冲击噪声下基于混合LL2 -L1 优化求解的CSR 参数估计

针对冲击噪声环境下压缩感知雷达参数估计性能急剧下降的问题,提出一种新的鲁棒性参数估计方法。首先,根据压缩感知雷达参数估计的稀疏线性模型,基于Lorentzian 范数和L1 范数稀疏正则化构造冲击噪声背景下稀疏重构的混合LL2-L1 范数优化模型;然后,利用迭代加权最小二乘法和阈值收缩函数推导上述模型优化求解的一步迭代公式;最后,从理论上对文中算法的收敛性进行证明,并给出算法计算复杂度的定量分析。计算机仿真实验表明,文中算法在冲击噪声下支撑集的重构更精确、重构信号的精度更高、重构的计算量更小。

Parameter Estimation for CSR under Impulsive Noise Based on Mixed LL2-L1 Optimization

In the presence of impulsive noise, the degeneracy of the robustness of most existing sparse recovery algorithms results in a sharp decline in the performance of parameter estimation for compressed sensing radar (CSR). In this paper, a novel robust parameter estimation method used in impulsive noise environment LTSIRLS (Lorentzian based Threshold Shrinkaged IRLS) was proposed. Firstly, the mixed LL2-L1 optimization model for sparse recovery under impulsive noise environment was built based on Lorentzian constrained L1 regularization. Secondly, the iterative formulation was deduced by exploiting the IRLS (Iteratively Re-weighted Least Squares) and the threshold shrinkage function. Thirdly, the convergence property of the proposed algorithm was theoretically proved and the computational complexity was quantitatively analyzed. It is verified that the proposed method results in more accurate support and signal recovery, smaller computational burden.