Additive Noise Research Articles

Existence and continuity of random exponential attractors for stochastic 3D globally modified non-autonomous Navier-Stokes equation

In this paper, we deal with four problems. (i) Based on criteria for a continuous non-autonomous deterministic dynamical system (NDDS) and a continuous non-autonomous random dynamical system (NRDS), we construct an exponential attractor for a continuous NDDS and a family of random exponential attractors for a family of continuous non-autonomous random dynamical systems (NRDS), respectively. (ii) We prove that this family of random exponential attractors is continuous (or stable, robust, i.e., upper and lower semi-continuous) in the sense of the symmetric Hausdorff distance as the intensity of stochastic perturbations approaches zero. (iii) We prove that for two conjugate NRDS, if one has a random exponential attractor, then the other has a random exponential attractor, and that for two families of conjugate NRDS, if a family of random exponential attractors for one family is continuous, then a corresponding family of random exponential attractors for the other family is continuous. (iv) We apply our abstract result to study the existence and continuity of random exponential attractors for 3D globally modified non-autonomous Navier-Stokes equation with additive noise.

Strong approximation of the time-fractional Cahn–Hilliard equation driven by a fractionally integrated additive noise

Strong approximation of the time-fractional Cahn–Hilliard equation driven by a fractionally integrated additive noise

Ensemble responses of auditory midbrain neurons in the cat to speech stimuli at different signal-to-noise ratios

Originally reserved for those who are profoundly deaf, cochlear implantation is now common for people with partial hearing loss, particularly when combined with a hearing aid. This combined intervention enhances speech comprehension and sound quality when compared to electrical stimulation alone, particularly in noisy environments, but the physiological basis for the benefits is not well understood. Our long-term aim is to elucidate the underlying physiological mechanisms of this improvement, and as a first step in this process, we have investigated in normal hearing cats, the degree to which the patterns of neural activity evoked in the inferior colliculus (IC) by speech sounds in various levels of noise allows discrimination between those sounds. Neuronal responses were recorded simultaneously from 32 sites across the tonotopic axis of the IC in anaesthetised normal hearing cats (n=7). Speech sounds were presented at 20, 40 and 60dB SPL in quiet and with increasing levels of additive noise (signal-to-noise ratios (SNRs) –20, –15, –10, –5, 0, +5, +10, +15, +20dB). Neural discrimination was assessed using a Euclidean measure of distance between neural responses, resulting in a function reflecting speech sound differentiation across various SNRs. Responses of IC neurons reliably encoded the speech stimuli when presented in quiet, with optimal performance when an analysis bin-width of 5-10ms was used. Discrimination thresholds did not depend on stimulus level and were best for shorter analysis binwidths. This study sheds light on how the auditory midbrain represents speech sounds and provides baseline data with which responses to electro-acoustic speech sounds in partially deafened animals can be compared.

A hybrid CMOS-memristor based adaptable Bidirectional Associative Memory neural network for pattern recognition applications

Abstract This research presents a circuit-level hybrid CMOS memristor architecture for constructing Bidirectional Associative Memory (BAM). Initially, a synaptic circuit structure was built by employing a voltage threshold memristor in a crossbar architecture. This synaptic structure is adaptable and flexible for generating a wide range of synaptic weights. It is then deployed in the BAM network to perform an associative function. To aid in better name recall, this BAM network has been trained to associate Greek and mathematical symbols with their first letters in English, and vice versa. The designed circuit was validated using MATLAB and the EDA (Electronic Design Automation) Tool: Cadence Virtuoso. The addition of noise further evaluates the performance of the BAM network. When tested with noise levels of 10%, 20%, and 30%, the input patterns were retrieved at 100% in both directions. Furthermore, the proposed synaptic circuit is validated for variations in RON, ROFF and its performance is compared with other memristor models. It is also found that the average power consumption of the proposed synaptic circuit is 1.22mW. These results, which were experimentally confirmed, demonstrate the precision and noise isolation of the proposed BAM design. With appropriate tuning of memristor, the synaptic weights can be mapped easily with the memristor conductance value. This circuit can be effectively used in the field of image processing, neural network, and neuromorphic computation, which helps to associate and restore original or damaged binary images, showing strong robustness and accuracy.

