Compressed Sensing-based Imaging Methods For High-Resolution Radar

The theory of compressed sensing(CS) suggests that sparse or compressible signals can be accurately reconstructed from their highly undersampled measurements. By the fact that backscattering of radar targets in the high-frequency region is usually dominated by a small number of scattering centers, such a theory is applicable to high-resolution radar imaging. Hopefully, by exploiting the data compression ability of the theory, CS-based high-resolution radar imaging may achieve high-quality image reconstruction from measurements that are much less than those required by the traditional imaging method. Clearly, this behavior can significantly reduce the cost of the radar system in data collection, storage and transmission.This dissertation focuses on CS-based imaging methods for high-resolution radar. The main efforts are devoted to dealing with the key problem encountered in the existing CS-based imaging approaches. Specifically, the research in the dissertation consists of several aspects which are listed as follows.Chapter 1 introduces the background and significance of the research conducted in the dissertation. Subsequently, it overviews the investigations on the theory of CS and the subject of CS-based high-resolution radar imaging. Also, it points out the necessity for conducting further investigations into that subject.Chapter 2 describes the principle of high-resolution radar imaging based on CS. Firstly, the mathematical model for signal reconstruction in CS is introduced, the existing CS reconstruction methods are reviewed and the echo models for high-resolution radar imaging are derived. Subsequently, based on the above work, a general scheme for high-resolution radar imaging based on CS is presented. Also, simulation results based on the presented scheme and the existing CS reconstruction methods are provided. Based on these results, the key problem encountered in the existing CS reconstruction methods is pointed out, namely, dictionary mismatch incurring considerable imaging performance degradation.By utilizing the strategy of dictionary refinement, Chapter 3 proposes an accurate reconstruction algorithm for CS of complex sinusoids. To deal with the dictionary mismatch problem, the algorithm models the sparsifying dictionary of complex sinusoids as a parameterized Fourier dictionary, with the sampled frequency grid points viewed as the underlying parameters. As a result, the sparsifying dictionary is dynamically refinable during the signal reconstruction process, and its refinement can be realized via the tuning of the frequency grid. To carry out the above line of thought, the proposed algorithm alternates between sparse coefficients recovery and frequency grid update by employing the variational expectation-maximization(EM) algorithm. Results of extensive experiments based on both simulated and anechoic chamber data demonstrate that the proposed algorithm is effective in coping with dictionary mismatch and can generate high-quality high-resolution range profiles.To solve the problem that the reconstruction algorithm based on dictionary refinement has relatively high computational complexity, Chapter 4 focuses on fast reconstruction of complex sinusoids. Firstly, by applying the first order Taylor approximation to the true sparsifying dictionary of the original signal, a new sparse representation model is established. The model is more accurate for sparse representation of practical complex sinusoids. Based on this model, signal reconstruction is then reformulated as a problem in which two sparse coefficient vectors over two known dictionaries are sought under the constraint that the vectors share the same support. To solve the above problem, an iterative algorithm is developed under the framework of variational Bayesian inference. The algorithm involves no matrix inversions, and employs the FFT to compute all dictionary-vector multiplications. These behaviors indicate that the algorithm has quite low computational complexity. Results of extensive experiments based on both simulated and anechoic chamber data show that the proposed algorithm deals with the dictionary mismatch problem effectively while maintaining a low computational cost.Chapter 5 seeks the two dimensional(2-D) high-resolution radar imaging method that is immune to dictionary mismatch. Firstly, based on the first order Taylor approximation technique, a more accurate sparse representation model for 2-D radar imaging is established. With such a model, 2-D radar imaging is recast as a problem that recovers three sparse vectors over three known dictionaries under the constraint that all the vectors share the same support. To solve this problem, an inference procedure under the variational Bayesian inference framework is then derived, and an iterative algorithm is developed to perform the procedure. Specifically, the sparsifying dictionaries utilized in the algorithm have the form of 2-D DFT matrices, which spares the algorithm form the large memory cost in explicitly generating dictionary entries and also allows dictionary-vector multiplications to be implemented using the 2-D FFT. To validate the proposed algorithm, a wide range of experiments are conducted by using data simulated, collected in an anechoic chamber and generated via a software for high-frequency electromagnetic scattering computation. The experimental results demonstrate that the proposed algorithm has the ability to deal with the dictionary mismatch problem and can generate high-quality 2-D images based on highly undersampled measurements.Chapter 6 provides concluding remarks, and also points out the directions for future research.