微波成像中的参数化稀疏表征模型

李刚 张颢 孟华东 刘一民 王希勤

摘 要：稀疏表征的任务是找到一个基信号矩阵，在雷达回波数据域和稀疏域之间构建一个线性映射。经典稀疏表征模型中，基信号矩阵是预先设定的，例如：傅里叶矩阵、小波矩阵等等，而且在稀疏求解过程中是固定不变的。然而，雷达目标往往存在非合作运动，这将给雷达回波带来未知的距离徙动和频率调制，导致传统基矩阵无法实现非合作目标回波信号的稀疏表征。为解决这一难题，提出了参数化稀疏表征模型，构建了以目标特征状态为参数的基信号矩阵，并实现了目标运动状态估计与稀疏恢复的联合求解。仿真和实测雷达数据实验表明，参数化稀疏表征模型能够有效地提高雷达图像质量。

关键词：压缩感知 雷达成像 稀疏表征 字典学习

Abstract：The goal of sparse representation is to find a dictionary matrix that maps radar signals onto a sparse domain.In traditional models of sparse representation，the dictionary is pre-designed and fixed during the solution process.The popular dictionaries include Fourier and Wavelet matrices.However，the non-cooperative motion of the target causes unknown range migration and frequency modulation. Therefore，traditional dictionaries cannot ensure the sparse representation of the echo from a non-cooperative target.To solve this problem，we propose parametric sparse representation model，create the dictionary related to target motion status parameters，and simultaneously achieve the sparse representation and the parameter estimation.Simulations and experiments on real radar data show that parametric sparse representation is helpful to improve the quality of radar images.

Key Words：Compressed sensing；Radar imaging；Sparse representation；Dictionary learning

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