Information limits and Thouless-Anderson-Palmer equations for spiked matrix models with structured noise

We consider a prototypical problem of Bayesian inference for a structured spiked model: a low-rank signal is corrupted by additive noise. While both information-theoretic and algorithmic limits are well understood when the noise is a Gaussian Wigner matrix, the more realistic case of structured noise still remains challenging. To capture the structure while maintaining mathematical tractability, a line of work has focused on rotationally invariant noise. However, existing studies either provide suboptimal algorithms or are limited to a special class of noise ensembles. In this paper, using tools from statistical physics (replica method) and random matrix theory (generalized spherical integrals) we establish the characterization of the information-theoretic limits for a noise matrix drawn from a general trace ensemble. Remarkably, our analysis unveils the asymptotic equivalence between the rotationally invariant model and a surrogate Gaussian one. Finally, we show how to saturate the predicted statistical limits using an efficient algorithm inspired by the theory of adaptive Thouless-Anderson-Palmer (TAP) equations. Published by the American Physical Society 2025

Fourier energy spectrum centroid: a robust and efficient approach for shear wave speed estimation in ω–k space

Objective.The propagation speed of a shear wave, whether externally or internally induced, in biological tissues is directly linked to the tissue's stiffness. The group shear wave speed (SWS) can be estimated using a class of time-of-flight (TOF) methods in the time-domain or phase speed-based methods in the frequency domain. However, these methods suffer from biased estimations or time-consuming computations, and they are especially prone to wave distortions inin vivocases. In this work, we present a parameter-free, robust, and efficient group SWS estimation method coined as Fourier energy spectrum centroid (FESC).Approach.The proposed FESC method is based on the center of mass inω-kspace. It was evaluated on data from computer simulations with additive Gaussian noise, a commercial elasticity phantom, anex vivopig liver, andin vivobiceps brachii muscles of three young healthy male subjects. The FESC method was compared with two 2D frequency-domain methods: Max-fre, which considers phase SWS at the peak ofk-space, and Fre-regre, which applies linear regression of phase SWS within a fixed bandwidth. Two additional benchmarks included time-domain methods based on cross-correlation (X-Corr) and radon sum transformation (RD).Main results.Statistical results showed that our FESC method and the RD method had comparable accuracy and robustness, outperforming the other benchmark methods. In the simulation and phantom studies, when the signal-to-noise ratio was higher than 25 dB, our FESC showed higher accuracy than RD. In thein vivostudy, our FESC method had better repeatability than RD. Furthermore, the proposed FESC method was 100 times faster than the runner-up method, X-Corr, and 3,000 times faster than the least efficient method, RD.Significance.All results indicated that our proposed Fourier-based method shows promise in reliably and efficiently providing reference values for group SWS in homogeneous bulk media.

Neural network solutions for artificial intelligence based on the new MIU-Net model for segmentation of the lung images in the diagnosis and treatment of lung diseases

The purpose of this research is to segment the chest on X-rays, a crucial step in medical image processing pivotal for diagnosing and treating lung diseases. By employing modifications to the U-Net model, this study endeavors to enhance chest segmentation on X-rays. The approach includes introducing alterations to the basic architecture of the U-Net model, integrating Inception blocks, and a using a squeeze-and-excitation mechanism to improve segmentation accuracy. The Shenzhen dataset, comprising chest radiographs, serves as the subject of investigation, highlighting the practical application of these modifications. The utilization of the MIU-Net model for automatic chest organ segmentation underscores its significance in the realm of lung disease diagnosis and treatment. Experimental methodologies encompass two types of data augmentation: Contrast Limited Adaptive Histogram Equalization (CLAHE) and the introduction of Gaussian noise, to test the model's robustness under various conditions. A comparative analysis is conducted against both the baseline U-Net and U-Net with Inception blocks. The results show that the improved U-Net model that includes Inception and Squeeze-and-Excitation (SE) is a lot better than the original U-Net. Specifically, the Dice coefficient for the improved model stands at 0.9040 for the original data, 0.9306 with CLAHE application, and 0.9232 with Gaussian noise addition. These findings underscore the importance of the research, emphasizing the significance of improving the accuracy of chest segmentation on X-rays for early disease detection and treatment optimization, which are the practical implications of this study. The research’s implications extend beyond academic interest, offering potential enhancements in clinical practices for lung disease management.

Information Geometry for Decoding

We revisit the idea of using elements of information geometry for decoding low-density parity-check (LDPC) codes, as introduced by Ikeda et al. In this work, we explicitly compute the m-projection to an e-flat submanifold, in the case of a binary symmetric channel and the Gaussian channel. We exemplify the algorithm by testing moderate size Gallager codes. To approach decoding problems, we show general theorems based on alternating projections in the framework of information geometry, inspired by von Neumann’s theorem for the convergence of alternating projections in Hilbert spaces. More precisely, consider the manifold S of the probability distributions on the n-dimensional hypercube (i.e., the set of binary sequences of length n). Let p be in S. In the case of two intersecting m-flat or e-flat submanifolds, the method of alternating projections on the two submanifolds converges to the projection of p on their intersection. This result is also generalized to a finite family of submanifolds of S.

