本文關(guān)鍵詞： 逆散射 屬性散射模型 稀疏貝葉斯學習 稀疏表示 壓縮感知　出處：《清華大學》2015年博士論文　論文類型：學位論文

【摘要】：根據(jù)目標散射響應(yīng)與目標幾何結(jié)構(gòu)、雷達頻率、角度和極化之間的依賴關(guān)系,從極化電磁散射測量數(shù)據(jù)反演目標幾何結(jié)構(gòu)參數(shù)是一個重要的逆散射問題,具有非線性和不適定性。一般來說,問題模型的低維近似和模型參數(shù)的離散化可以將不適定問題轉(zhuǎn)化為適定問題,且提高維度和減小離散間隔會在改善建模精度的同時增加求解難度。本文研究的主要目的就是改善建模精度和克服不適定性。理想點散射模型由于只有兩個自由度而成為應(yīng)用最廣泛的參數(shù)化模型。圖像重建的本質(zhì)就是通過離散化這種模型的參數(shù)來求解逆散射問題的。特別是,超分辨和稀疏表示成像算法利用參數(shù)的離散值生成冗余字典矩陣,并通過引入先驗信息改善成像質(zhì)量,然而超線性增長的計算量和固有的網(wǎng)格誤差使其無法求解較大規(guī)模問題。為此,本文構(gòu)建了基于字典更新的p范數(shù)稀疏表示方法用于抑制網(wǎng)格誤差,同時,提出了基于外推濾波策略的子帶分解方法用于降低計算復(fù)雜度。理想點散射模型忽略了頻率和角度依賴等與目標局部結(jié)構(gòu)緊密相關(guān)的重要信息。根據(jù)幾何繞射理論提出的屬性散射模型,通過引入頻率和角度依賴改善了建模精度。然而,屬性散射模型存在方位依賴函數(shù)與標準散射體散射模型不一致、無法適應(yīng)弧形散射體建模、未考慮散射體遷移效應(yīng)和遮蔽效應(yīng)等缺陷。為了改善建模精度,本文從修改方位依賴函數(shù)、增加指向角依賴、引入位移遷移因子和增加窗函數(shù)等方面改進這種模型,使其從數(shù)學形式上統(tǒng)一球、圓臺、圓柱、二面角、三面角和矩形平板等六種標準散射體,實驗結(jié)果驗證了所提模型的表征能力。相比而言,改進屬性散射模型具有較高的自由度,這就意味著基于字典矩陣的逆散射方法將面臨無法承受的計算量。為此,本文使用推廣的復(fù)數(shù)域增量稀疏貝葉斯學習算法求解逆散射。這種算法使用導數(shù)直接優(yōu)化連續(xù)參數(shù),不僅可以避免字典矩陣帶來的計算負擔和網(wǎng)格誤差,還可以有效提升解的稀疏性及求解精度,復(fù)雜形狀目標逆散射實驗驗證了逆散射算法的有效性。在上述工作的基礎(chǔ)上,本文根據(jù)基本型多任務(wù)稀疏貝葉斯學習算法,提出了擴展算法用于求解極化逆散射問題,經(jīng)過重新設(shè)計先驗?zāi)Ｐ?避免了不相關(guān)任務(wù)間的信息共享。此外,還針對壓縮感知逆散射問題,提出了廣義迭代自適應(yīng)算法和引入矩陣濾波的改進增量稀疏貝葉斯學習算法,逆散射實驗驗證了算法的性能。今后還將研究極化雙站逆散射和三維逆散射等問題。
[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.
【學位授予單位】：清華大學
【學位級別】：博士
【學位授予年份】：2015
【分類號】：TN011

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