X光相位對比成像法之研究

Abstract

傳統X光成像法利用X光穿透過物體後，能量被吸收的特性進行成像，然而在醫學檢測上比較重要的癌細胞或微小細胞，在體內吸收的對比度較低，因此傳統吸收式X光成像法在微小細胞的檢驗上，無法獲得有效的應用。X光相位對比成像技術的出現，改善了傳統式的缺點，但目前相位對比成像法都建立在單色光的假設下，因此為了提高相位對比成像法之實際應用價值，本論文第一部分運用多色光譜積分法，模擬相位對比演算法之計算，藉由增加入射光光譜的數量，運用最小平方法來提升重建的品質，此方法能夠提供較解析解法佳的重建效果。本論文第二部分研究三維的相位資訊迭代重建法，迭代重建法是一種將影像投影的過程轉換成矩陣線性運算的方法，轉換的方法及投影矩陣之設計將在文中加以探討，當投影的矩陣被建立，斷層掃瞄重建即可當成解大型線性系統問題，本研究使用加權最小平方共軛梯度法進行重建的電腦模擬，為了提高重建的品質及速度，我們計算雜訊的統計特徵做為加權矩陣，並且分別討論使用不同的條件矩陣及參數下之重建結果，經過電腦的模擬，可以知道有使用加權矩陣的重建結果可以獲得較多高頻的特徵，相對的誤差也較小。

The conventional X-ray radiography relies on the attenuation of X-ray energy to produce an image that describes the absorption property of the object. However, the small contrast between cancer tissues and normal tissues makes the conventional X-ray radiography ineffective in cancer diagnosis. Thanks to the emergence of X-ray phase-contrast imaging techniques, the low contrast of tissues can then be overcome. However, almost all the existing phase retrieval algorithms assume that incident beams are monochromatic, which usually are not available in modern clinical X-ray tubes. In order to implement the phase-contrast imaging in the clinical system, a quantitative polychromatic X-ray phase contrast imaging for tissue characterization was investigated in the first part of this thesis. It is a method that reconstructs the thickness distribution of the object that consists of a few homogeneous parts of known composition. By taking use of more incident spectra, we can apply the least-squares method to improve the reconstruction performance. The second part of this thesis is the iterative reconstruction of phase contrast tomography. It used the linear algebra operation to express the Radon transform. Since the phase retrieval process can result in a large noise amplification in the low frequency, the low frequency noise reduction became an important issue. In this study, the weighted least-squares conjugate-gradient method was utilized to reconstruct three-dimensional refractive index distribution. The statistical properties of the projected phase images were calculated as a priori information. This statistical properties could be taken into consideration to enhance the reconstruction quality and provided the reconstructed images with lower relative errors.