Off-Grid Ultrasound Imaging by Stochastic Optimization

Ultrasound images formed by delay-and-sum (DAS) beamforming are plagued by artifacts that only clear up after compounding many transmissions. One promising way to mitigate this is posing imaging as an inverse problem. Inverse problem-based imaging approaches can yield high image quality with few transmits, but existing methods require a very fine image grid and are not robust to changes in measurement model parameters. We present inverse grid-free estimation of reflectivities (INFER), an off-grid and stochastic algorithm that finds a solution to the inverse scattering problem in ultrasound imaging. Our method jointly optimizes for the locations of the gridpoints, their reflectivities, and the speed of sound. This approach allows us to use fewer gridpoints than existing methods. At the same time, it obtains $2\times $ - $3\times $ higher far-field lateral resolution and 6%-68% higher generalized contrast-to-noise ratio (gCNR) on in vivo data, and it is robust to speed of sound changes of up to ±100 m/s. The use of stochastic optimization enables solving for multiple transmissions simultaneously without increasing the required memory or computational load per iteration. We show that our method works on both phantom and in vivo data and compares favorably against existing beamforming methods. The source code and the dataset to reproduce the results in this article are available at ww.w.github.com/vincentvdschaft/off-grid-ultrasound.