LaRoque Samuel J, Sidky Emil Y, Pan Xiaochuan
University of Chicago, Department of Radiology, Chicago, Illinois 60637, USA.
J Opt Soc Am A Opt Image Sci Vis. 2008 Jul;25(7):1772-82. doi: 10.1364/josaa.25.001772.
We present a method for obtaining accurate image reconstruction from highly sparse data in diffraction tomography (DT). A practical need exists for reconstruction from few-view and limited-angle data, as this can greatly reduce required scan times in DT. Our method does this by minimizing the total variation (TV) of the estimated image, subject to the constraint that the Fourier transform of the estimated image matches the measured Fourier data samples. Using simulation studies, we show that the TV-minimization algorithm allows accurate reconstruction in a variety of few-view and limited-angle situations in DT. Accurate image reconstruction is obtained from far fewer data samples than are required by common algorithms such as the filtered-backpropagation algorithm. Overall our results indicate that the TV-minimization algorithm can be successfully applied to DT image reconstruction under a variety of scan configurations and data conditions of practical significance.
我们提出了一种在衍射断层扫描（DT）中从高度稀疏数据获得精确图像重建的方法。实际中存在从少视图和有限角度数据进行重建的需求，因为这可以大大减少DT所需的扫描时间。我们的方法通过最小化估计图像的总变差（TV）来实现这一点，条件是估计图像的傅里叶变换与测量的傅里叶数据样本相匹配。通过模拟研究，我们表明TV最小化算法能够在DT的各种少视图和有限角度情况下实现精确重建。从比诸如滤波反投影算法等常用算法所需的数据样本少得多的情况下就能获得精确的图像重建。总体而言，我们的结果表明，TV最小化算法可以在各种具有实际意义的扫描配置和数据条件下成功应用于DT图像重建。
