Noise Correlation Research Articles

A 128-channel receive array for cortical brain imaging at 7 T.

A 128-channel receive-only array for brain imaging at 7 T was simulated, designed, constructed, and tested within a high-performance head gradient designed for high-resolution functional imaging. The coil used a tight-fitting helmet geometry populated with 128 loop elements and preamplifiers to fit into a 39 cm diameter space inside a built-in gradient. The signal-to-noise ratio (SNR) and parallel imaging performance (1/g) were measured in vivo and simulated using electromagnetic modeling. The histogram of 1/g factors was analyzed to assess the range of performance. The array's performance was compared to the industry-standard 32-channel receive array and a 64-channel research array. It was possible to construct the 128-channel array with body noise-dominated loops producing an average noise correlation of 5.4%. Measurements showed increased sensitivity compared with the 32-channel and 64-channel array through a combination of higher intrinsic SNR and g-factor improvements. For unaccelerated imaging, the 128-channel array showed SNR gains of 17.6% and 9.3% compared to the 32-channel and 64-channel array, respectively, at the center of the brain and 42% and 18% higher SNR in the peripheral brain regions including the cortex. For R = 5 accelerated imaging, these gains were 44.2% and 24.3% at the brain center and 86.7% and 48.7% in the cortex. The 1/g-factor histograms show both an improved mean and a tighter distribution by increasing the channel count, with both effects becoming more pronounced at higher accelerations. The experimental results confirm that increasing the channel count to 128 channels is beneficial for 7T brain imaging, both for increasing SNR in peripheral brain regions and for accelerated imaging.

A stopping criterion for iterative proton CT image reconstruction based on correlated noise properties.

Whereas filtered back projection algorithms for voxel-based CT image reconstruction have noise properties defined by the filter, iterative algorithms must stop at some point in their convergence and do not necessarily produce consistent noise properties for images with different degrees of heterogeneity. A least-squares iterative algorithm for proton CT (pCT) image reconstruction converges toward a unique solution for relative stopping power (RSP) that optimally fits the protons. We present a stopping criterion that delivers solutions with the property that correlations of RSP noise between voxels are relatively low. This provides a method to produce pCT images with consistent noise properties useful for proton therapy treatment planning, which relies on summing RSP along lines of voxels. Consistent noise properties will also be useful for future studies of image quality using metrics such as contrast to noise ratio, and to compare RSP noise and dose of pCT with other modalities such as dual-energyCT. With simulated and real images with varying heterogeneity from a prototype clinical proton imaging system, we calculate average RSP correlations between voxel pairs in uniform regions-of-interest versus distance between voxels. We define a parameter r, the remaining distance to the unique solution relative to estimated RSP noise, and our stopping criterion is based on r falling below a chosenvalue. We find large correlations between voxels for larger values of r, and anticorrelations for smaller values. For r in the range of 0.5-1, voxels are relatively uncorrelated, and compared to smaller values of r have lower noise with only slight loss of spatialresolution. Iterative algorithms not using a specific metric or rationale for stopping iterations may produce images with an unknown and arbitrary level of convergence or smoothing. We resolve this issue by stopping iterations of a least-squares iterative algorithm when r reaches the range of 0.5-1. This defines a pCT image reconstruction method with consistent statistical properties optimal for clinical use, including for treatment planning with pCTimages.

Surpassing spectator qubits with photonic modes and continuous measurement for Heisenberg-limited noise mitigation

Noise is an ever-present challenge to the creation and preservation of fragile quantum states. Recent work suggests that spatial noise correlations can be harnessed as a resource for noise mitigation via the use of spectator qubits to measure environmental noise. In this work we generalize this concept from spectator qubits to a spectator mode: a photonic mode which continuously measures spatially correlated classical dephasing noise and applies a continuous correction drive to frequency-tunable data qubits. Our analysis shows that by using many photon states, spectator modes can surpass many of the quantum measurement constraints that limit spectator qubit approaches. We also find that long-time data qubit dephasing can be arbitrarily suppressed, even for white noise dephasing. Further, using a squeezing (parametric) drive, the error in the spectator mode approach can exhibit Heisenberg-limited scaling in the number of photons used. We also show that spectator mode noise mitigation can be implemented completely autonomously using engineered dissipation. In this case no explicit measurement or processing of a classical measurement record is needed. Our work establishes spectator modes as a potentially powerful alternative to spectator qubits for noise mitigation.

10-channel phased-array coil for carotid wall MRI at 3T.

