Band-pass filtering for optimal displacement estimation in the presence of grating lobes at large beam steering angles

Multi-dimensional ultrasound displacement estimation accuracy can be improved by projecting high resolution radio frequency (RF) based axial (along the beam) displacements estimated at multiple beam steering angles. When the beam steering angle increases or when the ratio between ultrasound frequency and element pitch becomes larger, grating lobe artifacts increase, which distorts the displacement estimation. This study investigates the effect of low-pass filtering with various cut-off frequencies on the displacement estimation accuracy. The goal is to determine if there is a frequency cut-off point below which the grating lobe distortion ceases to dominate the increase in displacement estimation accuracy due to the addition of main lobe signal. Ultrasound RF data were obtained of a homogeneous block phantom (10×10×4 cm³) before and after 400 μm vertical displacement applied using a micromanipulator. An L11-3 (Sonos 7500, Philips) and an L5-13 (Accuvix V10, Samsung) linear array transducer were used to acquire RF data at beam-steering angles of 0°, 10°, 20° and 30°. Both transducers had -20 dB bandwidths of 3-13 MHz. The measurements were repeated more than fifteen times. Pre- and post-displacement datasets were created after band-pass filtering with upper frequency cut-off points varying between 3.5 and 13.5 MHz in steps of 1 MHz. The lower frequency cut-off was kept fixed at 2.5 MHz. Axial displacements for each dataset were determined using a coarse-to-fine 2D cross-correlation based algorithm. The angular axial displacement fields were projected vertically and the root mean squared errors of the displacements were calculated. It was found that for optimal displacement estimation accuracy it was beneficial not to fully remove the grating lobe signal by low-pass filtering, but to set the upper frequency cut-off slightly higher. In that way, an essential part of the main lobe signal was maintained - nd the major part of the grating lobe artifacts was removed.