基于基尼系数和改进压缩感知的ISAR成像新方法研究

Compressed sensing(CS) supplies a new signal acquisition and reconstruction method.Although ISAR imaging based on CS has obtained some achievements at present, there are some problems to be solved. To improve the performance of compressed sensing ISAR imaging method, the project intends to carry out the the following work: (1) At present, l1, lp or l0 norm are popularly used in CS to measure the sparsity of signal. But these norms quantify sparsity in a way that runs counter to an intuitive understanding of sparsity. Gini index, as a more effective measure of sparsity, is to be explored to improve reconstruction performance. (2) In compressed sensing ISAR imaging, discretization of continuous parameters can make that these is mismatch between the used basis and actual basis, and then the performance of imaging degenerates greatly. To overcome the shortcoming, a reconstruction algorithm which can self correct perturbation is to be studied and a linear estimator is to be employed to improve the estimate accuracy of strong scattering points' amplitude and phase. (3) In CS based ISAR maneuvering target imaging, an imaging method in direction based on joint optimization and an imaging method in range based on modified-CS method will be studied. The research of the project will improve and extend existing CS theory, supply theory and technology foundation for CS applying into ISAR actual imaging, and has important significance for pushing the application of CS.

压缩感知（CS）提供了一种新的信号获取和重构方式，目前它在ISAR成像中已取得了一些成果，但仍存在一些问题需要解决。为了提高压缩感知ISAR成像方法的性能，拟开展以下工作：（1）目前，CS中一般采用l1、lp或l0范数来衡量信号的稀疏性，但这些范数确定稀疏的方式并不符合人们对稀疏的直觉理解。拟采用一种更加有效的稀疏测度-基尼系数提高重构性能。（2）在压缩感知ISAR成像中，连续参数的离散化会使得使用的基函数与真正的基函数不一致，此时成像性能明显下降。为了克服这个缺陷，拟研究一种能够自校正扰动的重构算法，并采用线性估计器提高强散射点幅度和相位的估计精度。（3）在基于CS的ISAR机动目标成像中，拟研究基于联合优化的方位维成像方法和基于CS修正方法的距离维成像方法。本项目的研究将完善和扩展现有的CS理论，为CS方法用于ISAR实际成像提供理论和技术基础，对推动CS的应用具有重要的意义。

压缩感知在ISAR成像中已取得了一些成果，但仍存在一些问题需要解决。本项目的主要研究内容包括：（1）为了提高压缩感知ISAR成像的质量，研究了基于基尼系数和log-sum最小化的稀疏重构算法；（2）为了减小压缩感知中偏离栅格对ISAR成像质量的影响，研究了基于偏离栅格的正弦信号重构算法和ISAR成像方法；（3）为了突破目前压缩感知仅用于ISAR平稳运动目标成像的局限，研究了基于压缩感知的机动目标ISAR成像方法。得到的重要结果：（1）得到了基于log-sum最小化的压缩感知ISAR成像方法，并为此方法提供了一种新的解释。与基于l1范数的方法相比，它能基于更少的测量值，或在更宽松的稀疏条件，或以更小的重构误差恢复信号。将此方法用于仿真正弦信号的频谱估计和实测ISAR数据的成像都得到了很好的结果。（2）得到了正弦信号偏离栅格的压缩感知重构算法，即将稀疏重构问题转换为联合优化问题，采用联合优化和线性估器计解决正弦信号偏离栅格的问题。（3）得到了基于时频基函数的压缩感知ISAR成像方法，将它用于美国海军研究实验室V.C.CHEN提供的MIG-25飞机成像中，不仅可以提高成像质量，而且能够抑制噪声。本项目的研究完善和扩展了现有的压缩感知理论，为压缩感知用于ISAR实际成像提供了理论和技术基础，对推动压缩感知的应用具有重要的意义。