Removing Random-Valued Impulse Noises by a Two-Staged Nonlinear Filtering Method

Digital images are frequently contaminated by impulse noise(IN)during acquisition and transmission.The removal of this noise from images is essential for their further processing.In this paper,a two-staged nonlinear filtering algorithm is proposed for removing random-valued impulse noise(RVIN)from digital images.Noisy pixels are identified and corrected in two cascaded stages.The statistics of two subsets of nearest neighbors are employed as the criterion for detecting noisy pixels in the first stage,while directional differences are adopted as the detector criterion in the second stage.The respective adaptive median values are taken as the replacement values for noisy pixels in each stage.The performance of the proposed method was compared with that of several existing methods.The experimental results show that the performance of the suggested algorithm is superior to those of the compared methods in terms of noise removal,edge preservation,and processing time.

Applying nonlinear filtering in reverberation time measurement under strong background noise

Nonlinear filtering of impulse response obtained by M-sequence correlation method under strong background noise is presented. The research shows that the new method works very efficiently without the need to cut off impulse response data. Even if the ratio of signal to noise is below -15 dB, the same decay curve ranges can still be obtained as when S/N > 40

An Optimized Implementation of a Novel Nonlinear Filter for Color Image Restoration

Image processing is becoming more popular because images are being used increasingly in medical diagnosis,biometric monitoring,and character recognition.But these images are frequently contaminated with noise,which can corrupt subsequent image processing stages.Therefore,in this paper,we propose a novel nonlinear filter for removing“salt and pepper”impulsive noise from a complex color image.The new filter is called the Modified Vector Directional Filter(MVDF).The suggested method is based on the traditional Vector Directional Filter(VDF).However,before the candidate pixel is processed by the VDF,theMVDF employs a threshold and the neighboring pixels of the candidate pixel in a 3×3 filter window to determine whether it is noise-corrupted or noise-free.Several reference color images corrupted by impulsive noise with intensities ranging from 3%to 20%are used to assess theMVDF’s effectiveness.The results of the experiments show that theMVDF is better than the VDF and the Generalized VDF(GVDF)in terms of the PSNR(Peak Signal-to-Noise Ratio),NCD(Normalized Color Difference),and execution time for the denoised image.In fact,the PSNR is increased by 6.554%and 12.624%,the NCD is decreased by 20.273%and 44.147%,and the execution time is reduced by approximately a factor of 3 for the MVDF relative to the VDF and GVDF,respectively.These results prove the efficiency of the proposed filter.Furthermore,a hardware design is proposed for the MVDF using the High-Level Synthesis(HLS)flow in order to increase its performance.This design,which is implemented on the Xilinx ZynqXCZU9EG Field-ProgrammableGate Array(FPGA),allows the restoration of a 256×256-pixel image in 2 milliseconds(ms)only.

Nonlinear Teager-Kaiser Infomax Boost Clustering Algorithm for Brain Tumor Detection Technique

Brain tumor detection and division is a difficult tedious undertaking in clinical image preparation.When it comes to the new technology that enables accurate identification of the mysterious tissues of the brain,magnetic resonance imaging(MRI)is a great tool.It is possible to alter the tumor’s size and shape at any time for any number of patients by using the Brain picture.Radiologists have a difficult time sorting and classifying tumors from multiple images.Brain tumors may be accurately detected using a new approach called Nonlinear Teager-Kaiser Iterative Infomax Boost Clustering-Based Image Segmentation(NTKFIBC-IS).Teager-Kaiser filtering is used to reduce noise artifacts and improve the quality of images before they are processed.Different clinical characteristics are then retrieved and analyzed statistically to identify brain tumors.The use of a BraTS2015 database enables the proposed approach to be used for both qualitative and quantitative research.This dataset was used to do experimental evaluations on several metrics such as peak signal-to-noise ratios,illness detection accuracy,and false-positive rates as well as disease detection time as a function of a picture count.This segmentation delivers greater accuracy in detecting brain tumors with minimal time consumption and false-positive rates than current stateof-the-art approaches.

