Adaptive Gaussian Noise Image Removal Algorithm Using Filtering-Based Noise Estimation

This paper proposes a spatially denoising algorithm using filtering-based noise estimation for an image corrupted by Gaussian noise.The proposed algorithm consists of two stages:estimation and elimination of noise density.To adaptively deal with variety of the noise amount,a noisy input image is firstly filtered by a lowpass filter.Standard deviation of the noise is computed from different images between the noisy input and its filtered image.In addition,a modified Gaussian noise removal filter based on the local statistics such as local weighted mean,local weighted activity and local maximum is used to control the degree of noise suppression.Experiments show the effectiveness of the proposed algorithm.

Noise estimation and filtering method of MEMS gyroscope based on EMMAP

Aiming at the problems of low measurement accuracy,uncertainty and nonlinearity of random noise of the micro electro mechanical system(MEMS)gyroscope,a gyroscope noise estimation and filtering method is proposed,which combines expectation maximum(EM)with maximum a posterior(MAP)to form an adpative unscented Kalman filter(UKF),called EMMAP-UKF.According to the MAP estimation principle,a suboptimal unbiased MAP noise statistical estimation model is constructed.Then,EM algorithm is introduced to transform the noise estimation problem into the mathematical expectation maximization problem,which can dynamically adjust the variance of the observed noise.Finally,the estimation and filtering of gyroscope random drift error can be realized.The performance of the gyro noise filtering method is evaluated by Allan variance,and the effectiveness of the method is verified by hardware-in-the-loop simulation.

A maximum noise fraction transform with improved noise estimation for hyperspectral images

Feature extraction is often performed to reduce spectral dimension of hyperspectral images before image classification. The maximum noise fraction （MNF） transform is one of the most commonly used spectral feature extraction methods. The spectral features in several bands of hyperspectral images are submerged by the noise. The MNF transform is advantageous over the principle component （PC） transform because it takes the noise information in the spatial domain into consideration. However, the experiments described in this paper demonstrate that classification accuracy is greatly influenced by the MNF transform when the ground objects are mixed together. The underlying mechanism of it is revealed and analyzed by mathematical theory. In order to improve the performance of classification after feature extraction when ground objects are mixed in hyperspectral images, a new MNF transform, with an improved method of estimating hyperspectral image noise covariance matrix （NCM）, is presented. This improved MNF transform is applied to both the simulated data and real data. The results show that compared with the classical MNF transform, this new method enhanced the ability of feature extraction and increased classification accuracy.

Carrier frequency offset and impulse noise estimation for underwater acoustic orthogonal frequency division multiplexing

The carrier frequency offset（CFO）and impulse noise always affect the performance of underwater acoustic communication_systems.The CFO and impulse noise could be estimated by using the null subcarriers to cancel the effects of the two types of interference.The null subcarriers estimation methods include optimal separate estimation and joint estimation.The separate estimation firstly estimates the CFO value and then estimates the impulse noise value.However,the CFO and impulse noise always affect each other when either of them is estimated separately.The performance could be improved by using the joint estimation.The results of simulations and experiments have showed that these two optimization methods have good performance and the joint estimation has better performance than the separate estimation method.There is 3 dB performance gain at the BER value of 10^（-2）when using the joint estimation method.Thus these methods could improve the system robustness by using the CFO compensation and impulse noise suppression.

Noise estimation for deep sub-micron integrated circuits

Noise analysis and avoidance are an increasingly critical step in the design of deep sub-micron (DSM) integrated circuits (ICs). The crosstalk between neighboring interconnects gradually becomes the main noise sources in DSM ICs. We introduce an efficient and accurate noise-evaluation method for capacitively coupled nets of ICs. The method holds for a victim net with arbitrary number of aggressive nets under ramp input excitation. For common RC nets extracted by electronic design au-tomation (EDA) tools, the deviation between our method and HSPICE is under 10% .

Automatic estimation and removal of noise on digital image

An spatially adaptive noise detection and removal algorithm is proposed.Under the assumption that an observed image and its additive noise have Gaussian distribution,the noise parameters are estimated with local statistics from an observed degraded image,and the parameters are used to define the constraints on the noise detection process.In addition,an adaptive low-pass filter having a variable filter window defined by the constraints on noise detection is used to control the degree of smoothness of the reconstructed image.Experimental results demonstrate the capability of the proposed algorithm.

