Gaussian Mixture Noise Research Articles

Hider: A Hyperspectral Image Denoising Transformer With Spatial-Spectral Constraints for Hybrid Noise Removal.

Hyperspectral image (HSI) qualities are limited by a mixture of Gaussian noise, impulse noise, stripes, and deadlines during the sensor imaging process, resulting in weak application performance. To enhance HSI qualities, methods based on convolutional neural networks have been successively applied to restore clean data from the observed data. However, the architecture of these methods lacks spectral and spatial constraints, and the convolution operators have limited receptive fields and inflexible model inferences. Thus, in this study, we propose an efficient end-to-end transformer, named HSI denoising transformer (Hider), for mixed HSI noise removal. First, a U-shaped 3-D transformer architecture is built for multiscale feature aggregation. Second, a multihead global spectral attention module within the spectral transformer block is designed to excavate information in different spectral patterns. Finally, an additional locally enhanced cross-spatial attention module within the spatial-spectral transformer block is constructed to build the long-range spatial relationship to avoid the high computational complexity of global spatial self-attention. Through the imposition of global correlations along spectrum and spatial self-similarity constraints on the transformer, our proposed Hider aims to capture long-range spatial contextual information and cluster objects with the same spectral pattern for HSI denoising. To verify the effectiveness and efficiency of Hider, we conducted extensive simulated and real experiments. The denoising results on both simulated and real-world datasets show that Hider achieves superior evaluation metrics and visual assessments compared with other state-of-the-art methods.

A multi-user cognitive radio full-duplex channel under imperfect spectrum sensing: Achievable rates and energy efficiency

In this work, the achievable rates and energy efficiency of a multi-user cognitive radio (CR) uplink channel with full-duplex (FD) are studied. For this multi-user CR channel, secondary users can work in FD mode to simultaneously transmit and listen to the channel. We consider a realistic scenario in which both FD operation and spectrum sensing are imperfect. At first, we examine the sensing performance and the rate region through the evaluation of the probability of miss-detection and the probability of false alarm when the primary user (PU) activity is assumed to be non-time-slotted. Due to an imperfect sensing operation, the cognitive radio channel is modeled as a non-Gaussian channel impacted by a Gaussian-mixture (GM) noise plus PU interference. Under this practical assumption, it is not possible to calculate the achievable rates and the rate region directly. Instead, we derive simple approximations of these metrics which can be easily calculated with arbitrarily small errors. In the second part of the paper, we further evaluate the derivatives of these achievable rates at low-power regimes. This calculation helps us evaluate the energy efficiency and obtain the minimum energy per bit Eb/N0min when Gaussian and discrete input signals are used.

The Gain-Scheduled Filter With Probability Density Function Compensator for Stochastic System With Missing Measurements and Gaussian Mixture Noise

The Gain-Scheduled Filter With Probability Density Function Compensator for Stochastic System With Missing Measurements and Gaussian Mixture Noise

Signal detection for FTN system under unknown noise model with imperfect CSI

The problem of signal detection for faster-than-Nyquist (FTN) signaling system with imperfect channel state information (CSI) is studied. Also, the non-Gaussian noise in real applications is considered. A general model, Gaussian mixture noise (GMN) model, is applied to describe the unknown probability density function (PDF) of the non-Gaussian noise. After that, a framework over variational inference is constructed to simplify the problem through finding an auxiliary PDF with factorization form. Based on the factor graph over the signal, joint response and the parameters of GMN, an iterative solution is obtained. Simulations demonstrate the effectiveness of the proposed approach.

Vehicular visible light communications noise analysis and modeling.

Vehicular visible light communications (VVLC) is promising intelligent transportation systems technology with the utilization of light-emitting diodes. The main degrading factor for the performance of VVLC systems is noise. Traditional VVLC systems noise modeling is based on the additive white Gaussian noise assumption in the form of shot and thermal noise. In this paper, to investigate both time correlated and white noise components of the VVLC channel noise, we propose a noise analysis based on Allan variance, which provides a time-series analysis method to identify noise from the data. The results show that white noise and random walk are observed in the VVLC systems. We also propose a motion detection algorithm based on the adaptive Gaussian mixture (GM) model to generate a double Gaussian model of VVLC channel noise. We further present a study on the error performance of a VVLC system considering channel noise to be a mixture of Gaussian components. We derive the analytical expressions of probability of error for binary phase-shift keying and quadrature phase-shift keying constellations. It has been observed that, in the presence of GM noise, the system performance degrades significantly from the usual one expected in a Gaussian noise environment and becomes a function of the mixing coefficients of the GM distribution.

