Edge-adaptive \begin{document}$ \ell_2 $\end{document} regularization image reconstruction from non-uniform Fourier data
Edge-adaptive \begin{document}$ \ell_2 $\end{document} regularization image reconstruction from non-uniform Fourier data
复制标题
非均匀傅立叶数据的边缘自适应 egin{document}$ ell_2 $end{document} 正则化图像重建
DOI：
10.3934/ipi.2019042
复制
发表时间：
2018
影响因子：
1.3
通讯作者：
Anne Gelb
中科院分区：
文献类型：
--
作者：
V. Churchill;Richard Archibald;Anne Gelb
从基于边缘稀疏性的重建方法恢复的信号和图像在边缘域中可能不是真正稀疏的，并且经常导致质量差的重建。迭代重加权方法在精度上提供了一些改进，但以延长运行时间为代价。本文研究了以非均匀傅里叶样本形式获取数据时的此类方法，然后提出了一种新的非迭代加权正则化方法，该方法首先对数据进行预处理，以确定边缘域中非零值的精确位置。我们的新方法是准确和有效的，并优于加权正则化方法在几个数值实验。
Signals and images recovered from edge-sparsity based reconstruction methods may not truely be sparse in the edge domain, and often result in poor quality reconstruction. Iteratively reweighted methods provide some improvement in accuracy, but at the cost of extended runtime. This paper examines such methods when data are acquired as non-uniform Fourier samples, and then presents a new non-iterative weighted regularization method that first pre-processes the data to determine the precise locations of the non-zero values in the edge domain. Our new method is both accurate and efficient, and outperforms reweighted regularization methods in several numerical experiments.