Theoretical and experimental analysis of phase noise in semiconductor lasers biased below threshold

Abstract We report a theoretical and experimental study of phase noise in semiconductor lasers when the bias current is below the threshold value. The theoretical study is performed by using two types of rate equations, with additive and multiplicative noise terms. We find the conditions for which the evolution in those rate equations can be described by 1-dimensional and two dimensional Brownian motions, respectively. The main statistical differences between the additive and multiplicative noise models are then illustrated by using the simplified Brownian motion models. Additive and multiplicative noise models predictions are compared with measurements of the phase noise with a coherent receiver using a 90o optical hybrid. We develop a novel method to extract the phase noise directly from our measurements, that in contrast to the usual direct method is not based on the analysis of the phase noise difference. The method permits a direct visualization of the phase noise trajectories and a calculation of the averages and the distribution that is valid in the short-time limit. Our results are in very good agreement with the results obtained with the method based on the phase noise difference. Our experimental results show that the variance of the phase noise grows linearly in time and has Gaussian statistics, supporting the modelization of the phase noise statistics with the additive noise model.

On the Privacy of Sublinear-Communication Jaccard Index Estimation via Min-hash

The min-hash sketch is a well-known technique for low-communication approximation of the Jaccard index between two input sets. Moreover, there is a folklore belief that min-hash sketch-based protocols protect the privacy of the inputs. In this paper, we consider variants of private min-hash sketch based-protocols and investigate this folklore to quantify the privacy of the min-hash sketch. We begin our investigation by presenting a highly-efficient two-party protocol for estimating the Jaccard index while ensuring differential privacy. This protocol adds Laplacian noise to the min-hash sketch counts to provide privacy protection. Then, we aim to understand what privacy, if any, is guaranteed if the results of the min-hash are released without any additional noise, such as in the case of historical data. We begin our investigation by considering the privacy of min-hash in a centralized setting where the hash functions are chosen by the min-hash functionality and are unknown to the participants. We show that in this case the min-hash output satisfies the standard definition of differential privacy (DP) without any additional noise. We next consider a more practical distributed setting, where the hash function must be shared among all parties and is typically public. Unfortunately, we show that in this public hash function setting, the min-hash output is no longer DP. We therefore consider the notion of distributional differential privacy (DDP) introduced by Bassily et al. (FOCS 2013). We show that if the honest party's set has sufficiently high min-entropy, the min-hash output achieves DDP without requiring noise. Our findings provide guidance on how to use the min-hash sketch for private Jaccard index estimation and clarify the extent to which min-hash protocols protect input privacy, refining the common belief in their privacy guarantees.

A CO2–Δ14CO2 inversion setup for estimating European fossil CO2 emissions

Abstract. Independent estimation and verification of fossil CO2 emissions on a regional and national scale are crucial for evaluating the fossil CO2 emissions and reductions reported by countries as part of their nationally determined contributions (NDCs). Top-down methods, such as the assimilation of in situ and satellite observations of different tracers (e.g., CO2, CO, Δ14CO2, XCO2), have been increasingly used for this purpose. In this paper, we use the Lund University Modular Inversion Algorithm (LUMIA) to estimate fossil CO2 emissions and natural fluxes by simultaneously inverting in situ synthetic observations of CO2 and Δ14CO2 over Europe. We evaluate the inversion system by conducting a series of observing system simulation experiments (OSSEs). We find that in regions with a dense sampling network, such as western/central Europe, adding Δ14CO2 observations in an experiment where the prior fossil CO2 and biosphere fluxes are set to zero allows LUMIA to recover the time series of both categories. This reduces the prior-to-truth root mean square error (RMSE) from 1.26 to 0.12 TgC d−1 in fossil CO2 and from 0.97 to 0.17 TgC d−1 in biosphere fluxes, reflecting the true total CO2 budget by 91 %. In a second set of experiments using realistic prior fluxes, we find that in addition to retrieving the time series of the optimized fluxes, we are able to recover the true regional fossil CO2 budget in western/central Europe by 95 % and in Germany by 97 %. In all experiments, regions with low sampling coverage, such as southern Europe and the British Isles, show poorly resolved posterior fossil CO2 emissions. Although the posterior biosphere fluxes in these regions follow the seasonal patterns of the true fluxes, a significant bias remains, making it impossible to close the total CO2 budget. We find that the prior uncertainty of fossil CO2 emissions does not significantly impact the posterior estimates, showing similar results in regions with good sampling coverage like western/central Europe and northern Europe. Finally, having a good prior estimate of the terrestrial isotopic disequilibrium is important to avoid introducing additional noise into the posterior fossil CO2 fluxes.

