Backpropagation in turbid media

Abstract

We extend the backpropagation algorithm of standard diffraction tomography to backpropagation in turbid media. We analyze the behavior of the backpropagation algorithm both for a single-view geometry, as is common in mammography, and for multiple views. The most general form of the algorithm permits arbitrary placement of sources and detectors in the background medium. In addition, we specialize the algorithm for the case of a planar array of detectors, which permits the backpropagation algorithm to be implemented with fast-Fourier-domain noniterative algebraic methods. In this case the algorithm can be used to reconstruct three-dimensional images in a minute or less, depending on the number of views. We demonstrate the theoretical results with computer simulations.