Impact of starting model on waveform inversion in ultrasound tomography

Abstract

The convergence of waveform inversion in ultrasound tomography is heavily impacted by the choice of starting model. Ray tomography is often used as the starting model for waveform inversion; however, artifacts resulting from ray tomography can continue to persist during waveform inversion. On the other hand, a homogeneous starting model for waveform inversion may result in cycle skipping artifacts if the frequency of the transmitted waveform is too high or the error between the starting model and ground-truth is too large. Clinical in vivo breast data suggests that waveform inversion from a homogeneous starting model is sufficient for an accurate reconstruction of the speed of sound if the starting model is close enough to the average speed of sound in the medium and the starting frequency for waveform inversion is sufficiently low to avoid cycle skipping. Comparing the results of waveform inversion using ray tomography and a homogeneous sound speed as initial models, the homogeneous starting model avoids oscillatory artifacts produced by ray tomography at the edges of the breast. Although the RMS error between the two waveform inversion results is 29.6 m/s, most of the error is the result of reconstruction artifacts at the edges of the breast. When the RMS error is measured inside the breast away from its boundaries, this RMS error drops down to 11.5 m/s.

Imaging stroke through the skull using ultrasound tomography

“…The artifacts present in this work can be overcome by addressing two sets of issues that can be loosely grouped into hardware and software concerns. Hardware concerns which must be addressed include low signal to noise ratio (SNR) at our desired imaging frequencies (i..e, sub-600 kHz levels), and a complete lack of signal at sub-300 kHz levels, leading to cycle skipping artifacts 13 . As the skull attenuates ultrasound waves significantly more than soft tissue, additional techniques such as virtual sources may also be investigated in order to improve SNR in transmission imaging.…”

“…The FWI process is repeated every 10 kHz from 50 kHz to 700 kHz with three iterations per frequency. Full details of the FWI reconstruction algorithm can be found in 13 .…”

“…1C; TransducerWorks, LLC, Centre Hall, PA; 3 MHz center frequency, 1-4 MHz Bandwidth) 14 . The transducer was driven at 700 kHz to ensure appropriate low frequency content in the waveform to begin full waveform inversion image reconstruction 13 . For all UST images in this work, reconstruction was performed using FWI techniques (350-900 kHz, 50 kHz step size) to generate sound speed and attenuation images, while traditional reflection images were also generated to aid with localization of the features.…”

Efficient Helmholtz equation solver for frequency domain waveform inversion based on the decomposition into one-way wave equations

“…Please see our prior work 16 for full details on how the Helmholtz equation is used within FWI. We test three different numerical solvers for the Helmholtz equation within an FWI code: 1) block LU decomposition 13 with 9-point stencil, 12 2) one-way wave equation decomposition with the Fourier split-step method, 14 and 3) one-way wave equation decomposition with PSPI.…”

“…We test three different numerical solvers for the Helmholtz equation within an FWI code: 1) block LU decomposition 13 with 9-point stencil, 12 2) one-way wave equation decomposition with the Fourier split-step method, 14 and 3) one-way wave equation decomposition with PSPI. 15 Raw ultrasound channel data from a whole-breast ultrasound tomography system 16,17 (22-cm diameter ring; 1024 elements) was used to reconstruct sound speed and attenuation in the breast using FWI. The FWI reconstructions for each choice of Helmholtz equation solver are compared.…”