Phase vs. magnitude information in functional magnetic resonance imaging time series: toward understanding the noise

Although it has been shown that the phase of the MR signal from the brain is particularly prone to variation due to respiration, the overall physiological information contained in phase time series is not well understood. Here, we explore the different physiological processes contributing to the phase time series noise, identify their spatiotemporal characteristics and examine their relationship to BOLD-related and non-BOLD-related physiological noise in the magnitude time series. This was performed by manipulating the contribution of physiological noise to the total signal variance by modulating the TE and voxel volume, and using a short TR in order to adequately sample physiological signal fluctuations. The phase and magnitude signals were compared both before and after removal of signal fluctuations at the primary respiratory and cardiac frequencies with RETROICOR. We found that the temporal phase noise increased with TE at a faster rate than predicted by 1/TSNR as a result of physiological noise. As suggested by previous studies, the primary contributor to phase physiological noise was respiration-related effects which were manifested at a large scale (>1 cm). Notably, RETROICOR removed respiration-related large-scale artifacts and this resulted in considerable improvements in the temporal phase stability (7–90%). Physiological noise in the magnitude time series after RETROICOR consisted of low-frequency BOLD-related fluctuations (<0.13 Hz) localized to gray matter and the vasculature, and fluctuations in the vasculature correlated with slow (<0.1 Hz) variations in respiration volume and cardiac rhythm. Physiological noise in the phase signal after RETROICOR also occurred in frequencies below 0.13 Hz and was consistent with (1) residual large-scale magneto-mechanical effects correlated with slow variations in respiration volume and cardiac rhythm over time, and (2) local scale (<1 cm) effects localized in gray matter and vasculature most likely due to vascular dephasing mediated by a BOLD susceptibility change. While BOLD-related magnitude noise exhibited a TE dependence similar to BOLD, the ‘BOLD-related’ noise in the phase data increased with increasing TE and thus caused the overall phase noise to increase at a faster rate with TE than predicted by 1/TSNR. Interestingly, the spatial specificity of this effect was more evident for the higher resolution phase data, as opposed to the magnitude data, suggesting that at a higher spatial resolution the phase signal may contain more information on physiological processes than the magnitude signal.     

The effect of flicker noise on the phase noise of opto-electronic oscillator

A new analytic theory model of opto-electronic oscillator (OEO) is derived and verified by experiments in this paper, where the flick and white noise are both considered. Based on this model, the effect of flick noise on the phase noise is analyzed and results show that our model can describe the phase noise characteristics of OEO more accurately than traditional model.     

Inductive shielding of NMR phase noise

We report on a solution to the problem of phase noise in nuclear magnetic resonance (NMR) experiments. Phase noise refers to the variation in the phases of NMR signals from successive acquisitions due to an unstable applied field. Such a situation exists in high-field resistive Bitter magnets and, for sufficiently long timescales, can cause serious signal degradation upon signal averaging. An inductive shield, formed by a highly conducting metal tube placed around the sample and along the applied field, provides screening of the AC components of the applied field and thereby retains phase coherence over long periods. Although simple in principle there are technical difficulties for practical implementation of this method. We present demonstrations of the utility of this approach. In particular, we show a significant extension of the effective transverse coherence time of the ¹³C resonance in doubly ¹³C-labeled glycerol in a resistive Bitter magnet. This was accomplished through the use of a highly conducting aluminum shield, cooled to 4 K with liquid helium.     

Quantum Fisher information of the GHZ state due to classical phase noise lasers under non-Markovian environment

The dynamics of N$N$-qubit GHZ state quantum Fisher information (QFI) under phase noise lasers (PNLs) driving is investigated in terms of non-Markovian master equation. We first investigate the non-Markovian dynamics of the QFI of N$N$-qubit GHZ state and show that when the ratio of the PNL rate and the system–environment coupling strength is very small, the oscillations of the QFIs decay slower which corresponds to the non-Markovian region; yet when it becomes large, the QFIs monotonously decay which corresponds to the Markovian region. When the atom number N$N$ increases, QFIs in both regions decay faster. We further find that the QFI flow disappears suddenly followed by a sudden birth depending on the ratio of the PNL rate and the system–environment coupling strength and the atom number N$N$, which unveil a fundamental connection between the non-Markovian behaviors and the parameters of system–environment couplings. We discuss two optimal positive operator-valued measures (POVMs) for two different strategies of our model and find the condition of the optimal measurement. At last, we consider the QFI of two atoms with qubit–qubit interaction under random telegraph noises (RTNs).     

