  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.