Improved differential evolution for RSSD-based localization in Gaussian mixture noise

Signal strength-based localization approaches are prevalent in wireless sensor networks due to their low cost and simplicity. However, factors such as human interference and heterogeneous sources make approaches based on Gaussian noise and known transmit power unreliable. To address these issues, a received signal strength difference (RSSD) based approach is proposed to localize a source with unknown transmit power and Gaussian mixture noise. First, an RSSD-based nonconvex maximum likelihood (ML) problem is formulated which does not require an approximation or good initial point. Then, an improved differential evolution (IDE) method is given to obtain a global solution. Opposition-based learning (OL) combined with a chaotic map (CM) is used to obtain a robust population and adaptive mutation (AM) with two subpopulations is employed to balance global exploration and convergence. The corresponding Cramér–Rao lower bound (CRLB) for Gaussian mixture noise is derived for comparison purposes. Numerical results are presented which show that the proposed OLAM-IDE method provides better localization accuracy than state-of-the-art approaches.

Double Extended Kalman Filter Algorithm Based on Weighted Multi-Innovation and Weighted Maximum Correlation Entropy Criterion for Co-Estimation of Battery SOC and Capacity.

Most of the traditional extended Kalman filter algorithms for the co-estimation of SOC and capacity of lithium-ion batteries are designed based on the minimum mean square error (MMSE) criterion, which may show superior performance in Gaussian noise scenes. However, due to the complexity of the battery operating environment, it is likely to face non-Gaussian noise (especially outlier noise), at which time the performance of the traditional extended Kalman filter algorithms will be seriously weakened. To solve the above problems, this paper first proposes a double extended Kalman filter algorithm based on weighted multi-innovation and weighted maximum correlation entropy (WMI-WMCC-DEKF) for the co-estimation of battery SOC and capacity. In this paper, the performance of the target algorithm is verified and compared by generating different types of noise from three noise models: weak Gaussian mixture noise, strong Gaussian mixture noise, and outlier noise. The maximum absolute error value (MAE) and root mean square error value (RMSE) of the WMI-WMCC-DEKF algorithm can achieve the highest performance improvement of 69.3 and 84.2% (SOC), 61.3, and 94.2% (capacity), respectively. The experimental results fully prove that the target algorithm has excellent performance against three kinds of noises.

Gaussian Mixture Midway-Merge for Object SLAM With Pose Ambiguity

In this letter, we propose a novel method to merge a Gaussian mixture on matrix Lie groups and present its application for a simultaneous localization and mapping problem with symmetric objects. The key idea is to predetermine the weighted mean called a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">midway point</i> and merge Gaussian mixture components at the associated tangent space. Through this rule, the covariance matrix captures the original density more accurately, and the need for the back-projection is spared when compared to the conventional merge. We highlight the midway-merge by numerically evaluating dissimilarity metrics of density functions before and after the merge on the rotational group. Furthermore, we experimentally discover that the rotational error of symmetric objects follows heavy-tailed behavior and formulate the Gaussian sum filter to model it by a Gaussian mixture noise. The effectiveness of our approach is validated through virtual and real-world datasets.

Non-Gaussian Pseudolinear Kalman Filtering-Based Target Motion Analysis with State Constraints

For the bearing-only target motion analysis (TMA), the pseudolinear Kalman filter (PLKF) solves the complex nonlinear estimation of the motion model parameters but suffers serious bias problems. The pseudolinear Kalman filter under the minimum mean square error framework (PL-MMSE) has a more accurate tracking ability and higher stability compared to the PLKF. Since the bearing signals are corrupted by non-Gaussian noise in practice, we reconstruct the PL-MMSE under Gaussian mixture noise. If some prior information, such as state constraints, is available, the performance of the PL-MMSE can be further improved by incorporating state constraints in the filtering process. In this paper, the mean square and estimation projection methods are used to incorporate PL-MMSE with linear constraints, respectively. Then, the linear approximation and second-order approximation methods are applied to merge PL-MMSE with nonlinear constraints, respectively. Simulation results demonstrate that the constrained PL-MMSE algorithms result in lower mean square errors and bias norms, which demonstrates the superiority of the constrained algorithms.

