稀疏激励的极化逆散射理论研究

发布时间：2018-02-28 11:30

本文关键词： 逆散射属性散射模型稀疏贝叶斯学习稀疏表示压缩感知　出处：《清华大学》2015年博士论文　论文类型：学位论文

【摘要】：根据目标散射响应与目标几何结构、雷达频率、角度和极化之间的依赖关系,从极化电磁散射测量数据反演目标几何结构参数是一个重要的逆散射问题,具有非线性和不适定性。一般来说,问题模型的低维近似和模型参数的离散化可以将不适定问题转化为适定问题,且提高维度和减小离散间隔会在改善建模精度的同时增加求解难度。本文研究的主要目的就是改善建模精度和克服不适定性。理想点散射模型由于只有两个自由度而成为应用最广泛的参数化模型。图像重建的本质就是通过离散化这种模型的参数来求解逆散射问题的。特别是,超分辨和稀疏表示成像算法利用参数的离散值生成冗余字典矩阵,并通过引入先验信息改善成像质量,然而超线性增长的计算量和固有的网格误差使其无法求解较大规模问题。为此,本文构建了基于字典更新的p范数稀疏表示方法用于抑制网格误差,同时,提出了基于外推滤波策略的子带分解方法用于降低计算复杂度。理想点散射模型忽略了频率和角度依赖等与目标局部结构紧密相关的重要信息。根据几何绕射理论提出的属性散射模型,通过引入频率和角度依赖改善了建模精度。然而,属性散射模型存在方位依赖函数与标准散射体散射模型不一致、无法适应弧形散射体建模、未考虑散射体迁移效应和遮蔽效应等缺陷。为了改善建模精度,本文从修改方位依赖函数、增加指向角依赖、引入位移迁移因子和增加窗函数等方面改进这种模型,使其从数学形式上统一球、圆台、圆柱、二面角、三面角和矩形平板等六种标准散射体,实验结果验证了所提模型的表征能力。相比而言,改进属性散射模型具有较高的自由度,这就意味着基于字典矩阵的逆散射方法将面临无法承受的计算量。为此,本文使用推广的复数域增量稀疏贝叶斯学习算法求解逆散射。这种算法使用导数直接优化连续参数,不仅可以避免字典矩阵带来的计算负担和网格误差,还可以有效提升解的稀疏性及求解精度,复杂形状目标逆散射实验验证了逆散射算法的有效性。在上述工作的基础上,本文根据基本型多任务稀疏贝叶斯学习算法,提出了扩展算法用于求解极化逆散射问题,经过重新设计先验模型,避免了不相关任务间的信息共享。此外,还针对压缩感知逆散射问题,提出了广义迭代自适应算法和引入矩阵滤波的改进增量稀疏贝叶斯学习算法,逆散射实验验证了算法的性能。今后还将研究极化双站逆散射和三维逆散射等问题。
[Abstract]:According to the dependence between target scattering response and target geometry, radar frequency, angle and polarization, it is an important inverse scattering problem to retrieve the geometric structure parameters from polarimetric electromagnetic scattering measurement data. Generally speaking, the low dimensional approximation of the problem model and the discretization of the model parameters can transform the ill-posed problem into a suitable one. The main purpose of this paper is to improve the modeling accuracy and overcome the ill-posed problem. The ideal point scattering model has only two freedoms. The essence of image reconstruction is to discretize the parameters of this model to solve the inverse scattering problem. Super-resolution and sparse representation imaging algorithms generate redundant dictionary matrices using discrete values of parameters and improve imaging quality by introducing prior information. However, the computational complexity of superlinear growth and the inherent grid error make it impossible to solve the larger scale problem. In this paper, a dictionary updated p-norm sparse representation method is proposed to suppress the grid error. A subband decomposition method based on extrapolation filtering strategy is proposed to reduce the computational complexity. The ideal point scattering model ignores important information closely related to the local structure of the target, such as frequency and angle dependence. On the attribute scattering model, The precision of the model is improved by introducing frequency and angle dependence. However, the azimuth dependent function of the attribute scattering model is inconsistent with the standard scattering model, so it can not adapt to the arc scattering model. In order to improve the modeling accuracy, this paper improves this model by modifying the azimuth dependent function, increasing the direction-angle dependence, introducing the displacement migration factor and increasing the window function, etc. Six kinds of standard scatterers, such as sphere, platform, cylinder, dihedral angle, trihedral angle and rectangular plate, are unified in mathematical form. The experimental results verify the characterization ability of the proposed model. The improved attribute scattering model has a higher degree of freedom, which means that the inverse scattering method based on dictionary matrix will face unbearable computation. In this paper, the generalized incremental sparse Bayesian learning algorithm in complex domain is used to solve the inverse scattering. In this algorithm, the derivative is used to directly optimize the continuous parameters, which can not only avoid the computational burden and the grid error caused by the dictionary matrix. It can also improve the sparsity and accuracy of the solution effectively. The inverse scattering experiment of complex shape objects verifies the effectiveness of the inverse scattering algorithm. Based on the above work, the basic multi-task sparse Bayesian learning algorithm is used in this paper. An extended algorithm is proposed to solve the polarization inverse scattering problem. A priori model is redesigned to avoid the information sharing between unrelated tasks. In addition, the compressed sensing inverse scattering problem is also proposed. A generalized iterative adaptive algorithm and an improved incremental sparse Bayesian learning algorithm with matrix filtering are proposed. The inverse scattering experiment verifies the performance of the algorithm. In the future, the problems of polarized bistatic inverse scattering and three-dimensional inverse scattering will be studied.
【学位授予单位】：清华大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：TN011

【相似文献】