First of all, thank you for actively developing k-Wave and maintaining this forum.
I would like to simulate realistic speckle in 2D/3D B-mode ultrasound images (7.6 MHz centre freq., 75% bandwidth). To to this, I added Gaussian noise to the density field. Next, I performed a convergence study (no attenuation, constant SOS of 1500 m/s) and noticed that the SNR of the simulated speckle converged very slowly.
To find the cause, I simplified the model by using a centre frequency of 1 Mhz in 1D. Instead of speckle, I simulated a discontinuous transition by prescribing a steep increase in the density field (from 1000 to 1100). I recorded the reflection of the wave and determined the maximum amplitude, for various grid spacings (between 5-150 um, which corresponds to 300-10 points per wavelength at the centre freq.).
The max. amplitude converges to the analytical solution (dashed line), although very slowly, see Figure 1. In an attempt to improve convergence, I tried to describe a band-limited discontinuous transition, using the rectangular function (sampled in the Fourier domain using the sinc function). This however, did not improve convergence, see Figure 2.
As I did not expect these results, I decided to have a look at k-Wave's code itself.
I noticed that the inverted rho_0 field was interpolated to the staggered grid using linear interpolation. I expected that a band-limited interpolation would be more accurate for band-limited signals, and I implemented this interpolation within k-Wave's code. I redid the convergence study with this modified code, and noticed the maximum reflection amplitude converged much faster with the band-limited discontinuous transition (convergence at already ~150 um).
This leads me to the following questions. Is this slow convergence for reflected waves typical, and are there other ways to improve it? Is the band-limited interpolation for the inverted rho_0 field a valid approach?
I would appreciate hearing your opinion on this.
Jan-Willem Muller
PhD candidate, PULS/e group, Eindhoven University of Technology
Figure 1:
Figure 2:
Download figures:
https://imgur.com/a/YbDi3hc