Sampling the Fourier transform along radial lines

TL;DR

This paper explores total variation minimization for recovering point sources from Fourier transform samples along radial lines, providing a numerical algorithm and theoretical insights into the sampling and recovery process.

Contribution

It introduces a novel numerical algorithm for this infinite dimensional problem and establishes theoretical links between sampling operators and source recoverability.

Findings

Developed a numerical algorithm for Fourier sampling along radial lines.

Established theoretical conditions for successful point source recovery.

Enhanced understanding of the sampling operator’s role in source recoverability.

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.