Noise level estimation method with application to EMD-based signal denoising

This paper proposes a new signal noise level estimation approach by local regions. The estimated noise variance is applied as the threshold for an improved empirical mode decomposition（EMD） based signal denoising method. The proposed estimation method can effectively extract the candidate regions for the noise level estimation by measuring the correlation coefficient between noisy signal and a Gaussian filtered signal. For the improved EMD based method, the situation of decomposed intrinsic mode function（IMFs） which contains noise and signal simultaneously are taken into account. Experimental results from two simulated signals and an X-ray pulsar signal demonstrate that the proposed method can achieve better performance than the conventional EMD and wavelet transform（WT） based denoising methods.

Joint DOA and polarization estimation for unequal power sources based on reconstructed noise subspace

In most literature about joint direction of arrival（DOA） and polarization estimation, the case that sources possess different power levels is seldom discussed. However, this case exists widely in practical applications, especially in passive radar systems. In this paper, we propose a joint DOA and polarization estimation method for unequal power sources based on the reconstructed noise subspace. The invariance property of noise subspace（IPNS） to power of sources has been proved an effective method to estimate DOA of unequal power sources. We develop the IPNS method for joint DOA and polarization estimation based on a dual polarized array. Moreover, we propose an improved IPNS method based on the reconstructed noise subspace, which has higher resolution probability than the IPNS method. It is theoretically proved that the IPNS to power of sources is still valid when the eigenvalues of the noise subspace are changed artificially. Simulation results show that the resolution probability of the proposed method is enhanced compared with the methods based on the IPNS and the polarimetric multiple signal classification（MUSIC） method. Meanwhile, the proposed method has approximately the same estimation accuracy as the IPNS method for the weak source.

Research on Restoration of Murals Based on Diffusion Model and Transformer

Due to the limitations of a priori knowledge and convolution operation,the existing image restoration techniques cannot be directly applied to the cultural relics mural restoration,in order to more accurately restore the original appearance of the cultural relics mural images,an image restoration based on the denoising diffusion probability model(Denoising Diffusion Probability Model(DDPM))and the Transformer method.The process involves two steps:in the first step,the damaged mural image is firstly utilized as the condition to generate the noise image,using the time,condition and noise image patch as the inputs to the noise prediction network,capturing the global dependencies in the input sequence through the multi-attentionmechanismof the input sequence and feedforward neural network processing,and designing a long skip connection between the shallow and deep layers in the Transformer blocks between the shallow and deep layers using long skip connections to fuse the feature information of global and local outputs to maintain the overall consistency of the restoration results;In the second step,taking the noisy image as a condition to direct the diffusion model to back sample to generate the restored image.Experiment results show that the PSNR and SSIM of the proposedmethod are improved by 2%to 9%and 1%to 3.3%,respectively,which are compared to the comparison methods.This study proposed synthesizes the advantages of the diffusionmodel and deep learningmodel to make themural restoration results more accurate.

HMM-based noise estimator for speech enhancement

A noise estimator was presented in this paper by modeling the log-power sequence with hidden Markov model （HMM）. The smoothing factor of this estimator was motivated by the speech presence probability at each frequency band. This HMM had a speech state and a nonspeech state, and each state consisted of a unique Gaussian function. The mean of the nonspeech state was the estimation of the noise logarithmic power. To make this estimator run in an on-line manner, an HMM parameter updated method was used based on a first-order recursive process. The noise signal was tracked together with the HMM to be sequentially updated. For the sake of reliability, some constraints were introduced to the HMM. The proposed algorithm was compared with the conventional ones such as minimum statistics （MS） and improved minima controlled recursive averaging （IM- CRA）. The experimental results confirms its promising performance.

