最佳化正則參數於擴散光造影反算及驗證

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吳唸督(Nian-Du Wu) 查詢紙本館藏

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機械工程學系

論文名稱

最佳化正則參數於擴散光造影反算及驗證

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至系統瀏覽論文 (2026-4-1以後開放)

摘要(中)

擴散光斷層造影(Diffuse optical imaging, DOI)，是將近紅外光入射生理組織，由光偵測器蒐集離開組織光資訊，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反算兩個部分。前向計算藉有限元素法（Finite element method, FEM）求解擴散方程式呈現光在組織中傳遞情形，獲得不同位置的光資訊；逆向反算則通過牛頓法進行疊代，藉著將量測資料與前向計算的差值最小化，重建組織光學係數分佈，進而判斷腫瘤大小及位置。逆向反算因屬於非線性且病態的問題，故加入Tikhonov正則化限制縮小解的範圍，而正則化項用來穩定重建結果。
在重建DOI圖像時，不易在迭帶計算過程手動調整正則參數，而其選定影響圖像品質。本論文透過單頻率及多頻率電源驅動光源，以不同置入物的個數大小、離心距及光學係數對比度的仿體進行數值模擬和實驗，然後對所選擇固定的正則參數以及L曲線和U曲線準則獲得的正則參數，進行圖像重建影像評估與分析。而從實驗結果可得知L曲線準則在計算時，有最小的解範數及殘差範數為最佳正則參數，但兩者為最小值不一定為平衡的狀態，以至於在下一次迭代時，L曲線呈現倒置L型，無法獲取最佳正則參數，導致呈現過擬合的狀態；U曲線準則無論在模擬或實驗結果，基本都能重建出置入物的位置，且能有效地抑制雜訊，在重建過程中U曲線準則能以較少的運算時間及迭代次數達到設定的誤差閥值。在固定正則參數的圖像重建中，正則參數為0.02時，經常會發生過擬合的現象，而正則參數為50時，則是會發生欠擬合的現象，正則參數為1時，大致能重建出置入物的位置。使用CSD分析模擬及實驗資料影像可得知，U曲線準則在模擬結果中，有3例獲得最佳吸收係數解析度，有7例獲得最佳散射係數解析度，而實驗結果中，有1例獲得最佳吸收係數解析度，有2例獲得最佳散射係數解析度，U曲線準則均能從吸收或散射係數解析度其一得到較好的結果。

摘要(英)

Diffuse optical tomography (DOT), in which laser light enters the tissue, and the light information is collected by detector. There are two parts in the image reconstruction: forward calculation and inverse reconstruction. The forward calculation uses the finite element method (FEM) to solve the diffusion equation to present the light transmission in the tissue and obtain the light information at different positions; The inverse calculation was performed by Newton′s method to minimize the difference between the measured data and the forward calculation, to reconstruct the tissue optical coefficient distribution, and to determine the size and location of the tumor. Since the inverse calculation is a non-linear and ill-conditioned problem, Tikhonov′s regularization is added to limit the range of solutions, and the regularization term is used to stabilize the reconstruction results.
In the reconstruction of DOI images, it is not easy to manually adjust the regularization parameters during the iterative band calculation, and the selection affects the image quality. In this paper, we conduct numerical simulations and experiments with different imitations of object size, centroid distance, and optical coefficient contrast by driving the light source with single frequency and multi-frequency power sources, and then evaluate and analyze the image reconstruction with the selected fixed regularization parameters and the regularization parameters obtained from the L-curve and U-curve method. The L-curve method has the minimum solution and residual norm as the optimal regular parameter, but the minimum value of both is not necessarily balanced, so that the L-curve shows an inverted L-shape in the next iteration, and the optimal regular parameter cannot be obtained, resulting in an overfitting state; The U-curve method is able to reconstruct the position of the object in both simulation and experimental results, and can effectively suppress noise. In the image reconstruction with fixed regular parameters, overfitting often occurs when the regular parameter is 0.02, underfitting occurs when the regular parameter is 50, and the position of the object can be reconstructed roughly when the regular parameter is 1. Using CSD to analyze the simulated and experimental data images, it was found that the U curve method obtained the best absorption coefficient resolution in 3 cases and the best scattering coefficient resolution in 7 cases in the simulated results, while the experimental results obtained the best absorption coefficient resolution in 1 case and the best scattering coefficient resolution in 2 cases, and the U curve method obtained better results from either absorption or scattering coefficient resolution.

關鍵字(中)

★ 擴散光學斷層造影
★ 有限元素法
★ Tikhonov正則化
★ 影像重建
★ 正則參數
★ L曲線
★ U曲線

關鍵字(英)

★ Diffuse optical tomography
★ finite element method
★ Tikhonov regularization
★ image reconstruction
★ regular parameter
★ L curve
★ U curve

論文目次

摘要 I
Abstract II
致謝 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 乳房組織光學特性與醫學影像造影..... 2
1-2-1 乳房組織光學特性......................... 2
1-2-2 醫學影像造影................................. 5
1-3 文獻回顧........................................ 6
1-3-1 正則參數最佳化......................... 6
1-3-2 實驗室先前基礎........................ 7
1-4 論文架構................................ 8
第二章理論基礎............................... 10
2-1 擴散光學理論.......................... 10
2-1-1 擴散方程式............................ 10
2-1-2 邊界條件......................... 13
2-2 前向計算..................................... 14
2-3 影像重建逆向問題...................... 16
2-3-1 Jacobian矩陣.............................. 16
2-3-2 Jacobian正規化(normalization)....... 18
2-4 Tikhonov正則化 ........................ 18
第三章基於L曲線/U曲線準則之正則化參數最佳化 ...... 20
3-1 SVD的運用................................... 20
3-2 L曲線準則與其特性 ................ 21
3-3 U曲線準則與其特性.................... 22
3-4 L曲線/U曲線準則應用於DOpIm ..................... 23
3-4-1 DOpIm概述..................................... 23
3-4-2 介面修改與功能介紹...................... 24
第四章數值模擬驗證................................................ 26
4-1 模擬仿體設計................................. 26
4-2 影像重建.......................................... 29
4-3 模擬資料驗證............................. 29
4-4 影像評估與分析........................... 46
4-5 運算效率比較............................. 50
第五章影像重建實驗驗證................................ 55
5-1 實驗系統架構.............................. 55
5-2 實驗仿體設計.............................. 56
5-3 影像重建.......................................... 56
5-3-1 單頻率光資訊................................ 56
5-3-2 多頻率光資訊.................................. 62
第六章結論與未來展望.................................... 65
6-1 結論................................................. 65
6-2 未來展望............................................. 65
參考文獻 66

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指導教授

潘敏俊(Min-Chun Pan)

審核日期

2023-3-23

推文