Homogeneous Noise Research Articles

Optimizing magnetometers arrays and analysis pipelines for multivariate pattern analysis

BackgroundMultivariate pattern analysis (MVPA) has proven an excellent tool in cognitive neuroscience. It also holds a strong promise when applied to optically-pumped magnetometer-based magnetoencephalography. New methodTo optimize OPM-MEG systems for MVPA experiments this study examines data from a conventional MEG magnetometer array, focusing on appropriate noise reduction techniques for magnetometers. We determined the least required number of sensors needed for robust MVPA for image categorization experiments. ResultsWe found that the use of signal space separation (SSS) without a proper regularization significantly lowered the classification accuracy considering a sub-array of 102 magnetometers or a sub-array of 204 gradiometers. We also found that classification accuracy did not improve when going beyond 30 sensors irrespective of whether SSS has been applied. Comparison with existing methodsThe power spectra of data filtered with SSS has a substantially higher noise floor that data cleaned with SSP or HFC. Consequently, MVPA decoding results obtained from the SSS-filtered data are significantly lower compared to all other methods employed. ConclusionsWhen designing MEG system based on SQUID magnetometers optimized for multivariate analysis for image categorization experiments, about 30 magnetometers are sufficient. We advise against applying SSS filters without a proper regularization to data from MEG and OPM systems prior to performing MVPA as this method, albeit reducing low-frequency external noise contributions, also introduces an increase in broadband noise. We recommend employing noise reduction techniques that either decrease or maintain the noise floor of the data like signal-space projection, homogeneous field correction and gradient noise reduction.

A conservative stochastic Dirac-Klein-Gordon system

Considered herein is a particular nonlinear dispersive stochastic system consisting of Dirac and Klein-Gordon equations. They are coupled by nonlinear terms due to the Yukawa interaction. We consider a case of homogeneous multiplicative noise that seems to be very natural from the perspective of the least action formalism. We are able to show existence and uniqueness of a corresponding Cauchy problem in Bourgain spaces. Moreover, the regarded model implies charge conservation, known for the deterministic analogue of the system, and this is used to prove a global existence result for suitable initial data.

Predictors of Speech-in-Noise Understanding in a Population of Occupationally Noise-Exposed Individuals.

Understanding speech in noise is particularly difficult for individuals occupationally exposed to noise due to a mix of noise-induced auditory lesions and the energetic masking of speech signals. For years, the monitoring of conventional audiometric thresholds has been the usual method to check and preserve auditory function. Recently, suprathreshold deficits, notably, difficulties in understanding speech in noise, has pointed out the need for new monitoring tools. The present study aims to identify the most important variables that predict speech in noise understanding in order to suggest a new method of hearing status monitoring. Physiological (distortion products of otoacoustic emissions, electrocochleography) and behavioral (amplitude and frequency modulation detection thresholds, conventional and extended high-frequency audiometric thresholds) variables were collected in a population of individuals presenting a relatively homogeneous occupational noise exposure. Those variables were used as predictors in a statistical model (random forest) to predict the scores of three different speech-in-noise tests and a self-report of speech-in-noise ability. The extended high-frequency threshold appears to be the best predictor and therefore an interesting candidate for a new way of monitoring noise-exposed professionals.

Adaptive target detection for an FDA-MIMO radar in a mainlobe deceptive jamming and a partially homogeneous noise

In this paper, we investigate the adaptive target detection problem for a collocated frequency diverse array multiple-input multiple-output (FDA-MIMO) radar in the presence of mainlobe deceptive jamming and partially homogeneous noise with an unknown covariance matrix and scaling factor. Precisely, we establish a received signal model that includes the true target and false counterparts echoes in the presence of Gaussian noise (it includes thermal noise, interference suppression, and clutter after range compensation.). Furthermore, we consider that the range information of the true target and mainlobe deceptive targets is not identical. Therefore, we project the corresponding transmit steering vectors onto different subspaces with known subspace matrices but unknown coordinates. On the other hand, the true and false targets' receive steering vectors are considered to be from the same subspace. Finally, following the generalized likelihood ratio test (GLRT), the Rao and the Wald criteria, we design three adaptive detectors with two-step criteria, i.e., TGLRT, TRao, and TWald. We note that the proposed detectors maintain a constant false alarm rate (CFAR) against the scaling factor and the noise covariance matrix. The extensive numerical simulation results have validated the effectiveness of the proposed detectors.

