Blind calibration for arrays with an aberration layer in ultrasound imaging

We consider the scenario of finding the transfer function of an aberrating layer in front of an ultrasound array. We are interested in blindly estimating this transfer function without prior knowledge of the unknown ultrasound sources or ultrasound contrast image. The algorithm gives an exact solution if the matrix representing the aberration layer's transfer function is full rank, up to a scaling and reordering of its columns, which has to be resolved using some prior knowledge of the matrix structure. We provide conditions for the robustness of blind calibration in noise. Numerical simulations show that the method becomes more robust for shorter wavelengths, as the transfer function matrices then tend to be less ill-conditioned. Image reconstruction from simulated data using the k-Wave toolbox show that a well calibrated model removes some of the distortions introduced by an uncalibrated model, and improves the resolution for some of the sources.