本論文提出一數值方法，主要目的為重建非均勻介電物體之成像。於逆散射方面，將逆散射問題轉換為最佳化問題之後，首先利用遺傳演算法(genetic algorithm)，得一最佳化解或可接受之解，再串疊牛頓迭代法(Newton-type iterative method)，以快速收斂至更精確之解。 數值方法之執行過程，其入射波採用多方向連續照射之方式，以收集較完整之材質特性資訊。於理論推導方面，本研究考慮完整之非線性公式，以提高解之精確度。即使介電物體具有較複雜之材質特性分佈(不平滑)，或者介電體材質特性分佈與環境之材質特性具有較高之對比度，此數值方法亦能適用。 就大部分較簡單之例子而言，遺傳演算法即可得到相當良好之解。然而，對於較複雜之例子，即考驗著遺傳演算法之強健性。本論文以演傳演算法所得之解，當作牛頓法之初始猜測值。藉由遺傳演算法之全域搜尋特性，以求得可接受之解，期望此解對於區域性搜尋之牛頓法而言，可能為適當之初始猜測值。串疊之方法比較單一遺傳演算法，或者單一牛頓迭代法，其解之精確度勢必較高。本研究模擬之數值結果顯示，此串疊之數值方法運用於重建非均勻介電物體之材質特性分佈，得到良好之重建結果。 In this paper, we propose a method, which combines a genetic algorithm (GA) with a Newton-type iteration for the reconstruction of permittivity distribution of two-dimensional (2-D) dielectric objects. The method is based on a multi-illumination multiview processing. In particular, by taking account into the complete nonlinear formulations, the permittivity distribution of the objects could be highly-contrasted and complicated inhomogeneous. First, the inverse problem is recast as a global nonlinear optimization problem, which is solved by a GA. Then, the solution obtained by the GA is taken as an initial guess for the Newton-type iteration method. This method is tested by considering several numerical examples, and it is found that the performance of this combination method is better than the individual GA and the individual Newton-type iteration method. Numerical results show that satisfactory reconstruction has been obtained.
