Ultrasonic imaging through aberrating layers using covariance matching

We consider the scenario of finding the transfer function of an aberrating layer in front of a receiving ultrasound (US) array, assuming a separate non-aberrated transmit source. We propose a method for blindly estimating this transfer function without exact knowledge of the ultrasound sources or acoustic contrast image, and without directly measuring the transfer function using a separate controlled calibration experiment. Instead, the measurement data of many unknown random images is collected, such as from blood flow, and its second-order statistics are exploited. A measurement model is formulated that explicitly defines the layer's transfer function. A covariance domain problem is then defined to eliminate the image variable, and it is solved for the layer's transfer function using manifold-based optimization. The proposed approach and calibration algorithm are evaluated on a range of challenging and realistic simulations using the k-Wave toolbox. Our results show that, given a sufficiently efficient parameterization of the layer's transfer function, and by jointly estimating the transfer function at multiple frequencies, the proposed algorithm is able to obtain an accurate estimate. Subsequent simulated imaging experiments using the obtained transfer function also show increased imaging performance in various aberrating layers, including a skull layer.