An optically pumped magnetic gradiometer for the detection of human biomagnetism

We realise an intrinsic optically pumped magnetic gradiometer based on non-linear magneto-optical rotation. We show that our sensor can reach a gradiometric sensitivity of 18 fT cm−1Hz−1 and can reject common mode homogeneous magnetic field noise with up to 30 dB attenuation. We demonstrate that our magnetic field gradiometer is sufficiently sensitive and resilient to be employed in biomagnetic applications. In particular, we are able to record the auditory evoked response of the human brain, and to perform real-time magnetocardiography in the presence of external magnetic field disturbances. Our gradiometer provides complementary capabilities in human biomagnetic sensing to optically pumped magnetometers, and opens new avenues in the detection of human biomagnetism.

Escape-rate response to noise of all amplitudes in leaky chaos

We study the effect of homogeneous noise on the escape rate of strongly chaotic area-preserving maps with a small opening. While in the noiseless dynamics the escape rate analytically depends on the instability of the shortest periodic orbit inside the hole, adding noise overall enhances escape, which, however, exhibits a non-trivial response to the noise amplitude, featuring an initial plateau and a successive rapid growth up to a saturation value. Numerical analysis is performed on cat maps with a hole, and the salient traits of the response to noise of the escape rate are reproduced analytically by an approximate model.

Long-time behavior of stochastic Hamilton-Jacobi equations

The long-time behavior of stochastic Hamilton-Jacobi equations is analyzed, including the stochastic mean curvature flow as a special case. In a variety of settings, new and sharpened results are obtained. Among them are (i) a regularization by noise phenomenon for the mean curvature flow with homogeneous noise which establishes that the inclusion of noise speeds up the decay of solutions, and (ii) the long-time convergence of solutions to spatially inhomogeneous stochastic Hamilton-Jacobi equations. A number of motivating examples about nonlinear stochastic partial differential equations are presented in the appendix.

Continuity in law for solutions of SPDES with space-time homogeneous Gaussian noise

In this paper, we study the continuity in law of the solutions of two linear multiplicative SPDEs (the parabolic Anderson model and the hyperbolic Anderson model) with respect to the spatial parameter of the noise. The solution is interpreted in the Skorohod sense, using Malliavin calculus. We consider two cases: (i) the regular noise, whose spatial covariance is given by the Riesz kernel of order [Formula: see text], in spatial dimension [Formula: see text]; (ii) the rough noise, which is fractional in space with Hurst index [Formula: see text], in spatial dimension [Formula: see text]. We assume that the noise is colored in time.

Medical federated learning with joint graph purification for noisy label learning

In terms of increasing privacy issues, Federated Learning (FL) has received extensive attention in medical imaging. Through collaborative training, FL can produce superior diagnostic models with global knowledge, while preserving private data locally. In practice, medical diagnosis suffers from intra-/inter-observer variability, thus label noise is inevitable in dataset preparation. Different from existing studies on centralized datasets, the label noise problem in FL scenarios confronts more challenges, due to data inaccessibility and even noise heterogeneity. In this work, we propose a federated framework with joint Graph Purification (FedGP) to address the label noise in FL through server and clients collaboration. Specifically, to overcome the impact of label noise on local training, we first devise a noisy graph purification on the client side to generate reliable pseudo labels by progressively expanding the purified graph with topological knowledge. Then, we further propose a graph-guided negative ensemble loss to exploit the topology of the client-side purified graph with robust complementary supervision against label noise. Moreover, to address the FL label noise with data silos, we propose a global centroid aggregation on the server side to produce a robust classifier with global knowledge, which can be optimized collaboratively in the FL framework. Extensive experiments are conducted on endoscopic and pathological images with the comparison under the homogeneous, heterogeneous, and real-world label noise for medical FL. Among these diverse noisy FL settings, our FedGP framework significantly outperforms denoising and noisy FL state-of-the-arts by a large margin. The source code is available at https://github.com/CUHK-AIM-Group/FedGP.

