基于低秩矩阵的非均匀采样NMR波谱重建进展

多维核磁共振（Nuclear Magnetic Resonance，NMR）利用多维波谱来分析分子结构，被广泛用于化学、生物学和医学等领域，但信号采样时间随波谱维度和采样点数增加而迅速增长．非均匀采样通过降低间接维采样点数来加速数据采集，并引入合理的重建方法获得完整的NMR波谱．如何快速重建高质量的波谱，是NMR信号处理研究的前沿．本文主要综述近年来基于低秩矩阵的NMR波谱重建方法的发展．首先介绍了低秩矩阵的相关数学基础；然后从一般低秩矩阵和结构化低秩汉克尔矩阵两个角度来论述重建模型，并讨论相关的NMR波谱应用；最后分析了该技术存在的不足，并展望其未来发展的趋势．     

基于压缩感知/重采样的NMR噪声抑制新方法

发展高灵敏检测方法是分析化学的永恒主题之一,提高信号强度和降低噪声水平是增强灵敏度的根本途径.在核磁共振波谱(NMR)分析中,通常采用高磁场强度的谱仪或复杂的脉冲实验方法来提高信号强度,或通过使用超低温探头来降低噪声水平,但这无疑会提高实验成本或增加实验难度.相较而言,利用数据后处理方法辨识和抑制噪声,是更为经济的提高信噪比(SNR)的途径.因此,该文在前期研究中发展的基于统计学中重采样原理的数据后处理方法(NASR)的基础上,通过引入压缩感知(CS)技术,对重采样方法进行了优化改进,所发展的NMR数据处理新方法(CS_NASR)可有效排除主观因素影响,提高处理结果的鲁棒性.     

基于稀疏贝叶斯学习的复杂网络拓扑估计

提出了一种噪声环境下复杂网络拓扑估计方法, 仅利用含噪时间序列估计未知结构混沌系统的动力学方程和参数, 以及由混沌系统组成的复杂网络的拓扑结构、节点动力学方程、所有参数、 节点间耦合方向和耦合强度.通过采用动力学方程的统一形式, 将动力系统方程结构和参数估计看成线性回归问题的系数估计, 该估计问题利用贝叶斯压缩传感的信号重建算法求解, 含噪信号的模型重建使用相关向量机方法,即通过稀疏贝叶斯学习求解稀疏欠定线性方程得到上面提到的可估计对象.以单个Lorenz系统及由200个 Lorenz系统组成的无标度网络为例说明方法的有效性. 仿真结果表明,提出的方法对噪声有很强的鲁棒性,收敛速度快,稳态误差极小, 克服了最小二乘估计方法收敛速度慢、 稳态误差大以及压缩传感估计方法对噪声鲁棒性不强的缺点.     

相干X射线衍射成像的数字模拟研究

相位重建是实现X 射线相干衍射成像的关键, 它利用远场采集的样品傅里叶相干衍射花样、结合过采样理论,再采用迭代算法复原样品的相位信息. 文中采用数字模拟的方法, 利用小尺寸二维非周期性图形作为物场, 研究了过采样比对重构结果的影响, 研究发现, 迭代次数为1000 次时最佳过采样比的范围是3—7 之间. 利用噪声模拟方法, 研究了噪声对相位重建的影响, 找到了完成相位重建的噪声限是信噪比不能低于10. 分析了重构结果中孪生像以及随机平移的产生原因, 并给出了相应的解决办法, 结果表明, 此方法可有效地提高重构图像的质量. 关键词： 相干X射线衍射成像 过采样 相位重建算法 显微成像     