Lightweight Noise Robust Spoofing Attack Detection using Cochleagram and ResNet Amalgamated Features

Abstract Speaker verification, like other biometric technologies, is vulnerable to spoofing attacks. An attacker impersonates a specific target speaker using impersonation, replay, Text-to-Speech (TTS), or Voice conversion (VC) techniques to gain unauthorized access to the system. The work in this paper, proposes a solution that uses an amalgamation of Cochleagram and Residual Network (ResNet) to implement the frontend feature extraction phase of an Audio Spoof Detection (ASD) system. Cochleagram generation, feature extraction-dimensionality reduction and classification are the three main phases of the proposed ASD system. In the first phase, the recorded audios have been converted into Cochleagrams by using Equivalent Rectangular Bandwidth (ERB) based gammatone filters. In the next phase, three variants of Residual Network (ResNet), ResNet50, ResNet41 and ResNet27, one by one, have been used for extracting dynamic features and Resnet50, ResNet41 that are fed to Linear Decrement Analysis (LDA) for dimensionality reduction. At last, in the classification phase, the LDA reduced features have been used for training four different machine learning classifiers such as Random Forest, Naïve Bayes, K-Nearest Neighbour (KNN), and eXtreme Gradient Boosting (XGBoost), individually. The proposed work in this paper concentrates on synthetic, replay, and deepfake attacks. The state-of-the-art ASVspoof 2019 Logical Access (LA), Physical Access (PA), Voice Spoofing Detection Corpus (VSDC) and DEepfake CROss-lingual (DECRO) datasets are utilised for training and testing the proposed ASD system. Additionally, we have assessed the performance of our proposed system under the influence of additive noise. Airplane noise at different SNR rate (0, dB 5dB, 10dB and -5dB) has been added to training and testing audios for the same. From the obtained results, it can be concluded that combination of Cochleagram and ResNet50 with XGBoost classifier outperforms all other implemented systems for detecting fake audios under noisy environment.

Machine Learning Approach to Energy Detection Based Spectrum Sensing for Cognitive Radio Networks

AbstractCognitive radio is an intelligent technology for wireless communication that optimizes the use of available frequency bands. Machine learning techniques can play an important role in spectrum sensing for cognitive radio networks to meet the rising traffic demand of wireless communication systems. The reliability of spectrum sensing methods depends on the prior knowledge of the noise to set a threshold. On the other hand, the success of a machine learning model relies on both the datasets and the accuracy of its learning algorithms. In this paper, we propose a spectrum sensing method for cognitive radio based on a machine learning algorithm in the conventional energy detection technique that removes the requirement to calculate the threshold. Initially, we introduce a method to build the dataset using the general concept of spectrum sensing based on the energy detection technique. The Naive Bayes supervised machine learning classification algorithm is implemented on the generated dataset for training, validation, and testing to sense the available spectrum. The proposed method is evaluated and tested using performance metrics such as confusion matrix, accuracy, precision, recall, F1 score, probability of detection, and probability of false alarm. In the simulation, the quadrature phase‐shift keying (QPSK) modulation scheme over the additive white Gaussian noise (AWGN) channel is considered. The experimental outcomes of the proposed method provide satisfactory and acceptable performance for spectrum sensing in cognitive radio networks. © 2025 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.

Design of an Underwater Acoustic Waveform and Integrated System for Communication and Detection

Combining underwater communication and detection can reduce system size and power consumption as well as improve secrecy. This paper presents a waveform that integrates continuous phase modulation (CPM) for data communication with linear frequency modulation (LFM) for detection. It is shown that the velocity ambiguity and range performance with this waveform are similar to those with only LFM. An integrated underwater acoustic system is also proposed to achieve simultaneous communication and detection. A symbol suffix (SS) is introduced into the signal frame at the transmitter and a two-step algorithm is employed at the receiver for frequency and phase offset estimation. Results are presented, showing that this decreases the sensitivity to CPM and reduces the range ambiguity side lobes. Further, the proposed system can effectively recover the data from the received signal. The bit error rate (BER) is shown to be better than that of traditional systems without a symbol suffix. With changes in the signal-to-noise ratio (SNR), the bit error rate (BER) in underwater acoustic environments is comparable to that in an additive white Gaussian noise (AWGN) channel, indicating a significant improvement in communication performance within the underwater acoustic channel.

Generalized Adaptive Diversity Gradient Descent Bit-Flipping with a Finite State Machine.

