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A Radon-transform-based formula for reconstructing acoustic sources from the scattered fields

Xiaodong Liu, Jing Wang

Abstract

We propose a novel indicator function for reconstructing acoustic sources from multi-frequency near-field measurements. The theoretical basis is established by a formula relating the scattered field to the source function through the Radon transform. Such a representation enables us to recover the source function directly. The efficiency and robustness of the novel indicator function are verified by several numerical examples.

A Radon-transform-based formula for reconstructing acoustic sources from the scattered fields

Abstract

We propose a novel indicator function for reconstructing acoustic sources from multi-frequency near-field measurements. The theoretical basis is established by a formula relating the scattered field to the source function through the Radon transform. Such a representation enables us to recover the source function directly. The efficiency and robustness of the novel indicator function are verified by several numerical examples.
Paper Structure (3 sections, 1 theorem, 14 equations, 4 figures, 1 algorithm)

This paper contains 3 sections, 1 theorem, 14 equations, 4 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. A novel indicator
  3. Numerical examples and discussions

Key Result

Theorem 2.1

Let $S(z)\in L^2({\mathbb R}^2)$ be a real-valued source function with compact support $\Omega\subset B_R(0)$, then

Figures (4)

  • Figure 1: The true sources.
  • Figure 2: Reconstructions of Example 1.
  • Figure 3: Reconstructions of Example 2.
  • Figure 4: Reconstructions of Example 3.

Theorems & Definitions (2)

  • Theorem 2.1
  • proof