基于谱图分解的宽带通信信号智能检测算法

对于宽带通信信号检测问题,针对目前基于深度学习的信号检测算法不适应于处理大带宽和大时宽的宽带信号以及对信号时频参数估计存在的固有偏差问题,提出基于谱图分解的宽带通信信号智能检测算法,完成对大带宽接收信号中窄带信号的高效准确检测。首先将由宽带信号转化而来的灰度时频谱图通过谱图分解得到适合于目标检测网络输入大小的子谱图,然后使用改进的无锚框YOLOx目标检测算法对子谱图中的窄带信号进行检测,最后将子谱图的信号检测结果融合得到窄带信号的时频参数等检测结果。经过实验测试得出,该算法能够适应复杂的噪声环境,与其他深度学习算法和传统算法相比,具有较高的信号检测概率,较低的虚警概率,较小的信号参数估计平均误差,其检测精度更高,鲁棒性、实用性、通用性更强。     

应用CS理论实现同步采样压缩成像

为了减轻图像数据存储负担,实现图像在网络上的快速传输和实时处理,对一种新的压缩传感(CS)理论进行了研究。介绍了压缩传感理论的主要思想和基于压缩传感理论的光学成像系统,给出了一种新型图像重建算法—和谐正交匹配追踪算法,并进行了相应的模拟实验。实验结果显示,该成像机制可同步完成图像的采样与数据压缩,同时可获得良好的图像重建效果。由于该方法所要传输的信号数据量较小,所以十分有利于远距离的图像传输。     

基于压缩传感的纯相位物体相位恢复

传统的相位恢复算法通过双强度或者单强度测量的数据进行迭代运算以恢复丢失的相位信息, 它要求采样数据必须满足香农采样定理.当成像的分辨率较高时, 大量的测量数据势必会对数据采样设备提出更多的要求.因此, 为减少采样负担, 本文提出了一种基于压缩传感的相位恢复算法, 通过在傅里叶面的少量单强度测量数据, 应用改进的混合输入输出算法来恢复纯相位物体的相位分布.在采样数据远小于采样定理所需的条件时, 该算法仍能精确地恢复相位分布具有分块均匀特征的纯相位物体.数值仿真实验表明该算法具有良好的收敛性能. 关键词： 相位恢复 压缩传感     

基于压缩感知成像系统的动态背景去噪

为了消除背景光强动态变化引起的非线性误差,提出了基于压缩感知成像系统的动态背景去噪算法.算法将测量中不同背景光强下所得测量值的平均值之差作为补偿系数,通过补偿系数消除动态背景噪声对压缩感知成像系统的非线性影响.仿真结果表明,在总数为900次的采样过程中,背影噪声动态变化300次时,算法能够将重建图像的峰值信噪比由29.5dB提高到62dB;在动态背景噪声的影响下,本文算法能够大大提高目标图像的可读性,提高成像质量,增加压缩感知成像系统的鲁棒性.     

改进的最小方差算法在超声成像中的应用

为了提高最小方差超声成像算法的分辨率、对比度以及对噪声的鲁棒性,提出一种改进的最小方差成像算法。该方法首先基于回波信号中期望信号与噪声信号的可分离性将信号划分为期望信号和噪声信号,然后根据最小方差原理,求出加权向量使期望信号功率最小,同时,为了增加算法对噪声的鲁棒性,对信号方向向量增加一对约束条件,进一步提高图像质量。在全发全收和合成孔径模式下对点目标和吸声斑进行仿真,结果表明所提算法在全发全收模式下,-6 dB处分辨率在最小方差基础上提高了1倍左右,在合成孔径模式下,对比度在特征空间最小方差算法基础上提高了8 dB,且远优于传统延时叠加算法。最后通过实验进一步表明改进的最小方差算法图像在分辨率、对比度及对噪声的鲁棒性等方面表现更优,可以有效的改善超声图像的质量。      

CT不完全投影数据重建算法综述

本文主要针对计算机断层成像(computed tomography,CT)不完全投影数据重建中探测器全覆盖稀疏角度重建和探测器部分覆盖截断数据重建问题,综述了其在研究方法上国内外的进展.在探测器对被检测物体可以完全覆盖的情况下,针对稀疏均匀采样和视角受限采样,探讨了离散模型迭代重建算法和压缩感知采样重建算法.在探测器对被检测物体不能完全覆盖的情况下,探讨了锥束螺旋BPF重建算法、加型迭代重建算法和锥束FDK改进算法.论文可以为CT重建领域的研究工作者提供全面的方法梳理和总结,并指出了当前研究的重点和未来研究的方向.     

