Optimum Quadratic Filters for Nonlinear Ultrasonic Imaging

In this paper, we present a novel method of a quadratic filter (QF) design for separating nonlinearity in pulse–echo signals in order to improve the quality of ultrasound images. The design of QFs is performed in frequency domain. The two-dimensional (2D) frequency response of the optimum QF is composed of two 2D Gaussian functions with different spreads in their major and minor axes. The centers of the Gaussian functions are positioned at frequency pairs where the contrast-to-tissue (CTR) ratio is maximal along the main diagonal, i.e., major axis, of 2D frequency plane. The different spreads in major and minor axes offer two degrees of freedom in maximizing the CTR and axial resolution simultaneously. This avoids the inherent tradeoff between contrast and axial resolution when linear filters are used (e.g. in second harmonic imaging). We demonstrate the performance of the approach with echo data from two imaging targets, i.e., a flow phantom and a quality assurance phantom.