CT和定点式SAR中的直接傅立叶重建算法研究

【作者】 王洋；

【导师】 汪元美；

【作者基本信息】 浙江大学 ， 生物医学工程， 2004， 硕士

【摘要】 计算机层析成像技术(CT)和综合孔径雷达(SAR)是图像重建技术应用的两个重要领域。卷积反投影(CBP)与直接傅立叶重建(DF)同是图像重建中变换法的典型算法。一般说来，DF算法原理简单，重建速度快，但缺乏准确、高效的插值算法，致使重建质量不如CBP法。因而，进一步开展DF重建算法在CT和SAR图像重建领域中的应用研究具有重要的理论价值和现实意义。 论文从系统模型的建立入手，根据DF算法与CBP算法的内在联系，推算出使用雅可比加权的二维周期sinc核插值器的DF算法就等价于CBP算法，然后基于这一结论分别在CT和SAR系统模型中进行了仿真实现。文中讨论的各种形式的sinc核插值DF重建算法，都可概括为以下两步： (ⅰ)使用雅可比加权的二维周期sinc核插值器(或简化形式的sinc核插值器)，对非笛卡尔形的傅立叶数据进行插值； (ⅱ)二维傅立叶反变换。 由于SAR系统中近似笛卡尔形的采样数据使其插值过程简易化，因而DF算法在SAR中更具优势。对小角度采样的SAR而言，简单的低阶插值即可获得很好的DF重建。 要说明的是，雅可比加权的sinc核插值并不是最优插值器。也即，使用理想插值器的DF算法可望获得优于CBP法的重建效果。总之，寻求准确高效的DF层析重建算法就等同于寻求DF中准确高效、近似理想的插值方法。再者，用以FFT优化的DSP芯片的推陈出新，使得DF算法具有广阔的发展前景。更多还原

【Abstract】 Computerized tomography (CT) and synthetic aperture radar (SAR) are two of the most important fields in image reconstruction. Both convolution Backprojection (CBP) method and direct-Fourier (DF) Reconstruction method are the representative algorithms of transform methods in image reconstruction. Generally speaking, DF algorithm has the simple theory and the fast reconstruction, but the lack of good efficient interpolation makes the quality of reconstruction is inferior to that of CBP method. Thus, the further investigation of DF algorithm has the important theoretic value and practical meaning in the image reconstruction field of CT and SAR.In this paper, we begin with system modeling. Then, according to the internal relations of DF and CBP, we show that the CBP algorithm is equivalent to DF reconstruction by using a Jacobian-weighted 2D sine-kernel interpolator. At last, this conclusion is applied to the simulations of CT and S AR. All reconstruction algorithms discussed in this thesis can be considered as a method of implementing a two-step reconstruction procedure: (i) Interpolation of non-Cartesian Fourier data, using a 2D Jacobian-weightedsinc-kernal (or simplified version of the sine-kernel) interpolator; (ii) 2D inverse FFT.For the S AR nearly Cartesian shape of the sampling grid makes interpolation more facilitation, DF method used in SAR has more advantages than those in CT. When the data collection angle is very small, the DF method performs very well with interpolators of low complexity.It is point out that this interpolator using a Jacobian-weighted 2D sine-kernel is not optimal, i.e. DF algorithms utilizing optimal interpolators may surpass CBP in image quality. In conclusion, searching for accurate and efficient tomographic reconstruction algorithms is equivalent to that for accurate and efficient methods for approximating the optimal interpolator in DF reconstruction. Furthermore, many new DSP chips are optimized for FFT operations, which make DF algorithms of great promise.更多还原