In this paper, we introduce a novel gradient descent bit-flipping algorithm with a finite state machine (GDBF-wSM) for iterative decoding of low-density parity-check (LDPC) codes. The algorithm utilizes a finite state machine to update variable node potentials-for each variable node, the corresponding finite state machine adjusts the update value based on whether the node was a candidate for flipping in previous iterations. We also present a learnable framework that can optimize decoder parameters using a database of uncorrectable error patterns. The performance of the proposed algorithm is illustrated for various regular LDPC codes, both in a binary symmetric channel (BSC) and the channel with additive white Gaussian noise (AWGN). The numerical results indicate a performance improvement when comparing our algorithm to previously proposed GDBF-based approaches.

Comparison of coseismic velocity changes estimated by cross-correlation of ambient seismic noise for earthquakes in south Korea and Japan

Ambient noise cross-correlation has been widely used to observe post-earthquake temporal velocity variations. Comparative studies are essential for assessing seismic hazards and clarifying the relationship between velocity variation and magnitude. However, very few comparative studies by earthquake magnitude have been conducted, particularly for magnitudes smaller than 6. In 2016 and 2017, southeastern Korea experienced the two most damaging earthquakes of the past 250 years: the Pohang earthquake (M 5.4) and Gyeongju earthquake (M 5.8). This study compared the coseismic velocity variations of these earthquakes with those observed in the M 7.3 Kumamoto and M 6.6 Tottori earthquakes, which occurred in Japan in 2016. In this study, the moving window cross-spectral analysis revealed different curves for bidirectional cross-correlations, a difference that has not been addressed in previous studies. This discrepancy was most likely caused by data deficiencies due to prolonged aftershocks or by instability from small-magnitude earthquakes recorded by surface seismometers in Korea. The average velocity decrease between forward and reverse order pairs correlated well with earthquake magnitude, except in the case of the Korean earthquake. Our devised measure based on aftershock activity suggests that the large decrease in the Pohang earthquake was due to non-coseismic noise in addition to instability.

Colored stochastic multiplicative processes with additive noise unveil a third-order partial differential equation, defying conventional Fokker-Planck equation and Fick-law paradigms

Colored stochastic multiplicative processes with additive noise unveil a third-order partial differential equation, defying conventional Fokker-Planck equation and Fick-law paradigms

A comparative analysis of perceptual noise in lateral and depth motion: Evidence from eye tracking.

The characterization of how precisely we perceive visual speed has traditionally relied on psychophysical judgments in discrimination tasks. Such tasks are often considered laborious and susceptible to biases, particularly without the involvement of highly trained participants. Additionally, thresholds for motion-in-depth perception are frequently reported as higher compared to lateral motion, a discrepancy that contrasts with everyday visuomotor tasks. In this research, we rely on a smooth pursuit model, based on a Kalman filter, to quantify speed observational uncertainties. This model allows us to distinguish between additive and multiplicative noise across three conditions of motion dynamics within a virtual reality setting: random walk, linear motion, and nonlinear motion, incorporating both lateral and depth motion components. We aim to assess tracking performance and perceptual uncertainties for lateral versus motion-in-depth. In alignment with prior research, our results indicate diminished performance for depth motion in the random walk condition, characterized by unpredictable positioning. However, when velocity information is available and facilitates predictions of future positions, perceptual uncertainties become more consistent between lateral and in-depth motion. This consistency is particularly noticeable within ranges where retinal speeds overlap between these two dimensions. Significantly, additive noise emerges as the primary source of uncertainty, largely exceeding multiplicative noise. This predominance of additive noise is consistent with computational accounts of visual motion. Our study challenges earlier beliefs of marked differences in processing lateral versus in-depth motions, suggesting similar levels of perceptual uncertainty and underscoring the significant role of additive noise.

Frequency and damping factor estimation of damped sinusoid by using DFT and DTFT

An algorithm for estimating the frequency and damping factor of damped complex sinusoidal signal is presented. After the rough estimation of frequency by discrete Fourier transform (DFT), the fine estimation of frequency and damping factor is achieved by utilizing the DFT bin with the maximum magnitude and two arbitrarily spaced discrete time Fourier transform (DTFT) spectral lines located on the same side of the maximum DFT spectrum bin. Then the theoretical mean square error (MSE) in additive white noise is analyzed. Simulation results show that the proposed algorithm tracks the Cramer-Rao lower bound (CRLB), and the parameters estimation accuracy is higher than the competing algorithms in most situations. The computational requirements are almost the same as several existing methods.

Achievable Cutoff Rates of the Additive Exponential Noise Channels

Achievable Cutoff Rates of the Additive Exponential Noise Channels