Suppression of sampling artefacts in high-resolution four-dimensional NMR spectra using signal separation algorithm

The development of non-uniform sampling (NUS) strategies permits to obtain high-dimensional spectra with increased resolution in significantly reduced experimental time. We extended a previously proposed signal separation algorithm (SSA) to process sparse four-dimensional NMR data. It is employed for two experiments carried out for a partially unstructured 114-residue construct of chicken Engrailed 2 protein, namely 4D HCCH-TOCSY and 4D C,N-edited NOESY. The SSA allowed us to obtain high-quality spectra using only as little as 0.16% of the available samples, with low sampling artefacts approaching the thermal noise level in most spectral regions. It is demonstrated that NUS 4D HCCH-TOCSY is dominated by sampling noise and requires efficient artefact suppression. On the other hand, 4D C,N-edited NOESY is a particularly attractive experiment for NUS, as the absence of diagonal peaks renders the problem of artefacts less critical. We also present a transverse-relaxation optimized sequence for HMQC that is especially designed for longer evolution periods in the indirectly detected proton dimension in high-dimensional pulse sequences. In conjunction with novel sampling strategies and efficient processing methods, this improvement enabled us to obtain unique structural information about aliphatic-amide contacts.     

基于核磁共振的统计全相关谱在大鼠肾脏组织中的应用

生物组织是基于NMR的代谢组学研究的主要对象之一，广泛应用于分子病理学、毒理学、生物医学等众多领域. 但是，为了保证测定的准确，组织的NMR实验往往需要在较低的温度下和较短时间内完成，以防止由于组织内酶的降解和扩散而导致的某些代谢物质的分析信息被破坏. 统计全相关谱(Statistical Total Correlation Spectroscopy, STOCSY)是依靠一维谱来实现二维谱的一些功能的方法，不需要额外的实验时间，已经被广泛应用于代谢组学研究中. 本文采用STOCSY方法，通过对一系列¹H高分辨魔角旋转谱的统计分析和计算，得到了肾脏组织的准二维相关谱，其中共振峰之间的相关较为准确的反应了物质之间的耦合信息，为物质的归属提供了帮助.     

129Xe NMR study of Xe adsorption on multiwall carbon nanotubes

¹²⁹Xe NMR spectroscopy has been used to study the adsorption of Xe on multi-wall carbon nanotubes (MWCNT). The results obtained have shown the ¹²⁹Xe NMR ability to probe the intercrystalline (aggregate) and the inner porosity of CNT. In particular, the effects on porosity of tubes openings by hydrogen exposure and of ball milling were examined. Dramatic changes observed in the ¹²⁹Xe NMR spectra after moderate ball milling of MWCNTs were attributed to the destruction of the initial intercrystalline pore structure and to the Xe access inside the nanotubes. To examine the exchange dynamics the mixture of as-made and milled MWCNTs was studied with one- and two-dimensional (1D and 2D) ¹²⁹Xe NMR. The exchange between the interior of milled nanotubes and the aggregate pores of as-made MWCNTs was fast on the NMR acquisition time scale. The Xenon exchange between the interior of the as-made MWCNTs and the large aggregate pores occurred on a longer time scale of 10 ms, as was established by 2D ¹²⁹Xe NMR exchange spectroscopy. Variable temperature ¹²⁹Xe NMR data were also discussed and analyzed in terms of the fast exchange approximation.     

