Maximum entropy: A complement to Tikhonov regularization for determination of pair distance distributions by pulsed ESR
Maximum entropy: A complement to Tikhonov regularization for determination of pair distance distributions by pulsed ESR
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DOI：
10.1016/j.jmr.2005.07.021
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发表时间：
2005-12-01
影响因子：
2.2
通讯作者：
Freed, JH
中科院分区：
文献类型：
--
作者：
Chiang, YW;Borbat, PP;Freed, JH
Tikhonov正则化(TIKR)已被证明是直接从脉冲ESR信号确定双标记生物分子中自旋对距离分布的一种有效而有价值的方法。TIKR是一种直接方法，不需要迭代，因此提供了一种快速和唯一的解决方案。然而，在有限噪声存在的情况下，所得到的分布往往表现出负部分的振荡漂移，特别是在分布的外围区域。概率分布的Shannon-Jaynes熵为概率分布提供了所有内在的非负性约束，并提供了一种从不完全数据中获取信息的无偏方法。我们描述了如何应用最大熵正则化方法(MEM)来解决脉冲ESR中偶极子信号的不适定性。我们利用它来抑制距离分布的负漂移，提高偶极子信号对噪声的容忍度。模型研究和实验数据表明，将MEM所需的初始概率分布或种子概率分布作为TIKR结果，则MEM能够提供正则化的解。对于非负性约束，它在处理TIKR中有问题的噪声方面是有效的。此外，我们还在我们的MEM方法中加入了提取分子间偶极分量的能力，这嵌入在原始实验数据中。我们发现，使用TIKR结果作为种子，迭代实现的MEM最小化得到了极大的加速，并且收敛更成功。因此，我们认为MEM方法是对TIKR的补充，它确保了正对距离分布，提高了TIKR的精度。(C)2005 Elsevier Inc.保留所有权利。
Tikhonov regularization (TIKR) has been demonstrated as a powerful and valuable method for the determination of distance distributions of spin-pairs in bi-labeled biomolecules directly from pulsed ESR signals. TIKR is a direct method, which requires no iteration, and, therefore, provides a rapid and unique solution. However, the distribution obtained tends to exhibit oscillatory excursions with negative portions in the presence of finite noise, especially in the peripheral regions of the distribution. The Shannon-Jaynes entropy of a probability distribution provides ail intrinsic non-negativity constraint on the probability distribution and an unbiased way of obtaining information from incomplete data. We describe how the maximum entropy regularization method (MEM) may be applied to solve the ill-posed nature of the dipolar signal in pulsed ESR. We make use of it to suppress the negative excursions of the distance distribution and to increase the tolerance to noise in the dipolar signal. Model studies and experimental data are investigated, and they show that, with the initial or "seed" probability distribution that is required for MEM taken as the TIKR result, then MEM is able to provide a regularized solution, subject. to the non-negativity constraint, and it is effective in dealing with noise that is problematic for TIKR. In addition we have incorporated into Our MEM method the ability to extract the intermolecular dipolar component, which is embedded in the raw experimental data. We find that MEM minimization, which is implemented iteratively, is greatly accelerated using the TIKR result as the seed, and it converges more successfully. Thus we regard the MEM method as a complement to TIKR by securing a positive pair distance distribution and enhancing the accuracy of TIKR. (c) 2005 Elsevier Inc. All rights reserved.