Sparse ISAR Imaging Algorithm Based on Bayesian-Lasso
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摘要: 逆合成孔径雷达(ISAR)目标回波具有明显的稀疏特征，传统的凸优化稀疏ISAR成像算法涉及繁琐的正则项系数调整，严重限制了超分辨成像的精度及便捷程度。针对此问题，该文面向非约束Lasso正则化模型，建立分层贝叶斯概率模型，将非约束的
$ {\ell _1}$ 范数正则化问题等效转化成稀疏拉普拉斯先验建模问题，并在分层贝叶斯Lasso模型中建立正则项系数依赖的概率分布，从而为实现完全自动化参数调整提供便利条件。考虑到目标稀疏散射特征和多超参数的高维统计特性，该文应用吉布斯(Gibbs)随机采样方法，实现对ISAR目标稀疏特征的求解，并同步获取包括正则项系数在内的多参数估计。基于该文研究方法可实现全部参数均通过数据学习获得，从而有效避免繁琐的参数调整过程，提升算法的自动化程度。仿真及实测数据均可证明该方法的有效性和优越性。Abstract: Due to the echoes of the Inverse Synthetic Aperture Radar (ISAR) imagery are spatially sparse, the conventional convex optimization for the sparse image recovery involves tedious adjustment for the regularization parameter, which seriously limits the accuracy and the convenience of the image formation. In this paper, the unconstrained least absolute shrinkage and selection operator (Lasso) model is introduced for the$ {\ell _1}$ regularization problem, and it is equivalently transformed into sparse Bayesian inference under the Laplacian prior. More specifically, a hierarchical Bayesian model is established. In such cases, multiple hyper-parameters with multi-level conditional probability distribution are introduced. Due to the equivalent transformation, the manual choice of the regularization parameter can be replaced by automatic determination under the hierarchical Bayesian model, which provides convenience of fully conditional probability adjustment. Considering the high dimensions of sparse image responses and multiple hyper-parameters, the Gibbs sampler is adopted, where the Bayesian posterior of the ISAR image and high-dimensional hyper-parameters can be solved with fully confidence. Based on the research in this paper, all parameters can be attained by data, therefore tedious parameter adjustment can be avoided, and the automation level of the algorithm can be improved. The effectiveness and superiority of this method are proved by both simulated and measured data experiments. -
表 1 贝叶斯Lasso算法流程
(1) 初始化${{{X}}^{\left( 0 \right)}}$, ${\beta ^{\left( 0 \right)}}$, ${{{\alpha}} ^{\left( 0 \right)}}$和${\lambda ^{\left( 0 \right)}}$并构造字典${{A}}$； (2) 设置老化期门限$T$和迭代次数$k$=$1,2, ··· ,K$，其中$K$为迭代总次数且$T < K$，开始循环采样； (3) 根据式(15)噪声精度$\beta $的条件后验概率密度分布$p\left( {\beta \left| {{{X}},{{Y}},{{\alpha}} ,\lambda } \right.} \right)$对$\beta $进行采样； (4) 根据式(16)正则化系数$\lambda $所服从的条件后验概率密度分布$p\left( {\lambda \left| {{{X}},{{Y}},{{\alpha}} ,\beta } \right.} \right)$对$\lambda $进行采样； (5) 根据式(17)超参数${{\alpha}} $所服从的条件后验概率密度分布$p\left( {{{\alpha}} \left| {{{X}},{{Y}},\lambda ,\beta } \right.} \right)$对${{\alpha}} $进行采样； (6) 根据式(19)目标${{X}}$所服从的条件后验概率密度分布$p\left( {{{X}}\left| {{{Y}},{{\alpha}} ,\lambda ,\beta } \right.} \right)$对${{X}}$进行采样； (7) 若$k > T$，收集${{X}}$的采样样本$\left[ {{{{X}}^{\left( T \right)}},{{{X}}^{\left( {T + 1} \right)}}, ··· ,{{{X}}^{\left( K \right)}}} \right]$，重复步骤(3)—步骤(6)直至收敛。 
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