隨著科技文明的發達，影像重建議題廣泛應用在許多領域，舉凡醫學、電腦、工業、交通到民生等方面均會使用到，尤其在保全上深具應用價值。另外，在國防安全、影像雷達方面，此技術扮演不可或缺的角色，亦是未來發展的重點之ㄧ。因此，本研究分成水面上與水面下兩部份之影像重建為研究主軸。在第一部份中，以雷達波入射目標物體，然後收集回波，藉由這些回波配合演算法便可把目標物體的形狀推算出來，可應用於飛機與船艦等的雷達目標探測。
在陸地上的微波，國內外有許多學者在做微波成像的相關研究，由於微波成像技術不必將儀器與被測的物體做直接的接觸，因此可以廣泛被運用在工業上的非破壞性檢測，軍事上的雷達影像、以及醫學上做人體內部的影像處理。但如果直接運用到水下或者是海洋環境，則會因為電磁波在水中的衰減率極高，在實際運用上會受到相當大的限制。然而在水域環境中，聲波比起光波和電磁波較不容易被吸收，是水中遠距離傳播最好的選擇，所以聲波是水中最佳的探測工具。因此在第二部份中，將此理論推廣至水面下，將雷達波改為聲波入射，同樣藉由這些散射波推知水面下物體的形狀。
此論文主要是使用動差法來推算出散射值，所以使用到大型矩陣，此種陣列結構在實際應用上有急速增加的趨勢，數值分析最引人入勝之處在於它可靠的正確性，也因此近年來研究人員花費了龐大的努力在此方面。本研究也成功將逆散射問題改寫成一個求最小值的問題，為了求最小值的問題，本論文是利用粒子群演算法(Particle swarm optimization, PSO)。粒子群演算法是一種藉由隨機的選擇，在參數空間中進行最佳化的搜尋法則；在運算的過程中，數值計算不需要進行微分的動作，因此，不會陷於區域的最佳解，即使假設的初始值與精確值相差甚遠時，此法亦能避開區域極值而收斂到問題的整體極值。利用粒子群演算法來求得該最小值問題的解，這種強韌的特性，就可重建出在自由空間中二維散射體的形狀。

The image reconstruction techniques have been applied to many areas, including medicine, computer, industry, traffic and human life, especially in the safety control. The image reconstruction also plays an important role in national defense. It will be well developed in the future. Therefore, this research was focused on the image reconstruction of both terrestrial and underwater environments. In the first part, the target is illuminated by plane electromagnetic waves. The scattered waves are then collected for imaging by signal processing techniques. This technology can be applied to the aircraft and ship detection.
There have been many studies involved in the terrestrial microwave imaging. Through the imaging techniques, the target objects do not need to appear near the instrument. The microwave has been widely applied to non-destructive detection in industry, radar images in military, and image processing of human body in medicine. However, the microwave is not suitable in underwater environments due to its limited propagation distance. Alternatively, the acoustic wave can propagate very far and thus becomes a good candidate of underwater imaging. In the second part, we extend the terrestrial microwave imaging technique to treat underwater acoustic imaging.
In this thesis, we utilize the moment method to calculate the scattered fields of objects.
This method has been proved to be accurate and efficient by many researchers. The inverse scattering problem was successfully transformed into the minimization of a cost function. This cost function was minimized by the PSO (particle swarm optimization) method. As the minimum of the cost function is reached, the shape of the target object was reconstructed simultaneously. The PSO algorithm is an ideal searching principle on parameter space by using random choice. During the calculation, there is no differential operation. Nearly global optimum can be ficiently achieved by the PSO algorithm. In this study, the PSO was successfully applied to both the terrestrial microwave and underwater acoustic imaging.

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