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Machine learning classifiers are increasingly widely used. This research note explores how a particular widely used classifier, the Random Forest, performs when faced with samples which are imbalanced and noisy data. Both are known to affect accuracy, but if their effects are independent or not has not been explored. Based on an experiment using synthetic data generated for the study we find that the effects of noise and sample balance interact with each other; classification accuracy is worse when faced with both noisy data and sample imbalance. This has implications for the use of RF in market research, but also for how methods to address either sample imbalance or noise are assessed. [ABSTRACT FROM AUTHOR]

Traditionally, stress fluctuations in flowing and deformed materials are overlooked, with an obvious focus on average stresses in a continuum mechanical approximation. However, these fluctuations, often dismissed as "noise," hold the potential to provide direct insights into the material structure and its structure-stress coupling, uncovering detailed aspects of fluid transport and relaxation behaviors. Despite advancements in experimental techniques allowing for the visualization of these fluctuations, their significance remains largely untapped as modeling efforts continue to target Newtonian fluids within the confines of Gaussian noise assumptions. In the present work, a comparative analysis of stress fluctuations in two distinct microstructural models is carried out: the temporary network model and the hydrodynamic dumbbell model. Despite both models conforming to the upper convected Maxwell model at a macroscopic level, the temporary network model predicts non-Gaussian fluctuations. We find that stress fluctuations within the temporary network model exhibit more pronounced abruptness at the local scale, with only an enlargement of the control volume leading to a gradual Gaussian-like noise, diminishing the differences between the two models. These findings underscore the heightened sensitivity of fluctuating rheology to microstructural details and the microstructure–flow coupling, beyond what is captured by macroscopically averaged stresses. [ABSTRACT FROM AUTHOR]

Surface microseismic monitoring is widely used in hydraulic fracturing. Real‐time monitoring data collected during fracturing can be used to perform surface‐microseismic localization, which aids in assessing the effects of fracturing and provides guidance for the process. The accuracy of localization critically depends on the quality of monitoring data. However, the signal‐to‐noise ratio of the data is often low due to strong coherent and random noise, making denoising essential for processing surface monitoring data. To suppress noise more effectively, this paper introduces a novel denoising method that integrates the Ramanujan subspace with dynamic time warping and adaptive singular value decomposition. The new method consists of two steps: First, a Ramanujan subspace is constructed to suppress periodic noise. Then, dynamic time warping and adaptive singular value decomposition are applied to eliminate remaining coherent and random noise. The method has been evaluated using both synthetic and field data, and its performance is compared with traditional microseismic denoising techniques, including bandpass filtering and empirical mode decomposition. [ABSTRACT FROM AUTHOR]

ABSTRACT Non‐negative Matrix Factorization (NMF) is an effective algorithm for multivariate data analysis, including applications to feature selection, pattern recognition, and computer vision. Its variant, Semi‐Nonnegative Matrix Factorization (SNF), extends the ability of NMF to render parts‐based data representations to include mixed‐sign data. Graph Regularized SNF builds upon this paradigm by adding a graph regularization term to preserve the local geometrical structure of the data space. Despite their successes, SNF‐related algorithms to date still suffer from instability caused by the Frobenius norm due to the effects of outliers and noise. In this paper, we present a new L2,1$$ {L}_{2,1} $$ SNF algorithm that utilizes the noise‐insensitive L2,1$$ {L}_{2,1} $$ norm. We provide monotonic convergence analysis of the L2,1$$ {L}_{2,1} $$ SNF algorithm. In addition, we conduct numerical experiments on three benchmark mixed‐sign datasets as well as several randomized mixed‐sign matrices to demonstrate the performance superiority of L2,1$$ {L}_{2,1} $$ SNF over conventional SNF algorithms under the influence of Gaussian noise at different levels. [ABSTRACT FROM AUTHOR]

ABSTRACT The Kalman filter provides an optimal estimation for a linear system with Gaussian noise. However, when the noises are non‐Gaussian in nature, its performance deteriorates rapidly. For non‐Gaussian noises, maximum correntropy Kalman filter (MCKF) is developed which provides a more accurate result. In a scenario, where the actual system model differs from nominal consideration, the performance of the MCKF degrades. For such cases, in this article, we have proposed a new robust filtering technique for a linear system which maximizes a cost function defined by exponential of weighted past and present errors weighted with the kernel bandwidth. During filtering, at each time step, the kernel bandwidth is selected by maximizing the correntropy function of error. Further, a convergence condition of the proposed algorithm is derived. Numerical examples are presented to show the usefulness of the proposed filtering technique. [ABSTRACT FROM AUTHOR]

Condition health monitoring and fault diagnosis is able to safeguard against potential threats to machines. Nevertheless, the acquired signals by using a plenty of sensors are often accompanied by noise and meanwhile the useful information contained in the signals is not both complete and reliable, thereby together reducing the accuracy and stability of the fault diagnosis. Therefore, this paper proposes a noise-enhanced intelligent fault diagnosis method with multi-channel information fusion. Here, it would inject the varying levels of Gaussian noise into multi-channel input data as well as intelligent diagnostic models, with a view to elucidating the benefits of noise. Furthermore, the proposed method is validated through three experiments. The experimental results demonstrate that the diagnostic accuracy of the hydraulic motor and the two different bearings reaches 99.85%, 99.89%, and 99.85% by using the proposed method, respectively, which are increased by 2.50%, 4.09%, and 2.50%, respectively, compared with one without the injection of noise. In addition, by comparing the diagnostic accuracy of ones with single-channel and multi-channel information fusion under the optimal noise level in both cases, it is found that one with multi-channel information fusion shows an average of 3.20% increase than the single-channel one. [ABSTRACT FROM AUTHOR]

This study focuses on examining the issues of extended dissipative-based composite anti-disturbance reliable tracking control for stochastic Takagi–Sugeno fuzzy systems afflicted by sensor faults and multiple disturbances. Explicitly, the multiple disturbances include the autonomous Wiener process and non random noises with partly known information that are generated by an exogenous plant. To address the difficulty of estimating the non random disturbance while considering the partially known information, the study incorporates a fuzzy stochastic disturbance observer. Furthermore, to solve the output tracking issue of the system under consideration, a modified repetitive tracking control is implemented. Then, combining the methodologies of disturbance observer-based control technique with modified repetitive control, a composite anti-disturbance reliable tracking control strategy is developed for achieving the intended tracking goal despite the multiple disturbances and sensor faults encountered. Additionally, the proposed approach involves extended dissipativity scheme, which includes $ H_\infty $ H∞, passivity, dissipativity, and $ \mathfrak {L}_2 - \mathfrak {L}_\infty $ L2−L∞ performances in a unified framework. In particular, by employing Lyapunov–Krasovskii functional approach, the essential stability criteria for the proposed closed-loop system are articulated in the form of linear matrix inequalities. Additionally, numerical illustrations are presented to exemplify the application and efficiency of the developed control protocol. [ABSTRACT FROM AUTHOR]

