Yang Xiaoli, Hofmann Ralf, Dapp Robin, van de Kamp Thomas, dos Santos Rolo Tomy, Xiao Xianghui, Moosmann Julian, Kashef Jubin, Stotzka Rainer
Opt Express. 2015 Mar 9;23(5):5368-87. doi: 10.1364/OE.23.005368.
High-resolution, three-dimensional (3D) imaging of soft tissues requires the solution of two inverse problems: phase retrieval and the reconstruction of the 3D image from a tomographic stack of two-dimensional (2D) projections. The number of projections per stack should be small to accommodate fast tomography of rapid processes and to constrain X-ray radiation dose to optimal levels to either increase the duration of in vivo time-lapse series at a given goal for spatial resolution and/or the conservation of structure under X-ray irradiation. In pursuing the 3D reconstruction problem in the sense of compressive sampling theory, we propose to reduce the number of projections by applying an advanced algebraic technique subject to the minimisation of the total variation (TV) in the reconstructed slice. This problem is formulated in a Lagrangian multiplier fashion with the parameter value determined by appealing to a discrete L-curve in conjunction with a conjugate gradient method. The usefulness of this reconstruction modality is demonstrated for simulated and in vivo data, the latter acquired in parallel-beam imaging experiments using synchrotron radiation.
软组织的高分辨率三维（3D）成像需要解决两个逆问题：相位恢复以及从二维（2D）投影的断层图像堆栈重建3D图像。每个堆栈的投影数量应较少，以适应快速过程的快速断层扫描，并将X射线辐射剂量限制在最佳水平，以便在给定的空间分辨率目标下增加体内延时序列的持续时间和/或在X射线照射下保持结构。在压缩采样理论的意义上解决3D重建问题时，我们建议通过应用一种先进的代数技术来减少投影数量，该技术以重建切片中的总变差（TV）最小化为条件。这个问题以拉格朗日乘数的方式表述，参数值通过结合共轭梯度法诉诸离散L曲线来确定。这种重建方式的有效性在模拟数据和体内数据中得到了证明，后者是在使用同步辐射的平行光束成像实验中获取的。
