Resampling of data between arbitrary grids using convolution interpolation
Resampling of data between arbitrary grids using convolution interpolation
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DOI：
10.1109/42.774166
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发表时间：
1999-05-01
影响因子：
10.6
通讯作者：
Eggers, H
中科院分区：
文献类型：
--
作者：
Rasche, V;Proksa, R;Eggers, H
对于某些医疗应用，需要重新采样数据。在磁共振断层扫描（MRT）或计算机断层扫描（CT）中，例如，可以在傅立叶域中的非直线网格上对数据进行采样。对于图像重建，可以应用卷积插值算法（通常称为网格化）来将数据重建到直线网格上。需要将数据从直线网格恢复到非直线网格，例如，本文介绍了卷积插值在任意网格上的应用，其基本算法可分为两步。首先，将数据从任意输入网格重新采样到直线网格上，其次，将直线数据重新采样到任意输出网格上。此外，我们想引入一种新的技术来获得我们的算法的第一步所需的采样密度函数。为了快速、独立于采样模式地确定采样密度函数，计算样本分布的Voronoi图。每个样本周围的Voronoi单元的体积被用作采样密度的度量。它表明，引入的重采样技术允许快速重采样数据之间的任意网格。此外，它表明，建议的方法来获得的采样密度函数是适合的，即使是任意的采样模式，例子中所提出的技术已被应用于沿着螺旋，径向和任意轨迹采集的数据的重建和快速计算的投影给定的直线采样图像。
For certain medical applications resampling of data is required. In magnetic resonance tomography (MRT) or com puter tomography (CT), e.g., data may be sampled on non-rectilinear grids in the Fourier domain. For the image reconstruction a convolution-interpolation algorithm, often called gridding, can be applied for resampling of the data onto a rectilinear grid. Resampling of data from a rectilinear onto a nonrectilinear grid are needed, e.g., if projections of a given rectilinear data set are to be obtained.In this paper we introduce the application of the convolution interpolation for resampling of data from one arbitrary grid onto another, The basic algorithm can be split into two steps. First, the data are resampled from the arbitrary input grid onto a rectilinear grid and second, the rectilinear data is resampled onto the arbitrary output grid. Furthermore, we like to introduce a new technique to derive the sampling density function needed for the first step of our algorithm. For fast, sampling-pattern-independent determination of the sampling density function the Voronoi diagram of the sample distribution is calculated. The volume of the Voronoi cell around each sample is used as a measure for the sampling density.It is shown that the introduced resampling technique allows fast resampling of data between arbitrary grids. Furthermore, it is shown that the suggested approach to derive the sampling density function is suitable even for arbitrary sampling patterns, Examples are given in which the proposed technique has been applied for the reconstruction of data acquired along spiral, radial, and arbitrary trajectories and for the fast calculation of projections of a given rectilinearly sampled image.