Sunaguchi Naoki, Yuasa Tetsuya, Sun Fengrong, Gupta Rajiv, Ando Masami
Opt Express. 2015 Apr 20;23(8):9717-29. doi: 10.1364/OE.23.009717.
This paper describes an algebraic reconstruction algorithm that uses total variation (TV) regularization for differential phase contrast computed tomography (DPC-CT) using a limited number of views. In order to overcome over-flattening inherent in TV regularization, a two-step reconstruction process is used: we first reconstruct tomographic images of gradient refractive index from differential projections with TV regularization; these images are then used to compute tomographic images of refractive index by solving the Poisson equation. We incorporate TV regularization in the reconstruction process because the distribution of gradient refractive index is much more flattened than the refractive index. Simulations of the proposed method demonstrate that it can achieve satisfactory image quality from a much smaller number of projections than is required by the Nyquist sampling theorem. We experimentally prove the feasibility of the proposed method using dark field imaging optics at PF-14C beamline at the Photon Factory, KEK. The differential phase contrast projection data was experimentally acquired from a biological sample and DPC-CT images were reconstructed. We show that far fewer projections are needed when the proposed algorithm is used.
本文描述了一种代数重建算法，该算法在使用有限数量视图的微分相衬计算机断层扫描（DPC-CT）中采用全变差（TV）正则化。为了克服TV正则化中固有的过度平滑问题，采用了两步重建过程：首先，我们使用TV正则化从微分投影重建梯度折射率的断层图像；然后通过求解泊松方程，利用这些图像计算折射率的断层图像。我们在重建过程中纳入TV正则化，是因为梯度折射率的分布比折射率更加平滑。对所提方法的模拟表明，与奈奎斯特采样定理要求的投影数量相比，它可以从少得多的投影数量中获得令人满意的图像质量。我们在日本高能加速器研究机构（KEK）光子工厂的PF-14C光束线使用暗场成像光学系统，通过实验证明了所提方法的可行性。从生物样本中实验获取了微分相衬投影数据，并重建了DPC-CT图像。我们表明，使用所提算法时所需的投影数量要少得多。
