Sampling the Fourier transform along radial lines

Charles Dossal; Vincent Duval; Clarice Poon

doi:10.1137/16M1108807

Sampling the Fourier transform along radial lines

Charles Dossal, Vincent Duval, Clarice Poon

Department of Mathematical Sciences

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

11 Citations (SciVal)

Abstract

This article considers the use of total variation minimization for the recovery of a superposition of point sources from samples of its Fourier transform along radial lines. We present a numerical algorithm for the computation of solutions to this infinite dimensional problem. The theoretical results of this paper make precise the link between the sampling operator and the recoverability of the point sources.

Original language	English
Pages (from-to)	2540-2564
Number of pages	25
Journal	SIAM Journal on Numerical Analysis
Volume	55
Issue number	6
Early online date	2 Nov 2017
DOIs	https://doi.org/10.1137/16M1108807
Publication status	Published - 31 Dec 2017

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abstract = "This article considers the use of total variation minimization for the recovery of a superposition of point sources from samples of its Fourier transform along radial lines. We present a numerical algorithm for the computation of solutions to this infinite dimensional problem. The theoretical results of this paper make precise the link between the sampling operator and the recoverability of the point sources.",

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AB - This article considers the use of total variation minimization for the recovery of a superposition of point sources from samples of its Fourier transform along radial lines. We present a numerical algorithm for the computation of solutions to this infinite dimensional problem. The theoretical results of this paper make precise the link between the sampling operator and the recoverability of the point sources.

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DO - 10.1137/16M1108807

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JO - SIAM Journal on Numerical Analysis

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Sampling the Fourier transform along radial lines

Abstract

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