本論文研究穿牆多導體影像問題，利用非同步粒子群聚法(Asynchronous Particle Swarm Optimization)來處理埋藏於牆壁之後的電磁成像問題。
    將未知形狀的物體，埋藏在牆壁之後，從外部入射電磁波照射埋藏在牆壁之後的未知物體，並在牆壁外部量測其散射場，利用在導體表面的邊界條件及量測到的散射電場，可推導出一組非線性積分方程，將散射場積分方程式透過動差法求得散射電場相關資訊。在此使用傅立葉級數展開及描述物體的形狀，將電磁成像問題轉化為求解最佳化問題，並在演算法中使用非同步粒子群聚法重建埋藏於牆後之雙導體之形狀。藉由將量測而得的散射場和非同步粒子群聚法所計算出的散射場數值相比較，若兩個散射場之差值越小，則表示重建出來的未知物體越良好。
    不論初始的猜測值如何，非同步粒子群聚法總會收斂到全域極值(Global Extreme)，因此，在數值模擬顯示中，即使最初的猜測值與實際值相差甚遠，我們仍然可求得準確的數值解，成功的重建出物體形狀函數，量測的散射場即使加入高斯分佈的雜訊，依然可以得到良好的重建結果。

This paper presents an inverse scattering problem for the through-wall imaging problem. Two separate perfect-conducting cylinders of unknown shapes are hidden behind a homogeneous building wall and illuminated by the transverse magnetic(TM) plane wave.
    After an integral formulation, a discretization using the method of moment (MoM) is applied. The through-wall imaging (TWI) problem is recast as a nonlinear optimization problem with an objective function defined by the norm of a difference between the measured and calculated scattered electric field. Thus, the shape of metallic cylinder can be obtained by minimizing the objective function.
    The Asynchronous particle swarm optimization is employed to find out the global extreme solution of the object function. Numerical results demonstrate even when the initial guesses are far away from the exact shapes, and then the multiple scattered fields between two conductors are serious the good reconstruction can be obtained.
In addition, the effect of Gaussian noise on the reconstruction result is investigated and through the numerical simulation shows that we can still get good results of reconstructions.

第一章	簡介…………………………………………………1
1.1節	研究動機與相關文獻………………………………1
1.2節	本研究之貢獻………………………………………7
1.3節	各章內容簡述………………………………………7
第二章	多導體在半空間中的逆散射理論…………………9
2.1節	正散射的理論公式推導……………………………9 
2.2節	數值方法……………………………………………15
2.2.1節	動差法於積分方程式的應用………………………15
2.2.2節	非同步粒子群聚最佳化法…………………………17
第三章	數值模擬結果………………………………………22
3.1節	Fourier series描述重建的形狀之數值模擬…………22
第四章	結論…………………………………………………42
參考文獻………………………………………………………43
圖 2-1 二維雙導體在穿牆的示意圖…………………………………14
圖 2-2 非同步粒子群聚法流程圖……………………………………19
圖 2-3 二維問題中，不同邊界條件示意圖…………………………21
圖 3-1(a) 例子1雙導體在穿牆的形狀函數的重建情形。加號線(+)代表實際的形狀函數，虛線(--)代表初始猜測的形狀，實線則代表最後所重建之圖形。…………………………25
圖 3-1(b) 參數相對誤差隨代數變化趨勢圖………………………26
圖 3-1(c) 例子1在不同準位的雜訊干擾下對DR值的影響………27
圖 3-1(d) 例子1雙導體在穿牆兩物體距離小於一波長形狀函數的重建情形。+號線(++)代表實際的形狀函數，虛線(--)代表初始猜測的形狀，實線代表最後所重建之圖形。…………28
圖 3-1(e) 兩物體小於一波長時參數相對誤差隨代數變化趨勢圖…29
圖 3-2(a) 例子2雙導體在穿牆的形狀函數的重建情形。加號線(++)代表實際的形狀函數，虛線(--)代表初始猜測的形狀，實線則代表最後所重建之圖形。…………………………31
圖 3-2(b) 參數相對誤差隨代數變化趨勢圖………………………32
圖 3-2(c) 例子2在不同準位的雜訊干擾下對DR值的影響………33
圖 3-2(d) 例子2雙導體在穿牆兩物體距離小於一波長形狀函數的重建情形。+號線(++)代表實際的形狀函數，虛線(--)代表初始猜測的形狀，實線代表最後所重建之圖形。………34
圖 3-2(e) 兩物體小於一波長時參數相對誤差隨代數變化趨勢圖…35
圖 3-3(a) 例子3雙導體在穿牆的形狀函數的重建情形。加號線(++)代表實際的形狀函數，虛線(--)代表初始猜測的形狀，實線則代表最後所重建之圖形。…………………………37
圖 3-3(b) 參數相對誤差隨代數變化趨勢圖………………………38
圖 3-3(c) 例子3在不同準位的雜訊干擾下對DR值的影響………39
圖 3-3(d) 例子3雙導體在穿牆兩物體距離小於一波長形狀函數的重建情形。+號線(++)代表實際的形狀函數，虛線(--)代表初始猜測的形狀，實線代表最後所重建之圖形。…………40
圖 3-3(e) 兩物體小於一波長時參數相對誤差隨代數變化趨勢圖…41

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