Isotropic Noise Research Articles

Surface wave imaging with stationary-phase noise sources based on ultrashort traffic-induced data: An application in karst cave detection

Abstract In urban environments, abundant traffic-induced noise data are analyzed through crosscorrelation to retrieve high-frequency (> 1 Hz) surface waves, providing a cost-effective technique for detecting near-surface structures. The isotropic noise source distribution is an essential prerequisite for the correct reconstruction of the Green’s function. The azimuth of traffic noise sources, however, can change with human activities in highly populated urban areas, resulting in non-random distributions in time and space. Due to the uneven distribution of traffic noise sources, spurious signals are generated in the noise crosscorrelation functions and phase velocities calculated from the retrieved surface waves are overestimated, leading to incorrect S-wave velocity profiles. By analyzing the noise source distribution of each segment, we selected the stationary-phase segments to improve the retrieval of surface waves. We processed approximately one-day ultrashort continuous recordings to obtain virtual shot gathers with larger multichannel-coherency coefficients and dispersion images with more surface-wave dispersion data. S-wave velocity profiles for different arrays, including a 3D S-wave velocity model, were produced by inverting the surface-wave dispersion data to reveal the distribution of karst caves beneath the surface. The results demonstrate the effectiveness of the strategy of the stationary-phase segment selection and the great potential of traffic-induced surface waves in monitoring subsurface changes in urban areas.

Representation learning with unconditional denoising diffusion models for dynamical systems

Abstract. We propose denoising diffusion models for data-driven representation learning of dynamical systems. In this type of generative deep learning, a neural network is trained to denoise and reverse a diffusion process, where Gaussian noise is added to states from the attractor of a dynamical system. Iteratively applied, the neural network can then map samples from isotropic Gaussian noise to the state distribution. We showcase the potential of such neural networks in proof-of-concept experiments with the Lorenz 1963 system. Trained for state generation, the neural network can produce samples that are almost indistinguishable from those on the attractor. The model has thereby learned an internal representation of the system, applicable for different tasks other than state generation. As a first task, we fine-tune the pre-trained neural network for surrogate modelling by retraining its last layer and keeping the remaining network as a fixed feature extractor. In these low-dimensional settings, such fine-tuned models perform similarly to deep neural networks trained from scratch. As a second task, we apply the pre-trained model to generate an ensemble out of a deterministic run. Diffusing the run, and then iteratively applying the neural network, conditions the state generation, which allows us to sample from the attractor in the run's neighbouring region. To control the resulting ensemble spread and Gaussianity, we tune the diffusion time and, thus, the sampled portion of the attractor. While easier to tune, this proposed ensemble sampler can outperform tuned static covariances in ensemble optimal interpolation. Therefore, these two applications show that denoising diffusion models are a promising way towards representation learning for dynamical systems.

An analytical model of spatial correlation between vector fields of surface generated noise in a stratified ocean.

Traditionally, hydrophone-based acoustic pressure information has been utilized for underwater detection, but the advent of vector sensors has enabled the utilization of particle velocity of sound waves. A vector sensor adds three-axis particle velocity vector components to the conventional acoustic pressure sensor, representing spatial correlation not as a scalar function but as a matrix of four vector components. While analytical solutions exist for vector sensor spatial correlation in the case of simple isotropic noise, such noise fails to reflect the medium properties of the ocean, such as sound speed or density. Previous investigation reflecting the ocean environment derived a pressure spatial correlation model for surface generated noise in a stratified ocean, but this model is limited in the applicability to vector sensors. In this work, we extend the pressure spatial correlation model to vector fields, and by comparing with isotropic noise, we have confirmed that ocean environmental factors significantly influence the spatial correlation of vector sensors.

Eigenvalues of the noise covariance matrix in ocean waveguides.

The eigenvalue (EV) spectra of the theoretical noise covariance matrix (CM) and observed sample CM provide information about the environment, source, and noise generation. This paper investigates these spectra for vertical line arrays (VLAs) and horizontal line arrays (HLAs) in deep and shallow water numerically. Empirically, the spectra are related to the width of the conventional beamforming output in angle space. In deep water, the HLA noise CM tends to be isotropic regardless of the sound speed profile. Thus, the EV spectrum approaches a step function. In contrast, the VLA noise CM is non-isotropic, and the EVs of the CM jump in two steps. The EVs before the first jump are due to sea surface noise, while those between the first and second jump are due to bottom-reflected noise. In shallow water, the VLA noise CM is affected by the environment (sound speed profile and seabed density, sound speed, attenuation, and layers) and array depth, the EVs have a more complicated structure. For Noise09 VLA experimental data, the noise sample CM EVs match the waveguide noise model better than the three-dimensional isotropic noise model.