Major Development Under Gaussian Filtering Since Unscented Kalman Filter

Filtering is a recursive estimation of hidden states of a dynamic system from noisy measurements.Such problems appear in several branches of science and technology,ranging from target tracking to biomedical monitoring.A commonly practiced approach of filtering with nonlinear systems is Gaussian filtering.The early Gaussian filters used a derivative-based implementation,and suffered from several drawbacks,such as the smoothness requirements of system models and poor stability.A derivative-free numerical approximation-based Gaussian filter,named the unscented Kalman filter(UKF),was introduced in the nineties,which offered several advantages over the derivativebased Gaussian filters.Since the proposition of UKF,derivativefree Gaussian filtering has been a highly active research area.This paper reviews significant developments made under Gaussian filtering since the proposition of UKF.The review is particularly focused on three categories of developments:i)advancing the numerical approximation methods;ii)modifying the conventional Gaussian approach to further improve the filtering performance;and iii)constrained filtering to address the problem of discrete-time formulation of process dynamics.This review highlights the computational aspect of recent developments in all three categories.The performance of various filters are analyzed by simulating them with real-life target tracking problems.

Skew t Distribution-Based Nonlinear Filter with Asymmetric Measurement Noise Using Variational Bayesian Inference

This paper is focused on the state estimation problem for nonlinear systems with unknown statistics of measurement noise.Based on the cubature Kalman filter,we propose a new nonlinear filtering algorithm that employs a skew t distribution to characterize the asymmetry of the measurement noise.The system states and the statistics of skew t noise distribution,including the shape matrix,the scale matrix,and the degree of freedom(DOF)are estimated jointly by employing variational Bayesian(VB)inference.The proposed method is validated in a target tracking example.Results of the simulation indicate that the proposed nonlinear filter can perform satisfactorily in the presence of unknown statistics of measurement noise and outperform than the existing state-of-the-art nonlinear filters.

Optimal State Estimation and Fault Diagnosis for a Class of Nonlinear Systems

This study proposes a scheme for state estimation and,consequently,fault diagnosis in nonlinear systems.Initially,an optimal nonlinear observer is designed for nonlinear systems subject to an actuator or plant fault.By utilizing Lyapunov's direct method,the observer is proved to be optimal with respect to a performance function,including the magnitude of the observer gain and the convergence time.The observer gain is obtained by using approximation of Hamilton-Jacobi-Bellman(HJB)equation.The approximation is determined via an online trained neural network(NN).Next a class of affine nonlinear systems is considered which is subject to unknown disturbances in addition to fault signals.In this case,for each fault the original system is transformed to a new form in which the proposed optimal observer can be applied for state estimation and fault detection and isolation(FDI).Simulation results of a singlelink flexible joint robot(SLFJR)electric drive system show the effectiveness of the proposed methodology.

A Hybrid Nonlinear Active Noise Control Method Using Chebyshev Nonlinear Filter

Investigations into active noise control(ANC)technique have been conducted with the aim of effective control of the low-frequency noise.In practice,however,the performance of currently available ANC systems degrades due to the effects of nonlinearity in the primary and secondary paths,primary noise and louder speaker.This paper proposes a hybrid control structure of nonlinear ANC system to control the non-stationary noise produced by the rotating machinery on the nonlinear primary path.A fast version of ensemble empirical mode decomposition is used to decompose the non-stationary primary noise into intrinsic mode functions,which are expanded using the second-order Chebyshev nonlinear filter and then individually controlled.The convergence of the nonlinear ANC system is also discussed.Simulation results demonstrate that proposed method outperforms the FSLMS and VFXLMS algorithms with respect to noise reduction and convergence rate.

A Review of Nonlinear Kalman Filter Appling to Sensorless Control for AC Motor Drives

Sensorless control of AC motor drives,which takes the advantages of cost saving,higher reliability,and less hardware,has been developed for several decades.Among the existing speed sensorless control methods,nonlinear Kalman filter-based one has attached widespread attention due to its superb estimation accuracy and inherent resistibility to noise.However,the determination of noise covariance matrix and robustness of model uncertainties are still open issues in practice.A great number of studies try to solve these problems in resent years.This paper reviews the application of extended Kalman filter(EKF),unscented Kalman filter(UKF),and cubature Kalman filter(CKF)in speed sensorless control for AC motor drives.As an iterative algorithm,EKF has advantages in processor implementation.However,EKF suffers from the linearization error and model uncertainties when applying to sensorless control system.This paper presents the predominant improvements of EKF which is also applicative in UKF and CKF mostly.

