A stochastic approach to delays optimization for narrowband transmit beam pattern in medical ultrasound

In ultrasound imaging, state-of-the-art methods for transmit beam pattern (TBP) optimization have well-known drawbacks like non-uniform beam width over depth, significant side lobes, and quick energy drop-out beyond the focal region. To overcome these limitations, we develop a TBP optimization approach by focusing on its narrowband approximation and considering transmit delays as free variables instead of linked to specific focal depths. We formulate a non-linear Least Squares problem to minimize the difference between the TBP corresponding to a set of delays and the desired one, modeled as a 2D rectangle elongated along the beam axis. Three metrics are defined to quantitatively evaluate the results. Results obtained by synthetic simulations show that the main lobe width is considerably more intense ( \(+31.5\%\) $+31.5\%$ on average) and uniform ( \(+28.7\%\) $+28.7\%$ on average) over the whole depth range compared to classical focalized Beam Patterns. The application of the method to elastography shows improvements in the ultrasound energy concentration along a desired axis.