2D sparse sampling algorithm for ND Fredholm equations with applications to NMR relaxometry

Ariel Hafftka, H. Celik, A. Cloninger, W. Czaja, R. Spencer
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引用次数: 6

Abstract

In [1], Cloninger, Czaja, Bai, and Basser developed an algorithm for compressive sampling based data acquisition for the solution of 2D Fredholm equations. We extend the algorithm to N dimensional data, by randomly sampling in 2 dimensions and fully sampling in the remaining N-2 dimensions. This new algorithm has direct applications to 3-dimensional nuclear magnetic resonance relaxometry and related experiments, such as T1-D-T2 or T1-T1,ρ-T2. In these experiments, the first two parameters are time-consuming to acquire, so sparse sampling in the first two parameters can provide significant experimental time savings, while compressive sampling is unnecessary in the third parameter.
ND Fredholm方程的二维稀疏采样算法及其在核磁共振弛豫测量中的应用
在[1]中,Cloninger、Czaja、Bai和Basser开发了一种基于压缩采样的数据采集算法,用于求解二维Fredholm方程。我们将算法扩展到N维数据,在2维中随机采样,在剩下的N-2维中完全采样。该算法可直接应用于三维核磁共振弛豫测量及相关实验,如T1-D-T2或T1-T1,ρ-T2。在这些实验中,前两个参数的获取比较耗时,因此对前两个参数进行稀疏采样可以显著节省实验时间,而对第三个参数则不需要进行压缩采样。
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