High-resolution 2D NMR spectra in inhomogeneous fields based on intermolecular multiple-quantum coherences with efficient acquisition schemes

High-resolution 2D NMR spectra in inhomogeneous fields can be achieved by the use of intermolecular multiple-quantum coherences and shearing reconstruction of 3D data. However, the long acquisition time of 3D spectral data is generally unbearable for in vivo applications. To overcome this problem, two pulse sequences dubbed as iDH-COSY and iDH-JRES were proposed in this paper. Although 3D acquisition is still required for the new sequences, the high-resolution 2D spectra can be obtained with a relatively short scanning time utilizing the manipulation of indirect evolution period and sparse sampling. The intermolecular multiple-quantum coherence treatment combined with the raising and lowering operators was applied to derive analytical signal expressions for the new sequences. And the experimental observations agree with the theoretical predictions. Our results show that the new sequences possess bright perspective in the applications on in vivo localized NMR spectroscopy.     

迭代软阈值法压缩感知重建谱峰较宽的二维固体谱

压缩感知技术可以打破传统奈奎斯特采样定理的限制,利用优化算法对欠采数据进行重建,并获得高质量的结果,因此在核磁共振领域得到了广泛的关注．但是当核磁共振谱的谱峰很宽时,基于共轭梯度方法的压缩感知重建却难以得到令人满意的谱图．因此,该文采用凸优化非线性重建算法,使用基于谱图域软阈值的压缩感知算法重建固体二维宽谱（¹H双量子-单量子谱或MQMAS谱）,有效地解决了宽峰在重建时变弱的问题．     

Theory of mirrored time domain sampling for NMR spectroscopy

A generalized theory is presented for novel mirrored hypercomplex time domain sampling (MHS) of NMR spectra. It is the salient new feature of MHS that two interferograms are acquired with different directionality of time evolution, that is, one is sampled forward from time t=0 to the maximal evolution time tmax, while the second is sampled backward from t=0 to -tmax. The sampling can be accomplished in a (semi) constant time or non constant-time manner. Subsequently, the two interferograms are linearly combined to yield a complex time domain signal. The manifold of MHS schemes considered here is defined by arbitrary settings of sampling phases ('primary phase shifts') and amplitudes of the two interferograms. It is shown that, for any two given primary phase shifts, the addition theorems of trigonometric functions yield the unique linear combination required to form the complex signal. In the framework of clean absorption mode (CAM) acquisition of NMR spectra being devoid of residual dispersive signal components, 'secondary phase shifts' represent time domain phase errors which are to be eliminated. In contrast, such secondary phase shifts may be introduced by experimental design in order to encode additional NMR parameters, a new class of NMR experiments proposed here. For generalization, it is further considered that secondary phase shifts may depend on primary phase shifts and/or sampling directionality. In order to compare with MHS theory, a correspondingly generalized theory is derived for widely used hypercomplex ('States') sampling (HS). With generalized theory it is shown, first, that previously introduced 'canonical' schemes, characterized by primary phases being multiples of π/4, afford maximal intensity of the desired absorptive signals in the absence of secondary phase shifts, and second, how primary phases can be adjusted to maximize the signal intensity provided that the secondary phase shifts are known. Third, it is demonstrated that theory enables one to accurately measure secondary phase shifts and amplitude imbalances. Application to constant time 2D [13C, 1H]-HSQC spectra recorded for a protein sample with canonical MHS/HS schemes showed that accurate CAM data acquisition can be readily implemented on modern spectrometers for experiments based on through-bond polarization transfer. Fourth, when moderate variations of secondary phase shifts with primary phase shift and/or sampling directionality are encountered, generalized theory allowed comparison of the robustness of different MHS/HS schemes for CAM data acquisition, and thus to identify the scheme best suited to suppress dispersive peak components and quadrature image peaks. Moreover, it is shown that for spectra acquired with several indirect evolution periods, the best suited scheme can be identified independently for each of the periods.     

