BME Seminar Series: Andrew J. Hesford
Fast Forward and Inverse Methods for Acoustic Scattering by Human Tissue
University of Rochester
Iterative inverse scattering methods such as the distorted Born iterative method have promising applications in clinical medical imaging. By repeatedly solving a linearized approximation to the nonlinear inverse problem, these techniques gradually reconstruct a solution that can accommodate large-scale, high-contrast objects. Careful formulation of the solution allows reconstructions to proceed without explicit representations of the Fréchet derivative that maps image corrections to differences between measured acoustic response and the predicted response for an image. The result is an improved memory footprint and lower asymptotic computational complexity at the expense of repeated forward scattering solutions. By pairing the methods with a Kaczmarz-like iterative scheme and a fast forward solution, the expense of repeated forward solutions can be reduced.
Despite recent advancements in the efficiency of the full-wave forward methods, repeated simulations of large-scale scattering remain too costly for inverse scattering applications. Reduced-physics models such as the parabolic wave equation offer a reduction in computational complexity by several orders of magnitude at the expense of reduced accuracy. Split-step Fourier propagation methods for the solution of the parabolic wave equation are well suited to the simulation of scattering by penetrable media and are extremely efficient. Error can be reduced with high-order approximations to the parabolic operator and a multi-pass approach to incorporate backscatter.
The step-wise nature of split-step Fourier propagation methods makes them ideally suited to execution on graphical processing units (GPUs). Severe memory constraints make large-scale, full-wave solutions difficult in such environments. In contrast, split-step Fourier propagation requires that only a single cross section of the scattering structure be resident in memory for each step. When the high performance of GPUs is coupled with the inherent efficiency of parabolic wave methods, full wave solutions that take hours on thousands of CPUs can be approximated in minutes on a single GPU.