Ultrasonic Computed Tomography On Non-uniform Fourier Transform

As one of modern medical imaging techniques, ultrasound imaging technique has its irreplaceable role. X-ray imaging technique can accurately obtain information on human tissue, but it is not ideal for soft tissues. X-ray imaging has a huge impact on the human body due to associated radiation hazards, so there are limits in application. Ultrasound imaging equipment is used highly frequency in the hospital for its cheap, non-ionizing radiation, and it could be made into portable devices. B-mode ultrasonic can be applied to common physical examination or routine fetal examination and so on, but the quality of imaging is fuzzy, to judge the situation on the human body need to rely on the experience of doctors which affect the individual's subjective judgments of the results, so the quantitative ultrasound imaging for human become an important area. Computed Tomography is an imaging technology which illuminating an object from many different directions and reconstructing the cross-section image of the object according to transmission data or reflection data.We discussed the ultrasound diffraction tomography problem that a security energy-ultrasonic image the human tissue quantitatively in the case of scatter in this paper. The main work and contribution of this dissertation can be summarized as follows:According to the Fourier diffraction projection theorem, the frequency domain interpolation (Gridding) algorithm is interpolating the scattered field data that transformed into the frequency domain to get the value on the uniform grid. We get the imaging of the media plane through inverse 2-D Fourier transform.Non-uniform Fourier transform include forward and backward NUFT. We can get the fast forward NUFT through interpolating the over-sampling FFT transform of the data in the frequency domain. Adopt to the min-max method to optimize the parameters in the interpolation, We get the non-uniform fast Fourier transform algorithm based on min-max. We discussed the backward NUFT samples from the non-uniform to uniform samples that the inverse transform of the forward NUFT problem in the two-dimensional. Because the calculation is large, we can?t solve the inverse matrix using direct method. We introduce the least square method idea using the iterative algorithm (CG) closing to the optimal resolve gradually. Using the imaging results in the in the interpolation method as the initial value of iteration, we can reduce the number of iterations and reduce the computation. Through test analysis , imaging effect is improved using this method.Access to the simulation data are discussed .In the case of weak scattering, we can get the values of Shepp-Logan model in the frequency domain at any point using the analytic solution based on the Fourier projection theorem. We can get the simulated data without introducing any error based on this. The multi-frequency ultrasonic projections can reduce the imaging time. The standpoint is a good development of medical images. The less integrity projection occured in the imaging process, we analyze the effect of the adequate extent and data redundancy on the imaging to reduce the projector or sampling points, the utilization of information becomes higher. Analysing the information in the transmission and reflection mode scattering, we can get the transmission and reflection data without increasing the sampling time. We can improve the image quality with combining the data.