Deep Unfolding Network for Efficient Mixed Video Noise Removal

Existing image and video denoising algorithms have focused on removing homogeneous Gaussian noise. However, this assumption with noise modeling is often too simplistic for the characteristics of real-world noise. Moreover, the design of network architectures in most deep learning-based video denoising methods is heuristic, ignoring valuable domain knowledge. In this paper, we propose a model-guided deep unfolding network for the more challenging and realistic mixed noise video denoising problem, named DU-MVDnet. First, we develop a novel observation model/likelihood function based on the correlations among adjacent degraded frames. In the framework of Bayesian deep learning, we introduce a deep image denoiser prior and obtain an iterative optimization algorithm based on the maximum a posterior (MAP) estimation. To facilitate end-to-end optimization, the iterative algorithm is transformed into a deep convolutional neural network (DCNN)-based implementation. Furthermore, recognizing the limitations of traditional motion estimation and compensation methods, we propose an efficient multistage recursive fusion strategy to exploit temporal dependencies. Specifically, we divide video frames into several overlapping groups and progressively integrate these frames into one frame. Toward this objective, we implement a multiframe adaptive aggregation operation to integrate feature maps of intragroup with those of intergroup frames. Extensive experimental results on different video test datasets have demonstrated that the proposed model-guided deep network outperforms current state-of-the-art video denoising algorithms such as FastDVDnet and MAP-VDNet.

Optimal encoding of oscillators into more oscillators

Bosonic encoding of quantum information into harmonic oscillators is a hardware efficient approach to battle noise. In this regard, oscillator-to-oscillator codes not only provide an additional opportunity in bosonic encoding, but also extend the applicability of error correction to continuous-variable states ubiquitous in quantum sensing and communication. In this work, we derive the optimal oscillator-to-oscillator codes among the general family of Gottesman-Kitaev-Preskill (GKP)-stablizer codes for homogeneous noise. We prove that an arbitrary GKP-stabilizer code can be reduced to a generalized GKP two-mode-squeezing (TMS) code. The optimal encoding to minimize the geometric mean error can be constructed from GKP-TMS codes with an optimized GKP lattice and TMS gains. For single-mode data and ancilla, this optimal code design problem can be efficiently solved, and we further provide numerical evidence that a hexagonal GKP lattice is optimal and strictly better than the previously adopted square lattice. For the multimode case, general GKP lattice optimization is challenging. In the two-mode data and ancilla case, we identify the D4 lattice—a 4-dimensional dense-packing lattice—to be superior to a product of lower dimensional lattices. As a by-product, the code reduction allows us to prove a universal no-threshold-theorem for arbitrary oscillators-to-oscillators codes based on Gaussian encoding, even when the ancilla are not GKP states.

Decoherence of Single‐Excitation Entanglement over Duan‐Lukin‐Cirac‐Zoller Quantum Networks Caused by Slow‐Magnetic‐Field Fluctuations and Protection Approach

AbstractAtomic spin‐wave (SW) memory is a building block for quantum repeater. However, due to decoherence caused by atomic motions and magnetic‐field gradients, SW retrieval efficiency decays with storage time. Slow magnetic‐field fluctuations (SMFFs) lead to shot‐to‐shot phase noises of SWs, but have not been considered in previous repeater protocols. Here, a SW model including a homogeneous phase noise caused by SMFFs is developed, and then revealed that such phase noise induces decoherence of single‐excitation entanglement between two atomic ensembles in a repeater link. For verifying this conclusion, single‐excitation entanglement between two SWs in a cold atomic ensemble is experimentally prepared and observed entanglement decoherence induced by SMFFs. Limited by SMFFs, the evaluated lifetime of the single‐excitation entanglement over a repeater link is ≈135 ms, even if the link uses optical‐lattice atoms as nodes. Then an approach that may overcome such limitations and extend this lifetime to ≈1.7 s is presented.

