The approach functions by linearly simulating scattered wavefronts at shallow depths, and then time-shifting these wavefronts to deeper depths. The simulation only requires specification of the first and last scatterers encountered by a multiply reflected wave and a third point that establishes the arrival time of the reverberation. To maintain appropriate 2D correlation, this set of three points is fixed for the entire simulation and is shifted as with a normal linear simulation scattering field. We show example images, and we compute first order speckle statistics as a function of scatterer density. We perform ex vivo measures of reverberation where we find that the average speckle SNR is 1.73, which we can simulate with 2 reverberation scatterers per resolution cell. We also compare ex vivo lateral speckle statistics to those from linear and pseudo non-linear simulation data. Finally, the van Cittert-Zernike curve was shown to match empirical and theoretical observations.
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Brett Byram, Jasmine Shu, "A pseudo non-linear method for fast simulations of ultrasonic reverberation," Proc. SPIE 9790, Medical Imaging 2016: Ultrasonic Imaging and Tomography, 97900U (1 April 2016);