微波與無線電波相比，微波有頻率高、波長短、訊息量大、方向性佳還有能穿透電離層等優點。微波成像是一種以微波作為訊號傳遞的成像方法，屬於電磁逆散射問題。其原理是用微波照射被測物體，然後通過物體外部散射場的測量值來重建物體的形狀或介電係數分布。由於介電系數與生物組織的含水量密切相關，所以微波成像常用來作生物組織的成像。
    本論文是在探討非平坦表面下之非均勻物體進行物體重建的問題，吾人利用已知邊界條件及量測到的散射場值，可以推導出一組積分方程式，再由散射場積分方程式算出電場，將逆散射問題轉換成最佳化問題，接著使用自我適應之動態差異型演化法(SADDE)重建出物體位置及介電系數分佈，並比較其對非均勻物體重建之蒐尋速度及穩定性。
    將一週期性函數設定為已知表面，將非均勻介質物體，先推導其數學式，利用等效電流算出物體之積分方程式，再使用動差法將其轉換成矩陣，在電腦程式中計算散射場，進行數值模擬。最後利用自我適應之動態差異型演化法重建出非平坦表面下之非均勻介質物體，在任何的初始猜測值中，自我適應之動態差異型演化法都有辦法收斂到整體的極值，所以在數值模擬中，即使一開始的猜測值遠大於實際值，吾人還是可以求得準確的物體之介電系數分佈，且在散射場中加入雜訊後，仍可以得到良好的重建結果。

This thesis is to explore the problem of reconstruction of non-uniform objects under the surface. We initially consider objects as two-dimensional square matrix, and each cell puts different dielectric coefficients to indicate that the object is a non-uniform medium object. By placing the square matrix in the half space below the non-flat surface and calculating the dielectric constant of these square arrays, the position and dielectric coefficient distribution of the object can be reconstructed.
In this paper, we will use the non-uniform medium object as the main axis to explore the number of different objects and the distribution of dielectric coefficients in this environment. We use the self-adaptive dynamic differential evolution method (SADDE) reconstruction to simulate the non-uniform objects. Search speed and stability of reconstruction.
Set a periodic function to a known surface, derive the mathematical expression from the non-uniform medium object, calculate the integral equation of the object using the equivalent current, and convert it into a matrix using the motion difference method, and calculate it in the computer program. Scattering field for numerical simulation. Finally, the self-adaptive dynamic difference evolution method is used to reconstruct the non-uniform medium object under the surface. In any initial guess, the self-adaptive dynamic difference evolution method has a way to converge to the global extremum, so in numerical simulation In the mean, even if the initial guess is much larger than the actual value, we can still obtain the accurate distribution of the dielectric coefficient of the object, and after adding noise to the scattering field, good reconstruction results can still be obtained.

目錄
誌謝	I
中文摘要	II
Abstract	IV
圖目錄   VIII 
第一章簡介	1
1.1 研究動機與相關文獻	1
1.2 本研究之貢獻	10
1.3 各章內容簡述	10
第二章非平坦介質表面在半空間中的正散射理論	12
2.1 正散射的理論公式推導	12
2.2 動差法求正散射公式	16
2.3 正散射的理論數值驗證	20
第三章 演算法	22
3.1自我適應之動態差異型演化法(Self-Adaptive Dynamic Differential Evolution)	22
3.2非同步粒子群聚最佳化法(Asynchronous Particle Swarm Optimization)	30
3.3正則化法(Regularization)	40
第四章數值分析及結果模擬	42
第五章結論	60
參考文獻	61


圖目錄
圖2-1 週期性非平坦表面及掩埋物示意圖	13
圖2-2 驗證正散射模擬示意圖	21
圖3-1 自我適應之動態差異型演化法流程圖	23
圖3-2 自我適應之動態差異型演化法中突變方法一的示意圖	25
圖3-3 自我適應之動態差異型演化法中突變方法二的示意圖	26
圖3-4自我適應之動態差異型演化法中的交配向量於一個二維目標函數等位線圖描述的示意圖	28
圖3-5粒子群聚法流程圖	32
圖3-6粒子群聚法中於二維目標函數等位線圖	33
圖3-7三種邊界條件示意圖	35
圖3-8非同步粒子群聚法流程圖	39
圖4-1-1物體切割數為4X4之介質物體原始介電系數分佈	45
圖4-1-2例子一使用SADDE經過500次疊代之成像結果	46
圖4-1-3例子一以SADDE加入不同正則化因子後重建出的DEPS	46
圖4-1-4例子一以SADDE加上正則化因子10^(-5)重建之500代成像結果	47
圖4-1-5例子一之DEPS、DP趨勢圖	47
圖4-2-1物體切割數為6X6之介質物體原始介電系數分佈	49
圖4-2-2例子二以SADDE重建之500代介電系數分佈結果	49
圖4-2-3例子二以SADDE加入不同正則化因子後重建出的DEPS	50
圖4-2-4例子二以SADDE加上正則化因子10^(-5)重建之500代成像結果	50
圖4-2-5例子二之DEPS、DP趨勢圖	51
圖4-2-6例子二以特殊條件重建之500代介電系數分佈結果	52
圖4-2-7例子二以特殊條件加入不同正則化因子後重建出的DEPS	52
圖4-2-8例子二以特殊條件加上正則化因子10^(-5)重建之500代成像結果	53
圖4-3-1物體切割數為6X6之矩形介質物體原始介電系數分佈	55
圖4-3-2例子三以SADDE重建之500代介電系數分佈結果	56
圖4-3-3例子三以SADDE加入不同正則化因子後重建出的DEPS	56
圖4-3-4例子三以SADDE加上正則化因子10^(-6)重建之500代成像結果	57
圖4-3-5例子三之DEPS、DP趨勢圖	57
圖4-3-6例子三以APSO重建之500代介電系數分佈結果	58
圖4-3-7例子三以APSO加入不同正則化因子後重建出的DEPS	58
圖4-3-8例子三以APSO加上正則化因子10^(-5)重建之500代成像結果	59

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