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Source splitting via the point source method

Potthast, Roland, Fazi, Filippo and Nelson, Philip A. (2010) Source splitting via the point source method Inverse Problems, 26, (4), p. 45002. (doi:10.1088/0266-5611/26/4/045002).

Record type: Article

Abstract

We introduce a new algorithm for source identification and field splitting based on the point source method (Potthast 1998 A point-source method for inverse acoustic and electromagnetic obstacle scattering problems IMA J. Appl. Math. 61 119–40, Potthast R 1996 A fast new method to solve inverse scattering problems Inverse Problems 12 731–42). The task is to separate the sound fields uj, j = 1, ..., n of n \in \mathbb {N} sound sources supported in different bounded domains G1, ..., Gn in \mathbb {R}^3 from measurements of the field on some microphone array—mathematically speaking from the knowledge of the sum of the fields u = u1 + sdotsdotsdot + un on some open subset ? of a plane. The main idea of the scheme is to calculate filter functions g_1, \ldots, g_n, n\in \mathbb {N} , to construct uell for ell = 1, ..., n from u|? in the form

u_{\ell }(x) = \int _{\Lambda } g_{\ell,x}(y) u(y) {\,\rm d}s(y), \qquad \ell =1,\ldots, n.

We will provide the complete mathematical theory for the field splitting via the point source method. In particular, we describe uniqueness, solvability of the problem and convergence and stability of the algorithm. In the second part we describe the practical realization of the splitting for real data measurements carried out at the Institute for Sound and Vibration Research at Southampton, UK. A practical demonstration of the original recording and the splitting results for real data is available online.

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More information

Published date: 1 March 2010
Keywords: inverse problems, source localization and parameter estimation, acoustic array systems and processing, beam-forming
Organisations: Inst. Sound & Vibration Research, Fluid Dynamics & Acoustics Group

Identifiers

Local EPrints ID: 147103
URI: http://eprints.soton.ac.uk/id/eprint/147103
ISSN: 0266-5611
PURE UUID: 91ab92c3-68f0-4037-8986-68116a2bad4f

Catalogue record

Date deposited: 23 Apr 2010 09:10
Last modified: 18 Jul 2017 23:03

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