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Mathematical Analysis of Ultrafast Ultrasound Imaging

by G. S. Alberti and H. Ammari and F. Romero and T. Wintz

(Report number 2016-24)

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.

Keywords: Ultrafast ultrasound imaging, singular value decomposition, Casorati matrix, blood flow imaging.

@Techreport{AARW16_661,
  author = {G. S. Alberti and H. Ammari and F. Romero and T. Wintz},
  title = {Mathematical Analysis of Ultrafast Ultrasound Imaging},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2016-24},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2016/2016-24.pdf },
  year = {2016}
}

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