Current inspection strives to perform a detailed elaboration of the Tsallis entropy‐based magnetocaloric effect (MCE) of GaAs quantum dot (QD) doped with Gaussian impurity and under applied Gaussian white noise. Noise takes additive and multiplicative pathways for its entry to the doped QD. MCE has been found to decrease following the enhancement of temperature. The enquiry manifests magnetic field‐induced confinement and consequent decline in the disorder of the system during the gradual variation of several physical parameters. However, harnessing the extent of above confinement involves extremely sensitive and delicate control over the resultant influence of the particular physical parameter undergoing change, its range of magnitude, application of noise and its mode of inclusion. Importantly, MCE has been found to maximize only during the change in the strength of the dopant potential under multiplicative noise. And, on most occasions, multiplicative noise profoundly raises the MCE over its value under the state devoid of noise and under additive noise. [ABSTRACT FROM AUTHOR]

By considering that the predators have some additional foods apart from the focal prey and the prey take refuge, a predator–prey model with the effect of seasonality in a fluctuating environment is investigated in this study. Gaussian white noises, created by random fluctuation of water level, are introduced on the prey’s growth rate and predator’s mortality rate. Both the deterministic and stochastic systems are analyzed mathematically as well as numerically. Our analytical findings show that the intensity of environmental noise, additional foods and prey refuge play significant roles in survival as well as extinction of both prey and predator populations in the aquatic system. Our numerical results show that the effectual level of additional foods, depending on water level, has positive as well as negative effects on the predator and prey populations. We find that both species strongly persist at certain water level and for the low intensity of noise. However, for an increased value of noise intensity, they persist weakly and then go to extinction. Overall, our findings show that the variations of water level together with additional food and white noise plays crucial roles in persistence and extinction of species in the ecosystem. [ABSTRACT FROM AUTHOR]

This paper reports fractal patterns identified in the complex musical composition DIAPHONIES by Michael Paouris via power-law fractal analysis with sliding-windows of size 1024. From 7,647,232 analysed musical segments of DIAPHONIES, 3,222,832 (42.4%) are fractional Brownian motion (fBm) fractal segments and 4,424,400 (57.6%) are fractional Gaussian noise (fGn) stochastic ones. From the fBm fractal segments 295,294 (9.1%) exhibit strong persistency-P with power-law segments in the range of 2.3 ≤ b ≤ 3 . These are the very strong fractal areas in DIAPHONIES. Numerous segments with strong antipersistency 1.7 ≤ b < 2 are reported together with segments with AP changes ( 1.7 ≤ b < 2.3 ). In DIAPHONIES continuous fractal fBm areas are dipped in non-fractal fGn areas of deterministic music. The results are within the fBm fractal areas reported in existing papers. Very importantly, the simple composition called Nocturnal-Angel by Michael Paouris, exhibited limited fBm areas of average b ¯ = 1.98 ( σ = 0.3 ), namely of pure statistical, deterministic music, while simultaneously, the fractal analysis profile was completely different from the profiles of DIAPHONIES, hence reinforcing, the fractal findings of DIAPHONIES in relation to trivial music harmony. [ABSTRACT FROM AUTHOR]

Air pollution poses significant public health risks, necessitating accurate and efficient monitoring of particulate matter (PM). These organic compounds may be released from natural sources like trees and vegetation, as well as from anthropogenic, or human-made sources including industrial activities and motor vehicle emissions. Therefore, measuring PM concentrations is paramount to understanding people's exposure levels to pollutants. This paper introduces a novel image processing technique utilizing photographs/pictures of Do-it-Yourself (DiY) sensors for the detection and quantification of P M 10 particles, enhancing community involvement and data collection accuracy in Citizen Science (CS) projects. A synthetic data generation algorithm was developed to overcome the challenge of data scarcity commonly associated with citizen-based data collection to validate the image processing technique. This algorithm generates images by precisely defining parameters such as image resolution, image dimension, and PM airborne particle density. To ensure these synthetic images mimic real-world conditions, variations like Gaussian noise, focus blur, and white balance adjustments and combinations were introduced, simulating the environmental and technical factors affecting image quality in typical smartphone digital cameras. The detection algorithm for P M 10 particles demonstrates robust performance across varying levels of noise, maintaining effectiveness in realistic mobile imaging conditions. Therefore, the methodology retains sufficient accuracy, suggesting its practical applicability for environmental monitoring in diverse real-world conditions using mobile devices. [ABSTRACT FROM AUTHOR]

Laser point clouds are commonly affected by Gaussian and Laplace noise, resulting in decreased accuracy in subsequent surface reconstruction and visualization processes. However, existing point cloud denoising algorithms often overlook the local consistency and density of the point cloud normal vector. A feature map learning algorithm which integrates point normal constraints, Dirichlet energy, and coupled orthogonality bias terms is proposed. Specifically, the Dirichlet energy is employed to penalize the difference between neighboring normal vectors and combined with a coupled orthogonality bias term to enhance the orthogonality between the normal vectors and the subsurface, thereby enhancing the accuracy and robustness of the learned denoising of the feature maps. Additionally, to mitigate the effect of mixing noise, a point cloud density function is introduced to rapidly capture local feature correlations. In experimental findings on the anchor public dataset, the proposed method reduces the average mean square error (MSE) by 0.005 and 0.054 compared to the MRPCA and NLD algorithms, respectively. Moreover, it improves the average signal-to-noise ratio (SNR) by 0.13 DB and 2.14 DB compared to MRPCA and AWLOP, respectively. The proposed algorithm enhances computational efficiency by 27% compared to the RSLDM method. It not only removes mixed noise but also preserves the local geometric features of the point cloud, further improving computational efficiency. [ABSTRACT FROM AUTHOR]