Nonparametric VSS-APA based on precise background noise power estimate

The adaptive algorithm used for echo cancellation(EC) system needs to provide 1) low misadjustment and 2) high convergence rate. The affine projection algorithm(APA) is a better alternative than normalized least mean square(NLMS) algorithm in EC applications where the input signal is highly correlated. Since the APA with a constant step-size has to make compromise between the performance criteria 1) and 2), a variable step-size APA(VSS-APA) provides a more reliable solution. A nonparametric VSS-APA(NPVSS-APA) is proposed by recovering the background noise within the error signal instead of cancelling the a posteriori errors. The most problematic term of its variable step-size formula is the value of background noise power(BNP). The power difference between the desired signal and output signal, which equals the power of error signal statistically, has been considered the BNP estimate in a rough manner. Considering that the error signal consists of background noise and misalignment noise, a precise BNP estimate is achieved by multiplying the rough estimate with a corrective factor. After the analysis on the power ratio of misalignment noise to background noise of APA, the corrective factor is formulated depending on the projection order and the latest value of variable step-size. The new algorithm which does not require any a priori knowledge of EC environment has the advantage of easier controllability in practical application. The simulation results in the EC context indicate the accuracy of the proposed BNP estimate and the more effective behavior of the proposed algorithm compared with other versions of APA class.

A new information fusion white noise deconvolution estimator

The white noise deconvolution or input white noise estimation problem has important applications in oil seismic exploration, communication and signal processing. By the modern time series analysis method, based on the autoregressive moving average （ARMA） innovation model, a new information fusion white noise deconvolution estimator is presented for the general multisensor systems with different local dynamic models and correlated noises. It can handle the input white noise fused filtering, prediction and smoothing problems, and it is applicable to systems with colored measurement noises. It is locally optimal, and is globally suboptimal. The accuracy of the fuser is higher than that of each local white noise estimator. In order to compute the optimal weights, the formula computing the local estimation error cross-covariances is given. A Monte Carlo simulation example for the system with Bernoulli-Gaussian input white noise shows the effectiveness and performances.

INFORMATION FUSION STEADY-STATE WHITE NOISE DECONVOLUTION ESTIMATORS WITH TIME-DELAYED MEASUREMENTS AND COLORED MEASUREMENT NOISES

White noise deconvolution or input white noise estimation problem has important appli-cation backgrounds in oil seismic exploration,communication and signal processing.By the modern time series analysis method,based on the Auto-Regressive Moving Average(ARMA) innovation model,under the linear minimum variance optimal fusion rules,three optimal weighted fusion white noise deconvolution estimators are presented for the multisensor systems with time-delayed measurements and colored measurement noises.They can handle the input white noise fused filtering,prediction and smoothing problems.The accuracy of the fusers is higher than that of each local white noise estimator.In order to compute the optimal weights,the formula of computing the local estimation error cross-covariances is given.A Monte Carlo simulation example for the system with 3 sensors and the Bernoulli-Gaussian input white noise shows their effectiveness and performances.

SPEECH ENHANCEMENT USING CONSTRAINED SPECTRAL AMPLITUDE SUBTRACTION BASED ON NONCAUSAL A PRIORI SNR

Two gain forms of spectral amplitude subtraction are derived theoretically without neglecting the correlation of speech and noise spectrum during the period of a fralne. In the implementation, the constrained gain is expressed as a function of noncausal a priori SNR （Signal-to-Noise Ratio）. Noise and noncausal a priori SNR are estimated from the multitaper spectrum of the noisy signal with algorithms modified to be suitable for the multitaper spectruln. Objective evaluations show that in case of white Gaussian noise the proposed method outperforms some methods based on LSA （Log Spectral Amplitude） in terms of MBSD （Modified Bark Spectral Distortion）, segmental SNR and overall SNR, and informal listening tests show that speech reconstructed in this way has little speech distortion and musical noise is nearly inaudible even at low SNR.

Application of Adaptive Divided Difference Filter on GPS/IMU Integrated Navigation System

The efficient and accurate approximate nonlinear filters have been widely used in the estimation of states and parameters of dynamical systems. In this paper, an adaptive divided difference filter is designed for precise estimation of states and parameters of micromechanical gyro navigation system. Based on the investigation of nonlinear divided difference filter the adaptive divided difference filter(ADDF) was designed, which takes account of the incorrect time-varying noise statistics of dynamical systems and compensation of the nonlinearity effects neglected by linearization. And its performance is superior to that of DDF and extended Kalman filter(EKF). Simulation results indicate that the advantages of the proposed nonlinear filters make them attractive alternatives to the extended Kalman filter.

