在壓縮性感知中，最重要的步驟是如何將一個壓縮後的訊號恢復成它原本的樣子，也就是所謂的稀疏訊號重建問題。
　　本論文主要的貢獻在於提出一個能不斷更新與更正追蹤匹配所製造出解的演算法，追蹤匹配是用於做稀疏訊號重建的一個著名演算法。我們的演算法命名為漸進式正交追蹤匹配演算法，因為它不斷地更新欲重建的訊號，並漸進式地找出正確的解。這篇論文主要的貢獻在於提升重建的效能，同時不增加所需要的取樣數，換句話說，利用較多的運算時間來達到節省硬體成本的目的。
　　除此之外，本論文也提出漸進式過度偵測正交追蹤匹配演算法，用來處理實際應用中，當稀疏性未知的重建問題，這同時也是一個尚未被完美處理的追蹤匹配問題。本論文提出的演算法能夠快速地解出稀疏訊號重建問題，並同時保有相當好的重建表現。

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