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A reconstruction algorithm is derived for parallel beam transmission computed tomography through two-dimensional structures in which diffraction of the insonifying beam must be taken into account. The algorithm is found to be completely analogous to the filtered backprojection algorithm of conventional transmission tomography with the exception that the backprojection operation has to be replaced by a back propagation process whereby the complex phase of a field measured over a line outside the object is made to propagate back through the object space. The algorithm is applicable to diffraction tomography within either the first Born or Rytov approximations. Application of the algorithm to three-dimensional structures is also discussed.

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Inverse problems are of interest and importance across many branches of physics, mathematics, engineering and medical imaging. In this text, the foundations of imaging and wavefield inversion are presented in a clear and systematic way. The necessary theory is gradually developed throughout the book, progressing from simple wave equation based models to vector wave models. By combining theory with numerous MATLAB based examples, the author promotes a complete understanding of the material and establishes a basis for real world applications. Key topics of discussion include the derivation of solutions to the inhomogeneous and homogeneous Helmholtz equations using Green function techniques; the propagation and scattering of waves in homogeneous and inhomogeneous backgrounds; and the concept of field time reversal. Bridging the gap between mathematics and physics, this multidisciplinary book will appeal to graduate students and researchers alike. Additional resources including MATLAB codes and solutions are available online at www.cambridge.org/9780521119740.

Time-reversal-based imaging and inverse scattering of multiply scattering point targets

The treatment of time-reversal imaging of multiply scattering point targets developed by the present authors in Gruber et al. ͓"Time-reversal imaging with multiple signal classification considering multiple scattering between the targets," J. Acoust. Soc. Am., 115, 3042-3047 ͑2004͔͒ is reformulated and extended to the estimation of the target scattering strengths using the Foldy-Lax multiple scattering model. It is shown that the time-reversal multiple signal classification ͑MUSIC͒ pseudospectrum computed using the background Green function as the steering vector yields accurate estimates of the target locations, even in the presence of strong multiple scattering between the targets, and that the target scattering strengths are readily computed from the so-determined target locations using a nonlinear iterative algorithm. The paper includes computer simulations illustrating the theory and algorithms presented in the paper.