Presence Of Gaussian Noise Research Articles

Dynamical behavior of obligatory mutualistic-cheater interactions under the influence of white noise

Intraspecific mutualism is vital for ecosystems. Some interactions involve one species benefiting without reciprocating. Recent experiments suggest stable co-existence between mutualists and cheaters. This paper focuses on interactions between obligate mutualistic species and their cheaters, using a modified Lotka-Volterra model to analyze the negative impact of cheaters. We establish conditions for stability and verify a diffusive system's stability under spatial effects. Additionally, we study population dynamics fluctuations in the presence of Gaussian noise.

Generalized nonconvex nonsmooth four-directional total variation with overlapping group sparsity for image restoration

In this paper, we address the challenge of image deblurring in the presence of Gaussian noise. To achieve high-quality image restoration, we introduce an optimization framework that integrates four-directional total variation regularization, overlapping group sparsity, and a range of nonconvex penalties. This novel model effectively mitigates the staircase artifacts associated with total variation regularization and enhances restoration quality by leveraging domain-specific information about image pixels. Compared to the ℓ1 norm, the nonconvex penalty applied to overlapping groups promotes sparsity in image gradients at the group level. To solve this nonconvex optimization problem, we propose a proximal alternating reweighted minimization algorithm, which has a proximal alternating scheme with a reweighted approximation of its subproblem. Theoretically, we establish that the sequences generated by the proposed algorithm converge to a critical point using the Kurdyka–Łojasiewicz property. Experimental results validate the superiority of our approach over competing methods.

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

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

Enhanced Noise-Resilient Pressure Mat System Based on Hyperdimensional Computing.

Traditional systems for indoor pressure sensing and human activity recognition (HAR) rely on costly, high-resolution mats and computationally intensive neural network-based (NN-based) models that are prone to noise. In contrast, we design a cost-effective and noise-resilient pressure mat system for HAR, leveraging Velostat for intelligent pressure sensing and a novel hyperdimensional computing (HDC) classifier that is lightweight and highly noise resilient. To measure the performance of our system, we collected two datasets, capturing the static and continuous nature of human movements. Our HDC-based classification algorithm shows an accuracy of 93.19%, improving the accuracy by 9.47% over state-of-the-art CNNs, along with an 85% reduction in energy consumption. We propose a new HDC noise-resilient algorithm and analyze the performance of our proposed method in the presence of three different kinds of noise, including memory and communication, input, and sensor noise. Our system is more resilient across all three noise types. Specifically, in the presence of Gaussian noise, we achieve an accuracy of 92.15% (97.51% for static data), representing a 13.19% (8.77%) improvement compared to state-of-the-art CNNs.

Data Assimilation Using Time-Delay Nudging in the Presence of Gaussian Noise

Data Assimilation Using Time-Delay Nudging in the Presence of Gaussian Noise

Noise induced dynamics of two-qubit entangled Bell’s states

The stability of different types two-qubit entangled states was analyzed by a direct calculations of the time dependent probability to find the system in its initial state in the presence of Gaussian noise. The entangled states time evolution was studied in the presence of both classical and quantum noise. It was demonstrated that one pair of Bell’s states is robust to the Gaussian fluctuations, while the another one decays. The decay law of unstable entangled states is determined by the noise correlation function. The developed general formalism was applied for analysis the dynamics of entangled states in the presence of fluctuations produced by the electron–phonon interaction. It was revealed that unstable entangled states interacting with phonon bath can demonstrate the crossover between short time exponential decay law and long time power law decay. Obtained results can be effectively exploited for quantum computation, in which it is essential to be able to retrieve information about the initial quantum state even in the presence of interaction with the environment.

Cyclic Correlation‐Based Blind SNR Estimation for Cyclic Prefix‐Less OFDM System

AbstractThis paper tackles the problem of the signal‐to‐noise ratio estimation for cyclic prefix (CP)‐Less orthogonal frequency division multiplexing (OFDM) system in the presence of Gaussian noise over multipath fading channels. First, we introduce the cyclic correlation of the CP‐Less OFDM signal with CP, and analyze the cyclic correlations for Gaussian noise and received signal. Second, we isolate the Gaussian noise power from the signal power. Finally, we obtain the close form expression of SNR estimation by using cyclic correlations. Computer simulation results verify the effectiveness of the proposed method.

Reconstruction based on adaptive group least angle regression for fluorescence molecular tomography.