The effect of physiological noise in phase functional magnetic resonance imaging: from blood oxygen level-dependent effects to direct detection of neuronal currents

Recently, the possibility to use both magnitude and phase image sets for the statistical evaluation of fMRI has been proposed, with the prospective of increasing both statistical power and the spatial specificity. In the present work, several issues that affect the spatial and temporal stability in fMRI phase time series in the presence of physiologic noise processes are reviewed, discussed and illustrated by experiments performed at 3 T. The observed phase value is a fingerprint of the underlying voxel averaged magnetic field variations. Those related to physiological processes can be considered static or dynamic in relation to the temporal scale of a 2D acquisition and will play out on different spatial scales as well: globally across the entire images slice, and locally depending on the constituents and their relative fractions inside the MRI voxel. The 'static' respiration-induced effects lead to magneto-mechanic scan-to-scan variations in the global magnetic field but may also contribute to local BOLD fluctuations due to respiration-related variations in arterial carbon dioxide. Likewise, the 'dynamic' cardiac-related effects will lead to global susceptibility effects caused by pulsatile motion of the brain as well as local blood pressure-related changes in BOLD and changes in blood flow velocity. Finally, subject motion may lead to variations in both local and global tissue susceptibility that will be especially pronounced close to air cavities. Since dissimilar manifestations of physiological processes can be expected in phase and in magnitude images, a direct relationship between phase and magnitude scan-to-scan fluctuations cannot be assumed a priori. Therefore three different models were defined for the phase stability, each dependent on the relation between phase and magnitude variations and the best will depend on the underlying noise processes. By experiments on healthy volunteers at rest, we showed that phase stability depends on the type of post-processing and can be improved by reducing the low-frequency respiration-induced mechano-magnetic effects. Although the manifestations of physiological noise were in general more pronounced in phase than in magnitude images, due to phase wraps and global Bo effects, we suggest that a phase stability similar to that found in magnitude could theoretically be achieved by adequate correction methods. Moreover, as suggested by our experimental data regarding BOLD-related phase effects, phase stability could even supersede magnitude stability in voxels covering dense microvascular networks with BOLD-related fluctuations as the dominant noise contributor. In the interest of the quality of both BOLD-based and nc-MRI methods, future studies are required to find alternative methods that can improve phase stability, designed to match the temporal and spatial scale of the underlying neuronal activity.     

The impact of physiologic noise correction applied to functional MRI of pain at 1.5 and 3.0 T

This study quantified the impact of the well-known physiologic noise correction algorithm RETROICOR applied to a pain functional magnetic resonance imaging (FMRI) experiment at two field strengths: 1.5 and 3.0 T. In the 1.5-T acquisition, there was an 8.2% decrease in time course variance (σ) and a 227% improvement in average model fit (increase in mean R²_a). In the 3.0-T acquisition, significantly greater improvements were seen: a 10.4% decrease in σ and a 240% increase in mean R²_a. End-tidal carbon dioxide data were also collected during scanning and used to account for low-frequency changes in cerebral blood flow; however, the impact of this correction was trivial compared to applying RETROICOR. Comparison between two implementations of RETROICOR demonstrated that oversampled physiologic data can be applied by either downsampling or modification of the timing in the RETROICOR algorithm, with equivalent results. Furthermore, there was no significant effect from manually aligning the physiologic data with corresponding image slices from an interleaved acquisition, indicating that RETROICOR accounts for timing differences between physiologic changes and MR signal changes. These findings suggest that RETROICOR correction, as it is commonly implemented, should be included as part of the data analysis for pain FMRI studies performed at 1.5 and 3.0 T.     

Geometric phase of a qubit driven by a phase noise laser under non-Markovian dynamics

Robustness of the geometric phase (GP) with respect to the environmental effects is a basic condition for an effective quantum computation. Here, we study quantitatively the GP of a two-level atom system driven by a phase noise laser under non-Markovian dynamics in terms of different parameters involved in the whole system. We find that with the change of the damping coupling, the GP is very sensitive to its properties exhibiting long collapse and revival phenomena, which play a significant role in enhancing the stabilization and control of the system dynamics. Moreover, we show that the GP can be considered as a tool for testing and characterizing the nature of the qubit–environment coupling. Due to the significance of how a system is quantum correlated with its environment in the construction of a scalable quantum computer, the entanglement dynamics between the qubit with its environment under external classical noise is evaluated and investigated during the time evolution.     

Simulation and evaluation of phase noise for optical amplification using semiconductor optical amplifiers in DPSK applications

A thorough simulation and evaluation of phase noise for optical amplification using semiconductor optical amplifier (SOA) is very important for predicting its performance in differential phase-shift keyed (DPSK) applications. In this paper, standard deviation and probability distribution of differential phase noise at the SOA output are obtained from the statistics of simulated differential phase noise. By using a full-wave model of SOA, the noise performance in the entire operation range can be investigated. It is shown that nonlinear phase noise substantially contributes to the total phase noise in case of a noisy signal amplified by a saturated SOA and the nonlinear contribution is larger with shorter SOA carrier lifetime. It is also shown that Gaussian distribution can be useful as a good approximation of the total differential phase noise statistics in the whole operation range. Power penalty due to differential phase noise is evaluated using a semi-analytical probability density function (PDF) of receiver noise. Obvious increase of power penalty at high signal input powers can be found for low input OSNR, which is due to both the large nonlinear differential phase noise and the dependence of BER vs. receiving power curvature on differential phase noise standard deviation.     