Accurate assessment of plaque accumulation near the carotid bifurcation is important for the effective prevention and treatment of stroke. However, vessel and plaque delineation using MRI can be limited by low contrast-to-noise ratio (CNR) and long acquisition times. In this work, a 10-channel phased-array receive coil design for bilateral imaging of the carotid bifurcation using 3T MRI is proposed. The proposed 10-channel receive coil was compared to a commercial 4-channel receive coil configuration using data acquired from phantoms and healthy volunteers (N = 9). The relative performance of the coils was assessed, by comparing signal-to-noise ratio (SNR), noise correlation, g-factor noise amplification, and the CNR between vessel wall and lumen using black-blood sequences. Patient data were acquired from 12 atherosclerotic carotid artery disease patients. The 10-channel coil consistently provided substantially increased SNR in phantoms (+77 ± 27%) and improved CNR in healthy carotid arteries (+62 ± 11%), or reduced g-factor noise amplification. Patient data showed excellent delineation of atherosclerotic plaque along the length of the carotid bifurcation using the 10-channel coil. The proposed 10-channel coil design allows for improved visualization of the carotid arteries and the carotid bifurcation and increased parallel imaging acceleration factors relative to a commercial 4-channel coil design.

Generating 1D depth profile of shear-wave velocity from ambient noise cross-correlation: application to Jakarta array

In the past decade, cross-correlations of ambient seismic noise have been exploited in various applications to model the shallow-to-deep structure of Earth’s interior through tomographic inversions. The stack of cross-correlations between a 2-station pair represents empirical Green’s function and comprises the information of the subsurface structure between those stations. In practice, noise correlation function (NCF) is analyzed to reconstruct surface wave group or phase velocity dispersion; then, the dispersion data is used to model shear-wave velocity (Vs). This study presents a case for temporary seismic networks deployed in the Jakarta Basin; we applied a two-step routine to obtain a representative 1D Vs profile beneath an array. First, we extracted our array’s average phase velocity dispersion based on the relationship between NCF’s spectra and the Bessel function. Then, we invert for the 1D depth profile of Vs using a transdimensional Bayesian inversion to allow for exploring a number of layers in parameterizations. We successfully generate a 1D Vs profile up to 5 km depth reflecting the regional stratigraphy of the Jakarta Basin. In general, a sedimentary basin fill covers the area reaching a depth of 650 m. We suggest that this simple routine can be undertaken for other ambient noise cross-correlation cases; such a 1D depth profile would be beneficial to be used as a reference model.

Migration of Mechanical Perturbations Estimated by Seismic Coda Wave Interferometry During the 2018 Pre‐Eruptive Period at Kīlauea Volcano, Hawaii

AbstractWe use seismic ambient noise correlation and coda wave interferometry to estimate velocity variations at high temporal resolution, during the pre‐eruptive period and the onset of the 2018 eruption of Kīlauea volcano. A progressive velocity increase is observed from March to the end of April. It is followed by rapid decrease starting a few days before the onset of the East Rift Zone (ERZ) eruption and then by sharp velocity drop when the eruption started. The change of trend from velocity increase to decrease is progressively delayed by a few days from the summit caldera toward the ERZ. The location of the velocity perturbations shows a migration of the sources of velocity changes from the summit caldera toward the ERZ before the eruption. Using a model of pressure source, we show that the simultaneous caldera inflation and velocity increase probably result from an anisotropic distribution of fault and crack orientations. The velocity decrease could be due to damaging processes above the shallow reservoir and to plastic deformations around the caldera. We introduce a forward model of rock damage associated with the volcano‐tectonic seismicity to calculate the velocity decrease. The good agreement between the calculated and the observed velocity variations shows that a large part of the velocity decrease results from damage of the medium. The delayed onsets of velocity decrease and the source migration of velocity perturbations are probably related to progressive fault openings in the Southern and Eastern parts of the caldera and to magma transfer toward the ERZ.

The impact of noise correlations on the information contained in visual cortical activity

The impact of noise correlations on the information contained in visual cortical activity

Impact of Double Time Delays on Regime Shift and Stochastic Resonance for a Species Population System Driven by Colored Correlated Multiplicative and Additive Noises

In this paper, the characteristics for the state transition between the boom state and the extinction one, varius stochastic resonance (SR) phenomena for a species population system induced by double time delays and colored cross-correlated Gaussian noises are investigated. The control of the species population system has an important effect on ecological balance and the development of human living environment. By means of the numerical calculation of the mean extinction time and the stationary probability density function (SPDF), we can figure out some fact: both external and internal noises, the noise correlation strength and its correlation time, one time delay can all reduce the ecological stability and shorten the survival time of the system; while the other time delay can enhance significantly the biological stability and postpone the extinction of the population. For the mean extinction time (MET) of the species population, it is found that noise correlation strength, time delay, the noise correlation time can all reduce the peak value of the MET, which leads to the reduction of the life cycle. Inversely, the other time delay will not change the maximum of the MET, and induce the peak value to shift to the left. With respect to the SNR, it is discovered that in the noise correlation strength and its correlation time, one-time delay mainly plays a prominent role in inhibiting the SR effect. On the contrary, the multiplicative noise can result in the enhancement of the resonant peak. In particular, the other time delay and the additive noise can stimulate the SR effect for the SNR during the initial period. However, the further increase of them will bring about the reduction of the resonant phenomenon.

