Kostenko Alexander, Batenburg K Joost, King Andrew, Offerman S Erik, van Vliet Lucas J
Department of Imaging Science & Technology, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlands.
Opt Express. 2013 May 20;21(10):12185-96. doi: 10.1364/OE.21.012185.
The reconstruction problem in in-line X-ray Phase-Contrast Tomography is usually approached by solving two independent linearized sub-problems: phase retrieval and tomographic reconstruction. Both problems are often ill-posed and require the use of regularization techniques that lead to artifacts in the reconstructed image. We present a novel reconstruction approach that solves two coupled linear problems algebraically. Our approach is based on the assumption that the frequency space of the tomogram can be divided into bands that are accurately recovered and bands that are undefined by the observations. This results in an underdetermined linear system of equations. We investigate how this system can be solved using three different algebraic reconstruction algorithms based on Total Variation minimization. These algorithms are compared using both simulated and experimental data. Our results demonstrate that in many cases the proposed algebraic algorithms yield a significantly improved accuracy over the conventional L2-regularized closed-form solution. This work demonstrates that algebraic algorithms may become an important tool in applications where the acquisition time and the delivered radiation dose must be minimized.
在线X射线相衬断层扫描中的重建问题通常通过解决两个独立的线性化子问题来处理：相位恢复和断层重建。这两个问题往往都是不适定的，需要使用正则化技术，而这会在重建图像中产生伪影。我们提出了一种新颖的重建方法，该方法通过代数方法解决两个耦合的线性问题。我们的方法基于这样的假设，即断层图像的频率空间可以分为能被准确恢复的频段和由观测无法确定的频段。这导致了一个欠定线性方程组。我们研究了如何使用基于总变差最小化的三种不同代数重建算法来求解这个系统。使用模拟数据和实验数据对这些算法进行了比较。我们的结果表明，在许多情况下，所提出的代数算法比传统的L2正则化闭式解具有显著提高的精度。这项工作表明，代数算法可能会成为在必须将采集时间和所传递的辐射剂量最小化的应用中的一种重要工具。
