Robust Waveform Design of Ultrasound Arrays for Medical Imaging

Abstract

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.