Three‐dimensional inverse scattering tomography using elastic waves

Abstract

A 3‐D ultrasound method that provides clinically significant (and diagnostically valuable) images of important tissue characteristics is described. This is made possible by an inverse‐scattering technique that provides accurate, independent images of speed of sound, density, and absorption (with extension to five viscoelastic constants) at the very high spatial resolution of 0.5 to 1.0 wavelength of the incident ultrasound energy. Image size has increased from 16×16 pixels to 200 × 200 pixels and to 32×32×96 voxels while maintaining accuracy and spatial resolution. No other methods, for example the B‐scan mode of diffraction tomography based on the Rytov or Born approximations, have come close to matching this achievement. Further improvement in tissue imaging is possible by using the inverse scattering method in conjunction with a high performance reflection mode imaging method called synthetic focusing. The synthetic focusing method in nearly homogeneous medium produces medium to very large size, high spatial resolution images. The synthetic focus method also can be made to produce excellent images in the moderately high refracting environment of the human body by applying time shift and attenuation corrections obtained from medium resolution inverse scattering images of speed of sound and absorption. Regularization and constrained optimization methods have been used to improve the conditioning and therefore the speed of the inverse scattering methods.