Ultrasonic Wave-Speed Diffraction Tomography With Undersampled Data Using Virtual Transducers

Ultrasonic diffraction tomography offers a way to achieve high-resolution imaging of the wave-speed map, and hence, has strong potential applications in medical diagnosis and nondestructive evaluation. Ideal images can be obtained with a complete array of sensors surrounding the scatterer, provided that the measurement data are fully sampled in space, obeying the Nyquist criterion. Spatial undersampling causes the image to be distorted and introduce unwanted circular artifacts. In this paper, we propose an iteration approach using virtual transducers to achieve high-resolution tomographic imaging with undersampled measurements. At each iteration stage, the extent constraint estimated from the shape of the object of interest is applied on the image space to obtain a regularized image, based on which the ultrasonic measurement data at virtual transducers are calculated using a forward model. The full data set composed of original and virtual measurements is then used for tomography in the next stage. A final image with sufficiently high resolution is obtained only after a few iterations. The new imaging method yields improvements in the robustness and accuracy of ultrasonic tomography with undersampled data. We present numerical results using complicated wave-speed maps from realistic corrosion profiles. In addition, an experiment using guided ultrasonic waves is performed to further evaluate the imaging method.