In this paper, we demonstrate the Wong–Zakai approximation results for two dimensional stochastic Cahn–Hilliard–Navier–Stokes model. The model consists of a Navier–Stokes system coupled with convective Cahn–Hilliard equations. It describes the motion of an incompressible isothermal mixture of two (partially) immiscible fluids under the influence of multiplicative noise. Our main result describes the support of the distribution of solutions. As in [2], both inclusions are proved by means of a general Wong–Zakai type result of convergence in probability for nonlinear stochastic PDEs driven by a Hilbert‐valued Brownian motion and some adapted finite‐dimensional approximation of this process. Note that the coupling between the Navier–Stokes system and the Cahn–Hilliard equations makes the analysis more involved. [ABSTRACT FROM AUTHOR]

In the present enquiry, an in‐depth analysis of internal energy, entropy, heat capacity, and Helmholtz free energy of GaAsquantum dot (QD) which contains Gaussian impurity as dopant and falls under the influence of applied Gaussian white noise (GWHN) is performed. GWHN takes additive and multiplicative routes for its entrance to the doped QD. In this study, highly delicate and complex interplay between temperature, presence/absence of GWHN, mode of incorporation of GWHN, and the particular physical parameters concerned is unveiled. The said interplay, in effect, designs the features of the thermal properties. The enquiry uncovers competitive behavior between thermal disorder and spatial disorder that also affects the said thermodynamic properties. [ABSTRACT FROM AUTHOR]

This paper studies the stochastic time-fractional heat diffusion equation involving a Caputo derivative in time of order α ∈ (1 2 , 1 ] , driven simultaneously by a random diffusion coefficient field and fractionally integrated multiplicative noise. First, the well-posedness of the underlying problem is established by proving the existence, uniqueness, and stability of the mild solution. Then a spatio-temporal discretization method based on a Milstein exponential integrator scheme and finite element method is constructed and analyzed. The strong convergence rate of the fully discrete solution is derived. Numerical experiments are finally reported to confirm the theoretical result. [ABSTRACT FROM AUTHOR]

We study the scaling properties of the non-equilibrium stationary states (NESS) of a reaction-diffusion model. Under a suitable smallness condition, we show that the density of particles satisfies a law of large numbers with respect to the NESS, with an explicit rate of convergence, and we also show that at mesoscopic scales the NESS is well approximated by a local equilibrium (product) measure, in the total variation distance. In addition, in dimensions d ≤ 3 we show a central limit theorem for the density of particles under the NESS. The corresponding Gaussian limit can be represented as an independent sum of a white noise and a massive Gaussian free field, and in particular it presents macroscopic correlations. [ABSTRACT FROM AUTHOR]

A complete kinematic error model that contains all potential error sources, is one of the fundamentals to ensure the best result of kinematic calibration. In the case of parallel manipulators, the complete error model includes items of passive joint motions. These motions usually cannot be accurately observed during the identification process but can be derived through kinematic analysis. However, due to kinematic errors, the obtained passive joint motions deviate from their actual values, causing motion errors of passive joints. In other words, the passive joints introduce input errors to the error model, which are of the same order of magnitude as kinematic errors and much larger than other measurement and random noises. This issue can significantly affect the stability and accuracy of parameter identification, but it has not been clearly recognized in the literature. To address this problem, this paper systematically analyzes the influence of passive joints' motion errors on the kinematic calibration of parallel manipulators. It is found that when the complete error model including the passive joints' motion errors is used for kinematic calibration of parallel manipulators, the variance of kinematic error parameters solved by the least squares (LS) method greatly increases, leading to iterative divergence even when the identification matrix is column full rank. To improve the stability and accuracy of parameter identification, this study employs the total least squares (TLS) method, which is a dedicated approach for handling input errors, in the identification process. Numerical simulations and experiments of kinematic calibration are conducted on several parallel manipulators. The results validate the correctness and effectiveness of the analysis of the influence of passive joints' motion errors on the kinematic calibration of parallel manipulators. Furthermore, the results indicate that the TLS method can efficiently and accurately accomplish the identification of kinematic parameters. • Input errors which drawn little attention in kinematic calibration, are analyzed. • Influence of passive joints' motion errors on kinematic calibration is revealed. • TLS method is employed, ensuring the stability of parameter identification. • Results of numerical simulations and experiments verify the analysis in this paper. [ABSTRACT FROM AUTHOR]

Digital communication systems usually suffer from two factors: inter-symbol interference and impulsive noise. To improve the performance of communication receivers, this paper proposes a good solution to a linear blind equalizer. Firstly, a new lower-order statistic with a lower influence of impulsive noise is constructed based on a nonlinear function. Secondly, an unconstrained optimization problem is formulated by minimizing the mean square error related to the new lower-order statistic, and a new equalization algorithm is derived to effectively compensate for the inter-symbol interference. Thirdly, to further enhance the robustness of the proposed algorithm, the iterative formula of the proposed algorithm is handled by normalizing samples. Finally, numerical simulation results demonstrate that the proposed algorithm achieves better performance under Gaussian and impulsive noise. [ABSTRACT FROM AUTHOR]

While the practical application of adaptive filters has indeed garnered substantial attention, two pressing issues persist that have a profound impact on their performance—system sparsity and the presence of contaminated Gaussian impulsive noise. In this research paper, we propose a novel approach to tackle both of these issues simultaneously by introducing the concept of a proportionate matrix. Specifically, we present a proportionate maximum total complex correntropy algorithm based on the errors-in-variables model. The paper presents a theoretical analysis of the steady-state weight error power under the influence of impulsive noise. Furthermore, it discusses the performance comparison in system identification and highlights the robustness of the proposed algorithm. To validate its effectiveness, a simulation involving stereophonic acoustic echo cancellation is conducted, and the results confirm the clear advantages of the proposed Proportionate Maximum Total Complex Correntropy algorithm. [ABSTRACT FROM AUTHOR]

The Support Vector Machine (SVM) is a cornerstone of machine learning algorithms. This paper proposes a novel cost-sensitive model to address the challenges of class-imbalanced datasets inherent to SVMs. Integrating soft-margin SVM with the asymmetric LINEX loss function, this approach effectively tackles issues in scenarios with noisy data or overlapping classes. The LINEX loss function, which resembles the hinge and square loss functions, facilitates efficient model training with reduced sample penalties. Despite the resulting model's nonsmooth nature due to a constraint inequality, optimization is achieved using a Primal–Dual method, capitalizing on the convexity of the optimization function. This method enhances the model's noise robustness while preserving its original form. Extensive experiments validate the model's effectiveness, showcasing its superiority over traditional methods. Statistical tests further corroborate these findings. • The study effectively applies Soft Margin SVM combined with LINEX. • Addresses challenges posed by Gaussian noise and imbalanced data in datasets. • Employs the Primal–Dual algorithm to solve the model without constraints. • Maintains the integrity of the original dataset form throughout the process. [ABSTRACT FROM AUTHOR]