Adaptive Jamming Attack Detection Under Noise Uncertainty in mmWave Massive MIMO Systems

This paper addresses jamming attack detection issue in a millimeter Wave (mmWave) massive MIMO system under noise uncertainty. Specifically, we apply the generalized likelihood ratio test (GLRT) to develop a one-step GLRT scheme for detecting jamming attack under the homogeneous and partially homogeneous noise environments, and exploit training data to estimate the unknown noise statistical information and replace it with resulting estimation in deriving GLRT procedure to obtain adaptive GLRT detection scheme. We also design a two-step GLRT scheme, where we first assume the unknown noise statistical information is known, and derive GLRT based on test data, and then replace it by the sample covariance matrix based on training data only to achieve a fully adaptive jamming attack detector. With the help of statistical signal subspace analysis and composite hypothesis testing theories, we further examine the statistical distributions of the jamming attack detection schemes and present the closed-form expressions of false alarm and detection probabilities for the proposed schemes under different noise environments. Finally, we implement extensive simulations to validate the theoretical results and evaluate the detection efficiency under various parameters.

A Feynman–Kac approach for the spatial derivative of the solution to the Wick stochastic heat equation driven by time homogeneous white noise

We consider the (unique) mild solution [Formula: see text] of a one-dimensional stochastic heat equation on [Formula: see text] driven by time-homogeneous white noise in the Wick–Skorokhod sense. The main result of this paper is the computation of the spatial derivative of [Formula: see text], denoted by [Formula: see text], and its representation as a Feynman–Kac type closed form. The chaos expansion of [Formula: see text] makes it possible to find its (optimal) Hölder regularity especially in space.

Phase-based vibration imaging for structural dynamics applications: Marker-free full-field displacement measurements with confidence measures

Inspired by the concept of thermal imaging, we develop a phase-based vibration imaging technique using marker-free full-field displacement measurements, which aims to determine vibrational energy distribution and possibly vibration parameters as the thermal imaging determining thermal energy distribution using colormap. In this study, accurate full-field measurements are conducted at the sub-pixel level by performing a full-field phase-based optical flow with three novel progresses. First, an image-preprocessing Gaussian smoothing gradient is applied to reduce the nonlinear phase caused by homogenous patterns and image noise. Second, two confidence measures (phase nonlinearity and filter response) are adopted to obtain reliable displacement measurements estimated from the multi-scale and multi-direction phases. Third, the combination of vector average and the intersection of constraints ensure the accuracy of integrating every pixel’s displacement components. The vibrations can then be imaged by analyzing the acquired full-field displacements using techniques such as mean absolute deviation and frequency analyses. The capability of the proposed technique is demonstrated through numerical experiments using artificial patterns. After then, experimental validation is performed, which includes full-field operational deflection shape extraction on a 5-story structure and vibration imaging of an in-service hydrogen charging station, further proving the effectiveness of the proposed vibration imaging technique.

On a class of mixed stochastic heat equations driven by spatially homogeneous Gaussian noise

In this paper, we study a class of nonlinear stochastic heat equations ∂∂tu(t,x)=Δ+aαΔα2+b⋅∇u(t,x)+σ(u(t,x))Ẇ(t,x), where Ẇ denotes the Gaussian noise which is white in time and spatially homogeneous in space. The existence, uniqueness and the Hölder continuity of the mild solution to the above equation are proved.

Residual Hearing Does Not Influence the Effectiveness of Beamforming when Using a Cochlear Implant in Conjunction with Contralateral Routing of Signals

