Application Of NUFFT And Extrapolation In Ultrasound Diffraction Tomography

Ultrasound computerized tomography(CT) have many advantages, such as non-invasion, low-cost and so on. And it has been widely used in many applications like medical imaging and industrial non-invasion detection. In the future it will be applied in more and more areas. The Fourier diffraction CT imaging method, which uses the Fourier diffraction theorem, bases on wave equation. This method takes the scatter field into consideration. The results, reconstructed from the scattered filed of ultrasound wave, carry more information about the object. So the reconstruction results are higher definition and more perceived. However, there are some issues about this reconstruction method. One is that the samples in the frequency domain distribute on some arcs. So they are not uniform distributed. The other problem is that these samples all limited in low frequency band (the transmission type). In this paper, we analyze these two issues and give solutions.First, we solve the issue about the non-uniform distribution samples. We apply a type of NUFFT method. We apply the approximation theorem to use a sequence to approximate the Fourier basis. And we get an approximate representation to solve the NDFT. So we now have a type of NUFFT algorithm and its implementation. The method includes three steps: interpolation , computing over-sampled data using FFTscaling. Among these steps, interpolation function is involved in interpolation process and scaling process, so the choice of interpolation function is the key to the performance of algorithm. We select the Gaussian window and the Kaiser-Bessel window as the approximate solution. And we estimate the errors and analyze computation complexity. The simulation shows the Kaiser-Bessel window can get a more promising result. And for the reconstruction in present of noise, we introduce an iterative reconstruction, making use of total variation regularization to improve the quality of the results. The simulation verifies that under the same conditions the method applied in this paper can achieve a more acceptable result compared with FBP and bilinear interpolation method.Second, we discuss the problem that all samples in frequency domain confined in the low-pass part. At first, we make use of G-P algorithm to get high frequency information from the image which is reconstructed using NUFFT method early discussed. The G-P method is an iterative procedure, which combine information about the Fourier transform of a function with independent space domain constraints. And then a modified non-linear extrapolation method is applied to enhance the high frequency part. Compared with the original method, the improved method replaces the global threshold with a parameter which reflects the local information about amplitudes changes in the image. So the new method can enhance the image uniformly.At last, combining these methods, we build a procedure which can reconstruct a high quality image from projections.