Data security and user privacy concerns are receiving increasing attention. Federated learning models based on differential privacy offer a distributed machine learning framework that protects data privacy. However, the noise introduced by the differential privacy mechanism may affect the model's usability, especially when reasonable gradient clipping is absent. Fluctuations in the gradients can lead to issues like gradient explosion, compromising training stability and potentially leaking privacy. Therefore, gradient clipping has become a crucial method for protecting both model performance and data privacy. To balance privacy protection and model performance, we propose the Adaptive Weight-Based Differential Privacy Federated Learning (AWDP-FL) framework, which processes model gradient parameters at the neural network layer level. First, by designing and recording the change trends of two-layer historical gradient sequences, we analyze and predict gradient variations in the current iteration and calculate the corresponding weight values. Then, based on these weights, we perform adaptive gradient clipping for each data point in each training batch, which is followed by gradient momentum updates based on the third moment. Before uploading the parameters, Gaussian noise is added to protect privacy while maintaining model accuracy. Theoretical analysis and experimental results validate the effectiveness of this framework under strong privacy constraints. [ABSTRACT FROM AUTHOR]

The Shuttle Radar Topography Mission (SRTM) is a digital representation of the terrain surface morphology that contains rich terrain information and is widely used in environmental analyses. However, SRTM is adversely affected by mixed noise, which typically include random and stripe noise. Mixed noise results in the significant loss of topographic information, which reduce the validity of related research. To eliminate mixed noise in SRTM data, we propose an adaptive low‐rank group sparse model based on edge preservation (ALGS_EP) to remove mixed noise from datasets. The method relies on a low‐rank group sparse model that considers the gradient features of the terrain. It calculates a terrain factor to adapt the noise elimination model to terrain changes. Additionally, it integrates with the edge structure of elevation data and applies a double‐gradient constraint to preserve the structural details of the elevation data. The proposed model, built upon the alternating direction multiplier method framework, enhances the traditional weighted kernel paradigm minimization algorithm by introducing variable weights that adjust according to the gradient of elevation data during iterations. Additionally, it incorporates the correlation between strip noise and residual data blocks when computing the iteration count, ensuring an iterative solution approach that converges to the optimal solution. We used ALGS_EP to process global SRTM 1 data and published a higher‐quality and higher‐precision elevation dataset. The elevation data noise before and after noise elimination were statistically analyzed. Simulated and empirical results show that the model is highly robust and more effective than existing methods in both visual and quantitative evaluations. The noise elimination rate was 97.6%, compared to the original data. Therefore, this research was valuable for applications that use digital elevation model as an important data layer. [ABSTRACT FROM AUTHOR]

Photoacoustic microscopy (PAM) enables label‐free imaging of the 3D vasculature and functional information with 2D lateral scan. The unique capacity in probing metabolism makes it ideal for animal research and clinical application. However, the high‐excitation power impedes the high‐speed monitoring of hemodynamics due to thermal accumulation and photon damage. To address this challenge, a self‐supervised photoacoustic single volume denoising (PSVD) approach, which combines 3D random sampling and noise augmentation to achieve 6 dB signal‐to‐noise‐ratio and contrast‐to‐noise‐ratio increases for the customized optical‐resolution photoacoustic microscope, is developed. Using PSVD, high‐quality PAM images of the mouse ear are acquired with only 10% fluence of normal excitation. Functional imaging is validated with this PSVD‐empowered low‐fluence PAM. Accurate oxygen saturation maps and high‐contrast flow kymographs are obtained. Moreover, the capability of this approach in the live mouse ear under hypercapnia is demonstrated. Further transformation into clinical imaging with low fluence will broaden the application of PAM. [ABSTRACT FROM AUTHOR]

Acoustic-resolution photoacoustic microscopy (AR-PAM) suffers from degraded lateral resolution due to acoustic diffraction. Here, a resolution enhancement strategy for AR-PAM via a mean-reverting diffusion model was proposed to achieve the transition from acoustic resolution to optical resolution. By modeling the degradation process from high-resolution image to low-resolution AR-PAM image with stable Gaussian noise (i.e., mean state), a mean-reverting diffusion model is trained to learn prior information of the data distribution. Then the learned prior is employed to generate a high-resolution image from the AR-PAM image by iteratively sampling the noisy state. The performance of the proposed method was validated utilizing the simulated and in vivo experimental data under varying lateral resolutions and noise levels. The results show that an over 3.6-fold enhancement in lateral resolution was achieved. The image quality can be effectively improved, with a notable enhancement of ∼66% in PSNR and ∼480% in SSIM for in vivo data. [ABSTRACT FROM AUTHOR]

We develop a general framework for state estimation in systems modeled with noise-polluted continuous time dynamics and discrete time noisy measurements. Our approach is based on maximum likelihood estimation and employs the calculus of variations to derive optimality conditions for continuous time functions. We make no prior assumptions on the form of the mapping from measurements to state-estimate or on the distributions of the noise terms, making the framework more general than Kalman filtering/smoothing where this mapping is assumed to be linear and the noises Gaussian. The optimal solution that arises is interpreted as a continuous time spline, the structure and temporal dependency of which is determined by the system dynamics and the distributions of the process and measurement noise. Similar to Kalman smoothing, the optimal spline yields increased data accuracy at instants when measurements are taken, in addition to providing continuous time estimates outside the measurement instances. We demonstrate the utility and generality of our approach via illustrative examples that render both linear and nonlinear data filters depending on the particular system. Application of the proposed approach to a Monte Carlo simulation exhibits significant performance improvement in comparison to a common existing method. [ABSTRACT FROM AUTHOR]

The inverse photoacoustic problem is an ill-posed mathematical physics problem. There are many methods of solving the inverse photoacoustic problem, from parameter reduction to the development of complex regularization algorithms. The idea of this work is that semiconductor physical properties are determined from phase characteristic measurements because phase measurements are more sensitive than amplitude measurements. To solve the inverse photoacoustic problem, the thermoelastic properties and thickness of the sample are estimated using a neural network approach. The neural network was trained on a large database of photoacoustic phases calculated from a theoretical Si n-type model in the range of 20 Hz to 20 kHz, to which random Gaussian noise was applied. It is shown that in solving the inverse photoacoustic problem, high accuracy and precision can be achieved by applying phase measurement and neural network approaches. This study showed that a multi-parameter inverse problem can be solved using phase networks. [ABSTRACT FROM AUTHOR]

