Acoustic imaging using under-determined inverse approaches: Frequency limitations and optimal regularization

A New Method for Determining Optimal Regularization Parameter in Near‐Field Acoustic Holography

“…Compared with prior strategy, the posterior strategy does not require the prior knowledge of the noise variance in advance. The generalized cross validation (GCV) method [25] and the L-curve method [26,27] as the posterior strategy are the two most widely used methods for selecting the optimal regularization parameters, both of which have good adaptability in the engineering application. Although the convergence of the GCV criterion has been proven theoretically, the GCV function curve sometimes is too flat, which makes it difficult to determine the minimum value of the GCV function.…”

Inverse problem with beamforming regularization matrix applied to sound source localization in closed wind-tunnel using microphone array

“…It is well known that the minimization problem without regularization is ill-conditioned [13][14][15], meaning that the solution can be very sensitive to measurement noise or model uncertainties, therefore a discrete smoothing norm is used to regularize the unknown solution q λβ . We can define the discrete smoothing norm as…”

Acoustic imaging in application to reconstruction of rough rigid surface with airborne ultrasound waves

“…This leads to ill-conditioned matrix with multiple inverse solutions. The matrix inverse is based on the singular value decomposition method (SVD) and variety of regularisation methods such as truncated SVD and Tikhonov regularisation technique in conjunction with the methods optimising the choice of regularisation parameter 9,12,13 . In this paper the direct method based on the Kirchhoff integral discretisation is employed to reconstruct the elevation profile of a static, rigid rough surface.…”

“…We also assume that q z in equation (8) is approximately constant for all the receivers with the value given by the direction specular to that of the source, q s z (x m ) = 2kz s /R s . The resulting ill-conditioned matrix can be regularised with the help of Tikhonov regularization technique 13 and the surface elevation at point x m can be approximated with…”

“…Equation (15) is conditioned with the Tikhonov regularisation parameter β identified with the help of generalised cross validation (GCV) technique 13 . The application of the SVD in equation (15) is performed with a library function available in commercial software Matlab R2015a.…”