Abstract: We have previously introduced an ultrasonic imaging
approach that combines harmonic-sensitive pulse sequences with a
post-beamforming quadratic kernel derived from a second-order
Volterra filter (SOVF). This approach is designed to produce images
with high sensitivity to nonlinear oscillations from microbubble
ultrasound contrast agents (UCA) while maintaining high levels of
noise rejection. In this paper, a two-step algorithm for computing the
coefficients of the quadratic kernel leading to reduction of tissue
component introduced by motion, maximizing the noise rejection and
increases the specificity while optimizing the sensitivity to the UCA
is presented. In the first step, quadratic kernels from individual
singular modes of the PI data matrix are compared in terms of their
ability of maximize the contrast to tissue ratio (CTR). In the second
step, quadratic kernels resulting in the highest CTR values are
convolved. The imaging results indicate that a signal processing
approach to this clinical challenge is feasible.