The safety of chemical processes is of critical importance. However, traditional fault monitoring methods have insufficiently studied the monitoring accuracy of multi-channel data and have not adequately considered the impact of noise on industrial processes. To address this issue, this paper proposes a neural network-based model, DSCBAM-DenseNet, which integrates depthwise separable convolution and attention modules to fuse multi-channel data features and enhance the model's noise resistance. We simulated a real environment by adding Gaussian noise with different signal-to-noise ratios to the Tennessee Eastman process dataset and trained the model using multi-channel data. The experimental results show that this model outperforms traditional models in both fault diagnosis accuracy and noise resistance. Further research on a compressor unit engineering instance validated the superiority of the model. [ABSTRACT FROM AUTHOR]

While the statistical inference of first-order autoregressive processes driven by independent and identically distributed noises has a long history, the statistical analysis for first-order autoregressive processes driven by dependent noises is more recent. This paper considers the problem of estimating all the unknown parameters in first-order autoregressive processes driven by the fractional Gaussian noise, which is a self-similar stochastic process used to model persistent or anti-persistent dependency structures in observed time series. The estimation procedure is built upon the marriage of the log-periodogram regression and the method of moments. The usual asymptotic properties, including consistency and asymptotic normality, are established under some mild conditions. Monte Carlo simulations are performed to demonstrate the feasibility and effectiveness of the proposed method. Finally, the estimation methods are applied to model some realized volatility time series, where we find that the realized volatility is rough. Moreover, the proposed model is compared with some alternative models, including the first-order autoregressive process driven by the standard Gaussian noise, the heterogeneous autoregression model with lag structure (1,5,21) (HAR(1,5,21)), the autoregressive fractionally integrated moving average model (ARFIMA(1,d,0)) and the scaled fractional Brownian motion, in forecasting the logarithmic realized volatility. [ABSTRACT FROM AUTHOR]

In this paper, we study the Cauchy problem for the stochastically perturbed high-dimensional modified Euler-Poincaré system (MEP2) on the torus T d , d ≥ 1. We first establish a local well-posedness framework in the sense of Hadamard for the MEP2 driven by general nonlinear multiplicative noises. Then two kinds of global existence and uniqueness results are demonstrated: One indicates that the MEP2 perturbed by nonlocal-type random noises with proper intensity admits a unique large global strong solution; The other one infers that, if the initial data is sufficiently small, then the MEP2 perturbed by linear multiplicative noise has a unique global solution with high probability. In the case of one dimension, we find that the stochastic MEP2 will break down in finite time when the initial data meets appropriate shape condition. [ABSTRACT FROM AUTHOR]

In this paper, a robust algorithm for enhancing indoor positioning accuracy utilizing time difference of arrivals is proposed. Addressing limitations of maximum likelihood estimation and traditional weighted least squares methods, which often suffer from matrix ill-conditioned problem and numerical instability, leading to significant biases and reduced accuracy, we propose a novel bias reduction technique based on QR factorization. Incorporating geometric relationship information, our method improves precision. Through rigorous analysis and simulation under zero-mean white Gaussian noise, the algorithm demonstrates superior performance, overcoming matrix ill-conditioned problem, surpassing traditional methods, and closely aligning with the Cramér-Rao lower bound. [ABSTRACT FROM AUTHOR]

An inerter system, based on electromechanical similarity theory and vibration mitigation and isolation technology, represents a category of vibration damping systems. These systems typically improve damping performance by increasing mass or inertia, a method often found to be inefficient, leading to inadequate damping and limited applicability in real-world engineering scenarios. The lightweight inerter system (LwIS) introduced herein offers a more flexible and efficient means of altering structural inertia. Initially, this paper establishes the motion control equations for LwIS, followed by a stochastic analysis to derive the analytical expression for the root mean square displacement under Gaussian white noise excitation. A parametric analysis of LwIS is subsequently conducted, developing a displacement-based parametric strategy. Design examples for single-degree-of-freedom (SDOF) engineering structures under various requirements are provided, demonstrating the validity of LwIS’s optimal parameters through responses to simple harmonic excitation and seismic impacts. The findings indicate that the optimization approach of LwIS, unlike traditional methods, simultaneously addresses the displacement performance of the primary structure and the deformation efficiency of the damping element, thereby facilitating comprehensive optimization. Four optimal design parameters for LwIS are identified, underscoring its applicability to stochastic excitation and a broader range of load cases, thus enhancing its practicality in engineering contexts. LwIS’s design philosophy aims to improve deformation efficiency through an increased deformation enhancement coefficient in the damping element, enhancing damping performance, controlling seismic responses, and achieving superior energy dissipation. The optimal parameters, smaller in value, maximize the potential of the inerter system, aligning with the dual objectives of performance optimization and lightweight design, consequently reducing engineering costs. [ABSTRACT FROM AUTHOR]

Medical image security is paramount in the digital era but remains a significant challenge. This paper introduces an innovative zero-watermarking methodology tailored for medical imaging, ensuring robust protection without compromising image quality. We utilize Sped-up Robust features for high-precision feature extraction and singular value decomposition (SVD) to embed watermarks into the frequency domain, preserving the original image's integrity. Our methodology uniquely encodes watermarks in a non-intrusive manner, leveraging the robustness of the extracted features and the resilience of the SVD approach. The embedded watermark is imperceptible, maintaining the diagnostic value of medical images. Extensive experiments under various attacks, including Gaussian noise, JPEG compression, and geometric distortions, demonstrate the methodology's superior performance. The results reveal exceptional robustness, with high Normalized Correlation (NC) and Peak Signal-to-noise ratio (PSNR) values, outperforming existing techniques. Specifically, under Gaussian noise and rotation attacks, the watermark retrieved from the encrypted domain maintained an NC value close to 1.00, signifying near-perfect resilience. Even under severe attacks such as 30% cropping, the methodology exhibited a significantly higher NC compared to current state-of-the-art methods. [ABSTRACT FROM AUTHOR]

