3-D Wave-Equation-Based Finite-Frequency Tomography for Ultrasound Computed Tomography

Ultrasound computed tomography (USCT) has great potential for 3-D quantitative imaging of acoustic breast tissue properties. Typical devices include high-frequency transducers, which makes tomography techniques based on numerical wave propagation simulations computationally challenging, especially in 3-D. Therefore, despite the finite-frequency nature of ultrasonic waves, ray-theoretical approaches to transmission tomography are still widely used. This article introduces a finite-frequency traveltime tomography to medical ultrasound. In addition to being computationally tractable for 3-D imaging at high frequencies, the method has two main advantages: 1) it correctly accounts for the frequency dependence and volumetric sensitivity of traveltime measurements, which are related to off-ray-path scattering and diffraction. 2) It naturally enables out-of-plane imaging and the construction of 3-D images from 2-D slice-by-slice acquisition systems. Our method rests on the availability of calibration data in water, used to linearize the forward problem and to provide analytical expressions of cross correlation traveltime sensitivity. As a consequence of the finite-frequency content, sensitivity is distributed in multiple Fresnel volumes, thereby providing out-of-plane sensitivity. To improve computational efficiency, we develop a memory-efficient implementation by encoding the Jacobian operator with a 1-D parameterization, which allows us to extend the method to large-scale domains. We validate our tomographic approach using laboratory measurements collected with a 2-D setup of transducers and using a cylindrically symmetric phantom. We then demonstrate its applicability for 3-D reconstructions by simulating a slice-by-slice acquisition system using the same data set.