Debiased conversion measurements based target tracking with direction cosine measurements

Phased array radar’s measurements include two direction cosine and range measurements,which can be obtained in the direction cosine coordinates.State equation of the target is nonlinear with the measurements and in order to solve the nonlinear problem,debiased conversion measurements based target tracking with direction cosine and range measurements in direction cosine coordinates named DCMKFPreDcos is proposed first in this paper,where the predicted information is introduced to calculate the converted measurement errors’statistical characteristics to eliminate the correlation between measurement noise and the converted measurement errors covariance.When range rate information can be obtained further,based on the above DCMKF-PreDcos’filtering result,the sequential filtering is adopted to process the additional range rate measurement and the DCMKF-PreDcos algorithm with extra range rate information is given.The predicted information is also introduced to calculate the involved statistical characteristics of converted measurements.The effectiveness of the proposed algorithms is shown in simulation results.

Measure of nonlinearity for underwater target tracking using hull-mounted sensor

Purpose-Doppler-Bearing Tracking(DBT)is commonly used in target tracking applications for the underwater environment using the Hull-Mounted Sensor(HMS).It is an important and challenging problem in an underwater environment.Design/methodology/approach-The system nonlinearity in an underwater environment increases due to several reasons such as the type of measurements taken,the speeds of target and observer,environmental conditions,number of sensors considered for measurements and so on.Degrees of nonlinearity(DoNL)for these problems are analyzed using a proposed measure of nonlinearity(MoNL)for state estimation.Findings-In this research,the authors analyzed MoNL for state estimation and computed the conditional MoNL(normalized)using different filtering algorithms where measurements are obtained from a single sensor array(i.e.HMS).MoNL is implemented to find out the system nonlinearity for different filtering algorithms and identified how much nonlinear the system is,that is,to measure nonlinearity of a problem.Originality/value-Algorithms are evaluated for various scenarios with different angles on the target bow(ATB)in Monte-Carlo simulation.Computation of root mean squared(RMS)errors in position and velocity is carried out to assess the state estimation accuracy using MATLAB.

A solution of UAV localization problem using an interacting multiple nonlinear fuzzy adaptive H_(∞)models filter algorithm

The purpose of this research is to improve the robustness of the autonomous system in order to improve the position and velocity estimation of an Unmanned Aerial Vehicle(UAV).Therefore, new integrated SINS/GPS navigation scheme based on Interacting Multiple Nonlinear Fuzzy Adaptive H_∞ Models(IMM-NFAH_∞) filtering technique for UAV is presented. The proposed IMM-NFAH_∞ strategy switches between two different Nonlinear Fuzzy Adaptive H_∞(NFAH_∞) filters and each NFAH_∞ filter is based on different fuzzy logic inference systems. The newly proposed technique takes into consideration the high order Taylor series terms and adapts the nonlinear H_∞ filter based on different fuzzy inference systems via adaptive filter bounds(di),along with disturbance attenuation parameter c. Simulation analysis validates the performance of the proposed algorithm, and the comparison with nonlinear H_∞(NH_∞) filter and that with different NFAH_∞ filters demonstrate the effectiveness of UAV localization utilizing IMM-NFAH_∞ filter.

