MODELLING ULTRASOUND IMAGING AS A LINEAR, SHIFT-VARIANT SYSTEM

James Ng, Richard Prager, Nick Kingsbury, Graham Treece and Andrew Gee

21 January 2005

We solve the equation that governs acoustic wave propagation in an inhomogeneous medium to show that the radio frequency ultrasound signal can be expressed as the result of filtering the tissue reflectivity by a point-spread function. We extend the analysis to make the link between the radio frequency ultrasound signal and the representation of ultrasound scatterers as small vectors with random phase in the complex plane. Others have previously performed parts of this analysis. The contribution of the present paper it to provide a single coherent treatment emphasizing the assumptions that have to be made and the physical consequences of the models derived. This leads to insights into the interaction of monopole and dipole scattering, useful techniques for simulating and analysing speckle statistics in the complex plane and a new expression for the normalised covariance of the analytic radio frequency ultrasound signal in terms of the complex envelope of the point-spread function.

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