压缩感知同步扫描重建及其采样方案的研究

压缩感知(compressed sensing,CS)-磁共振成像(magnetic resonance imaging,MRI)技术使用随机欠采样的k空间数据来重建图像,大大提高了成像速度.但典型的CS重建很费时,这也是CS-MRI临床应用的主要障碍之一.针对这一问题,该文提出了在扫描时同步进行CS图像重建的方案.在同步重建的过程中,可以实时显示重建图像的结果,用户可以根据图像质量来决定何时终止扫描,这样可以在节约扫描和重建时间的同时,更好地控制图像质量.由于预先无法确定最终的采样率,因此传统的变密度随机采样方法并不完全适用.该文设计了适用于同步重建过程的采样模式生成方案,同时提出了分段采样方法,把采样过程分为两个阶段,不同阶段使用不同的概率密度函数(probability density function,PDF)确定待采样的相位编码行.模拟实验的结果表明,与使用单一密度函数的采样方案相比,分段采样方案能够在整个同步扫描重建过程中始终获得更好的图像.     

2D separated-local-field spectra from projections of 1D experiments

A novel procedure for reconstruction of 2D separated-local-field (SLF) NMR spectra from projections of 1D NMR data is presented. The technique, dubbed SLF projection reconstruction from one-dimensional spectra (SLF-PRODI), is particularly useful for uniaxially oriented membrane protein samples and represents a fast and robust alternative to the popular PISEMA experiment which correlates (1)H-(15)N dipole-dipole couplings with (15)N chemical shifts. The different 1D projections in the SLF-PRODI experiment are obtained from 1D spectra recorded under influence of homonuclear decoupling sequences with different scaling factors for the heteronuclear dipolar couplings. We demonstrate experimentally and numerically that as few as 2-4 1D projections will normally be sufficient to reconstruct a 2D SLF-PRODI spectrum with a quality resembling typical PISEMA spectra, leading to significant reduction of the acquisition time.     