Fluorescence molecular tomography can combine two-dimensional fluorescence imaging with anatomical information to reconstruct three-dimensional images of tumors. Reconstruction based on traditional regularization with tumor sparsity priors does not take into account that tumor cells form clusters, so it performs poorly when multiple light sources are used. Here we describe reconstruction based on an "adaptive group least angle regression elastic net" (AGLEN) method, in which local spatial structure correlation and group sparsity are integrated with elastic net regularization, followed by least angle regression. The AGLEN method works iteratively using the residual vector and a median smoothing strategy in order to adaptively obtain a robust local optimum. The method was verified using numerical simulations as well as imaging of mice bearing liver or melanoma tumors. AGLEN reconstruction performed better than state-of-the-art methods with different sizes of light sources at different distances from the sample and in the presence of Gaussian noise at 5-25%. In addition, AGLEN-based reconstruction accurately imaged tumor expression of cell death ligand-1, which can guide immunotherapy.

$\ell _{0}$-Norm Minimization Based Robust Matrix Completion Approach for MIMO Radar Target Localization

In this paper, we propose a robust matrix completion approach based on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell _{0}$</tex-math></inline-formula> -norm minimization for target localization in sub-Nyquist sampled multiple-input multiple-output (MIMO) radar. Owing to the low-rank property of the noise-free MIMO radar transmit matrix, our approach is able to recover the missing data and resist impulsive noise from the receive matrix. We adopt proximal block coordinate descent and adaptive penalty parameter adjustment by complex Laplacian kernel and normalized median absolute deviation. We analyze the resultant algorithm convergence and computational complexity, and demonstrate through simulations that it outperforms existing methods in terms of pseudospectrum, mean square error, and target detection probability in non-Gaussian impulsive noise, even for the full sampling schemes. While in the presence of Gaussian noise, our approach performs comparably with other sub-Nyquist methods.

Gaussian inference for data-driven state-feedback design of nonlinear systems

Data-driven control of nonlinear systems with rigorous guarantees is a challenging problem as it usually calls for nonconvex optimization and often requires the knowledge of the true basis functions of the unknown system dynamics. To tackle these drawbacks, this work is based on a data-driven polynomial representation of general nonlinear systems exploiting Taylor polynomials. Thereby, we design state-feedback laws that render a known equilibrium globally asymptotically stable while operating with respect to a desired quadratic performance criterion. The calculation of the polynomial state feedback boils down to a sum-of-squares optimization problem, and hence to computationally tractable linear matrix inequalities. Moreover, we examine state-input data in presence of Gaussian noise by Bayesian inference to overcome the conservatism of deterministic noise characterizations from recent data-driven control approaches for Gaussian noise.

Tracking Point Vortices and Circulations via Advected Passive Particles: An Estimation Approach

We present a novel method for estimating the circulations and positions of point vortices in a two-dimensional (2D) environment using trajectory data of passive particles in the presence of Gaussian noise. The method comprises two algorithms: the first one calculates the vortex circulations, while the second one reconstructs the vortex trajectories. This reconstruction is done thanks to a hierarchy of optimization problems, involving the integration of systems of differential equations, over time sub-intervals all with the same amplitude defined by the autocorrelation function for the advected passive particles’ trajectories. Our findings indicate that accurately tracking the position of vortices and determining their circulations is achievable, even when passive particle trajectories are affected by noise.

Secure estimation against non‐fixed channel attacks in cyber‐physical systems

AbstractThis article studies the secure estimation problem for cyber‐physical systems (CPSs) with sparse attacks and noises. Instead of fixed attacked sensor channels, the malicious attack investigated in this work is ‐sparse and the set of attacked sensor channels is time‐varying. A novel ‐minimization based on QR decomposition, rather than minimizing the row support of the attack matrix directly, is designed to reconstruct malicious attacks. Furthermore, considering that the presence of Gaussian noises may produce estimation errors, a secure conservative estimation method based on Kalman filter is proposed to estimate the consolidated signal consisting of sparse attacks and measurement noises. Moreover, it is proved that robustness of the proposed estimation algorithm can be guaranteed with the upper bound of estimation error covariance. An illustrative example is utilized to show the effectiveness of the proposed methods.

