| 摘要: | 在本研究中,邊界保持正規化 (edge-preserving regularization) 首次被提議用來克服 擴散光學成像影像重建中的病態問題,避免利用 Tikhonov 正規化時,重建影像中不易 區分腫瘤與背景組織的邊界模糊化現像。在所提出的邊界保持正規化方法中,有邊界 保持特性的潛能函式被視為一調整項並引入至目標函式中;為了最小化所提出的目 標函式,採用半二次正規化 (half-quadratic regularization) 來簡化最佳化工作,並使用 疊代方式求解此最佳化問題。本研究中亦呈現其邊界保持正規化重建演算法具有相 當的彈性,該演算法中可採用不同之權重函式 (weighting function),包括:泛羅倫茲 函式 (generalized Lorentzian function)、指數函式 (exponential function) 和泛總變差函式 (generalized total variation function)。在結果中,利用數值模擬數據與實驗數據來驗證所 提議之方法;從重建影像得知,使用邊界保持正規化,比 Tikhonov 正規化方法的使用, 有較佳的影像品質;除此之外,基於吸收係數影像可進一步擴展成功能性影像之故, 在擴散光學成像影像重建中,建議使用泛羅倫茲權重函式之邊界保持正規化影像重建 演算法。為評估近紅外光擴散光學斷層影像之成像品質,本研究中提出客觀的 contrast-and- size detail (CSD) 分析方法,其概念源自於主觀的 contrast detial (CD) 分析方法。在 CSD 分析方法中,定義並利用了數值量化的光學對比解析度與尺寸解析度,來評估不同光 學對比度與尺寸內置物下之成像品質,且藉由影像灰階值顯示之方法,呈現影像評估 結果;除此之外,亦可計算固定光學對比、尺寸內置物下之平均尺寸解析度與光學對 比解析度,並繪製 CSD 解析度曲線,來評估不同成像方式之影像結果。在結果中,採 用 Tikhonov 正規化,與不同權重函式下之邊界保持正規化影像重建演算法,呈現此 CSD 分析方法之應用方式;評估結果顯示,使用泛羅倫茲權重函式之邊界保持正規化影像重建演算法,吸收係數影像有較佳之重建結果。In this study, we first propose the use of edge-preserving regularization in optimizing an ill-conditioned problem in the reconstruction procedure for diffuse optical tomography to prevent unwanted edge smoothing, which usually degrades the attributes of images for distinguishing tumors from background tissues when using Tikhonov regularization. In the edge-preserving regularization method presented here, a potential function with edge-preserving properties is introduced as a regularized term in an objective function. In order to minimize this proposed objective function, an iterative method solving this optimization problem is presented in which half-quadratic regularization is introduced to simplify the minimization task. Both numerical and experimental data are employed to justify the proposed technique. The reconstruction results indicate that the edge-preserving regularization performs superior to Tikhonov regularization.A flexible edge-preserving regularization algorithm based on the finite element method is proposed to reconstruct the optical-property images of near infrared diffuse optical tomography. This regularization algorithm can easily incorporate with varied weighting functions, such as a generalized Lorentzian function, an exponential function, or a generalized total variation function. To evaluate the performance, results obtained from Tikhonov or edge-preserving regularization are compared with each other. As found, the edge-preserving regularization with the generalized Lorentzian function is more attractive than that with other functions for the estimation of absorption-coefficient images concerning functional tomographic images to discover functional information of tested phantoms/tissues.Based on the concept derived from the subjective contrast detail (CD) analysis, an objective contrast-and-size detail (CSD) analysis for evaluating the image quality of near infrared diffuse optical tomography (NIR DOT) is proposed. We define a measure for numerical CSD analysis based on the resolution estimation of contrast and size. Following that, the contrast-and-size map of resolution can be calculated and displayed for each corresponding image in the map; furthermore, a CSD resolution curve can be characterized by calculating the average value of the projection along the physical quantity/axis (size or contrast). To provide some worked examples about the proposed CSD analysis evaluating the imaging performance of different reconstruction methods, Tikhonov regularization and edge-preserving regularization with different weighting functions were employed. Results suggested that using edge-preserving regularization with the generalized Lorentzian weighting function is the most attractive for the estimation of absorption-coefficient images. |
