http://www.k-wave.org/forum/topic/slow-reflection-ampitude-convergence-and-improvement-suggestion Support for the k-Wave MATLAB toolbox en-US Wed, 13 May 2026 00:22:10 +0000 http://bbpress.org/?v=1.0.2 q http://www.k-wave.org/forum/search.php http://www.k-wave.org/forum/topic/slow-reflection-ampitude-convergence-and-improvement-suggestion#post-8503 Mon, 25 Apr 2022 19:02:09 +0000 bencox 8503@http://www.k-wave.org/forum/ <p>Hi Jan-Willem,</p> <p>This is interesting. Did you get to the bottom of this behaviour? We tried something similar with the sound speed previously but it didn't improve matters. There's a discussion of the convergence of the reflection coefficient with the usual set-up in this paper<br /> <a href="https://doi.org/10.1121/1.4712021">https://doi.org/10.1121/1.4712021</a>.</p> <p>Best wishes<br /> Ben </p> http://www.k-wave.org/forum/topic/slow-reflection-ampitude-convergence-and-improvement-suggestion#post-8460 Tue, 22 Feb 2022 17:10:51 +0000 jw 8460@http://www.k-wave.org/forum/ <p>First of all, thank you for actively developing k-Wave and maintaining this forum.<br /> 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. </p> <p>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.).</p> <p>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.</p> <p>As I did not expect these results, I decided to have a look at k-Wave's code itself.<br /> 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). </p> <p>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?</p> <p>I would appreciate hearing your opinion on this.</p> <p>Jan-Willem Muller<br /> PhD candidate, PULS/e group, Eindhoven University of Technology</p> <p>Figure 1:<br /> <img src="https://i.imgur.com/JjHmSiV.jpeg" /></p> <p>Figure 2:<br /> <img src="https://i.imgur.com/6d41l2t.jpeg" /></p> <p>Download figures:<br /> <a href="https://imgur.com/a/YbDi3hc" rel="nofollow">https://imgur.com/a/YbDi3hc</a> </p>