Modeling the point spread function of paired angle multiplicative compounding in ultrasound

Spatial compounding has recently been introduced into modern commercial ultrasound systems. These systems are able to reduce angular dependent artifacts by averaging multiple images taken from different angles. In order to further reduce angular dependent artifacts, paired angle multiplicative compounding (PAMC) was recently introduced. The multiplication of pairs of images acquired from different angles reduces angular dependent artifacts while amplifying areas of signal. The quantification of improvement in PAMC images has proved difficult since images can become corrupt with high standard deviation background noise, limiting statistical evaluations from showing the true merit. In order to present a more theoretical understanding of PAMC, as well a way to gauge theoretical improvements, the point spread function (PSF) is used for analysis. This paper presents a simple geometrical model of the PAMC PSF based on the combination of two component Bscan PSFs. In order to validate the model, we compare it to a set of simulated PAMC PSFs created by varying the angle of paired multiplication. Both the theory and geometrical model are in agreement over the range [10°, 170°], allowing the optimal angle of paired multiplication to be determined to be 90°, yielding a PSF approximately 5x smaller than without pairing.