In this paper we propose a motion-aware variational approach to reconstruct moving objects from sparse dynamic data. The motivation of this work stems from X-ray imaging of plants perfused with a liquid contrast agent, aimed at increasing the contrast of the images and studying the phloem transport in plants over time. The key idea of our approach is to deploy 3D shearlets as a space-temporal prior, treating time as the third dimension. The rationale behind this model is that a continuous evolution of a cartoon-like object is well suited for the use of 3D shearlets. We provide a basic mathematical analysis of the variational model for the image reconstruction. The numerical minimization is carried out with primal-dual scheme coupled with an automated choice of regularization parameter. We test our model on different measurement setups: a simulated phantom especially designed to resemble a plant stem, with spreading points to simulate a spreading contrast agent; a measured agarose gel phantom to demonstrate iodide diffusion and geometry prior to imaging living sample; a measured living tree grown \textit{in vitro} and perfused with a liquid sugar-iodine-mix. The results, compared against a 2D static model, show that our approach provides reconstructions that capture well the time dynamic of the contrast agent onset and are encouraging to develop microCT as a tool to study phloem transport using iodine tracer.

中文翻译：

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稀疏动态断层扫描：植物茎中碘灌注的基于剪切波的方法

在本文中，我们提出了一种运动感知变分方法，用于从稀疏动态数据中重建运动对象。这项工作的动机源于灌注液体造影剂的植物的 X 射线成像，旨在增加图像的对比度并研究植物中韧皮部随时间的传输。我们方法的关键思想是将 3D 剪切波部署为时空先验，将时间视为第三维。该模型背后的基本原理是，卡通状物体的连续演化非常适合使用 3D 剪刀剪。我们为图像重建的变分模型提供了基本的数学分析。数值最小化是通过原始对偶方案与正则化参数的自动选择相结合进行的。我们在不同的测量设置上测试我们的模型：一个专门设计成类似于植物茎的模拟体模，带有扩散点来模拟扩散的造影剂；测量的琼脂糖凝胶体模，用于在对活体样品成像之前展示碘化物扩散和几何形状；一棵经过测量的活树生长\textit{体外} 并用液体糖碘混合物灌注。与 2D 静态模型相比，结果表明我们的方法提供的重建能够很好地捕捉造影剂开始的时间动态，并鼓励开发 microCT 作为使用碘示踪剂研究韧皮部运输的工具。一棵经过测量的活树生长\textit{体外} 并用液体糖碘混合物灌注。与 2D 静态模型相比，结果表明我们的方法提供的重建能够很好地捕捉造影剂开始的时间动态，并鼓励开发 microCT 作为使用碘示踪剂研究韧皮部运输的工具。一棵经过测量的活树生长\textit{体外} 并用液体糖碘混合物灌注。与 2D 静态模型相比，结果表明我们的方法提供的重建能够很好地捕捉造影剂开始的时间动态，并鼓励开发 microCT 作为使用碘示踪剂研究韧皮部运输的工具。