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姓名	林妤謙(YU-CHIAN LIN)  查詢紙本館藏	畢業系所	機械工程學系
論文名稱	最佳化邊緣保持正則反算之擴散光造影及驗證
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檔案	[Endnote RIS 格式]    [Bibtex 格式]    [相關文章]   [文章引用]   [完整記錄]   [館藏目錄]   至系統瀏覽論文 (2028-1-31以後開放)
摘要(中)	擴散光斷層造影(Diffuse optical imaging, DOI)為利用近紅外光射入生理組織，並由光偵測器蒐集離開組織光資訊來進行組織光學係數分佈影像重建，影像重建分為前向計算與逆向問題兩個部分。前向計算藉由擴散方程式呈現近紅外光在組織中的傳遞情形，並利用限元素法(Finite element method, FEM)來獲得不同位置的光資訊；逆向問題則通過牛頓法進行疊代，藉由將量測資料與前向計算的差值最小化來重建組織光學係數分佈，進而判斷腫瘤大小及位置，因其屬於非線性(Nonlinear)且病態(Ill-posed)的問題，在處理時需加入正則化項改善解不唯一導致求解過程數值不穩定的問題，因此正則化法與正則參數(λ)的選擇對於計算來說極為重要。本研究在影像重建時使用邊緣保留正則化(Edge-preserving regularization, EPR)來限制並縮小解的範圍，將其與先前已有的吉洪諾夫正則化(Tikhonov regularization, TR)做比較，透過在EPR及TR中加入U曲線準則使其能夠自動決定最佳化λ，以客觀決定正則化計算參數，不會因為使用者對影像反算熟悉程度不同而計算結果有差異，作為團隊先前已開發的DOpIm造影軟體系統影像重建的不同選擇；並透過在原RCSD中對Rcontrast分別加入置入物及背景的標準差，來修正原本對比及尺寸辨識率(CSD)僅考慮光學係數平均值所造成的過擬合問題，並在Rsize中加入背景區域光學係數的均方誤差修正僅考慮到置入物區域光學係數的均方誤差的問題，使RCSD數值更貼近主觀判斷的二維重建影像。 研究中設計不同置入物大小、個數、離心距及光學係數對比度的仿體分別進行8組數值模擬和6組實驗數據量測，使用EPR來比較三種所選擇固定的正則參數50、1、0.02與U曲線準則所選擇之最佳化λ其重建影像差異；進一步比較同樣使用U曲線準則時，使用EPR及TR兩種正則化法的重建影像品質差異。從二維重建影像及解析度結果可發現，相較於自定義之λ值，使用U曲線準則重建影像在各案例中均能得到較佳的結果；而由CSD計算可發現使用U曲線準則在模擬中有25%(模擬8組中的2組)獲得最佳吸收係數解析度，為上述五種正則參數及正則化法中第三佳的計算方式，在最佳散射係數解析度則有87.5%(模擬8組中的7組)，為上述五種正則參數及正則化法中最佳計算方式，在實驗中則有33.3%(實驗6組中的2組)獲得最佳吸收係數解析度，為上述五種正則參數及正則化法中第二佳的計算方式，在最佳散射係數解析度則有83.3%(實驗6組中的5組)，為上述五種正則參數及正則化法中最佳計算方式。由計算結果可發現，當模擬案例設計越複雜時所需的CPU計算時間越久，但使用U曲線準則時在不同案例中的CPU計算效率並無明顯變化，相較於自定義之λ值，能在較短的計算時間內獲得較佳的重建影像。比較U曲線EPR-λ與自定義λ可知，在逆向計算中其光學係數更新值會依每次疊代而不同，當以指定λ運算時不論光學係數更新值為何，在正則化計算中皆以相同正則參數作計算；而U曲線準則所選擇的λ則會依照每次疊代的光學係數更新值，來決定該次運算時的最佳λ，因此無法透過指定U曲線準則所決定的最佳λ值，來重現出與U曲線準則相同的重建結果。 進一步比較使用EPR與TR之U曲線準則影像重建可發現，TR的重建結果在散射係數解析度上較容易取得較佳的重建結果(50%,實驗6組中的3組)，且在重建影像背景中較無雜訊假影，但在置入物邊界判別能力上沒有EPR清晰，適用於追求穩定性且對特徵細節要求較低的狀況；反之，EPR在重建影像上雖相較TR有較多的雜訊假影，但在置入物影像位置及大小的辨別上更為清晰，且在實驗數據量測案例中，使用EPR之U曲線準則能在二維重建影像的吸收及散射係數特徵上獲得兩者平均較佳的結果，在三置入物的案例中也能重建的比TR清晰，適用於需高精度置入物特徵且對雜訊要求較低的狀況。
摘要(英)	Diffuse Optical Imaging (DOI) utilizes near-infrared light to probe biological tissues, with detectors collecting the transmitted light to reconstruct the spatial distribution of optical coefficients. The image reconstruction process consists of two main components: forward modeling and the inverse problem. Forward modeling describes the propagation of near-infrared light in tissue using the diffusion equation and employs the Finite Element Method (FEM) to obtain light distribution at different locations. The inverse problem, solved iteratively using Newton’s method, minimizes the difference between measured data and forward model predictions to reconstruct the optical coefficient distribution, enabling tumor size and location estimation. Since the inverse problem is inherently nonlinear and ill-posed, regularization is required to stabilize the solution and mitigate numerical instability caused by non-uniqueness. Thus, selecting an appropriate regularization method and parameter (λ) is crucial for accurate reconstruction. This study incorporates Edge-Preserving Regularization (EPR) to constrain and refine the solution space during image reconstruction and compares its performance with Tikhonov Regularization (TR). To objectively determine the optimal λ and minimize user-dependent variability in reconstruction outcomes, the U-curve criterion is integrated into both EPR and TR. This enhancement provides an alternative reconstruction approach for the DOpIm imaging software system developed by our team. Additionally, modifications were made to the Contrast and Size Detection Rate (CSD) metric to address overfitting issues caused by considering only the mean optical coefficient values. Specifically, standard deviations of the optical coefficients in the inclusion and background regions were incorporated into the original Rcontrast metric, while Rsize was refined by including the mean square error of background optical coefficients to correct for previous evaluations that only considered inclusion regions. These refinements ensure that the Revised CSD (RCSD) metric better aligns with subjective visual