Towards Freehand 3D Synthetic Aperture Imaging with a 1D Probe Using Differentiable Beamforming

We present a proof-of-concept approach to freehand 3D synthetic aperture imaging using a linear 1D probe without external tracking, based on differentiable beamforming. Differentiable beamforming treats delay-and-sum (DAS) as a differentiable function through which gradients can be back-propagated when optimizing an objective function. We simulated freehand sensorless 3D ultrasound scans with Field II. Channel data was simulated for 200 transmit and receive events with a diverging wave sequence, where the transducer was swept continuously (translation and rotation) in elevation over the imaging target. The 3D DAS reconstruction was implemented in JAX, parameterized as a function of the transducer poses in time, i.e. the probe trajectory. The trajectory was estimated from the raw channel data by finding the sequence of poses that minimized the image entropy, where gradients were backpropagated through the DAS beamformer to update the pose estimates. In multiple examples, the trajectories were estimated with sufficient precision to perform synthetic aperture imaging, resulting in sharply improved focusing of point targets in the field of view. Larger sweep trajectories were found to produce images with better spatial resolution, as expected of larger synthetic apertures. This work shows promise for freehand sensorless synthetic aperture imaging, enabled by differentiable beamforming.