White noise nonlinear system analysis in nuclear magnetic resonance spectroscopy

Nonlinear noise excitation in nuclear magnetic resonance is a form of nonlinear spectroscopy which exploits the nonlinear susceptibilities in a very direct way. The nonlinear susceptibilities are defined by perturbation theory in the frequency domain. In nonlinear system analysis, on the other hand, the system response is described by a Volterra series in the time domain. The kernels of the Volterra functionals carry the information about the system and are to be determined by experiment.The series expansion of a molecular, atomic or nuclear system response is derived in quantum mechanics by time dependent perturbation theory, leading to a Volterra series with time ordered, triangular kernels. The kernels are multi-dimensional products of decaying exponentials, which describe coherence decays of particular density matrix elements. The Fourier transforms of the triangular Volterra kernels are the susceptibilies, which are formally identical in NMR spectroscopy and nonlinear optical spectroscopy. The nonlinear susceptibilities are multi-dimensional spectra, which in NMR spectroscopy reveal the spin communication pathways. These are established by various forms of single quantum coherence connectivities, such as indirect coupling, chemical exchange, cross-relaxation, dipolar and quadrupolar coupling.If the functionals of the Volterra series are orthogonalized with respect to Gaussian white noise excitation, the Wiener series results. The Wiener kernels can be derived by multi-dimensional cross-correlation of the system response with different powers of the Gaussian white noise excitation.Cross-correlation of the transverse magnetization response to noise excitation in NMR leads to multi-dimensional time functions, the Fourier transforms of which closely resemble the nonlinear susceptibilities. The cross-correlation spectra differ from the susceptibilities in the governing Liouvillean and the dynamic density matrix, which are affected by saturation for continuous excitation. Cross-correlation spectra and susceptibilities converge for vanishing excitation power. Therefore the cross-correlation spectra are referred to as stochastic susceptibilities.In stochastic NMR spectroscopy only odd order susceptibilities exist for transverse magnetization. The first nonlinear order is the third, and the nonlinear spectral information is derived from the third order susceptibility. Higher order susceptibilities are not feasible to derive from experimental data. An important share of the nonlinear information is found on the six subdiagonal 2D cross-sections through the third order susceptibility. These cross-sections arise in three pairs, which carry distinct information, separated according to longitudinal magnetization and population effects, zero quantum coherences, and double quantum coherences.In practice a nonlinear 3D spectrum is computed from experimental data by an algorithm in the frequency domain, which yields access to selected regions in the 3D spectrum. This spectrum is the symmetrized stochastic third order susceptibility. All its sub-diagonal 2D cross-sections are equivalent. They are the average of the six different sub-diagonal 2D cross-sections through the asymmetric third order susceptibility.The stochastic excitation technique in NMR is characterized by several unique attributes. (1) There is no minimum time for a data acquisition cycle, so that, at the expense of signal-to-noise ratio, strong samples can be investigated faster with stochastic NMR than with pulsed FT NMR. (2) Stochastic excitation tests the sample extensively, and measures a maximum amount of information in a single experiment. This feature is of particular interest for investigation of short-lived samples and of samples with little a priori information. (3) An experiment with stochastic excitation is simple to perform, but the data processing is more complex than in FT spectroscopy. (4) The nonlinear information about spin communication pathways is derived for individual frequency regions only, which are identified in the stochastic ID spectrum. This information is located primarily on the sub-diagonal 2D cross-sections through the third order susceptibility. (5) Stochastic NMR spectra derived from random noise excitation are contaminated by systematic noise. In the sub-diagonal 2D cross-sections the noise is reduced by filtering and symmetrization during data processing. (6) Sub-diagonal 2D cross-sections are sensitive to experimental phase distortions in one direction only. They are readily adjusted in phase with the same parameters as the ID spectrum. (7) Stochastic multi-dimensional spectra can be computed at variable resolution from one and the same set of raw data.So far stochastic NMR spectroscopy is not applied routinely in analytical spectroscopy. More practical experience is needed to evaluate its merits in comparison with Fourier transform NMR.Stochastic excitation is distinguished from continuous wave and sparsely pulsed excitation by low input power in connection with large bandwidth. This important property cannot be exploited in high resolution NMR in liquids, because excitation power is not a restricting factor in this case. The situation is different in NMR imaging, where large field gradients require large bandwidths and the excitation power becomes a point of concern. For this reason stochastic RF excitation is being investigated in NMR imaging.The multi-dimensional cross-correlation functions obtained from random noise excitation generally are contaminated by systematic noise. The occurrence of systematic noise can be avoided if pseudo-random excitation is used in combination with a transformation of the system response to obtain the kernels. This technique is used successfully in Hadamard spectroscopy, where the linear Volterra kernel is the Hadamard transform of the linear response functional. Nonlinear transformations^(220,221) for retrieval of nonlinear kernels have not yet been realized in NMR spectroscopy.The cross-correlation technique underlying the data evaluation in stochastic nonlinear system analysis is equivalent to interferometry in optical spectroscopy. The Michelson interferometer is the most prominent optical correlator. The time resolution of the kernels derived by cross-correlation is determined by the inverse bandwidth of the excitation. With the Michelson interferometer a time resolution of 10⁻¹⁴ s is achieved in IR spectroscopy. Since the IR correlogramm is Fourier transformed for spectral analysis, the time resolution cannot be exploited otherwise. For analysis of fast time dependent processes a two-dimensional interferometer should be constructed, which performs a 2D cross-correlation of the system response to two in general different noise inputs. One input pumps the time dependent process, the other is used to investigate the time dependence spectroscopically. This technique is introduced by the name of ‘two-dimensional interferometry’. It uses low excitation power, but provides high time resolution at large response energy. Related work is pursued in nonlinear optical spectroscopy with incoherent excitation. In this area the use of broad band lasers is investigated for generation of echoes and for correlation based measurements of relaxation times.