validate the theory by numerical experiments.

KW - Convex optimization

KW - spherical harmonics

KW - super-resolution

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U2 - 10.1109/LSP.2015.2485281

DO - 10.1109/LSP.2015.2485281

M3 - مقالة

SN - 1070-9908

VL - 22

SP - 2383

EP - 2386

JO - IEEE Signal Processing Letters

JF - IEEE Signal Processing Letters

IS - 12

M1 - 7286741

ER -

Recovery of Sparse Positive Signals on the Sphere from Low Resolution Measurements

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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