Sparse Component Analysis And Its Applications In Radar Imaging Processing

Sparse component analysis(SCA) is an emerging method for signal analysis. Based on the overcomplete dictionaries, it can provide the sparse representation of a given signal from the limited observations. Such representation can capture the nature of the observed signal, mine its intrinsic driving source and improve the resolution in the transformation domain. Presently, SCA becomes an effective tool for signal processing. As one part of signal processing, radar imaging technique plays an important role in military and civil applications. Intrinsically speaking, radar imaging is one kind of signal representation. Moreover, the electromagnetic scattering of radar target in high frequency is a local behavior, therefore SCA can improve the quality of radar images and be beneficial to image analysis and target recognition.Aiming at the background of radar imaging, this thesis studies the theoretical and appliedproblems of SCA, including the general criterion to construct sparsity measure and theSCA-based algorithms for radar imaging, such as the formation of high resolution rangeprofiles, two-dimensional ISAR imaging and the technique of multi-band radar signal synthesis.In order to pave the way for relevant applications, the thesis firstly discusses the theoreticalproblems in SCA, such as the construction of sparsity measure and the analysis of correspondingalgorithms. In details, the author presents a general criterion for the construction of sparsitymeasure, and proves that those measure functions satisfying the proposed criterion cantheoretically lead to the sparsest representation. With the general class of measure functionssatisfying above-mentioned criterion, an effective optimization algorithm is put forward togenerate sparse solution with its convergence proven, which provides a generalized version ofFOCUSS algorithm developed by previous researchers. According to the criterion, somesparsity-preserving measure funchtions are recommended and their performance is validated bynumerical simulation.With the application of SCA, the construction of overcomplete dictionaries is discussed and corresponding algorithms are presented to generate sparse representation of high resolution range profile. Based on the GTD(Geometry Theory of Diffraction) model and ideal point scatterer model of radar target in high frequency domain, the overcomplete dictionaries matching with radar measurement model and the scattering models are constructed. With the structure characteristics of the dictionaries, the FFT-based and Toeplitz matrix-based fast algorithms are presented for the formation of supper-resolution range profile. When l1-norm is applied assparsity measure, a suboptimal linear programming algorithm is proposed, which can reduce the computation complexity and the demand of memory when comparing with basis pursuit. Eventually, the parameter estimation performance of SCA is analyzed. Theoretical analysis and numerical results indicate that the estimator of parameter is biased, where the bias and variance of the parameter estimation error depends on whether the corresponding atom is active in thegiven signal.Subsequently, several SCA-based ISAR imaging algorithms are studied. Aiming at the ideal point scatterer model, a two-dimensional overcomplete dictionary is constructed. Because it can not meet the demand of (quasi)real time imaging to compute the matrix-vector product by the matrix sparsity, an FFT-based two-dimensional united supperresolution algorithm is proposed. To reduce the imaging time much more, a Toeplitz matrix-based two-dimensional decoupled supperresolution algorithm is put forward on the basis of decopling the radar observation model. Furthermore, considering the nonuniform rotation of radar target, the concept of parameter-indexed dictionary family is proposed and a new method is developed to estimate the parameters of multi-component LFM signal with single degree of freedom, with which the instantaneous Doppler frequencies are resolved.Finally, the technique of multi-band and multi-resolution radar signal synthesis is studied with the application of sparse representation model of radar target. On the basis of GTD model and ideal point scatterer model, the observations of multi-band radars are analyzed and a SCA-based method is provided for the formation of range profile by synthesizing the multi-band signals. Besides the synthesis of wide-band signals, we also discuss the synthesis processing of multi-resolution radar signals for the purpose of sea-surface target detection. Practically, the range resolutions of different radars are not all the same, which is an obstacle for effective synthesis process. Based on the sparse distribution characteristics of the target, the technique of resolution matching processing is developed, which applies the prior of radar target and sea clutter to improve the range resolution and paves the way for signal synthesis.