Reconstruction of irregularly-sampled volumetric data in efficient box spline spaces.
Reconstruction of irregularly-sampled volumetric data in efficient box spline spaces.
复制标题
在有效的箱形样条空间中重建不规则采样的体积数据。
DOI：
10.1109/tmi.2012.2190616
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发表时间：
2012
影响因子：
10.6
通讯作者：
Entezari,Alireza
中科院分区：
文献类型：
--
作者：
Xu,Xie;Alvarado,AlexanderSingh;Entezari,Alireza
我们提出了一个变分框架，用于在非张量积、样条空间中重建不规则采样的体积数据。受体心立方 (BCC) 格子采样理论优势的启发，本文研究了变分设置中的 BCC 格子及其相关的箱形样条空间。我们引入了箱形样条的正则化方案，使我们能够在变分重建框架中利用 BCC 晶格。我们证明，通过选择 BCC 格子而不是常用的笛卡尔格子作为平移不变表示，可以提高信号重建的质量。此外，由于与相应的张量积 B 样条空间相比，箱形样条空间中的系统矩阵的带宽更小，因此 BCC 框架中重建过程的计算成本降低了。准确性的提高在我们使用合成和真实生物医学数据集的实验中进行了数值量化和可视化。
We present a variational framework for the reconstruction of irregularly-sampled volumetric data in, nontensor-product, spline spaces. Motivated by the sampling-theoretic advantages of body centered cubic (BCC) lattice, this paper examines the BCC lattice and its associated box spline spaces in a variational setting. We introduce a regularization scheme for box splines that allows us to utilize the BCC lattice in a variational reconstruction framework. We demonstrate that by choosing the BCC lattice over the commonly-used Cartesian lattice, as the shift-invariant representation, one can increase the quality of signal reconstruction. Moreover, the computational cost of the reconstruction process is reduced in the BCC framework due to the smaller bandwidth of the system matrix in the box spline space compared to the corresponding tensor-product B-spline space. The improvements in accuracy are quantified numerically and visualized in our experiments with synthetic as well as real biomedical datasets.