Automated construction of effective potential via algorithmic implicit bias

We introduce a novel approach for decomposing and learning every scale of a given multiscale objective function in Rd, where d⩾1. This approach leverages a recently demonstrated implicit bias of the optimization method of gradient descent [44], which enables the automatic generation of data that nearly follow Gibbs distribution with an effective potential at any desired scale. One application of this automated effective potential modeling is to construct reduced-order models. For instance, a deterministic surrogate Hamiltonian model can be developed to substantially soften the stiffness that bottlenecks the simulation, while maintaining the accuracy of phase portraits at the scale of interest. Similarly, a stochastic surrogate model can be constructed at a desired scale, such that both its equilibrium and out-of-equilibrium behaviors (characterized by auto-correlation function and mean path) align with those of a damped mechanical system with the original multiscale function being its potential. The robustness and efficiency of our proposed approach in multi-dimensional scenarios have been demonstrated through a series of numerical experiments. A by-product of our development is a method for anisotropic noise estimation and calibration. More precisely, Langevin model of stochastic mechanical systems may not have isotropic noise in practice, and we provide a systematic algorithm to quantify its covariance matrix without directly measuring the noise. In this case, the system may not admit closed form expression of its invariant distribution either, but with this tool, we can design friction matrix appropriately to calibrate the system so that its invariant distribution has a closed form expression of Gibbs.

PointCAT: Contrastive Adversarial Training for Robust Point Cloud Recognition.

Notwithstanding the prominent performance shown in various applications, point cloud recognition models have often suffered from natural corruptions and adversarial perturbations. In this paper, we delve into boosting the general robustness of point cloud recognition, proposing Point-Cloud Contrastive Adversarial Training (PointCAT). The main intuition of PointCAT is encouraging the target recognition model to narrow the decision gap between clean point clouds and corrupted point clouds by devising feature-level constraints rather than logit-level constraints. Specifically, we leverage a supervised contrastive loss to facilitate the alignment and the uniformity of hypersphere representations, and design a pair of centralizing losses with dynamic prototype guidance to prevent features from deviating outside their belonging category clusters. To generate more challenging corrupted point clouds, we adversarially train a noise generator concurrently with the recognition model from the scratch. This differs from previous adversarial training methods that utilized gradient-based attacks as the inner loop. Comprehensive experiments show that the proposed PointCAT outperforms the baseline methods, significantly enhancing the robustness of diverse point cloud recognition models under various corruptions, including isotropic point noises, the LiDAR simulated noises, random point dropping, and adversarial perturbations. Our code is available at: https://github.com/shikiw/PointCAT.

Optimal Pose Estimation and Covariance Analysis with Simultaneous Localization and Mapping Applications

This work provides a theoretical analysis for optimally solving the pose estimation problem using total-least-squares for vector observations from landmark features, which is central to applications involving simultaneous localization and mapping. First, the optimization process is formulated with observation vectors extracted from point-cloud features. Then, error-covariance expressions are derived. The attitude and position estimates obtained via the derived optimization process are proven to reach the bounds defined by the Cramér–Rao lower bound under the small-angle approximation of attitude errors. A fully populated observation noise-covariance matrix is assumed as the weight in the cost function to cover the most general case of the sensor uncertainty. This includes more generic correlations in the errors than previous cases involving an isotropic noise assumption. The proposed solution is verified using Monte Carlo simulations, a Gazebo simulation in a robotics operating system, and an experiment with an actual light detection and ranging sensor to validate the error-covariance analysis.

Fitting quantum noise models to tomography data

The presence of noise is currently one of the main obstacles to achieving large-scale quantum computation. Strategies to characterise and understand noise processes in quantum hardware are a critical part of mitigating it, especially as the overhead of full error correction and fault-tolerance is beyond the reach of current hardware. Non-Markovian effects are a particularly unfavourable type of noise, being both harder to analyse using standard techniques and more difficult to control using error correction. In this work we develop a set of efficient algorithms, based on the rigorous mathematical theory of Markovian master equations, to analyse and evaluate unknown noise processes. In the case of dynamics consistent with Markovian evolution, our algorithm outputs the best-fit Lindbladian, i.e., the generator of a memoryless quantum channel which best approximates the tomographic data to within the given precision. In the case of non-Markovian dynamics, our algorithm returns a quantitative and operationally meaningful measure of non-Markovianity in terms of isotropic noise addition. We provide a Python implementation of all our algorithms, and benchmark these on a range of 1- and 2-qubit examples of synthesised noisy tomography data, generated using the Cirq platform. The numerical results show that our algorithms succeed both in extracting a full description of the best-fit Lindbladian to the measured dynamics, and in computing accurate values of non-Markovianity that match analytical calculations.

