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研究生:嚴中成
研究生(外文):Chung-chen Yan
論文名稱:三維近紅外光擴散光學斷層影像重建之數值計算研究
指導教授:潘敏俊
指導教授(外文):Min-chun PAN
學位類別:碩士
校院名稱:國立中央大學
系所名稱:機械工程學系
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2016
畢業學年度:104
語文別:中文
論文頁數:65
中文關鍵詞:三維擴散光學斷層造影有限元素法Tikhonov正則化腫瘤特徵辨識影像評估
外文關鍵詞:three-dimensional diffuse optical tomographyfinite element methodTikhonov regularizationidentification of tumorquantitative evaluation of image quality
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本論文針對應用於乳癌檢測之近紅外光擴散光學斷層造影系統,發展三維組織光學係數影像重建演算法。組織光學重建以擴散方程式為模型,並將演算法分為前向計算與反向計算兩部分。在前向計算中使用有限元素法求解擴散方程式,以獲得在特定光源及光學係數分布下量測點的穿透光資訊。在逆向計算中為了藉由量測得的光資訊來重建模型中的光學係數分布使用牛頓法來疊代,並求出使量測與理論之光訊息差異最小化的光學係數分布,並加入Tikhonov正則化加強重建之結果。藉由設計不同仿乳房光學特性之模擬案例,驗證本研究演算法對於腫瘤之光學特性對比度、幾何尺寸、及腫瘤位置等特徵之計算辨識能力,並藉由一維剖面圖、重建影像之均方誤差來進行定量,以及腫瘤及背景組織特徵之解析度來評估影像重建結果。在採用直徑80 mm之圓柱體為幾何模型,並於光源調變頻率為100 MHz的設定下執行造影案例分析,根據結果可知,可以順利重建離心距離為0 mm,且對比度為2倍、直徑15 mm之腫瘤,但在直徑20 mm效果最好,,而對於腫瘤角度、深度位置特徵具辨識能力。在光學係數方面,當腫瘤光學係數對比度大於2.5倍時則重建結果可能會高估其對比度,而吸收係數及散射係數對比度差異高於1.5倍時則容易出現串擾現象。
This study focuses on developing three-dimensional image reconstruction algorithm of near-infrared diffuse optical tomography (NIR DOT) system for detecting breast cancer. The image reconstruction algorithm of DOT is based on the diffusion equation, and involves both the forward calculation and inverse reconstruction. The forward calculation solves the diffusion equation by using the finite element method (FEM) for calculating the distribution of transmitted light under the condition of presumed light source and optical coefficient (absorption and scattering coefficients) of the model. The inverse calculation reconstructs the distribution of the optical coefficient by using Newton's method to minimize the difference between theory and measured data. Due to ill-posed nature of the inverse problem, Tikhonov regularization is utilized to stabilize the reconstruction result. For verification of developed reconstruction algorithm, different designated simulation cases, including different optical coefficients, size, and location of tumor, were used. The reconstruction results then were assessed by a set of resolution measures that compare reconstructed image with target one, and provide the quantitatively evaluation for the reconstructed image quality. Moreover, reconstruction images were also quantitatively evaluated by using mean square error (MSE). The evaluation results shows that, under condition of using 80-mm-diamater cylinder phantom, tumor with diameter more than 15 mm, located at the off-center distance 0 mm and contrast of 2, can be reconstructed. However, if the optical contrast of tumor were more than 2.5, it would lead to over-estimation of optical properties. It also shows significant crosstalk issue between absorption and scattering coefficients if the ratio of absorption-contrast to scattering-contrast is more than 1.5.
摘要 I
Abstract II
誌謝 III
目錄 IV
圖目錄 VI
表目錄 VIII
第一章 緒論 1
1-1 研究動機與目的 1
1-2 乳房組織光學特性 2
1-3 文獻回顧 5
1-4 論文架構 6
第二章 正向問題 7
2-1 有限元素法求解擴散方程式 8
第三章 逆向問題 12
3-1 建立逆向問題 12
3-2 雅可比(Jacobian)矩陣 13
3-3 雅可比(Jacobian)矩陣之正規化(normalization) 14
3-4 逆向問題之正則化(regularization) 15
第四章 模擬與驗證 16
4-1 模擬資料建立 16
4-2 影像重建 20
4-3 模擬驗證 21
4-3-1 幾何特徵辨識 22
4-3-2 光學特徵辨識 33
4-4 影像評估與分析 37
第五章 結論與未來展望 47
5-1 結論 47
5-2 未來展望 48
參考文獻 49
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