Studies On 1-Bit Coded Synthetic Aperture Radar Sparse Imaging

Compressive sensing theory provides a new method for data acquisition and processing. When some conditions are satisfied, sparse signals can be stably recovered via sparse optimization from measurements which are sampled at lower sampling rate compared to the Nyquist sampling rate. In compressive sensing framework, the sampling and compression of the data are achieved simultaneously, and the signal can be recovered from the incomplete measurements. Recently, some researches have shown that only the sign information of the measurements can also guarantee stable signal reconstruction under certain conditions, i.e.1-bit compressive sensing. Different from the conventional compressive sensing theory,1-bit compressive sensing theory reduces the data amount by reducing the quantization bit depth rather than reducing the measurement sampling rate. It is much easier to be implemented. In this case, the quantizer becomes a comparator, which is fast, inexpensive, with the characteristics of low power consumption, robust to nonlinear distortion and saturation. In Synthetic Aperture Radar (SAR) imaging tasks, the demand of high resolution always results in large amount of echo data, and 1-bit quantization will significantly alleviate the burden of the radar system. In this paper, the technique of 1-bit coded SAR imaging based on compressive sensing is studied. For sparse imaging scene, the goal is to improve the imaging performance by 1-bit compressive sensing method.In the introduction part, the development history and current status of SAR technology is briefly introduced. Then, sparse SAR imaging method based on conventional compressive sensing theory is also provided. Finally, the development situation of 1-bit coded SAR imaging approaches is provided, and some existing problems are also pointed out, which are addressed in the rest of this paper.In chapter two, the 1-bit compressive sensing theory and methods are introduced. At the beginning of chapter three, the binary ε-stable embedding property of the convolution matrix built by linear frequency modulation signal is verified to ensure the feasibility of applying 1-bit compressive sensing theory to achieve sparse SAR imaging. Then, a 1-bit SAR imaging algorithm based on compressive sensing is proposed. Finally, simulation experiments demonstrate the effectiveness of the proposed algorithm, and the advantages of the 1-bit sparse SAR imaging method over conventional compressive sensing based sparse SAR imaging methods is illustrated. The resolution of 1-bit sparse SAR imaging method is also discussed.In chapter four, the problem of high noise corruption which may occurred in SAR imaging applications is considered, and a robust algorithm based on variational Bayesian inference is proposed. The Bayesian model is deduced from the noise distribution, and the parameters are estimated by variational inference. Simulations validate the robustness of the proposed algorithm in 1-bit SAR imaging application.Chapter five provides two solutions to the off-grid problem which results from basis mismatch when continuous parameter space is discretized into finite grid points. The first solution is based on the concept of atomic norm, which does not need to discretize the continuous parameter space and inherently overcome the off-grid problem. However, the computational cost is too large to apply to large imaging problem. Thus, we only study the 1-bit range profile application. The second solution adopts adaptive grid technique, which regards the target locations as unknown parameters, and adaptively updates the grid points to approach the targets. This method can provide high reconstruction accuracy with low computational cost. Simulations demonstrate the abilities of the both methods to deal with the off-grid problem.In chapter six, an algorithm based on approximated observation with low computational complexity is proposed to facilitate the implementation of large scaled 1-bit sparse SAR imaging task. The proposed algorithm incorporates the 1-bit compressive sensing method with the traditional FFT-based fast focusing approach to significantly reduce the computational complexity. Experiments on simulated and real raw SAR date validate the effectiveness of the proposed algorithm.