A General Approach to the Design of the Fractional-Order Superdirective Beamformer

The superdirective beamformer (SD) with a linear array exhibits the maximum directivity factor (DF) in the isotropic noise field. Previously, a fractional-order SD (FO-SD) has been designed to achieve a compromise between the robustness and the DF. However, this method may suffer from two limitations. First, it only considers the Jacobi-Anger expansion-based beampattern synthesis. Second, it cannot control the DF in spherically isotropic noise field. To address these problems, we propose a general approach to the design of the FO-SD, which is a linear combination of two SDs with the integer order that can be designed with any beampattern synthesis method. Moreover, the proposed approach is able to control the WNG and the DF in both spherically and cylindrically isotropic noise field. Computer simulations substantiate the effectiveness of the proposed FO-SD over the existing SDs.

Further results on maximal ratio combining under correlated noise for multi-carrier underwater acoustic communication using vector sensors

In the isotropic marine ambient noise field, the pressure and particle velocity signal processing based on the maximal ratio combining (MRC) algorithm can effectively improve the signal-to-noise ratio (SNR) for the underwater acoustic (UWA) communication using acoustic vector sensors (VS). However, the assumption of isotropic ambient noise is not always valid, especially when combined with VS manufacturing errors, which increase the correlation between pressure and velocity branches for the noise and reduce MRC performance. Therefore, a correlation coefficient weighted MRC (CCW-MRC) method is proposed to achieve the optimal combination under correlated noise. And we derive the optimal weighting factors and apply the CCW-MRC method to the multi-carrier M-ary Frequency Shift Keying (MFSK) based UWA communication system with the single acoustic VS. Simulation and the field trial results demonstrate that the proposed CCW-MRC method can improve the received SNR by 2-3 dB compared with the traditional MRC in the multicarrier MFSK based UWA communication system using the single acoustic VS.

Reversing skin cancer adversarial examples by multiscale diffusive and denoising aggregation mechanism

Reliable skin cancer diagnosis models play an essential role in early screening and medical intervention. Prevailing computer-aided skin cancer classification systems employ deep learning approaches. However, recent studies reveal their extreme vulnerability to adversarial attacks — often imperceptible perturbations to significantly reduce the performances of skin cancer diagnosis models. To mitigate these threats, this work presents a simple, effective, and resource-efficient defense framework by reverse engineering adversarial perturbations in skin cancer images. Specifically, a multiscale image pyramid is first established to better preserve discriminative structures in the medical imaging domain. To neutralize adversarial effects, skin images at different scales are then progressively diffused by injecting isotropic Gaussian noises to move the adversarial examples to the clean image manifold. Crucially, to further reverse adversarial noises and suppress redundant injected noises, a novel multiscale denoising mechanism is carefully designed that aggregates image information from neighboring scales. We evaluated the defensive effectiveness of our method on ISIC 2019, a largest skin cancer multiclass classification dataset. Experimental results demonstrate that the proposed method can successfully reverse adversarial perturbations from different attacks and significantly outperform some state-of-the-art methods in defending skin cancer diagnosis models.

Self-supervision for Tabular Data by Learning to Predict Additive Homoskedastic Gaussian Noise as Pretext

The lack of scalability of data annotation translates to the need to decrease dependency on labels. Self-supervision offers a solution with data training themselves. However, it has received relatively less attention on tabular data, data that drive a large proportion of business and application domains. This work, which we name the Statistical Self-Supervisor (SSS), proposes a method for self-supervision on tabular data by defining a continuous perturbation as pretext. It enables a neural network to learn representations by learning to predict the level of additive isotropic Gaussian noise added to inputs. The choice of the pretext transformation is motivated by intrinsic characteristics of a neural network fundamentally performing linear fits under the widely adopted assumption of Gaussianity in its fitting error and the preservation of locality of a data example on the data manifold in the presence of small random perturbations. The transform condenses information in the generated representations, making them better employable for further task-specific prediction as evidenced by performance improvement of the downstream classifier. To evaluate the persistence of performance under low-annotation settings, SSS is evaluated against different levels of label availability to the downstream classifier (1% to 100%) and benchmarked against self- and semi-supervised methods. At the most label-constrained, 1% setting, we report a maximum increase of at least 2.5% against the next-best semi-supervised competing method. We report an increase of more than 1.5% against self-supervised state of the art. Ablation studies also reveal that increasing label availability from 0% to 1% results in a maximum increase of up to 50% on either of the five performance metrics and up to 15% thereafter, indicating diminishing returns in additional annotation.