Wall-pressure spectra, spanwise correlation, and far-field noise measurements of a NACA 0008 airfoil under uniform and turbulent inflows

This paper discusses unique measurements of wall-pressure fluctuations (WPFs), spanwise correlation length, and far-field noise of a NACA 0008 airfoil subjected to uniform, non-turbulent and turbulent inflows. From these measurements, the near-field characteristics of trailing-edge (TE) and leading-edge (LE) noise of a thin airfoil are analyzed. The competing nature of the LE and TE noise mechanisms of an airfoil subjected to a turbulent inflow is also investigated. Experiments were performed in the Aeroacoustic Wind Tunnel of the University of Twente for a chord-based Reynolds number ranging from 3.2×105 to 9×105 for a uniform inflow and a rod-generated turbulent inflow with a turbulence intensity of approximately 18%. The effective angles of attack ranged from -5∘ to 5∘. Measurements of the boundary layer at the TE, the WPFs along the chord and span, and the far-field radiated noise were performed. For the uniform inflow case, laminar-boundary-layer noise, turbulent-boundary-layer (TBL) noise, and blunt TE noise sources are identified. The far-field noise spectrum presents similar components in the frequency domain as the WPF spectrum and the spanwise correlation length at the TE. The angle of attack mainly affects the WPF spectrum and spanwise correlation length for chord-based Strouhal numbers St<10. The angle of attack slightly affects the TE noise with a maximum variation of 3 dB for 10<St<60. For the turbulent inflow case, it is observed that the turbulence significantly affects the WPFs and spanwise correlation length along the chord, increasing considerably compared to the case of uniform inflow. The highest WPF spectral level and the larger spanwise correlation length occur at positions close to the LE. The results show that the turbulent inflow yields a higher WPF spectral level and larger spanwise correlation length at the TE, resulting in higher levels of TE noise. However, LE noise is still the dominant noise source for St<25.2. For higher frequencies, the TE noise level is expected to become higher than the LE noise level.

Discrete identification of continuous non-linear andnon-stationary dynamical systems that is insensitive to noise correlation and measurement outliers

Discrete identification of continuous non-linear andnon-stationary dynamical systems that is insensitive to noise correlation and measurement outliers

Impact of Spatial Noise Correlation on Bearing Accuracy in DIFAR Systems

Impact of Spatial Noise Correlation on Bearing Accuracy in DIFAR Systems

Tumor state transitions driven by Gaussian and non-Gaussian noises

Tumor state transitions between the excited (high-concentration) and nonexcited (low-concentration) basins under the Gaussian white noise and non-Gaussian colored noise are investigated via the most probable steady states (MPSS) and the first escape probability (FEP)-based stochastic basin of attraction (SBA), respectively. Reducing the non-Gaussian colored noise and then utilizing the unified colored noise approximation (UCNA), the Markov system is derived. The extremal controlling equation of stationary probability density function (SPDF) is derived to analyze the impacts of noise on transitions in terms of MPSS. The existence of the ‘color’ of the non-Gaussian colored noise induces the reappearance of the uncorrelated additive white noise parameter that had vanished from the extremal controlling equation, completely reversing the inability of the uncorrelated additive Gaussian white noise to operate on transitions. The FEP-dependent SBA characterizing the excited basin stability is performed to further analyze the role of noise on the likelihood of escaping to the nonexcited state. Results show that the cross-correlated noises play a dual role in regulating SBA. The increased SBA indicating more difficulty to escape to the nonexcited state reflects a worse therapeutic effect. Therefore, enhancing the negatively correlated noise intensities and augmenting the non-Gaussian noise correlation time is essential for destabilizing the excited basin and achieving optimal therapeutic efficacy.

