论文标题
从嘈杂和采样不足的傅立叶数据中恢复的顺序图像恢复
Sequential image recovery from noisy and under-sampled Fourier data
论文作者
论文摘要
开发了一种新的算法，以从嘈杂和采样不足的傅立叶数据中共同恢复图像的时间顺序。具体而言，我们考虑每个数据集缺失了阻止其（个人）准确恢复的重要信息的情况。我们的新方法旨在通过从序列中的其他图像中“借用”它来恢复每个单独图像中缺少的信息。结果，单个重建的{\ em all}产生的精度提高了。高分辨率傅立叶边缘检测方法的使用对于我们的算法至关重要。特别是，边缘信息是直接从傅立叶数据中获得的，该数据导致数据集之间的准确耦合项。此外，由于不需要粗糙的重建来处理图像间和图像内信息，因此很大程度上避免了数据丢失。提供了数值示例，以证明我们新方法的准确性，效率和鲁棒性。
A new algorithm is developed to jointly recover a temporal sequence of images from noisy and under-sampled Fourier data. Specifically, we consider the case where each data set is missing vital information that prevents its (individual) accurate recovery. Our new method is designed to restore the missing information in each individual image by "borrowing" it from the other images in the sequence. As a result, {\em all} of the individual reconstructions yield improved accuracy. The use of high resolution Fourier edge detection methods is essential to our algorithm. In particular, edge information is obtained directly from the Fourier data which leads to an accurate coupling term between data sets. Moreover, data loss is largely avoided as coarse reconstructions are not required to process inter- and intra-image information. Numerical examples are provided to demonstrate the accuracy, efficiency and robustness of our new method.
