非平坦表面下之週期性非均勻介質物體成像

Microwave Imaging of a Periodic Inhomogeneous Dielectric Object Buried in Rough Surfaces

洪博捷(Bo-Jie Hong)

指導教授 ： 丘建青

淡江大學/工學院/電機工程學系碩士班/碩士(2019年)

https://doi.org/10.6846/TKU.2019.00429

摘要

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。

關鍵字

微波成像 ； 非均勻介質物體 ； 自我適應之差異型演化法 ； 非同步粒子群聚法 ； 正則化

並列摘要

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.

並列關鍵字

Microwave Imaging ； Inhomogeneous Dielectric Object ； Self-Adaptive Dynamic Differential Evolution (SADDE) ； Asynchronous Particle Swarm Optimization(APSO) ； Regularization

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