Introduction: Contralateral routing of signals (CROS) overcomes the head shadow effect by redirecting speech signals from the contralateral ear to the better-hearing cochlear implant (CI) ear. Here we tested the performance of an adaptive monaural beamformer (MB) and a fixed binaural beamformer (BB) using the CROS system of Advanced Bionics. Methods: In a group of 17 unilateral CI users, we evaluated the benefits of MB and BB for speech recognition by measuring speech reception threshold (SRT) with and without beamforming. MB and BB were additionally evaluated with signal-to-noise ratio (SNR) measurements using a KEMAR manikin. We also assessed the effect of residual hearing in the CROS ear on the benefits of MB and BB. Speech was delivered in front of the listener in a background of homogeneous 8-talker babble noise. Results: With CI-CROS in omnidirectional settings with the T-mic active on the CI as a reference, BB significantly improved SRT by 1.4 dB, whereas MB yielded no significant improvements. The difference in effects on SRT between the two beamformers was, however, not significant. SNR effects were substantially larger, at 2.1 dB for MB and 5.8 dB for BB. CI-CROS with default omnidirectional settings also improved SRT and SNR by 1 dB over CI alone. Residual hearing did not significantly affect beamformer performance. Discussion: We recommend the use of BB over MB for CI-CROS users. Residual hearing in the CROS ear is not a limiting factor for fitting a CROS device, although a bimodal option should be considered.

Bound-state soliton gas as a limit of adiabatically growing integrable turbulence

We study numerically the integrable turbulence in the framework of the one-dimensional nonlinear Schrodinger equation (1D-NLSE) of the focusing type using a new approach called the “growing of turbulence”. In this approach, we add a small linear pumping term to the equation and start evolution from statistically homogeneous Gaussian noise. After reaching a certain level of average intensity, we switch off the pumping and examine the resulting integrable turbulence. For sufficiently small initial noise and pumping coefficient, and also for not very wide simulation box (basin length), we observe that the turbulence grows in a universal adiabatic regime, moving successively through the statistically stationary states of the integrable 1D-NLSE, which do not depend on the pumping coefficient, amplitude of the initial noise or basing length. Waiting longer in the growth stage, we transit from weakly nonlinear states to strongly nonlinear ones, characterized by a high frequency of rogue waves. Using the inverse scattering transform (IST) method to monitor the evolution, we observe that the solitonic part of the wavefield becomes dominant even when the (linear) dispersion effects are still leading in the dynamics and with increasing average intensity the wavefield approaches a dense bound-state soliton gas, whose properties are defined by the Fourier spectrum of the initial noise. Regimes deviating from the universal adiabatic growth also lead to solitonic states, but solitons in these states have noticeably different velocities and a significantly wider distribution by amplitude, while the statistics of wavefield indicates a much more frequent appearance of very large waves.

Enhancing distributed sensing with imperfect error correction

Entanglement has shown promise in enhancing information processing tasks in a sensor network, via distributed quantum sensing protocols. As noise is ubiquitous in sensor networks, error correction schemes based on Gottesman, Kitaev and Preskill (GKP) states are required to enhance the performance, as shown in [New J. Phys. 22, 022001 (2020)] assuming homogeneous noise among sensors and perfect GKP states. Here, we extend the analyses of performance enhancement to finite squeezed GKP states in a heterogeneous noise model. To begin with, we study different concatenation schemes of GKP-two-mode-squeezing codes. While traditional sequential concatenation schemes in previous works do improve the suppression of noise, we propose a balanced concatenation scheme that outperforms the sequential scheme in presence of finite GKP squeezing. We then apply these results to two specific tasks in distributed quantum sensing -- parameter estimation and hypothesis testing -- to understand the trade-off between imperfect squeezing and performance. For the former task, we consider an energy-constrained scenario and provide an optimal way to distribute the energy of the finite squeezed GKP states among the sensors. For the latter task, we show that the error probability can still be drastically lowered via concatenation of realistic finite squeezed GKP codes.

Spatial integral of the solution to hyperbolic Anderson model with time-independent noise

In this article, we study the asymptotic behavior of the spatial integral of the solution to the hyperbolic Anderson model in dimension d≤2, as the domain of the integral gets large (for fixed time t). This equation is driven by a spatially homogeneous Gaussian noise, whose covariance function is either integrable, or is given by the Riesz kernel. The novelty is that the noise does not depend on time, which means that Itô’s martingale theory for stochastic integration cannot be used. Using a combination of Malliavin calculus with Stein’s method, we show that with proper normalization and centering, the spatial integral of the solution converges to a standard normal distribution, by estimating the speed of this convergence in the total variation distance. We also prove the corresponding functional limit theorem for the spatial integral process.