Robust superdirective beamforming for arbitrary sensor arrays

This paper presents a method of designing robust superdirective beamformers for arbitrary sensor arrays. First, the optimal weighting vector is transformed into an equivalent form based on the eigen–decomposition of the noise correlation matrix in an isotropic uniform noise field, and its entries will be indexed using mode orders instead of element numbers. Second, a parameter is weighted at the maximum–order entry in the modified weighting vector. The beampattern, directivity factor, and error sensitivity function can be expressed as functions of the parameter. Adjusting the parameter will achieve arbitrary–order superdirective beampatterns with different directivity factors or error sensitivity functions. Third, the closed–form expression of the parameter can be derived given a desired directivity factor or error sensitivity function. The final robust broadband superdirective beampatterns can then be readily synthesized. The proposed method, which is an extension of that previously proposed for circular sensor arrays, provides flexible schemes to designing robust broadband superdirective beamformers for arbitrary arrays in simulations and experiments.

Unraveling-paired dynamical maps recover the input of quantum channels

We explore algebraic and dynamical consequences of unraveling general time-local master equations. We show that the ‘influence martingale’, the paramount ingredient of a recently discovered unraveling framework, pairs any time-local master equation with a one parameter family of Lindblad–Gorini–Kossakowski–Sudarshan master equations. At any instant of time, the variance of the influence martingale provides an upper bound on the Hilbert–Schmidt distance between solutions of paired master equations. Finding the lowest upper bound on the variance of the influence martingale yields an explicit criterion of ‘optimal pairing’. The criterion independently retrieves the measure of isotropic noise necessary for the structural physical approximation of the flow the time-local master equation with a completely positive flow. The optimal pairing also allows us to invoke a general result on linear maps on operators (the ‘commutant representation’) to embed the flow of a general master equation in the off-diagonal corner of a completely positive semi-group which in turn solves a time-local master equation that we explicitly determine. We use the embedding to reverse a completely positive evolution, a quantum channel, to its initial condition thereby providing a protocol to preserve quantum memory against decoherence. We thus arrive at a model of continuous-time error correction by a quantum channel.

High Signal-to-Noise Ratio MEMS Noise Listener for Ship Noise Detection

Ship noise observation is of great significance to marine environment research and national defense security. Acoustic stealth technology makes a variety of ship noise significantly reduced, which is a new challenge for marine noise monitoring. However, there are few high spatial gain detection methods for low-noise ship monitoring. Therefore, a high Signal-to-Noise Ratio (SNR) MEMS noise listener for ship noise detection is developed in this paper. The listener achieves considerable gain by suppressing isotropic noise in the ocean. The working principle and posterior end signal processing method of the listener are introduced in detail. A gain of 10 dB over the sound pressure detector is obtained by detecting the standard sound source. In addition, the traffic vessel noise monitoring experiment verifies that the listener can detect the ship noise. The results show that the listener has a very broad application prospect in the field of low-noise ship observation.

Anisotropic Diffusion in Consensus-Based Optimization on the Sphere

In this paper we are concerned with the global minimization of a possibly non-smooth and non-convex objective function constrained on the unit hypersphere by means of a multi-agent derivative-free method. The proposed algorithm falls into the class of the recently introduced Consensus-Based Optimization. In fact, agents move on the sphere driven by a drift towards an instantaneous consensus point, which is computed as a convex combination of agent locations, weighted by the cost function according to Laplaces principle, and it represents an approximation to a global minimizer. The dynamics is further perturbed by an anisotropic random vector field to favor exploration. The main results of this paper are about the proof of convergence of the numerical scheme to global minimizers provided conditions of well-preparation of the initial datum. The proof of convergence combines a mean-field limit result with a novel asymptotic analysis, and classical convergence results of numerical methods for SDE. The main innovation with respect to previous work is the introduction of an anisotropic stochastic term, which allows us to ensure the independence of the parameters of the algorithm from the dimension and to scale the method to work in very high dimension. We present several numerical experiments, which show that the algorithm proposed in the present paper is extremely versatile and outperforms previous formulations with isotropic stochastic noise.

