本研究的目標在於建立一個運用於PCB檢測的X射線非破壞性檢測的影像重建演算法。X射線具有可穿透性，可探測物體的物性與內部缺陷，但是單獨的X射線投影僅僅只記錄投影中的資訊，並無法正確判斷出內藏的瑕疵位置，所以必須建立一套影像重建演算法。本研究採用線型感測器的斷層掃瞄系統，嘗試從數個不同角度對PCB做投影掃瞄。雖然受限於待測物的幾何限制，使得系統掃瞄時會有投影角度的限制，使得投影資訊不足。由於檢測目標主要為BGA錫球，因此在只有單一物質一種吸收率下，可將問題簡化成為重建二值影像，因此採用線性規劃演算法( Linear Programming, LP)在有限投影角度下重建電腦斷層掃瞄影像(computed tomography, CT)。另外為了讓Linear Programming可重建多值影像，提出多值重建的Linear Programming修正演算法。為了有效減少重建時間，以及消除有雜訊的投影誤差，本研究分別提出局部重建法和Moving average method 來改善Linear Programming演算法，均有改善影像效果。

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