在波形网络中融合相位信息的骨导语音增强

已有骨导语音增强算法重点关注语音幅度谱增强,在波形合成时会因为相位不匹配导致语音质量下降。为解决该问题,提出了一种融合相位信息的波形网络(WaveNet)模型实现骨导语音增强波形生成。该方法以频带扩展WaveNet为基础,融合骨导语音相位谱信息与增强的语音幅度谱作为模型的条件特征,根据融合特征生成增强语音波形,实现了相位信息的有效利用。仿真实验综合对比了群时延谱和瞬时频率偏差谱相位特征,主客观结果表明,不论是采用串联融合还是卷积融合方式,骨导语音相位信息均有效补充了原有幅度谱条件特征,改善了语音增强效果。利用串联方式融合群时延谱特征可得到最佳结果,相比于原始骨导语音,平均意见得分(MOS)提升了约54.3%。     

Fisher information due to a phase noisy laser under non-Markovian environment

More recently, K. Berrada [Annals of Physics 340 (2014) 60-69] [1] studied the geometric phase of a two-level atom system driven by a phase noise laser under non-Markovian dynamics in terms of different parameters involved in the whole system, and collapse and revival phenomena were found for large class of states. In this paper, using this noise effect, we study the quantum fisher information (QFI) for a two-level atom system driven by a phase noise laser under non-Markovian dynamics. A new quantity, called QFI flow is used to characterize the damping effect and unveil a fundamental connection between non-Markovian behavior and dynamics of system–environment correlations under phase noise laser. It is shown that QFI flow has disappeared suddenly followed by a sudden birth depending on the kind of the environment damping. QFI flow provides an indicator to characterize the dissipative quantum system’s decoherence by analyzing the behavior of the dynamical non-Markovian coefficients.     

Ionic noise measurement in polymer electrolytes

Electrical noise associated with ion transport (termed as “ionic noise”) has been measured at different temperatures, using a lock-in amplifier and dynamic signal analyzer for a polymer electrolyte PEO:NH₄I and its CdS dispersed composite. The ionic noise suddenly increases as the polymer passes through its phase transition at T _g and T _m. The T _g-peak in the noise measurement appears more clearly than what it does in DTA/DSC or conductivity measurements. Therefore, we suggest the noise technique as a good probe for studying phase transitions in ion conducting solid electrolytes. Further, the present noise measurements also confirm the known results of DTA/DSC studies that both T _g and T _m of polymer electrolytes shift on the formation of composites.     

Photonic-delay homodyne technology for low-phase noise measurement

The sensitivity of photonic-delay homodyne phase noise measurement system is improved by using high-linear photodetector and low-phase noise amplifier in this paper. The phase noise model for microwave link is proposed and the sensitivity of photonic-delay based measurement system is analyzed with this theory model. Results show that phase noise sensitivity in this measurement system is −130 dBc/Hz at 1 kHz and −145 dBc/Hz at 10 kHz, and in my knowledge it is the highest sensitivity for photonic-delay homodyne technology without cross correlation.     

The phase shift index for marking functional asynchrony in Alzheimer's disease patients using fMRI

Our previous study suggested that the functional magnetic resonance imaging MRI (fMRI) COSLOF Index (CI) could be used as a quantitative biomarker for Alzheimer's disease (AD). The fMRI CI was lowest in the AD group (0.13+/-0.10), followed by the mild cognitive impairment (MCI) group (0.20+/-0.05) and the control group (0.34+/-0.09). The current study continues an investigation into which of the following two factors has a dominant role in determining the CI: the signal-to-noise ratio (SNR) or the phase shift of spontaneous low-frequency (SLF) components. By using a theoretical model for SLF components, we demonstrated that the normalized CI does not depend on the SNR of the SLF components. Further analysis shows that by taking the ratio of the cross-correlation coefficient to the maximum-shifted cross-correlation coefficient, the SNR factor can be canceled. Therefore, the determination of the phase shift index (PSI) method is independent of the SNR, and the PSI provides an accurate measure of the phase shift between SLF components. By applying this PSI method to the control, MCI and AD groups of subjects, experimental results demonstrated that the PSI was highest in the AD group (72.6+/-11.3 degrees ), followed by the MCI group (58.6+/-5.7 degrees ) and, finally, the control group (40.6+/-8.4 degrees ). These results suggest that the larger is the PSI value, the more asynchrony exists between SLF components.     