Retrieving High-Dimensional Quantum Steering from a Noisy Environment with N Measurement Settings.

One of the most often implied benefits of high-dimensional (HD) quantum systems is to lead to stronger forms of correlations, featuring increased robustness to noise. Here, we experimentally demonstrate the n-setting linear HD quantum steering criterion. We verify the large violation of the steering inequalities without full-state tomography. The lower bound of the violation is 2.24±0.01 in 11 dimensions, exceeding the bound (V<2) of two-setting criteria. Hence, a higher strength of steering has been revealed. Moreover, we demonstrate the method for enhancing the noise robustness without increasing dimension, alternatively, by increasing measurement settings. Using the entanglement in 11 dimensions, we experimentally retrieve steering nonlocality with 63.4±1.4% isotropic noise fraction, surpassing the 50% limitation of two-setting criteria. Our Letter offers the potential for practical one-sided device-independent quantum information processing that tolerates the noisy environment, lossy detection, and transcends the present transmission distance limitation.

Quality-relevant feature extraction method based on teacher-student uncertainty autoencoder and its application to soft sensors

Supervised representation learning based on the teacher-student framework can extract quality-related features for soft sensors, in which the teacher network extracts representation information for the student network as supervision information. In traditional applications, the teacher network is heavy and is difficult to train, so the teacher network is conventionally pre-trained. However, the pre-training of the teacher network is unnecessary if the training process is not complicated so that it is meaningful to joint optimize the teacher-student network. In our application, the teacher-student framework is used to extract quality-related representation information for soft sensors. The objective is to maximize the mutual information of representation information and supervision information, in which the inconsistency of distributions between observed information and supervisory information is modeled as isotropic Gaussian noise. The objective is decoupled through analysis under some approximate assumptions so that the alternative iteration method can be used to update the parameters of the model. The proposed quality-related feature extraction method is applied to soft sensors combined with a traditional just-in-time learning method. Our experiments show that the prediction performance of our representation extraction method is better than other existing representation extraction algorithms.

Non-Intrusive Binaural Speech Intelligibility Prediction From Discrete Latent Representations

Non-intrusive speech intelligibility (SI) prediction from binaural signals is useful in many applications. However, most existing signal-based measures are designed to be applied to single-channel signals. Measures specifically designed to take into account the binaural properties of the signal are often intrusive – characterised by requiring access to a clean speech signal – and typically rely on combining both channels into a single-channel signal before making predictions. This letter proposes a non-intrusive SI measure that computes features from a binaural input signal using a combination of vector quantization (VQ) and contrastive predictive coding (CPC) methods. vector quantized contrastive predictive coding (VQ-CPC) feature extraction does not rely on any model of the auditory system and is instead trained to maximise the mutual information between the input signal and output features. The computed VQ-CPC features are input to a predicting function parameterized by a neural network. Two predicting functions are considered in this letter. Both feature extractor and predicting functions are trained on simulated binaural signals with isotropic noise. They are tested on simulated signals with isotropic and real noise. For all signals, the ground truth scores are the (intrusive) deterministic binaural short-time objective intelligibility (STOI). Results are presented in terms of correlations and mean-squared error (MSE) and demonstrate that VQ-CPC features are able to capture information relevant to modelling SI and outperform all the considered benchmarks – even when evaluating on data comprising of different noise field types.

Rapid evaluation of the spectral signal detection threshold and Stieltjes transform

Accurate detection of signal components is a frequently-encountered challenge in statistical applications with a low signal-to-noise ratio. This problem is particularly challenging in settings with heteroscedastic noise. In certain signal-plus-noise models of data, such as the classical spiked covariance model and its variants, there are closed formulas for the spectral signal detection threshold (the largest sample eigenvalue attributable solely to noise) for isotropic noise in the limit of infinitely large data matrices. However, more general noise models currently lack provably fast and accurate methods for numerically evaluating the threshold. In this work, we introduce a rapid algorithm for evaluating the spectral signal detection threshold in the limit of infinitely large data matrices. We consider noise matrices with a separable variance profile (whose variance matrix is rank 1), as these arise often in applications. The solution is based on nested applications of Newton’s method. We also devise a new algorithm for evaluating the Stieltjes transform of the spectral distribution at real values exceeding the threshold. The Stieltjes transform on this domain is known to be a key quantity in parameter estimation for spectral denoising methods. The correctness of both algorithms is proven from a detailed analysis of the master equations characterizing the Stieltjes transform, and their performance is demonstrated in numerical experiments.