In this report we derive a model for a highly scattering medium, implemented as a set of MATLAB functions. This model is used to analyze an approach for using time-reversal to enhance the detection of a single frequency source in a highly scattering medium. The basic approach is to apply the singular value decomposition to the multistatic response matrix for a time-reversal array system. We then use the array in a purely passive mode, measuring the response to the presence of a source. The measured response is projected onto the singular vectors, creating a time-reversal pseudo-spectrum. We can then apply standard detection techniques to the pseudo-spectrum to determine the presence of a source. If the source is close to a particular scatterer in the medium, then we would expect an enhancement of the inner product between the array response to the source with the singular vector associated with that scatterer. In this note we begin by deriving the Foldy-Lax model of a highly scattering medium, calculate both the field emitted by the source and the multistatic response matrix of a time-reversal array system in the medium, then describe the initial analysis approach.
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