Noise Source Localization in an Attenuating Medium

Abstract

Abstract. In this paper we consider the problem of reconstructing the spatial support of noise sources from boundary measurements using cross correlation techniques. We consider media with and without attenuation and provide efficient imaging functionals in both cases. We also discuss the case where the noise sources are spatially correlated. We present numerical results to show the viability of the different proposed imaging techniques.AMS subject classifications. 35L05, 35R30; Secondary 47A52, 65J20Key words. Passive imaging, wave propagation, attenuation 1. Introduction. The main objective of this paper is to present an original approach for detecting the spatial support of noise sources in an attenuating electromagnetic or acoustic medium. The main application envisaged by our work concerns robotic sound or microwave noise source localization and tracking; see, for instance, [12,13,14,15,21]. It is a quite challenging problem to build an autonomous robotic system for finding, investigating, and modeling ambient electromagnetic or sound noise sources in the environment. On the other hand, a robot can be a rather significant source of electromagnetic and/or acoustic noise. Detecting or hiding the robot to reduce the risk of being detected is also another challenging problem. As will be seen in this paper, at least two robots have to be used in order to locate noise sources by cross correlation.Passive imaging from noisy signals has been a very active field. It has been shown that the Green's function of the wave equation in an inhomogeneous medium can be estimated by cross correlating the signals emitted by ambient noise sources and recorded by a passive sensor array [7,17,18]. The idea has been used for travel time estimation and background velocity estimation in geophysical contexts, and also for passive sensor imaging of reflectors [9,10], which consists of backpropagating or migrating the cross correlation matrix of the recorded signals. The relation between the cross correlation of ambient noise signals recorded at two observation points and the Green's function between these two points can be proved using the Helmholtz-Kirchhoff identity when the ambient noise sources surround the observation region [5,20] or using stationary phase arguments in the high-frequency regime when the support ambient noise sources are spatially limited [9,19].In [11] the noise source imaging problem is analyzed in a high-frequency asymptotic regime and the support of the noise sources is identified with a special Radon transform. Here we shall consider a general context in non-attenuating and attenuating media. In attenuating media, one can think to first pre-process the data as originally done in [4] and then backpropagate the cross correlation of the pre-processed data in a non-attenuating medium. However, this seems impossible because the recorded data are very long and usually contain a huge amount of additional measurement noise. Instead, we backpropagate the cross correlation of the recorded data with a regularized versi...

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