Ultrasound Diffractive Tomography

Abstract
This project is dealing with computerized diffraction tomography. Tomography is a scanning method that gives a cross-section image of an object. Diffraction is a phenomenon that is created when using low frequency waves, thus creating a wave phenomenon.

The problem
The diffraction in acoustic imaging requires the use of different algorithms than what straight ray tomography requires. These algorithms treat the distortion created by the diffraction. In this project different aspects of the diffraction influence on the reconstruction were examined using three algorithms. Computation time and errors were calculated and examines for each algorithm.

The solution

1. During the project the following algorithms were tested and compared: Gridding algorithm – makes use of a frequency domain interpolation of the non-uniform data to a uniform Cartesian grid using bilinear interpolation
2. The direct computation – Straightforward computation of the forward and the inverse non-uniform Fourier transform by creating the transform matrix and applying it to the picture in column stack
3. Reconstruction using Non Uniform Fast Fourier Transform- A method equivalent to a convolution regridding method on an over sampled grid using an optimal selection of a Gaussian kernel. This method makes the use of a fast reconstruction using the inverse FFT algorithm

Tools
The algorithms were implemented using Matlab TM

Conclusions

The direct transformation takes the longest time of computation but gives the most accurate results. On the other hand the NUFFT algorithm gives pretty good results compared with gridding algorithm and is much faster than using the direct computation.

Acknowledgment
We would like to thank Dr. Zibulevsky, Dr. Azhary, Alexander Bronstein and Michael Bronstein for supervising this project.
We are also grateful to the Ollendorf Minerva Center Fund for supporting this project.