Unknown Transmit Power RSSD-Based Localization in a Gaussian Mixture Channel

Localization is a critical task in wireless sensor networks (WSNs). However, accurate localization is difficult when there is noise from external sources and faulty nodes, especially when the transmit power is unknown. Signal strength-based localization methods are popular due to their low complexity and simple implementation. In this paper, robust localization based on the received signal strength difference (RSSD) is considered with unknown transmit power and Gaussian mixture noise in the presence of faulty nodes. A robust fault-tolerant localization (RFLT) technique is proposed by reformulating the original localization problem using a generalized trust-region subproblem (GTRS) framework. The resulting problem is non-convex so it is divided into two subproblems using a regularization item (RI) with a block-update surrogate function (BUSF). The active set method (ASM) is used to obtain an initial solution. The corresponding Cramer–Rao lower bound (CRLB) for Gaussian mixture noise is derived as a benchmark. Simulation results are presented which show that the performance of the proposed method is superior to other state-of-the-art methods.

Robust classification via clipping-based kernel recursive least lncosh of error

Classification as a supervised machine learning method predicts the class label from the features distribution and the training process. The traditional classifier algorithms are not robust in the presence of outliers and noisy features. In this study, we suggest a novel robust classifier using kernel recursive least lncosh (RC-KRLL), in which the clipping concept is used to ignore the effect of large noises. Instead of the conventional mean square error cost function, the suggested RC-KRLL method is derived from the lncosh loss function, being more suitable for non-Gaussian noise. The mean, mean-square convergence, and learning curve of the RC-KRLL are discussed theoretically. The simulation results show that the proposed method outperforms the other robust state-of-the-art classification algorithms in the presence of synthetic non-Gaussian noise over UCI data sets, such as the mixture of Gaussian noise with different variances, impulse, and Alpha–Beta noises. The obtained results over 500px data sets on social media with real outliers and mislabeled samples confirmed the acceptable performance of the proposed method.

Multi-sensor measurement fusion based on minimum mixture error entropy with non-Gaussian measurement noise

In this paper, a novel multi-sensor measurement fusion method is proposed based on minimum error entropy criterion for nonlinear state estimation in non-Gaussian measurement noise. Through cubature-quadrature transform, a mixture error entropy cost function is defined to capture the high order statistics of multi-source measurement error. Based on the centralized measurement model, a measurement fusion information filter is developed by minimizing the mixture error entropy cost. The fixed point iteration approach is employed to calculate the estimates, and the square root implementation of the proposed filter is also provided. Further, the convergence conditions of the proposed information filter are derived. Simulations are performed with different dimensional measurements to demonstrate the effectiveness of the proposed algorithm. It is shown that, the estimation performance of the proposed measurement fusion information filter is better than that of traditional Kalman and Huber's filter based fusion methods against outliers and Gaussian mixture noises.

Maximum Likelihood estimation for non-minimum-phase noise transfer function with Gaussian mixture noise distribution

In this paper a Maximum Likelihood estimation algorithm for a linear dynamic system driven by an exogenous input signal, with non-minimum-phase noise transfer function and a Gaussian mixture noise is developed. We propose a flexible identification technique to estimate the system model parameters and the Gaussian mixture parameters based on the Expectation–Maximization algorithm. The benefits of our proposal are illustrated via numerical simulations.

