Collimated beam ultrasound systems are a novel technology for imaging inside multi-layered structures such as geothermal wells. Such systems include a transmitter and multiple receivers to capture reflected signals. Common algorithms for ultrasound reconstruction use delay-and-sum (DAS) approaches; these have low computational complexity but produce inaccurate images in the presence of complex structures and specialized geometries such as collimated beams.
In this paper, we propose a multi-layer, ultrasonic, model-based iterative reconstruction algorithm designed for collimated beam systems. We introduce a physics-based forward model to accurately account for the propagation of a collimated ultrasonic beam in multi-layer media and describe an efficient implementation using binary search. We model direct arrival signals, detector noise, and a spatially varying image prior, then cast the reconstruction as a maximum a posteriori estimation problem. Using simulated and experimental data we obtain significantly fewer artifacts relative to DAS while running in near real time using commodity compute resources.