Robust Waveform Design of Ultrasound Arrays for Medical Imaging

Sound speed is an effective parameter in designing an optimal beamformer. In conventional ultrasound imaging systems, the beamformer is designed assuming a fixed value of speed, whereas the speed in a tissue is not known precisely and also may fluctuate by a great value. The errors in estimating sound speed may lead to a severe degradation in the reconstructed image, as mainlobe width and sidelobe level of the beampattern are sensitive to the speed variations. In this paper, we consider the design of a transmit beamformer, which is robust to the speed variations. The problem is formulated as a convex optimization problem versus the covariance matrix of the excitation waveforms to obtain a beampattern with predefined mainlobe width and a minimum sidelobe level for all possible variations of speed. Then, by eigen-analysis of the obtained covariance matrix, a set of nonidentical single-carrier short-pulses for the excitation waveforms were designed. Various simulations indicate that the proposed method can yield a robust beampattern whose mainlobe width and sidelobe level almost remain constant by 10% speed variations. In contrast, the beampatterns obtained by nonrobust methods suffer extensive changes.