论文标题
基于变异的总重建和衍射断层扫描的相位检索
Total variation-based reconstruction and phase retrieval for diffraction tomography
论文作者
论文摘要
在光学衍射断层扫描（ODT）中，通过一系列具有相干光线的照明恢复了围绕其中心旋转的微观物体的三维散射电位。重建算法（例如过滤后的反向传播）需要了解测量平面处的复杂值波，而通常仅在实践中可以使用强度，即，即无量的测量值。 我们提出了一种基于三种关键成分的未知阶段信息的ODT的新重建方法。首先，使用Born的近似值对光传播进行建模，从而使我们能够使用傅立叶衍射定理。其次，我们利用原始二次迭代稳定了不均匀的离散傅立叶变换的反转，这也产生了具有已知相的ODT的新型数值反转公式。第三个成分是混合输入输出方案。我们实现了令人信服的数值结果，这表明与无相位数据的ODT是可能的。所谓的2D和3D重建甚至与已知阶段的重建相当。
In optical diffraction tomography (ODT), the three-dimensional scattering potential of a microscopic object rotating around its center is recovered by a series of illuminations with coherent light. Reconstruction algorithms such as the filtered backpropagation require knowledge of the complex-valued wave at the measurement plane, whereas often only intensities, i.e., phaseless measurements, are available in practice. We propose a new reconstruction approach for ODT with unknown phase information based on three key ingredients. First, the light propagation is modeled using Born's approximation enabling us to use the Fourier diffraction theorem. Second, we stabilize the inversion of the non-uniform discrete Fourier transform via total variation regularization utilizing a primal-dual iteration, which also yields a novel numerical inversion formula for ODT with known phase. The third ingredient is a hybrid input-output scheme. We achieved convincing numerical results, which indicate that ODT with phaseless data is possible. The so-obtained 2D and 3D reconstructions are even comparable to the ones with known phase.
