Ct And Fixed-point-based Sar In The Direct Fourier Reconstruction Algorithm Research

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.