assessments of 2D reconstructed images. In this study, eight numerical simulations and six experimental measurements were conducted using phantoms with varying inclusion sizes, numbers, eccentricities, and optical contrast ratios. EPR was employed to compare the reconstructed image quality using three fixed regularization parameters (50, 1, and 0.02) versus the optimal λ determined by the U-curve criterion. Furthermore, image reconstruction results using the U-curve criterion were compared between EPR and TR. Analysis of the 2D reconstructed images and resolution results indicates that the U-curve-based reconstruction consistently outperforms predefined λ values across all cases. According to CSD calculations, in simulations, the U-curve criterion yielded the best absorption coefficient resolution in 25% (2 out of 8 cases) and the best scattering coefficient resolution in 87.5% (7 out of 8 cases). In experiments, it achieved the best absorption coefficient resolution in 33.3% (2 out of 6 cases) and the best scattering coefficient resolution in 83.3% (5 out of 6 cases). The results further show that as the complexity of simulation cases increases, the required computation time also increases. However, when using the U-curve criterion, computational efficiency remains stable across different cases. Compared to fixed λ values, the U-curve criterion enables faster computation while achieving superior reconstruction quality. Additionally, comparing U-curve EPR-λ with manually specified λ values reveals that in the inverse problem, the optical coefficient update varies at each iteration. With a fixed λ, the same regularization parameter is applied throughout all iterations regardless of coefficient updates. In contrast, the U-curve criterion dynamically adjusts λ in each iteration based on the current optical coefficient update, ensuring optimal regularization at each step. Consequently, it is not possible to replicate the U-curve-based reconstruction results solely by manually specifying the final λ value determined by the U-curve criterion. Further comparison of image reconstruction using the U-curve criterion with EPR and TR reveals distinct performance characteristics. TR achieves superior scattering coefficient resolution in 50% (3 out of 6 experimental cases) and exhibits lower noise artifacts in reconstructed image backgrounds. However, it lacks the boundary delineation clarity of EPR, making it more suitable for applications prioritizing stability over fine structural details. Conversely, while EPR produces more noise artifacts compared to TR, it provides clearer identification of inclusion locations and sizes. In experimental measurements, the U-curve-based EPR reconstruction consistently achieves a more balanced performance in both absorption and scattering coefficient resolution across 2D reconstructed images. Moreover, in cases involving three inclusions, EPR reconstructs images with greater clarity than TR, making it the preferred choice for applications requiring high-precision inclusion characterization where some tolerance for noise is acceptable.
關鍵字(中)	★ 擴散光學斷層造影 ★ 有限元素法 ★ Edge-preserving正則化 ★ Tikhonov正則化 ★ 影像重建 ★ 正則參數	關鍵字(英)
論文目次	摘要 i Abstract iii 目錄 vii 圖目錄 ix 表目錄 xii 專有名詞與符號說明 xiii 第一章 緒論 1 1-1 研究動機與目的 1 1-2 乳房組織光學特性與醫學影像造影 3 1-2-1 乳房組織光學特性 3 1-2-2 醫學影像造影 6 1-3 文獻回顧 7 1-3-1 反算正則化與正則參數 7 1-3-2 實驗室先前基礎 9 1-4 論文架構 11 第二章 影像重建基礎及前向計算 12 2-1 組織擴散光學理論 12 2-1-1 擴散方程式 12 2-1-2 邊界條件 14 2-2 前向計算 15 第三章 影像重建逆向問題 18 3-1 影像反算 18 3-1-1 Jacobian矩陣 19 3-1-2 Jacobian正規化(normalization) 20 3-1-3 Tikhonov正則化 21 3-2 Edge-preserving正則化 21 3-2-1 正則化參數最佳化 23 3-2-2 U曲線準則及特性 25 3-3 DOpIm程式更新 26 3-3-1 DOpIm概述 26 3-3-2 介面修改與功能介紹 27 第四章 影像重建數值模擬 28 4-1 影像重建 28 4-2 模擬仿體設計 29 4-3 個別正則化參數之影像重建 31 4-4 影像品質分析與評估 45 4-5 結果與討論 50 4-6 U曲線EPR-λ與自定義λ比較 52 第五章 影像重建實驗驗證 57 5-1 光資訊量測實驗架構 57 5-2 實驗仿體設計 58 5-3 個別正則化參數影像重建 60 5-4 結果與討論 71 第六章 結論與未來展望 73 6-1 結論 73 6-2 未來展望 74 參考文獻 75
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指導教授	潘敏俊	審核日期	2025-3-26
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