3-D Nonlinear Acoustic Inverse Scattering: Algorithm and Quantitative Results.

We describe a novel 3-D ultrasound technology, the quantitative transmission ultrasound system and algorithm to image a pendent breast in a water bath. Quantitative accuracy is verified using phantoms. Morphological accuracy is verified using cadaveric breast and in vivo images, and spatial resolution is estimated. This paper generalizes an earlier 2-D algorithm to a full 3-D inversion algorithm and shows the importance of such a 3-D algorithm for artifact suppression as compared with the 2-D algorithm. The resultant high-resolution ultrasound images, along with quantitative information regarding tissue speed of sound/stiffness, provide a more accurate depiction of the breast anatomy and lesions, contributing to improved breast care.

Non-linear inverse scattering: high resolution quantitative breast tissue tomography.

Recent published results in inverse scattering generally show the difficulty in dealing with moderate to high contrast inhomogeneities when employing linearized or iteratively linearized algorithms (e.g., distorted Born iterative method). This paper presents a fully nonlinear algorithm utilizing full wave field data, that results in ultrasound computed tomographic images from a laboratory breast scanner, and shows several such unique images from volunteer subjects. The forward problem, data collection process and inverse scattering algorithm used are discussed. A functional that represents the "best fit" between predicted and measured data is minimized, and therefore requires a very fast forward problem solver, Jacobian calculation, and gradient estimation, all of which are described. The data collection device is described. The algorithm and device yield quantitative estimates of human breast tissue in vivo. Several high resolution images, measuring ∼150 by 150 wavelengths, obtained from the 2D inverse scattering algorithms, using data collected from a first prototype, are shown and discussed. The quantitative values are compared with previous published work.

Nonperturbative diffraction tomography via Gauss-Newton iteration applied to the scattering integral equation.

A nonperturbational inverse scattering solution for the scattering integral equation (SIE) is presented. The numerical discretization of the SIE is performed by the moment method (MM) using sinc basis functions. Previous algorithms using the alternating variable (AV) nonlinear iteration with algebraic reconstruction technique (ART) solution of the linearizations are shown to diverge for high contrast/large size acoustic scatterers. This deficiency is alleviated by the use of the Gauss-Newton (GN) nonlinear iteration with conjugate gradient (CG) solution of the linearizations. Further numerical efficiency is attained by use of the biconjugate gradient (BCG) algorithm to solve the forward scattering problems. Test problem reconstructions of circular cylinders, using the Bessel series analytic solution to generate the scattering data, demonstrate the accuracy of the method. Inhomogeneous models of human cross-sections verify the high spatial resolution and high speed of sound contrast capability of the method.