Robust reconstruction of scattering surfaces using a linear microphone array

A statistical inverse method for the reconstruction of rough surfaces from acoustic scattering

“…The proposed method is here applied to the measured data acquired in Ref. [2] using a broadband source and a 34microphone array. 21 frequency lines between 16 kHz and 21 kHz are used, thus resulting in 34 × 21 = 714 complex sound pressure experimental values.…”

“…In this work, the Kirchhoff approximation [7] is used, yielding an explicit expression of the sound pressure p at a microphone position r as a function of the source position, wavenumber, and surface elevation profile ζ(x) [1,2,4],…”

Simultaneous parametric estimation of shape and impedance of a scattering surface using a multi-frequency fast indirect boundary element method

“…Acoustic scattering can be utilized for noninvasive material characterization including surface impedance characterization and surface shape reconstruction in free field. For rough surfaces, i.e., smooth perturbations of an otherwise flat plane [1], the characterization of surface shape, e.g., seafloor, sea waves, and river surfaces [2,3,4,5,6], is of vital importance in many applications such as weather forecast, flood prevention, and geophysical inspection. In these cases, the surface shape can be estimated by fitting an acoustic scattering model onto a measurement of the scattered field using a number of sensors placed in front of the surface of interest [7].…”

“…In these cases, the surface shape can be estimated by fitting an acoustic scattering model onto a measurement of the scattered field using a number of sensors placed in front of the surface of interest [7]. Two approaches for the surface reconstruction are common, namely inverting the boundary integral equations that define the forward problem [1,8,9,10,11], or alternatively iterative shape updating by an optimization framework seeking to minimize the difference between the predicted and observed acoustic field [12]. Most of the previous studies rely on approximation approaches such as Kirchhoff approximation [1,9], small perturbation expansion [8], Milder's operator expansion [10], and Rytov approximation [13].…”

“…Two approaches for the surface reconstruction are common, namely inverting the boundary integral equations that define the forward problem [1,8,9,10,11], or alternatively iterative shape updating by an optimization framework seeking to minimize the difference between the predicted and observed acoustic field [12]. Most of the previous studies rely on approximation approaches such as Kirchhoff approximation [1,9], small perturbation expansion [8], Milder's operator expansion [10], and Rytov approximation [13]. These approximations generally simplify the inversion of the system matrix and are computationally efficient to use.…”