Non-uniform Fast Fourier Transform And Its Application In SAR Imaging

Synthetic aperture radar(SAR) is a high resolution microwave imaging radar which is generally used to get images of the ground targets by exploiting the large virtual aperture synthesized by the mo tion of the radar platform. During the imaging process, the self-motion of the radar platform and envir onment factors, on the one hand, will cause the azimuth and range's coupling in echo data; on the othe r hand, will cause non-uniform space sampling under many circumstances which leads to large proces sing errors by using traditional data processing schemes. Non-uniform Fast Fourier Transform(NUFF T) mainly focus on the process of interpolation, oversampling FFT and adding windows to the non-un iform data which holds a good practicability in SAR imaging processing. In this thesis, based on the n on-uniform SAR data, the NUFFT formula was put forward in non-uniform sampling SAR processing, realized the correction of range migration and azimuth phase error in non-uniform sampling SAR dat a, improved the SAR imaging quality finally. The validity and feasibility of the method are proved by theoretical derivation and processing of simulation data. The main contributions are as follows:(1)Analyzed the imaging algorithms of SAR on range direction and azimuth direction, studied three kinds of classic algorithms as Range-Doppler algorithm, Chirp Scaling algorithm and ?k algorithm, and verified these algorithms by point target simulation. Studied the effect on remove the range migration of these algorithms from the algorithm computation and accuracy, provided theoretical basis for the application of NUFFT algorithm.(2)The principle of NUFFT algorithm is introduced through the study of NDFT problems, the formula of NUFFT algorithm based on Gauss window function is derived, and the complexity comparison and error analysis are carried out with the standard FFT algorithm. On the basis of these, the NUFFT algorithm is used to deal with the single frequency and multi frequency non uniformly sampled signals, and the error analysis is presented, the results are compared with the FFT algorithm, and the effectiveness of the NUFFT algorithm is verified.(3)The two-dimensional separable principle of the echo data in SAR signal processing is introdu ced and the rationality of using NUFFT algorithm to process it is also verified here.By discretizing the echo data,the RD algorithm based on NUFFT formula is deduced, then the point targ et imaging simulation is performed to demonstrate the effectiveness of the proposed algorithm. At the same time, the comparison between the new method and the traditional method are presented from the perspectives of imaging results and the complexity of the two method.(4) The imaging model of azimuth nonuniform sampling is formed, and the influence of the non uniform sampling on the azimuth focus is also analyzed. Under different error conditions, the imagin g simulations are conducted. In this issue, the azimuth compensation principle is combined with NUFFT to induce a formula, which is suitable for NUFFT algorithm. The simulation results show that the focus effect of the proposed method is equivalent to that of the traditional method which first using FFT and then performing auto-focus algorithm.