A marginalised particle filter with variational inference for non‐linear state‐space models with Gaussian mixture noise

This work proposes a marginalised particle filter with variational inference for non-linear state-space models (SSMs) with Gaussian mixture noise. A latent variable indicating the component of the Gaussian mixture considered at each time instant is introduced to specify the measurement mode of the SSM. The resulting joint posterior distribution of the state vector, the mode variable and the parameters of the Gaussian mixture noise is marginalised with respect to the noise variables. The marginalised posterior distribution of the state and mode is then approximated by using an appropriate marginalised particle filter. The noise parameters conditionally on each particle system of the state and mode variable are finally updated by using variational Bayesian inference. A simulation study is conducted to compare the proposed method with state-of-the-art approaches in the context of positioning in urban canyons using global navigation satellite systems.

Low-rank Gaussian mixture modeling of space-snapshot representation of microphone array measurements for acoustic imaging in a complex noisy environment

The microphone array can simultaneously obtain the multi-dimensional information (space-time-frequency) of sound sources, which is recognized as a fundamental and powerful tool in acoustic imaging. Acoustic Beamforming is one of the widely used methods in acoustic imaging. However, most of the applications of beamforming are based on the Gaussian noise assumption, which is not always accurate in on-site measurements. For example, shock noise with a skewed probability density function (PDF) may appear on the signal record when the turbulent eddies are not controlled. Thus, in this paper, the conventional Gaussian noise model is extended to a Gaussian mixture noise model, which can approximate any probability distribution of the noise in theory. The space-snapshot representation of microphone array measurements is further modeled as a combination of the low-rank matrix part (measurements from the sound sources) and a Gaussian mixture matrix part (measurement noise). The signal from the sources of interest is finally recovered by the Expectation–maximization algorithm, which iterates between the low-rank approximation of the sound sources and the estimation of the parameter of the Gaussian mixture model. The proposed method is further investigated with simulations and compared with robust principal component analysis (RPCA) and Gaussian-based probabilistic factor analysis (PFA). It is concluded that the proposed method outperforms the state-of-the-art denoising methods.

LR-Net: Low-Rank Spatial-Spectral Network for Hyperspectral Image Denoising.

Due to the physical limitations of the imaging devices, hyperspectral images (HSIs) are commonly distorted by a mixture of Gaussian noise, impulse noise, stripes, and dead lines, leading to the decline in the performance of unmixing, classification, and other subsequent applications. In this paper, we propose a novel end-to-end low-rank spatial-spectral network (LR-Net) for the removal of the hybrid noise in HSIs. By integrating the low-rank physical property into a deep convolutional neural network (DCNN), the proposed LR-Net simultaneously enjoys the strong feature representation ability from DCNN and the implicit physical constraint of clean HSIs. Firstly, spatial-spectral atrous blocks (SSABs) are built to exploit spatial-spectral features of HSIs. Secondly, these spatial-spectral features are forwarded to a multi-atrous block (MAB) to aggregate the context in different receptive fields. Thirdly, the contextual features and spatial-spectral features from different levels are concatenated before being fed into a plug-and-play low-rank module (LRM) for feature reconstruction. With the help of the LRM, the workflow of low-rank matrix reconstruction can be streamlined in a differentiable manner. Finally, the low-rank features are utilized to capture the latent semantic relationships of the HSIs to recover clean HSIs. Extensive experiments on both simulated and real-world datasets were conducted. The experimental results show that the LR-Net outperforms other state-of-the-art denoising methods in terms of evaluation metrics and visual assessments. Particularly, through the collaborative integration of DCNNs and the low-rank property, the LR-Net shows strong stability and capacity for generalization.

Spectrum Sensing With Non-Gaussian Noise Over Multi-Path Fading Channels Towards Smart Cities With IoT

As the limited communication spectrum can not meet the demand of the exponential growth of intelligent connected devices in the internet of things(IoT) and typical smart city applications, in this paper, we propose a tractable spectrum sensing method based on Rao detection over non-Gaussian noise, such as generalized Gaussian noise(GGN), Gaussian mixture noise(GMN) and symmetric alpha-stable distribution ( <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> ) noise, multi-path fading channels environment to alleviate the issue of spectrum scarcity. In this method, there are unknown parameters in the multi-path fading channels. When the probability density function (P.D.F.) of non-Gaussian noise has a closed-form expression, the spectrum sensing method based on Rao detection is used. Otherwise the P.D.F. for <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> noise is estimated firstly by using non-parametric kernel estimation method, which addresses the issue that <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> noise has no closed-form P.D.F. expression, and then the performance of spectrum sensing is derived based on the theory of Rao detection in multi-path fading channels over typical smart city applications. Simulation results show that the accuracy of estimated P.D.F. for <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> noise and the performance of spectrum sensing under different <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> values over indoor, outdoor, and vehicle fading channels environment.