In this paper, the authors present a new transfer-learning-based robust technique for detection and classification of multi-type faults in low-voltage power distribution grids. Three-phase current and voltage signals were initially measured and sampled at a medium-voltage/low-voltage substation upon occurrence of a certain type of fault. Subsequently, a Hilbert–Huang transform was applied to the corresponding sampled fault signals to construct a time–frequency energy matrix as a 35 × 35 pixel matrix of the digital image after passing through a band-pass filter. Additionally, and for the sake of comprehensiveness, a residual network (ResNet) was designed as a fault detector and classifier to accurately identify the location and type of faults, while guaranteeing the robustness of the proposed technique against both white and connection noises. For the sake of evaluation, a three-phase 10 kV test system was implemented in the MATLAB/Simulink environment under different faulty operating conditions designs. The performance of the introduced technique was also examined in the Python environment. Based on simulation results, several conclusions can be drawn: (i) The ResNet outshines the neural architecture search network, Inception, and Xception by elevating the average accuracy by 2.23%; (ii) the ResNet-101 model is robust against white Gaussian noise and electromagnetic interference with values of 20, 30, and 40 dB; (iii) the proposed technique enhances functional coverage up to a radius of 30 km for fault detection along 14 points in the test system; and (iv) in the presence of distributed energy resources, the proposed technique is superior to other network architectures with an average of 5.44%. [ABSTRACT FROM AUTHOR]

In the field of image processing, common noise types include Gaussian noise, salt and pepper noise, speckle noise, uniform noise and pulse noise. Different types of noise require different denoising algorithms and techniques to maintain image quality and fidelity. Traditional image denoising methods not only remove image noise, but also result in the detail loss in the image. It cannot guarantee the clean removal of noise information while preserving the true signal of the image. To address the aforementioned issues, an image denoising method combining an improved threshold function and wavelet transform is proposed in the experiment. Unlike traditional threshold functions, the improved threshold function is a continuous function that can avoid the pseudo Gibbs effect after image denoising and improve image quality. During the process, the output image of the finite ridge wave transform is first combined with the wavelet transform to improve the denoising performance. Then, an improved threshold function is introduced to enhance the quality of the reconstructed image. In addition, to evaluate the performance of different algorithms, different densities of Gaussian noise are added to Lena images of black, white, and color in the experiment. The results showed that when adding 0.010.01 variance Gaussian noise to black and white images, the peak signal-to-noise ratio of the research method increased by 2.58dB in a positive direction. The mean square error decreased by 0.10dB. When using the algorithm for denoising, the research method had a minimum denoising time of only 13ms, which saved 9ms and 3ms compared to the hard threshold algorithm (Hard TA) and soft threshold algorithm (Soft TA), respectively. The research method exhibited higher stability, with an average similarity error fluctuating within 0.89%. The above results indicate that the research method has smaller errors and better system stability in image denoising. It can be applied in the field of digital image denoising, which can effectively promote the positive development of image denoising technology to a certain extent. [ABSTRACT FROM AUTHOR]

Exact solution for the probability density function is considered for two coupled population growth models driven by Gaussian white noises. Moreover, n -moments of interactions of the Gompertz and Verhulst logistic models are obtained and analyzed. It is shown that interactions can modify the behaviors of the population growth models, i.e, the species may collaborate and/or compete between them. [ABSTRACT FROM AUTHOR]

In this paper, we investigate an overdamped bistable system subject to Gaussian white noise and logical inputs. By solving and estimating the steady distribution of the corresponding Fokker–Planck equation and considering the two essential features of the reliable logic operations (RLOs)—initial value independence and sign invariance—we establish the sufficient condition for RLO occurrence and identify parametric resonance phenomena in the system. Our numerical simulations confirm the reliability and accuracy of the theoretical results. This work offers insights into enhancing the accuracy of stochastic systems, particularly in the realm of logical stochastic resonance, thereby contributing to advancements in understanding and controlling stochastic dynamical systems. [ABSTRACT FROM AUTHOR]

The automotive speech recognition field has become an active research topic as it enables drivers to activate various in-car functionalities without being distracted. However, research in Arabic remains nascent compared to English, French, and German. Therefore, this paper presents a Moroccan Arabic automotive speech recognition system. Our system aims to enhance the driving experience to make it comfortable and safe while assisting individuals with disabilities. We created a speech dataset comprising 20 commonly used car commands. It consists of 5600 instances collected from Moroccan contributors and recorded in clean and noisy environments to increase its representativity. We used MFCC, weighted MFCC, and Spectral Subband Centroids (SSC) for feature extraction, as they demonstrated promising results in noisy settings. For classifier construction, we proposed a hybrid architecture, consisting of Bidirectional Long Short-Term Memory (Bi-LSTM) and the Convolutional Neural Network (CNN). Training our proposed model with WMFCC and SSC features achieved an accuracy of 98.48%, outperforming all baseline models we trained and outperforming the existing solutions in the state-of-the-art literature. Moreover, it shows promising results in a clean and noisy environment and maintains resilience to additive Gaussian noise while using few computational resources. [ABSTRACT FROM AUTHOR]

Accurate estimation of the mean fragment size is crucial for optimizing open-pit mining operations. This study presents an approach that combines clustering, hyperparameter optimization, and data augmentation to enhance prediction accuracy using the Xtreme Gradient Boosting (XGBoost) regression model. A dataset of 110 blasts was divided into 97 blasts for training and testing, whereas a separate set of 13 new, unseen blasts was used to evaluate the robustness and generalization of the model. Hierarchical Agglomerative (HA) and K-means clustering algorithms were used, with HA clustering providing a higher cluster quality. To address class imbalance and improve model generalization, a synthetic minority oversampling technique for regression with Gaussian noise (SMOGN) was employed. Hyperparameter tuning was conducted using HyperOpt by comparing Random Search (RS) with the Advanced Tree-structured Parzen Estimator (ATPE). The combination of ATPE with HA clustering and SMOGN in an expanded search space produced the best results, achieving superior prediction accuracy and reliability. The proposed HAC1-SMOGN model, which integrates HA clustering, ATPE tuning, and SMOGN augmentation, achieved a mean squared error (MSE) of 0.0002 and an R2 of 0.98 on the test set. This study highlights the synergistic benefits of clustering, hyperparameter optimization, and data augmentation in enhancing machine learning models for regression tasks, particularly in scenarios with class imbalance or limited data. [ABSTRACT FROM AUTHOR]

