Research On Cs-sar Imaging Theory And Algorithms Based On Sparse Representation In The Fractional Fourier Domain

Synthetic Aperture Radar(SAR), as an all-time, all-weather, and long-range active observation system, has great practical value and plays an important role in the defense and civilian fields. Resolution is crucial for characterizing the observed targets. With the continuous development of the actual demand, high resolution and ultra-high resolution SAR imaging has become one of the current research focus. While, the current high resolution SAR imaging system, which is based on the Shannon-Nyquist sampling theorem and the classical theory of digital signal processing, has issues of the following: the radar system is large scale, high-speed data acquisition and mass data storage and transmission are difficult to achieve, information is redundant but feature is difficult to extract. These issues have become a bottleneck of the development of high resolution SAR. Under certain conditions, the new emerging theory of compressed sensing(or compressive sampling, CS) can reconstruct the original signal with high probability by using less amount of data than the Shannon-Nyquist sampling theorem required. The emergence of the CS provides the possibility to solve the development bottleneck for the high resolution of SAR. This dissertation is focused on the CS-based SAR imaging theory and algorithm. The main contributions and innovations of the dissertation are summarized as follows:1. An range-direction undersampling CS-SAR imaging algorithm is proposed based on the fractional Fourier transform(FRFT). Signal sparsity and the incoherence of the sensing modality are the two principles which the CS relies on. Firstly, the echo sparsity of the pulse radar which transmits linear frequency modulated(LFM) signal is analyzed. Considering the characteristics of the echo, the sparsest representation of the echo is given in the simplified fractional Fourier domain(SFRFD). It shows that the sparse representation of the echo in SFRFD has physical meaning, that is, the sparse representation of the echo in the SFRFD is the range profile of the observed scene in the SFRFD and the echo of sparse scene has good sparsity in the SFRFD. Secondly, the restricted isometry property(RIP) of the given sensing modalities is analyzed. It shows that the inverse simplified fractional Fourier matrix(ISFRFM) is a unitary matrix. As the sparsify matrix, the ISFRFM has good incoherence with the four alternative random matrices which are random Gaussian matrix, partial identity matrix, partial Fourier matrix and partial Hadamard matrix. RIPs of the random sampling matrices of the ISFRFM, the observation matrix of SAR and the time domain matching filter matrix, which are the common used sparsify matrices in the CS-SAR, have been compared. The comparison results show that the randomly sampled ISFRFM has better RIP than the other two randomly sampled matrices and has advantages in recovering signals. Then, the FRFT-based SAR imaging algorithm is proposed by applying CS technology in range direction. Simulated data are used to verify the effectiveness of the proposed algorithm. The influence of the type of measurement matrix and the amount of measurements on imaging results are analyzed under different signal-to-noise ratio(SNR). The results of the analysis can provide reference for the application of different measurement matrix under different conditions. Finally, the RADARSAT-1 data are processed by the proposed algorithm. The achieved results show that the proposed algorithm is capable of reconstructing high-quality images with limited amount of measurements.2. A two-dimensional(2-D) undersampling CS-SAR imaging algorithm is proposed based on the FRFT. In order to further reduce the amount of measurements, the CS technology is applied in both the range and azimuth directions. In the matrix form 2-D undersampling CS-SAR imaging, the range cell migration correction(RCMC) is difficult. The range cell migration(RCM), which degrades the imaging quality, is ignored by the existing matrix form 2-D undersampling CS-SAR imaging algorithm. To obtain high-quality images, the matrix form FRFTbased 2-D undersampling CS-SAR imaging algorithm, which considers the RCM, is proposed after careful analysis of the relationship between undersampled echo and RCM. In the proposed algorithm, due to the artful design of the azimuth measurement matrix, the RCM is corrected as an intermediate step of the cascade of 1-D CS processing in the range and azimuth directions by using the FRFT-based reference function multiplication and chirp-z transform in the case of2-D undersampling. Then, comparisons between the proposed algorithm and the existing 2-D undersampling CS-SAR imaging algorithms are made in the aspects of signal model, reconstruction model, size of sensing matrix, and computation complexity. The effectiveness and robustness with regard to the amount of undersampling of the proposed algorithm are demonstrated by some numerical experiments. Simulation experiments are also made to compare the proposed algorithm and the existing 2-D undersampling CS-SAR imaging algorithms in terms of the storage burden, computational efficiency, and reconstruction effects. The results show that the proposed algorithm can efficiently realize high-quality imaging with small amount of storage space. The proposed algorithm and the existing 2-D undersampling CS-SAR imaging algorithm which ignores the RCM are applied to the RADARSAT-1 data. For different sparsity and dynamic range of the scene, the proposed algorithm still can efficiently realize high-quality imaging under the condition of 2-D undersampling but the other algorithm cannot.3. A matrix form joint CS-SAR imaging and autofocus algorithm is proposed. The deviation between actual movement of SAR platform and the ideal movement, the measurement error about the platform velocity, and the atmospheric effects can bring phase errors in the ideal echo. To solve the image defocus problem caused by the phase errors, a matrix form joint CS-SAR imaging and autofocus algorithm is proposed. Compared to the exist vector form joint CS-SAR imaging and autofocus algorithms, the proposed algorithm has higher computational efficiency. Firstly, a matrix form model of joint CS-SAR imaging and autofocus is set up. Then, an appropriate algorithm to solve the matrix form model is proposed. The proposed algorithm cycles through steps of matrix form CS-SAR imaging and phase error estimation.The analytical expression of the phase error is derived. The regularized smoothed ?0-norm(ReSL0) algorithm and the matrix form regularized SL0(MReSL0) algorithm are proposed for CS-SAR imaging in inaccurate model. The ReSL0 algorithm is compared with the original smoothed ?0-norm(SL0) algorithm by applying Monte Carlo simulation experiments in the aspects of computational efficiency, anti-noise, and error tolerance. The results show that the anti-noise and error tolerance ability of ReSL0 compares favourably with that of the original SL0. Finally, the SL0, ReSL0, and the MReSL0 are applied to the matrix form joint CS-SAR imaging and autofocus model with simulated and real data. The results demonstrate that the proposed recovery algorithms can efficiently realize high-quality imaging with limited amount of measurements in matrix form joint CS-SAR imaging and autofocus, but the SL0 cannot.