  Collimated beam ultrasound systems are a technology for imaging inside
multi-layered structures such as geothermal wells. These systems work by using
a collimated narrow-band ultrasound transmitter that can penetrate through
multiple layers of heterogeneous material. A series of measurements can then be
made at multiple transmit frequencies. However, commonly used reconstruction
algorithms such as Synthetic Aperture Focusing Technique (SAFT) tend to produce
poor quality reconstructions for these systems both because they do not model
collimated beam systems and they do not jointly reconstruct the multiple
frequencies.
  In this paper, we propose a multi-frequency ultrasound model-based iterative
reconstruction (UMBIR) algorithm designed for multi-frequency collimated beam
ultrasound systems. The combined system targets reflective imaging of
heterogeneous, multi-layered structures. For each transmitted frequency band,
we introduce a physics-based forward model to accurately account for the
propagation of the collimated narrow-band ultrasonic beam through the
multi-layered media. We then show how the joint multi-frequency UMBIR
reconstruction can be computed by modeling the direct arrival signals, detector
noise, and incorporating a spatially varying image prior. Results using both
simulated and experimental data indicate that multi-frequency UMBIR
reconstruction yields much higher reconstruction quality than either single
frequency UMBIR or SAFT.