We study the dynamics of shear startup of Johnson–Segalman and non-stretching Rolie-Poly models using nonlinear simulations. We consider startup to shear rates in both monotonic and nonmonotonic regions of the constitutive curve. For the Johnson–Segalman model, which exhibits a shear stress overshoot during startup, our nonlinear simulations show that transient shear banding is absent regardless of whether the startup shear rate is in the monotonic or nonmonotonic regions of the constitutive curve. In the latter case, while there is clearly an inhomogeneity en route to the banded state, the magnitude of the extent of banding is not substantially large compared to that of the eventual banded state. Marked inhomogeneity in the velocity profile is predicted for the nonstretching Rolie-Poly model only if the solvent to solution viscosity ratio is smaller than O (10 − 3) , but its occurrence does not appear to have any correlation with the stress overshoot during startup. The comparison of the present nonlinear results with the results obtained within the framework of linearized dynamics show that nonlinearities have a stabilizing effect and mitigate the divergence of perturbations (as predicted within the linearized dynamics) during shear startup. We argue that the neglect of inertia in the nonlinear simulations is not self-consistent if the solvent to solution viscosity ratio is very small, and that inertial effects need to be included in order to obtain physically realistic results. Furthermore, our study demonstrates a pronounced sensitivity of shear startup in the nonstretching Rolie-Poly model when a random white noise with zero mean is used as the initial perturbation. Finally, this study clearly emphasizes that stress overshoot during shear startup does not always result in transient shear banding, notwithstanding whether the shear rates is in the monotonic or nonmonotonic part of the constitutive curve. [ABSTRACT FROM AUTHOR]

Autoproducts are quadratic or higher products of frequency-domain acoustic fields that can mimic genuine fields at frequencies within or outside the original field's bandwidth. Past studies have found a variety of interesting autoproduct properties but have been limited to quadratic autoproducts. This paper presents cubic autoproduct theory and documents how noise suppression may be attained with the cubic frequency-difference autoproduct, a product of three frequency-domain acoustic fields. The cubic autoproduct's field equations, developed from the inhomogeneous Helmholtz equation, and analytical results in single- and two-path environments justify interpretating the cubic autoproduct as a pseudofield and underscore its similarities to the quadratic autoproducts. For nonzero field bandwidth, many frequency triplets satisfy the relationship for a single cubic autoproduct frequency. Thus, bandwidth averaging can lead to serendipitous noise suppression and is shown herein to facilitate field-phase-structure recovery from ideal free space fields corrupted by Gaussian noise. Cubic-autoproduct-based direction of arrival (DOA) estimation using signal and noise recordings collected in the ocean are found to be more accurate than conventional DOA estimates from the same data. In particular, cubic autoproduct results showed a 3–5 dB noise suppression advantage for 4- and 6-kHz direct- and reflected-path sounds broadcast 200 m to a four-element receiving array. [ABSTRACT FROM AUTHOR]

The fault diagnosis of rolling bearings is faced with the problem of a lack of fault data. Currently, fault diagnosis based on traditional convolutional neural networks decreases the diagnosis rate. In this paper, the developed adaptive residual shrinkage network model is combined with transfer learning to solve the above problems. The model is trained on the Case Western Reserve dataset, and then the trained model is migrated to a small-sample dataset with a scaled-down sample size and the Jiangnan University bearing dataset to conduct the experiments. The experimental results show that the proposed method can efficiently learn from small-sample datasets, improving the accuracy of the fault diagnosis of bearings under variable loads and variable speeds. The adaptive parameter-rectified linear unit is utilized to adapt the nonlinear transformation. When rolling bearings are in operation, noise production is inevitable. In this paper, soft thresholding and an attention mechanism are added to the model, which can effectively process vibration signals with strong noise. In this paper, the real noise is simulated by adding Gaussian white noise in migration task experiments on small-sample datasets. The experimental results show that the algorithm has noise resistance. [ABSTRACT FROM AUTHOR]

Accurately classifying the intra-pulse modulations of radar emitter signals is important for radar systems and can provide necessary information for relevant military command strategy and decision making. As strong additional white Gaussian noise (AWGN) leads to a lower signal-to-noise ratio (SNR) of received signals, which results in a poor classification accuracy on the classification models based on deep neural networks (DNNs), in this paper, we propose an effective denoising method based on a denoising diffusion probabilistic model (DDPM) for increasing the quality of signals. Trained with denoised signals, classification models can classify samples denoised by our method with better accuracy. The experiments based on three DNN classification models using different modal input, with undenoised data, data denoised by the convolutional denoising auto-encoder (CDAE), and our method's denoised data, are conducted with three different conditions. The extensive experimental results indicate that our proposed method could denoise samples with lower values of the SNR, and that it is more effective for increasing the accuracy of DNN classification models for radar emitter signal intra-pulse modulations, where the average accuracy is increased from around 3 to 22 percentage points based on three different conditions. [ABSTRACT FROM AUTHOR]

The detection of change in remote-sensing images is broadly applicable to many fields. In recent years, both supervised and unsupervised methods have demonstrated excellent capacity to detect changes in high-resolution images. However, most of these methods are sensitive to noise, and their performance significantly deteriorates when dealing with remote-sensing images that have been contaminated by mixed random noises. Moreover, supervised methods require that samples are manually labeled for training, which is time-consuming and labor-intensive. This study proposes a new unsupervised change-detection (CD) framework that is resilient to mixed random noise called self-supervised denoising network-based unsupervised change-detection coupling FCM_SICM and EMD (SSDNet-FSE). It consists of two components, namely a denoising module and a CD module. The proposed method first utilizes a self-supervised denoising network with real 3D weight attention mechanisms to reconstruct noisy images. Then, a noise-resistant fuzzy C-means clustering algorithm (FCM_SICM) is used to decompose the mixed pixels of reconstructed images into multiple signal classes by exploiting local spatial information, spectral information, and membership linkage. Next, the noise-resistant Earth mover's distance (EMD) is used to calculate the distance between signal-class centers and the corresponding fuzzy memberships of bitemporal pixels and generate a map of the magnitude of change. Finally, automatic thresholding is undertaken to binarize the change-magnitude map into the final CD map. The results of experiments conducted on five public datasets prove the superior noise-resistant performance of the proposed method over six state-of-the-art CD competitors and confirm its effectiveness and potential for practical application. [ABSTRACT FROM AUTHOR]