Fundamental limits in structured principal component analysis and how to reach them

How do statistical dependencies in measurement noise influence high-dimensional inference? To answer this, we study the paradigmatic spiked matrix model of principal components analysis (PCA), where a rank-one matrix is corrupted by additive noise. We go beyond the usual independence assumption on the noise entries, by drawing the noise from a low-order polynomial orthogonal matrix ensemble. The resulting noise correlations make the setting relevant for applications but analytically challenging. We provide characterization of the Bayes optimal limits of inference in this model. If the spike is rotation invariant, we show that standard spectral PCA is optimal. However, for more general priors, both PCA and the existing approximate message-passing algorithm (AMP) fall short of achieving the information-theoretic limits, which we compute using the replica method from statistical physics. We thus propose an AMP, inspired by the theory of adaptive Thouless-Anderson-Palmer equations, which is empirically observed to saturate the conjectured theoretical limit. This AMP comes with a rigorous state evolution analysis tracking its performance. Although we focus on specific noise distributions, our methodology can be generalized to a wide class of trace matrix ensembles at the cost of more involved expressions. Finally, despite the seemingly strong assumption of rotation-invariant noise, our theory empirically predicts algorithmic performance on real data, pointing at strong universality properties.

Full counting statistics of ultrafast quantum transport

Quantum transport in the presence of time-dependent drives is dominated by quantum interference and many-body effects at low temperatures. For a periodic driving, the analysis of the full counting statistics revealed the elementary events that determine the statistical properties of the charge transport. As a result, the noise correlations display quantum oscillation as functions of the ratio of the voltage amplitude and the drive frequency, reflecting the detailed shape of the drive. However, so far only continuous wave excitations were considered, but, recently, transport by few-cycle light pulses were investigated, and the need for a statistical interpretation became eminent. We address the charge transfer generated by single- or few-cycle light pulses. The fingerprints of these time-dependent voltage pulses are imprinted in the full counting statistics of a coherent mesoscopic conductor at zero temperature. In addition, we identify the elementary processes that occur in the form of electron–hole pair creations, which can be investigated by the excess noise. We study the quantum oscillations in the differential noise induced by a wave packet consisting of an oscillating carrier modulated by a Gaussian- or a box-shaped envelope. As expected, the differential noise exhibits an oscillatory behavior with increasing amplitude. In particular, we find clear signature of the so-called carrier-envelope phase in the peak heights and positions of these quantum oscillations. More carrier cycles under the Gaussian envelope diminish the influence of the carrier-envelope phase, while this is not true for the box pulses, probably related to the abrupt onset.

Experimental Investigation of Stochastically Forced Rijke-Type Supercritical Thermoacoustic Systems

Intense thermoacoustic oscillations may lead to severe deterioration due to the induced intolerable damage to combustors. A better understanding of unstable behaviors is important to prevent or suppress these oscillations. Active thermoacoustic coupling in practical combustors is caused primarily by two approaches: inherent turbulent fluctuations and the flame response to acoustic waves. Turbulent fluctuations are generally characterized by random noise. This paper experimentally expands on previous analytic studies regarding the influence of colored disturbances on the thermoacoustic response near the supercritical bifurcation point. Therein, a laboratory-scale Rijke-type thermoacoustic system is established, and both supercritical and subcritical bifurcations are observed. Then, Ornstein–Uhlenbeck (OU)-type external colored noise is introduced near the supercritical bifurcation point, and the effects of the corresponding correlation time τc and noise intensity D are studied. The experimental results show that these variables of the colored noise significantly influence the dynamics of thermoacoustic oscillations in terms of the most probable amplitude and autocorrelation properties. A resonance-like behavior is observed as the noise intensity or the autocorrelation time of the colored noise is continuously varied, which means that the coherent resonance occurs in the thermoacoustic system. Finally, when the system is configured closer to the stability boundary, the extent of the coherence motion is intensified in the stochastic system response. Meanwhile, the signal-to-noise ratios (SNRs) of the colored-noise-induced response are found to become more distinguished, the optimal colored noise intensity decreases, and the optimal autocorrelation time increases. These findings provide valuable guidance to predict the onset of thermoacoustic instabilities.

Noise-induced servo errors in optical clocks utilizing Rabi interrogation

We show that in optical clocks based on Rabi interrogation, both laser-frequency and magnetic-field flicker () noise with zero mean can lead to servo errors at the 10−18 level if the negative-detuning (red) and positive-detuning (blue) sides of the transition are always probed in the same order. This is due to the strong correlations of flicker noise in combination with an imbalance in the response of the servo discriminator to positive and negative differential frequency noise between the red- and blue-side probing. This imbalance is particularly large for a normalized discriminator. We derive an analytical expression for the servo error based on the correlation function of the laser-frequency or magnetic-field noise and compare it to numerical servo simulations to demonstrate how the error depends on the noise level, servo parameters, and probing sequence. We also show that the servo error can be avoided by normalizing the discriminator with a moving mean or by reversing the red/blue probing order for every second servo cycle.

