广义稀疏均匀重采样及其在MRI中的应用

Amir Kiperwas, D. Rosenfeld, Yonina C. Eldar
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引用次数: 1

摘要

提出了一种将数据从非均匀网格重采样到均匀网格的算法。我们的算法称为广义稀疏均匀重采样(GSURS),它采用了现代采样理论的方法。选取由紧支持生成核的整数平移生成的中间子空间,得到一个表示非均匀间隔样本与一系列广义样本之间关系的稀疏方程组。这种稀疏方程组可以用稀疏方程求解器有效地求解。校正滤波器随后应用于结果,以获得均匀间隔的信号样本。我们演示了新方法在非均匀间隔k空间样本中重建MRI数据的应用。在这种情况下,该算法首先用于计算均匀间隔的k空间样本,然后对这些样本进行逆FFT,以获得重建图像。通过数值模拟,比较了GSURS与其他重建方法的性能,特别是卷积网格和非均匀FFT。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
GSURS: Generalized sparse uniform resampling with application to MRI
We present an algorithm for resampling data from a non-uniform grid onto a uniform grid. Our algorithm termed generalized sparse uniform resampling (GSURS) uses methods from modern sampling theory. Selection of an intermediate subspace generated by integer translations of a compactly supported generating kernel produces a sparse system of equations representing the relation between the nonuniformly spaced samples and a series of generalized samples. This sparse system of equations can be solved efficiently using a sparse equation solver. A correction filter is subsequently applied to the result in order to attain the uniformly spaced samples of the signal. We demonstrate the application of the new method for reconstructing MRI data from nonuniformly spaced k-space samples. In this scenario, the algorithm is first used to calculate uniformly spaced k-space samples, and subsequently an inverse FFT is applied to these samples in order to obtain the reconstructed image. Simulations using a numerical phantom are used to compare the performance of GSURS with other reconstruction methods, in particular convolutional gridding and the nonuniform FFT.
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