Sequential Image Recovery from Noisy and Under-Sampled Fourier Data
Sequential Image Recovery from Noisy and Under-Sampled Fourier Data
复制标题
DOI：
10.1007/s10915-022-01850-7
复制
发表时间：
2022-06-01
影响因子：
2.5
通讯作者：
Song，Guohui
中科院分区：
文献类型：
--
作者：
Xiao，Yao;Glaubitz，Jan;Song，Guohui
开发了一种新的算法，用于从噪声和欠采样的傅立叶数据中联合恢复图像的时间序列。具体地说，我们考虑了这样一种情况，即每个数据集都丢失了重要信息，从而阻碍了其(单个)准确恢复。我们的新方法旨在通过从序列中的其他图像中“借用”信息来恢复每一张单独图像中缺失的信息。因此，所有的单独重建都产生了更高的精度。高分辨率傅立叶边缘检测方法的使用对我们的算法是至关重要的。特别是，边缘信息直接从傅立叶数据中获得，这导致了数据集之间的准确耦合项。此外，由于不需要粗略重建来处理图像间和图像内信息，因此在很大程度上避免了数据丢失。数值算例验证了该方法的准确性、有效性和稳健性。
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,allof 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.