Fast Forward Maximum entropy reconstruction of sparsely sampled data
Fast Forward Maximum entropy reconstruction of sparsely sampled data
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DOI：
10.1016/j.jmr.2012.07.002
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发表时间：
2012-10-01
影响因子：
2.2
通讯作者：
Vosegaard, Thomas
中科院分区：
文献类型：
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作者：
Balsgart, Nicholas M.;Vosegaard, Thomas
我们提出了一种使用快速傅立叶变换（FT）的分析算法，用于导出作为使用Hyberts和瓦格纳的前向最大熵重建（FM）过程的稀疏采样数据集的迭代重建的一部分所需的梯度[J. Am. Chem. Soc. 129（2007）5108]。原始算法的主要缺点是，它需要一个FT和一个评估的熵每个丢失的数据点，以建立梯度。在本研究中，我们证明，整个梯度可以得到使用只有两个FT的和一个评价的熵导数，从而实现了令人印象深刻的节省时间相比，原来的程序。举例来说：具有间接维度的稀疏采样的2D数据集，其中仅对512个复杂点中的75个进行采样（15%采样），将缺少（512 75）x 2 = 874个点/nu（2）切片。原始FM算法需要874个FT和熵函数评估来设置梯度，而在这种情况下，本算法的速度要快450倍，因为它只需要两个FT。这使得计算时间从几个小时减少到不到一分钟。通过3D数据集的2D重建可以实现更令人印象深刻的时间节省，其中原始算法在高性能计算集群上需要数天的CPU时间，而在具有新算法的普通笔记本电脑上只需要几分钟的计算。(C)2012 Elsevier Inc. All rights reserved.
We present an analytical algorithm using fast Fourier transformations (FTs) for deriving the gradient needed as part of the iterative reconstruction of sparsely sampled datasets using the forward maximum entropy reconstruction (FM) procedure by Hyberts and Wagner [J. Am. Chem. Soc. 129 (2007) 5108]. The major drawback of the original algorithm is that it required one FT and one evaluation of the entropy per missing datapoint to establish the gradient. In the present study, we demonstrate that the entire gradient may be obtained using only two FT's and one evaluation of the entropy derivative, thus achieving impressive time savings compared to the original procedure. An example: A 2D dataset with sparse sampling of the indirect dimension, with sampling of only 75 out of 512 complex points (15% sampling) would lack (512 75) x 2 = 874 points per nu(2) slice. The original FM algorithm would require 874 FT's and entropy function evaluations to setup the gradient, while the present algorithm is similar to 450 times faster in this case, since it requires only two FT's. This allows reduction of the computational time from several hours to less than a minute. Even more impressive time savings may be achieved with 2D reconstructions of 3D datasets, where the original algorithm required days of CPU time on high-performance computing clusters only require few minutes of calculation on regular laptop computers with the new algorithm. (C) 2012 Elsevier Inc. All rights reserved.