Diffusion adagrad minimum kernel risk sensitive mean p-power loss algorithm

The most diffusion algorithms based on the mean square error (MSE) criterion generally have good performance in the presence of Gaussian noise, however suffer from performance deterioration under non-Gaussian noises. To combat non-Gaussian noises, a diffusion minimum kernel risk sensitive mean p-power loss (DMKRSP) algorithm is first designed using a generalized robust kernel risk sensitive mean p-power loss (KRSP) criterion combined with stochastic gradient descent (SGD). Then, due to more error information than SGD, the adaptive gradient (Adagrad) is used in DMKRSP to generate a diffusion Adagrad minimum kernel risk sensitive mean p-power loss (DAMKRSP) algorithm. Finally, the theoretical analysis of DMKRSP and DAMKRSP is presented for steady-state performance analysis. Simulations on system identification show that both DMKRSP and DAMKRSP are superior to other classical algorithms in term of robustness and filtering accuracy.

Explosive synchronization in coupled nonlinear oscillators on multiplex network

We report the emergence of explosive synchronization in a multiplex network where oscillators on the first layer are coupled with attractive coupling and those on the second layer, coupled with repulsive coupling. With Stuart-Landau and FitzHugh-Nagumo oscillators as the nodal dynamics, we consider non-local and mean-field intralayer couplings. We establish that explosive synchronization occurs in the multiplex network in the presence of Gaussian noise, and the transition is first order with hysteresis to a state of complete intra-layer and in-phase interlayer synchronization. The width of the hysteresis depends on the range of intralayer attractive coupling, strength of interlayer coupling and noise. We also see how to have control over this induced transition so that the explosive nature, if undesirable, can be converted to continuous type by tuning the strength of repulsive coupling or noise.

A Low-Cost Multistage Cascaded Adaptive Filter Configuration for Noise Reduction in Phonocardiogram Signal.

Phonocardiogram (PCG), the graphic recording of heart signals, is analyzed to determine the cardiac mechanical function. In the recording of PCG signals, the major problem encountered is the corruption by surrounding noise signals. The noise-corrupted signal cannot be analyzed and used for advanced processing. Therefore, there is a need to denoise these signals before being employed for further processing. Adaptive Noise Cancellers are best suited for signal denoising applications and can efficiently recover the corrupted PCG signal. This paper introduces an optimal adaptive filter structure using a Sign Error LMS algorithm to estimate a noise-free signal with high accuracy. In the proposed filter structure, a noisy signal is passed through a multistage cascaded adaptive filter structure. The number of stages to be cascaded and the step size for each stage are adjusted automatically. The proposed Variable Stage Cascaded Sign Error LMS (SELMS) adaptive filter model is tested for denoising the fetal PCG signal taken from the SUFHS database and corrupted by Gaussian and colored pink noise signals of different input SNR levels. The proposed filter model is also tested for pathological PCG signals in the presence of Gaussian noise. The simulation results prove that the proposed filter model performs remarkably well and provides 8–10 dB higher SNR values in a Gaussian noise environment and 2-3 dB higher SNR values in the presence of colored noise than the existing cascaded LMS filter models. The MSE values are improved by 75–80% in the case of Gaussian noise. Further, the correlation between the clean signal and its estimate after denoising is more than 0.99. The PSNR values are improved by 7 dB in a Gaussian noise environment and 1-2 dB in the presence of pink noise. The advantage of using the SELMS adaptive filter in the proposed filter model is that it offers a cost-effective hardware implementation of Adaptive Noise Canceller with high accuracy.

Inverse boundary problem in estimating heat transfer coefficient of a round pulsating bubbly jet: design of experiment

ABSTRACT An inverse algorithm is developed to estimate the transient convective coefficient distribution of a pulsating bubbly jet impinging on a cylindrical thermal mass. Cooling of the thermal mass is simulated by solving the two-dimensional transient heat equation in a cylindrical coordinate system using the finite difference method. The sum of squared differences between calculated and measured temperature data is the objective functional. As this is a nonlinear IHCP, the adjoint method is employed to derive the gradient components of the objective function, needed for the implementation of CGM. The procedure is carried out for six gas Reynolds numbers changing continuously through ten seconds of the jet impingement. The inverse scheme is validated using noiseless temperature data. The accuracy and convergence rate of the algorithm is then assessed by simulating the cooling process of thermal mass with four different materials. Moreover, the effects of sensors’ location, as well as initial guess on the estimation, are evaluated. Time-varying heat transfer coefficients are then estimated in the presence of Gaussian noise, having four standard deviations. Results demonstrate that, despite the estimation is affected by the noise level, the adjoint method is most efficient and rapidly convergent for the thermal mass with moderate thermal conductivity having a noisy temperature field of 1 .