Industrial image anomaly detection achieves automated detection and localization of defects or abnormal regions in images through image processing and deep learning techniques. Currently, utilizing the approach of reverse knowledge distillation has yielded favourable outcomes. However, it is still a challenge in terms of the feature extraction capability of the image and the robustness of the decoding of the student network. This study first addresses the issue that the teacher network has not been able to extract global information more effectively. To acquire more global information, a vision transformer network is introduced to enhance the model's global information extraction capability, obtaining better features to further assist the student network in decoding. Second, for anomalous samples, to address the low similarity between features extracted by the teacher network and features restored by the student network, Gaussian noise is introduced. This further increases the probability that the features decoded by the student model match normal sample features, enhancing the robustness of the student model. Extensive experiments were conducted on industrial image datasets AeBAD, MvtecAD, and BTAD. In the AeBAD dataset, under the PRO performance metric, the result is 89.83%, achieving state‐of‐the‐art performance. Under the AUROC performance metric, it reaches 83.35%. Similarly, good results were achieved on the MvtecAD and BTAD datasets. The proposed method's effectiveness and performance advantages were validated across multiple industrial datasets, providing a valuable reference for the application of industrial image anomaly detection methods. [ABSTRACT FROM AUTHOR]

The fractional differential equation L^\beta u = f posed on a compact metric graph is considered, where \beta >0 and L = \kappa ^2 - \nabla (a\nabla) is a second-order elliptic operator equipped with certain vertex conditions and sufficiently smooth and positive coefficients \kappa,a. We demonstrate the existence of a unique solution for a general class of vertex conditions and derive the regularity of the solution in the specific case of Kirchhoff vertex conditions. These results are extended to the stochastic setting when f is replaced by Gaussian white noise. For the deterministic and stochastic settings under generalized Kirchhoff vertex conditions, we propose a numerical solution based on a finite element approximation combined with a rational approximation of the fractional power L^{-\beta }. For the resulting approximation, the strong error is analyzed in the deterministic case, and the strong mean squared error as well as the L_2(\Gamma \times \Gamma)-error of the covariance function of the solution are analyzed in the stochastic setting. Explicit rates of convergences are derived for all cases. Numerical experiments for {L = \kappa ^2 - \Delta, \kappa >0} are performed to illustrate the results. [ABSTRACT FROM AUTHOR]

Interacting particle or agent systems that exhibit diverse swarming behaviors are prevalent in science and engineering. Developing effective differential equation models to understand the connection between individual interaction rules and swarming is a fundamental and challenging goal. In this paper, we study the data-driven discovery of a second-order particle swarming model that describes the evolution of N particles in \mathbb {R}^d under radial interactions. We propose a learning approach that models the latent radial interaction function as Gaussian processes, which can simultaneously fulfill two inference goals: one is the nonparametric inference of the interaction function with pointwise uncertainty quantification, and the other is the inference of unknown scalar parameters in the noncollective friction forces of the system. We formulate the learning problem as a statistical inverse learning problem and introduce an operator-theoretic framework that provides a detailed analysis of recoverability conditions, establishing that a coercivity condition is sufficient for recoverability. Given data collected from M i.i.d trajectories with independent Gaussian observational noise, we provide a finite-sample analysis, showing that our posterior mean estimator converges in a Reproducing Kernel Hilbert Space norm, at an optimal rate in M equal to the one in the classical 1-dimensional Kernel Ridge regression. As a byproduct, we show we can obtain a parametric learning rate in M for the posterior marginal variance using L^{\infty } norm and that the rate could also involve N and L (the number of observation time instances for each trajectory) depending on the condition number of the inverse problem. We provide numerical results on systems exhibiting different swarming behaviors, highlighting the effectiveness of our approach in the scarce, noisy trajectory data regime. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a fully discrete approximation of stochastic diffusion-wave equation driven by additive tempered fractional Gaussian noise. This additive noise exhibits semi-long range dependence. The model involves two nonlocal terms in time, i.e., a Caputo fractional derivative and a tempered fractional Brownian motion. The space discretization is achieved via the spectral Galerkin method. The Caputo fractional derivative of order α ∈ (1 , 2) is approximated by using the Grünwald–Letnikov formula. Combining Mittag-Leffler function, Laplace transform and z -transform, we establish the error estimates of the full discretization in the sense of mean-squared L 2 -norm. Numerical experiments are presented to confirm the strong convergence rates. [ABSTRACT FROM AUTHOR]

Stochastic bifurcation of dynamical system induced by Lévy noise is investigated in this paper from the global viewpoint, which is demonstrated based on the global attractor obtained with the compatible cell mapping (CCM) method. Compared with the traditional cell mapping method, the efficiency of CCM method is greatly improved by concentrating the computational domain on the covering set of the global attractor rather than the whole state space. The computation time can be further reduced by a simple parallel procedure with the block matrix strategy. With the proposed method, the evolutionary process of global properties has been presented. It shows that the shape and size of stochastic attractors and stochastic saddles vary along the direction of unstable manifold with the parameters of Lévy noise. Stochastic bifurcation occurs when stochastic attractor collides with stochastic saddle. It can be also found that the global bifurcation under Lévy noise is discontinuous because of the jump property. The results are significantly different from those of Gaussian noise, which reveals a distinct global evolutionary mechanism of stochastic bifurcation. Furthermore, it also indicates that the CCM method with block matrix is an effective tool for global analysis. [ABSTRACT FROM AUTHOR]

Noise is inevitable when acquiring seismic data, and effective random noise attenuation is crucial for seismic data processing and interpretation. Training and inferencing two‐stage deep learning‐based denoising methods typically require massive noisy–clean or noisy–noisy pairs to train the network. In this paper, we propose an unsupervised seismic data denoising framework called a re‐visible blind block network. It is a training‐as‐inferencing one‐stage method and utilizes only single noisy data for denoising, thereby eliminating the effort to prepare training data pairs. First, we introduce a global masker and a corresponding mask mapper to obtain the denoised result containing all blind block information, enabling simultaneous optimization of all blind blocks via the loss function. The global masker consists of two complementary block‐wise masks. It is utilized to mask noisy data to obtain two corrupted data, which are then input into the denoising network for noise attenuation. The mask mapper samples the value of blind blocks in the denoised data and projects it onto the same channel to gather the denoised results of all blind blocks together. Second, the original noisy data are incorporated into the network training process to prevent information loss, and a hybrid loss function is employed for updating the network parameters. Synthetic and field seismic data experiments demonstrate that our proposed method can protect seismic signals while suppressing random noise compared with traditional methods and several state‐of‐the‐art unsupervised deep learning denoising techniques. [ABSTRACT FROM AUTHOR]