Response to multiplicative noise: The cross-spectrum of membrane voltage fluctuation and voltage-independent conductance noise

We reveal that the correlation of voltage fluctuation and voltage-independent conductance noise, rather than the magnitude of the latter, explains most of the former. Being the response function in the spectral domain, the cross-spectrum has an order-three scaling law originating in the imaginary part, and it can be divided into three phases: left the real part dominant phase; right the imaginary part dominant phase; and center the transition phase. Since the coherence in the left phase has a greater decay rate than that in the right phase, an additional peak appears in the transition phase. All of these results imply that the effects of conductance noise, being multiplicative, cannot be characterized by the concept of impedance—which is adopted from the field of equilibrium thermodynamics.

Shear Wave Velocities in the San Gabriel and San Bernardino Basins, California

AbstractWe construct a new shear velocity model for the San Gabriel, Chino and San Bernardino basins located in the northern Los Angeles area using ambient noise correlation between dense linear nodal arrays, broadband stations, and accelerometers. We observe Rayleigh and Love waves in the correlation of vertical (Z) and transverse (T) components, respectively. By combining Hilbert and Wavelet transforms, we obtain the separated fundamental and first higher mode of the Rayleigh wave dispersion curves based on their distinct particle motion polarization. Basin depths constrained by receiver functions, gravity, and borehole data are incorporated into the prior model. Our 3D shear wave velocity model covers the upper 3–5 km of the crust in the San Gabriel, Chino and San Bernardino basin area. The Vs model is in agreement with the geological and geophysical cross‐sections from other studies, but discrepancies exist between our model and a Southern California Earthquake Center community velocity model. Our shear wave velocity model shows good consistency with the CVMS 4.26 in the San Gabriel basin, but predicts a deeper and slower sedimentary basin in the San Bernardino and Chino basins than the community model.

Superferromagnetic Sensors

The strong ferromagnetic nanoparticles are analyzed within the band structure-based shell model, accounting for discrete quantum levels of conducting electrons. As is demonstrated, such an approach allows for the description of the observed superparamagnetic features of these nanocrystals. Assemblies of such superparamagnets incorporated into nonmagnetic insulators, semiconductors, or metallic substrates are shown to display ferromagnetic coupling, resulting in a superferromagnetic ordering at sufficiently dense packing. Properties of such metamaterials are investigated by making use of the randomly jumping interacting moments model, accounting for quantum fluctuations induced by the discrete electronic levels and disorder. Employing the mean-field treatment for such superparamagnetic assemblies, we obtain the magnetic state equation, indicating conditions for an unstable behavior. Respectively, magnetic spinodal regions and critical points occur on the magnetic phase diagram of such ensembles. The respective magnetodynamics exhibit jerky behavior expressed as erratic stochastic jumps in magnetic induction curves. At critical points, magnetodynamics displays the features of self-organized criticality. Analyses of magnetic noise correlations are proposed as model-independent analytical tools employed in order to specify, quantify, and analyze the magnetic structure and origin of superferromagnetism. We discuss some results for a sensor-mode application of superferromagnetic reactivity associated with spatially local external fields, e.g., the detection of magnetic particles. The transport of electric charge carriers between superparamagnetic particles is considered tunneling and Landau-level state dynamics. The tunneling magnetoresistance is predicted to grow noticeably with decreasing nanomagnet size. The giant magnetoresistance is determined by the ratio of the respective times of flight and relaxation and can be significant at room temperature. Favorable designs for superferromagnetic systems with sensor implications are revealed.

A 16-channel loop array for in vivo macaque whole-brain imaging at 7 T

Combining multimodal approaches with functional magnetic resonance imaging (fMRI) has catapulted the research on brain circuitries of non-human primates (NHPs) into a new era. However, many studies are constrained by a lack of appropriate RF coils. In this study, a single loop transmit and 16-channel receive array coil was constructed for brain imaging of macaques at 7 Tesla (7 T). The 16 receive channels were mounted on a 3D-printed helmet-shaped form closely fitting the macaque head, with fourteen openings arranged for multimodal devices around the cortical regions. Coil performance was evaluated by quantifying and comparing signal-to-noise ratio (SNR) maps, noise correlations, g-factor maps and flip-angle maps with a 28-channel commercial knee coil. The in vivo results suggested that the macaque coil has higher SNR in cortical regions and better acceleration ability in parallel imaging, which may benefit revealing mesoscale organizations in the brain.