Self-tuning weighted measurement fusion Kalman filter and its convergence

For multisensor systems,when the model parameters and the noise variances are unknown,the consistent fused estimators of the model parameters and noise variances are obtained,based on the system identification algorithm,correlation method and least squares fusion criterion.Substituting these consistent estimators into the optimal weighted measurement fusion Kalman filter,a self-tuning weighted measurement fusion Kalman filter is presented.Using the dynamic error system analysis （DESA） method,the convergence of the self-tuning weighted measurement fusion Kalman filter is proved,i.e.,the self-tuning Kalman filter converges to the corresponding optimal Kalman filter in a realization.Therefore,the self-tuning weighted measurement fusion Kalman filter has asymptotic global optimality.One simulation example for a 4-sensor target tracking system verifies its effectiveness.

Decoupled Wiener state fuser for descriptor systems

By the modem time series analysis method, based on the autoregressive moving average （ARMA） innovation models and white noise estimation theory, using the optimal fusion rule weighted by diagonal matrices, a distributed descriptor Wiener state fuser is presented by weighting the local Wiener state estimators for the linear discrete stochastic descriptor systems with multisensor. It realizes a decoupled fusion estimation for state components. In order to compute the optimal weights, the formulas of computing the cross-covariances among local estimation errors are presented based on cross-covariances among the local innovation processes, input white noise, and measurement white noises. It can handle the fused filtering, smoothing, and prediction problems in a unified framework. Its accuracy is higher than that of each local estimator. A Monte Carlo simulation example shows its effectiveness and correctness.

The frequency estimation of harmonic signals embedded in multiplicative and additive noise

A method to separate a harmonic signal from multiplicative and additive noises is proposed. The method is to square the signal x(t), which consists of a harmonic signal embedded in multiplicative and additive noises, to form another signal y(t) = x2(t)-E[x2(t)]. After y(t) having been gotten, the Fourier transform is imposed on it. Because the information of x(t) (especially about frequency) is included in y(t), the frequency of x(t) can be estimated from the power spectrum of y(t). According to the simulation, under the condition where frequencies divided by resolution dω are integer, the maximum relative error of estimated frequencies is less than 0.4% when the signal-to-noise ratio (SNR) is greater than -23 dB. If frequencies divided by resolution dω are not integer, the maximum relative error will be less than 2.9%. But it is still small in terms of engineering.

A noise cross PSD estimator for dual-microphone speech enhancement based on minimum statistics

Some two-microphone noise reduction techniques that work in the frequency domain exploit coherence function between two noisy signals. They have shown good results when noise signals on two sensors are uncorrelated, but their per-formance decreases with correlated noises. Coherence based methods can be improved when the cross power spectral density (CPSD) of correlated noise signals is available. In this paper, we propose a new method for estimation of the CPSD of the noise, which is based on the minimum tracking technique. Despite the fact that the proposed estimator does not need to implement a voice activity detector (VAD), its performance is comparable to a CPSD estimator that uses an ideal VAD.

A robust optimization method for label noisy datasets based on adaptive threshold: Adaptive-k

The use of all samples in the optimization process does not produce robust results in datasets with label noise.Because the gradients calculated according to the losses of the noisy samples cause the optimization process to go in the wrong direction.In this paper,we recommend using samples with loss less than a threshold determined during the optimization,instead of using all samples in the mini-batch.Our proposed method,Adaptive-k,aims to exclude label noise samples from the optimization process and make the process robust.On noisy datasets,we found that using a threshold-based approach,such as Adaptive-k,produces better results than using all samples or a fixed number of low-loss samples in the mini-batch.On the basis of our theoretical analysis and experimental results,we show that the Adaptive-k method is closest to the performance of the Oracle,in which noisy samples are entirely removed from the dataset.Adaptive-k is a simple but effective method.It does not require prior knowledge of the noise ratio of the dataset,does not require additional model training,and does not increase training time significantly.In the experiments,we also show that Adaptive-k is compatible with different optimizers such as SGD,SGDM,and Adam.The code for Adaptive-k is available at GitHub.