The influence of high-frequency phase distortion on the phase correction effect in atmospheric turbulence

By using the method of the power-spectrum inversion, the turbulence phase screen has been built up, and the propagation characteristics of high-frequency phase of laser beam in atmospheric turbulence have been analyzed; in addition, the phase correction effect of laser beams by using the adaptive deformable mirror has been simulated, and its affecting factors in turbulence have also been analyzed quantitatively. The results show that the phase correction effect of laser beams in turbulence is mostly determined by the percent of high-frequency phase in distorted wavefront. With the increase of the intensity of atmospheric turbulence and the propagation distance in turbulence, the percent of high-frequency phase in distorted wavefront increases, resulting in the degradation of the phase correction effect.     

Zero and first-order phase shift correction for field map estimation with dual-echo GRE using bipolar gradients

A simple phase error correction technique used for field map estimation with a generally available dual-echo gradient-echo (GRE) sequence is presented. Magnetic field inhomogeneity maps estimated using two separate GRE volume acquisitions at different echo times are prone to dynamic motion errors between acquisitions. By using the dual-echo sequence, the data are collected during two back-to-back readout gradients in opposite polarity after a single radio frequency pulse, and interecho motion artifacts and alignment errors in field map estimation can be factored out. Residual phase error from the asymmetric readout pulses is modeled as an affine term in the readout direction. Results from phantom and human data suggest that the first-order phase correction term stays constant over time and, hence, can be applied to different data acquired with the same protocol over time. The zero-order phase correction term may change with time and is estimated empirically for different scans.     

低相噪光学频率梳

光学频率梳是光钟的重要组成部分,相噪是光梳的基本特性。文章从光梳相噪的描述方法入手,对光学频率梳相噪产生的几种常见来源及相噪抑制技术进行了综述,详细介绍了业已实现的几种低相噪光学频率梳。文末展望了未来低相噪光学频率梳的发展新趋势。     

NMR phase noise in bitter magnets

We have studied the temporal instability of a high field resistive Bitter magnet through nuclear magnetic resonance (NMR). This instability leads to transverse spin decoherence in repeated and accumulated NMR experiments as is normally performed during signal averaging. We demonstrate this effect via Hahn echo and Carr--Purcell--Meiboom--Gill (CPMG) transverse relaxation experiments in a 23-T resistive magnet. Quantitative analysis was found to be consistent with separate measurements of the magnetic field frequency fluctuation spectrum, as well as with independent NMR experiments performed in a magnetic field with a controlled instability. Finally, the CPMG sequence with short pulse delays is shown to be successful in recovering the intrinsic spin--spin relaxation even in the presence of magnetic field temporal instability.     

Signal processing method of phase correction for laser heterodyne interferometry

A novel signal processing method of movement direction identification and phase correction is presented for laser heterodyne interferometry. Based on the reference signal, four intervals with phase difference of 90° each other are set up. The real-time movement direction identification and the integer fringe counting are realized by detecting the times that the rising-edge of the measurement signal crosses the intervals. The phase correction approach is proposed in detail to solve the fraction phase compensation when the initial phase difference is not equal to the zero phase difference. Three experiments of the stability test, the nanometer and micrometer displacement tests on bi-directional movement were performed to demonstrate the usefulness and feasibility of the presented signal processing method.     

远程干涉型光纤传感系统的非线性相位噪声分析

以远程干涉型光纤传感系统为背景, 研究了系统非线性相位噪声构成, 对各构成要素的具体影响进行了详细分析和综合评价, 简要讨论了噪声抑制方案. 研究表明, 系统相位噪声主要包括强度噪声转化而来的相位噪声、非线性效应引起激光 线宽展宽导致的相位噪声以及自相位调制和交叉相位调制引入的相位噪声. 受激布里渊散射和四波混频可引入强度噪声并转化为相位噪声, 对于探测带宽较窄的光纤传感系统, 四波混频引入的该部分噪声往往可以忽略. 受激布里渊散射、四波混频和调制不稳定性都可引起激光线宽展宽从而造成相位噪声的增大. 当系统信道数目较多时, 交叉相位调制对相位噪声的贡献不可忽略. 所得结论对远程干涉型光纤传感系统的实际应用具有重要的指导意义.     

An active noise barrier with unidirectional secondary sources

An active noise barrier with unidirectional secondary sources is investigated in this paper, where the unidirectional secondary source consists of two closely located loudspeakers with pre-adjusted phase difference. The secondary sound field of the unidirectional sources is adjusted to maximally match the primary sound field in the shadow zone behind the barrier. It is shown both numerically and experimentally that the noise reduction performance of the active noise barrier can be improved remarkably by replacing monopoles with the unidirectional sources. The mechanism for the improvement is also investigated.