Research on underwater target tracking based on Gaussian Hermitian Kalman Particle filter algorithm

The underwater target tracking environment usually has the characteristics of strong nonlinearity and non-Gaussian. The target tracking problem usually uses the nonlinear filtering algorithm, which combines the nonlinear measurement model with the linear system dynamics. The primary goal of target tracking is to extract accurate information about the real-time state of the target from the noise nonlinear observation obtained by the sensor. A new Gaussian Hermitt Kalman particle filter algorithm (GHKF-PF) is used to improve the tracking accuracy of the particle filter algorithm (PF). GHKF-PF uses the GHKF sampling method to sample particles from the posterior distribution of the target, calculates the mean and covariance for each particle, and uses the mean and variance to guide sampling. In the simulation experiment, the uniform linear motion model of underwater 3D target in the environment of Gaussian mixture noise (GMN) is established, and the application of GHKF-PF algorithm in 3D space is realized, and the accuracy is higher than that of PF. In order to further verify the effectiveness of the algorithm, a six-dimensional uniform acceleration motion model is established and compared with the extended particle filter (EPF) algorithm and the unscented particle filter (UPF) algorithm. The simulation results show that the performance of the GHKF-PF algorithm is similar to that of the UPF algorithm and better than the EPF algorithm.

Robotic cross-modal generative adversarial network based on variational Bayesian Gaussian mixture noise model

Multimodal fusion is essential for robots to fully perceive the external environment. Single modal information limits the ability of robots to recognize and grasp objects. Meanwhile, traditional cross-modal data generation methods produce poor images, resulting in the bad effects of multimodal fusion. To solve the problem of the poor image effects of multimodal generation and the lack of data for multimodal fusion, this study proposes a variational Bayesian Gaussian mixture-conditional generative adversarial network (BGM-CGAN) for generating diverse cross-modal noise data. With the variational Bayesian Gaussian mixture algorithm, a uniform distributed random noise group is generated into a single mixed variable. The generated mixed variable is then generated through a Gaussian mixture model to generate a series of Gaussian mixed noise groups. The generated mixed noise group is randomly selected into a single Gaussian noise and imported into a modal image and fused with the modal image to successfully generate a high-resolution heterogeneous modal image. The method restores the heterogeneous modal information and solves the problem of the insufficient information and poor quality of generated images under a single modal. In the end, we use a variety of evaluation indexes (IS, FID, SSIM, and PSNR) to compare the proposed BGM-CGAN and other algorithms for cross-modal image generation capabilities. Results show the effectiveness and feasibility of the proposed algorithm. In addition, the BGM-CGAN algorithm has wide application prospects and can be extended to cross-modal material retrieval, cross-modal texture recognition, and other fields.

MIMO Spectrum Sensing for Cognitive Radio-Based Internet of Things

The emerging cognitive radio-based Internet-of-Things (CR-IoT) network provides a novel paradigm solution for IoT devices to efficiently utilize spectrum resources. Spectrum sensing is a critical problem in the CR-IoT network which has been investigated extensively under the Gaussian noise/interference. Since most of the interference in an IoT network is non-Gaussian, in this article, we introduce a novel spectrum sensing method for CR-IoT with additive Gaussian mixture noise/interference. The introduced method maps the observation signal matrix from the original input space to a high-dimensional feature space by a nonlinear Gaussian kernel function and then constructs a kernelized test statistic in the feature space. The approximate analytical expressions of the false alarm and detection probability of the proposed scheme are derived under Gaussian mixture noise, and the decision threshold can be determined according to false alarm probability. The simulation results show that the introduced multiple-input-multiple-output (MIMO) spectrum sensing method achieves good performance under Gaussian mixture noise/interference and significantly outperforms existing detectors.