基于共圆方法的衍射层析成像中的运动检测
Motion Detection in Diffraction Tomography by Common Circle Methods
AI总结：
本文针对光学衍射层析成像中的刚性运动检测问题，提出两种基于傅里叶数据中共圆检测的方法，并通过球极投影将其转化为不限于过原点的共线方法，实现相对取向的完整重建。
摘要：
共线方法（common lines）是冷冻电子显微镜（cryo-EM）中一种成熟的重建技术，可用于在给定来自不同方向的层析投影图像时提取物体的相对取向。本文研究光学衍射层析成像中的一个类似问题。基于傅里叶衍射定理，我们证明物体的刚性运动（即旋转和平移）可以通过检测傅里叶变换数据中的共圆来确定。我们引入两种识别共圆的方法。第一种方法受投影图像的共线方法启发，通过参数化两幅图像中的共圆来检测相对取向。第二种方法假设运动随时间平滑变化，并通过共圆方法的无穷小版本计算旋转运动的角速度。有趣的是，利用球极投影（stereographic projection），两种方法都可以重新表述为共线方法，但与 cryo-EM 中使用的共线不同，这些直线不限于通过原点，从而允许对相对取向进行完整重建。数值概念验证示例展示了我们重建方法的性能。
英文摘要：
The method of common lines is a well-established reconstruction technique in cryogenic electron microscopy (cryo-EM), which can be used to extract the relative orientations of an object given tomographic projection images from different directions. In this paper, we deal with an analogous problem in optical diffraction tomography. Based on the Fourier diffraction theorem, we show that rigid motions of the object, i.e., rotations and translations, can be determined by detecting common circles in the Fourier-transformed data. We introduce two methods to identify common circles. The first one is motivated by the common line approach for projection images and detects the relative orientation by parameterizing the common circles in the two images. The second one assumes a smooth motion over time and calculates the angular velocity of the rotational motion via an infinitesimal version of the common circle method. Interestingly, using the stereographic projection, both methods can be reformulated as common line methods, but these lines are, in contrast to those used in cryo-EM, not confined to pass through the origin and allow for a full reconstruction of the relative orientations. Numerical proof-of-the-concept examples demonstrate the performance of our reconstruction methods.
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