Enhanced Channel Attention Network With Cross-Layer Feature Fusion for Spectral Reconstruction in the Presence of Gaussian Noise

Spectral reconstruction from RGB images has made significant progress. Previous works usually utilized the noise-free RGB images as input to reconstruct the corresponding hyperspectral images (HSIs). However, due to instrumental limitation or atmospheric interference, it is inevitable to suffer from noise (e.g., Gaussian noise) in the actual image acquisition process, which further increases the difficulty of spectral reconstruction. In this paper, we propose an enhanced channel attention network (ECANet) to learn a nonlinear mapping from noisy RGB images to clean HSIs. The backbone of our proposed ECANet is stacked with multiple enhanced channel attention (ECA) blocks. The ECA block is the dual residual version of channel attention block, which makes the network focus on key auxiliary information and features that are more conducive to spectral reconstruction. For the case that the input RGB images are disturbed by Gaussian noise, cross-layer feature fusion (CLFF) unit is used to concatenate the multiple feature maps at different depths for more powerful feature representations. In addition, we design a novel combined loss function as the constraint of the ECANet to achieve more accurate reconstruction result. Experimental results on two HSI benchmarks, CAVE and NTIRE 2020, demonstrate that the effectiveness of our method in terms of both visual and quantitative over other state-of-the-art methods.

Simultaneous calibration of instrument scale factor and drift rate in network adjustment for continental-scale gravity survey campaign

SUMMARY The scale factor of each relative gravimeter must be calibrated both before and after the fieldwork of a terrestrial gravity survey, to reduce uncertainties and ensure high precision. Conventionally, such calibration is a time-consuming process performed following well-established baselines. We propose a new Bayesian method to estimate the scale factor in a hybrid gravity network that includes several absolute gravity observation stations. In this approach, the scale factor is estimated as a hyperparameter using the Akaike Bayesian information criterion and using known absolute gravity stations in the network or/and calibrated instruments as constraints. Testing the sensitivity of the gravity values and the residuals of the gravity difference between two successive stations to the change of the scale factor demonstrates the robustness of this method. We also test the sensitivity of the estimated scale factor in the presence of Gaussian noise and the non-linear instrumental drift rate. Moreover, if the maximum absolute gravity interval is greater than 60 per cent of the range of gravity values in the network, or if the known scale factors of calibrated gravimeters are well calibrated, this approach can provide reasonable estimates of the daily drift rate and the unknown scale factors, where the latter has an error of &amp;lt;3 × 10−5. We apply this approach to real gravity campaign data from Yunnan in China and use a cross-validation method to compare estimated gravity values and corresponding gravity values obtained from absolute gravity observations at the same stations, to validate how the proposed method improves estimation accuracy of the gravity value at each station.

Robust Methods for Wideband Compressive Spectrum Sensing Under Non-Gaussian Noise

In a cognitive radio network, non-reconstruction-based wideband compressive spectrum sensing poses challenges under the non-Gaussian noise environment. The maximum correntropy criterion (MCC) is robust to impulsive noise whereas, the Parzen window Renyi entropy is a good choice for spectrum sensing in the presence of Gaussian noise at a low signal-to-noise ratio (SNR). However, the detection performance of these algorithms depends on the accuracy of measured noise variance, which is sensitive to impulse noise. In this letter, we improve the sensing performance of both the aforementioned algorithms in a non-Gaussian noise environment by modifying the kernel and threshold using robust statistics. The robust technique minimizes the influence of impulsive noise in the received signal. Finally, we carry out the simulation results to illustrate the superior performance of robust sensing algorithms under both Bernoulli’s distribution and symmetric <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> stable ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{S}\alpha \text{S}$ </tex-math></inline-formula> ) distribution channel noise. The performance is compared with the non-robust counterpart for sensing multi-carrier Universal-Filtered Multi-Carrier (UFMC) signal.

Neural Network Reconstruction of Plasma Space-Time

We explore the use of Physics-Informed Neural Networks (PINNs) for reconstructing full magnetohydrodynamic solutions from partial samples, mimicking the recreation of space-time environments around spacecraft observations. We use one-dimensional magneto- and hydrodynamic benchmarks, namely the Sod, Ryu-Jones, and Brio-Wu shock tubes, to obtain the plasma state variables along linear trajectories in space-time. These simulated spacecraft measurements are used as constraining boundary data for a PINN which incorporates the full set of one-dimensional (magneto) hydrodynamics equations in its loss function. We find that the PINN is able to reconstruct the full 1D solution of these shock tubes even in the presence of Gaussian noise. However, our chosen PINN transformer architecture does not appear to scale well to higher dimensions. Nonetheless, PINNs in general could turn out to be a promising mechanism for reconstructing simple magnetic structures and dynamics from satellite observations in geospace.