我們在這本論文裡提出了一種全新的基於壓縮感測理論具修正有限孔徑效應之光聲斷層掃瞄影像重建技術。將造成有限孔徑效應即切向解析度失真的探頭空間脈衝響應整合於壓縮感測的光聲斷層掃描影像重建模型上，利用數學上的反摺積方法，以有效地消除平面非聚焦式探頭帶來的有限孔徑效應。 同時透過非線性的凸型最佳化法，此重建僅需要相對少量的掃描角度數量。因此，在同一重建影像品質的基準上，此重建法相較於傳統的演算法，所需資料量較少所以資料擷取所需時間較短。同時，因探頭的空間脈衝響應形成的有限孔徑效應而離掃瞄中心愈遠隨之下降的切向解析度，也可透過我們所提出的重建技術而大幅地改善。透過本論文所提出之重建演算法，運用於光聲斷層掃描上，不僅能使用訊雜比較好且接收面積較大的平面式探頭，能有效的消除切向解析度失真的問題，更可以有效地降低資料擷取時間和資料量，針對環形陣列探頭的光聲斷層掃描系統，更能夠有效降低系統成功。模擬與實驗結果驗證了本篇論文提出的重建技術不僅能有效地消除有限孔徑效應，更能夠降低資料擷取時間。

In this study, we propose a new compressive sensing (CS) based image reconstruction method for photoacoustic tomography (PAT) where the finite aperture effect is corrected. To eliminate the finite aperture effect, the proposed method adopts the spatial impulse responses (SIRs) of the finite-sized unfocused transducer into the discrete linear PAT imaging model for CS. By using the nonlinear recovery algorithm based on convex optimization, PAT can be reconstructed with highly incomplete data. Therefore, the number of measurements and the system cost needed for a certain image quality can be significantly reduced. In the mean time, retrospective restoration of the tangential resolution can be achieved because the SIRs of the unfocused transducer is incorporated in the CS. Simulation and experimental results demonstrate that this method can not only reduce the data acquisition time but also improve the degraded tangential resolution for PAT with finite-sized unfocused transducers.

摘要 5
Abstract 6
表目錄 13
第一章 緒論 14
1.1 光聲斷層掃描簡介 14
1.2 逆投影演算法 15
1.3 有限孔徑效應 18
1.4 壓縮感測簡介 22
1.5 研究動機與目的 25
1.6 論文架構 26
第二章 有限孔徑效應修正之壓縮感測影像重建 27
2.1 光聲斷層掃描感測矩陣 27
2.2 壓縮感測理論於光聲斷層掃描重建 32
第三章 模擬與實驗 38
3.1 模擬參數及設定 38
3.2 模擬結果與討論 40
3.3 實驗Data重建 56
第四章 結論與未來工作 66
4.1 結論 66
4.2 未來工作 67
參考文獻 73

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