A Fast Filtered Backpropagation Algorithm for Ultrasound Tomography

Ultrasound tomography of acoustic objects having vari- able density and compressibility is addressed within the framework of diflaction tomography. The Jiltered backpropagation algorithm of diffraction tomography is reviewed for tomographic systems employing plane-wave insonification and fixed (nonrotating) measurement planes. For these systems it is shown that a fast version of the algorithm can be implemented that requires on the order of M X N, fewer discrete Fourier transforms (DFT's) than are required by the conventional fil- tered backpropagation algorithm where M is the total number of views and N, the length of the image array along the axis perpendicular to the receiver plane. The conventional and fast algorithms are imple- ' mented in Fortran on a microcomputer and tested in computer simu- lation studies. It is found that both algorithms yield identical recon- structions; however, the fast algorithm results in considerable savings of CPU time. A detailed discussion of the implementation of both the conventional and fast filtered backpropagation algorithms on a micro- computer as well as graphs and photographic images of reconstruction generated using readily available and inexpensive commercial software and hardware are included.