Mathematical Analysis of Ultrafast Ultrasound Imaging

TL;DR

This paper offers a mathematical framework for ultrafast ultrasound imaging, deriving the point spread function, modeling blood flow, and demonstrating clutter removal via singular value decomposition to enhance blood vessel imaging.

Contribution

It introduces a mathematical analysis of ultrafast ultrasound, including point spread function derivation and a novel clutter removal method using SVD for improved blood flow imaging.

Findings

Successful clutter removal using SVD

High-resolution blood vessel imaging achieved

Mathematical characterization of system properties

Abstract

This paper provides a mathematical analysis of ultrafast ultrasound imaging. This newly emerging modality for biomedical imaging uses plane waves instead of focused waves in order to achieve very high frame rates. We derive the point spread function of the system in the Born approximation for wave propagation and study its properties. We consider dynamic data for blood flow imaging, and introduce a suitable random model for blood cells. We show that a singular value decomposition method can successfully remove the clutter signal by using the different spatial coherence of tissue and blood signals, thereby providing high-resolution images of blood vessels, even in cases when the clutter and blood speeds are comparable in magnitude. Several numerical simulations are presented to illustrate and validate the approach.