任意曲面模型之三維擴散光學影像重建計算研究

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姓名

鄧慕旗(MUDENG, VICKY VENDY HENGKI) 查詢紙本館藏

畢業系所

光機電工程研究所

論文名稱

任意曲面模型之三維擴散光學影像重建計算研究
(Computation of Three-Dimensional Diffuse Optical Image Reconstruction with Arbitrary Surface Models)

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摘要(中)

本論文發展可應用於任意表面乳癌檢測之三維擴散光學斷層影像（Diffuse optical tomography, DOT）重建演算法。該DOT影像重建演算以擴散方程式為基礎，包含求解前向問題與逆向重建。在求解前向問題中，基於已知光源與光學係數（吸收與傳播散射係數）分佈之條件下，利用有限元素法（Finite element method, FEM）求解擴散方程式，計算入射光之強度與相位分佈。逆向重建中，則使用牛頓法最小化量測之數據與利用FEM所求得之理論值之間的差異，進而估測光學係數之分佈。由於逆向重建的病態特性（ill-posed nature），影像重建中使用Tikhonov正規化來穩定重建結果。
本論文中，使用不同位置、大小及光學係數對比度（相對於背景組織）腫瘤內置物之模擬案例下，來驗證前向問題（光強度與相位）與所發展之影像重建演算法。首先在仿乳幾何模型案例中，放置一直徑為20 mm之內置物於x = 15 mm，y = 0 mm，z = 40 mm，在此高度下（z = 40mm），此仿乳假體之直徑為80 mm。在內置物擁有相同的傳播散射係數與不同的吸收係數對比度條件下，利用FEM求解擴散方程式所得之理論數值結果顯示，越大的吸收係數對比度導致越大的光源強度上的差異；另一方面，在內置物擁有相同的吸收係數與不同的傳播散射係數對比度條件下，傳播散射係數對比度越大，則光強度與相位差異越大。影像重建結果顯示，在相同的傳播散射係數與不同的吸收係數對比度之內置物條件下，會高估腫瘤內置物的吸收係數，而低估傳播散射係數；利用相同的吸收係數與不同的傳播散射係數對比度內置物之條件下所得到之重建結果顯示，當傳播散射係數對比度為2倍，則會有高估內置物之吸收係數，與低估傳播散射係數之情形。

本研究中亦從核磁共振影像中擷取乳房幾何模型，並將直徑為20 mm腫瘤內置物嵌入於乳房模型中（x = 0 mm，y = -15 mm，z = 30 mm），進行影像重建。重建結果顯示，在相同的傳播散射係數與不同的吸收係數對比度下，所重建之內置物之傳播散射係數有低估之情形，而所重建之吸收係數隨著內置物吸收係數對比度的提高，而有高估越多之趨勢；而在相同的吸收係數與不同的傳播散射係數對比度下，當傳播散射係數對比度來到2.5倍時，則會高估其內置物吸收係數，且低估傳播散射係數。

摘要(英)

The work within this thesis develops three-dimensional image reconstruction algorithm of diffuse optical tomography (DOT) system with arbitrary surface models for breast cancer detection. The image reconstruction algorithm of DOT is based on the diffusion equation, and involves both the forward problem 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 reduced 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.

In this thesis, different designated simulation cases, including different position of inclusion (an embedded synthetic tumor), size, and contrast ratio of absorption and reduced scattering coefficient of inclusion respect to background were used for verifying the results of forward problem (light intesity and phase shift of photon density Φ(r)) and developed reconstruction algorithm. For case under condition by using 80 mm diameter breast-like phantom as a geometry, tumor with diameter of 20 mm, located at x = 15 mm, y = 0 mm, and z = 40 mm. The same reduced scattering coefficient and different absorption coefficients were performed first, then the same absorption coefficient and different reduced scattering coefficients were employed thereafter. The evaluation results show that, the greater absorption coefficient, the greater light intesity differences between homogenous and inhomogeneous condition. On the other hand, the greater reduced scattering coefficient, the greater light intensity and phase shift differences between homogenous and inhomogeneous condition. They also show that, the reconstruction results with same reduced scattering coefficient and different absorption coefficients will lead to over estimation of absorption coefficient. On the other hand, under estimation is occured for reduce scattering coefficient. By acquiring the reconstruction results of same absorption coefficient and different reduced scattering coefficients, they indicate absorption coefficients will lead to significant over estimation if the contrast ratio of reduced scattering coefficient for inclusion and background is equal to 2. Moreover, under estimation is occurred for reduced scattering coefficient.

For breast model from MRI image (Magnetic Resonance Imaging)/NMR (Nuclear Magnetic Resonance) imaging with tumor embedded within the model had diameter of 20 mm, located at x = 0 mm, y = -15 mm, and z = 30 mm, the evaluation results demonstrate that, with same reduced scattering coefficient and different absorption coefficients will lead to over estimation of absorption coefficient. The greater absorption coefficient of inclusion in exact conditon, the greater over estimation of absorption coefficient for inclusion respect to background in reconstructed image. On the other hand, under estimation is occured for reduced scattering coefficient. In addition, the reconstruction results of same absorption coefficient and different reduced scattering coefficients. They indicate absorption coefficients will lead to over estimation if the contrast ratio of reduced scattering coefficient for inclusion and background is equal to 2.5. Futhermore, under estimation is occurred for reduced scattering coefficient.

關鍵字(中)

★ 三維擴散光學斷層影像
★ 有限元素法
★ Tikhonov 正規化
★ 乳癌檢測
★ 影像重建

關鍵字(英)

★ three-dimensional diffuse optical tomography
★ finite element method
★ Tikhonov regularization
★ breast cancer detection
★ image reconstruction

論文目次

摘要 i

Abstract ii

Acknowledgement iv

Contents v

List of Figures vii

List of Tables xiv

1 Introduction 1
1.1 Background 1
1.2 Literature review 4
1.2.1 Diffuse optical tomography 4
1.2.2 DOI reconstruction through DICOM images transferred 3D solid models 6
1.3 Aim and outline of this thesis 7

2 Forward problem 9
2.1 Diffusion equation 9
2.2 Forward solution to the diffusion equation __ the finite element method 10

3 Inverse solution 14
3.1 Formulation of inverse problem in DOI 14
3.2 Construction of the Jacobian matrix 15
3.2.1 The direct method 16
3.2.2 The adjoint method 17
3.3 Normalization of Jacobian matrix 17
3.4 Tikhonov regularization 18?
4 Simulation and verification 20
4.1 Simulation data __ model information is embedded 20
4.1.1 Breast-like model 20
4.1.2 Breast-like model __ following investigation 24
4.1.3 Breast model from MRI image 35
4.2 Image reconstruction 45
4.3 Reconstructions of simulated data 48
4.3.1 Image reconstruction for breast-like model 48
4.3.2 Image reconstruction for breast model from MRI image 56
4.4 Reconstructed limitation 63
4.4.1 Breast-like model image limitation 64
4.4.2 Breast model from MRI image limitation 71
4.5 CSD correction of absorption images 78
4.5.1 Absorption images correction for breast-like model 79
4.5.2 Absorption images correction for breast model from MRI image 85
4.6 Minima factors of reconstructed image 91
4.6.1 Taguchi method 92
4.6.2 Minima factors for breast-like model 93
4.6.3 Minima factors for breast model from MRI image 97

5 Conclusion and future work 100
5.1 Conclusion 100
5.2 Future work 102

Babliography 103

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指導教授

潘敏俊(PAN, MIN-CHUN)

審核日期

2017-1-25

推文