Convergence Analysis of Splitting-Up Algorithm of the Zakai’s Equation with Correlated Noises

In the field of nonlinear filtering(NLF),it is well-known that the unnormalized conditional density of the states satisfies the Zakai’s equation.The splitting-up algorithm has been first studied in the independent noises case by Bensoussan,et al.(1990).In this paper,the authors extend this convergence analysis of the splitting-up algorithm to the correlated noises’case.Given a time discretization,one splits the solution of the Zakai’s equation into two interlacing processes(with possibly computational advantage).These two processes correspond respectively to the prediction and updating.Under certain conditions,the authors show that both processes tend to the solution of the Zakai’s equation,as the time step goes to zero.The authors specify the conditions imposed on the way of splitting-up to guarantee the convergence.The major technical difficulty in the correlated noises’case,compared with the independent case,is to control the gradient of the second process in some sense.To illustrate the potentially computational advantage of the schemes based on the splitting-up ways,the authors experiment on a toy NLF model using the feedback particle filter(FPF)developed based on the splitting-up method and the sampling importance and resampling(SIR)as comparison.The FPF outperforms in both accuracy and efficiency.

Ice bottom evolution derived from thermistor string-based ice mass balance buoy observations

Digital information on sea ice extent,thickness,volume,and distribution is crucial for understanding Earth's climate system.The Snow and Ice Mass Balance Apparatus(SIMBA)is used to determine snow and ice temperatures in Arctic,Antarctic,ice-covered seas,and boreal lakes.Snow depth and ice thickness are derived from SIMBA temperature regimes(SIMBA_ET and SIMBA_HT).In warm conditions,SiMBA_ET temperature-based ice thickness may have errors due to the isothermal vertical profile.SIMBA_HT provides a visible ice-bottom interface for manual quantification.We propose an unmanned approach,combining neural networks,wavelet analysis,and Kalman filtering(NWK),to mathematically establish NwK and retrieve ice bottoms from various SIMBA_HT datasets.In the Arctic,NWK-derived total thickness showed a bias range of-5.64 cm to 4.01 cm and a correlation coefficient of 95%-99%.For Baltic Sea ice,values ranged from 1.31 cm to 2.41 cm(88%-98%correlation),and for boreal lake ice,-0.7 cm to 2.6 cm(75%-83%correlation).During ice growth,thermal equilibrium,and melting,the bias varied from-3.93 cm to 2.37 cm,-1.92 cm to 0.04 cm,and-4.90 cm to 3.96 cm,with correlation coefficients of 76%-99%.These results demonstrate NWK's robustness in retrieving ice bottom evolution in different water environments.

Real-Time Optimal State Estimation-Based Feedback Control for Stochastic Quantum Systems in the Non-Markovian Case

This paper studies the real-time optimal state estimation-based feedback control for twolevel stochastic quantum systems in the non-Markovian case.The system model is established by combining the time-convolutionless non-Markovian master equation and the stochastic master equation.A nonlinear filter based on the state-dependent Riccati equation is designed in order to achieve the realtime optimal estimation of quantum states.A quadratic function multiplied with an exponential term is selected as the Lyapunov function,and a continuous-time control law is deduced via the stochastic Lyapunov stability theorem to realize eigenstate feedback control based on real-time optimal state estimation.Numerical simulation results illustrate that the proposed control scheme is capable of steering the two-level quantum system from an arbitrary initial state to the desired eigenstate with a fidelity higher than 99%within a time of 3 a.u.

A novel strong tracking cubature Kalman filter and its application in maneuvering target tracking

The fading factor exerts a significant role in the strong tracking idea. However, traditional fading factor introduction method hinders the accuracy and robustness advantages of current strong-tracking-based nonlinear filtering algorithms such as Cubature Kalman Filter(CKF) since traditional fading factor introduction method only considers the first-order Taylor expansion. To this end, a new fading factor idea is suggested and introduced into the strong tracking CKF method.The new fading factor introduction method expanded the number of fading factors from one to two with reselected introduction positions. The relationship between the two fading factors as well as the general calculation method can be derived based on Taylor expansion. Obvious superiority of the newly suggested fading factor introduction method is demonstrated according to different nonlinearity of the measurement function. Equivalent calculation method can also be established while applied to CKF. Theoretical analysis shows that the strong tracking CKF can extract the thirdorder term information from the residual and thus realize second-order accuracy. After optimizing the strong tracking algorithm process, a Fast Strong Tracking CKF(FSTCKF) is finally established. Two simulation examples show that the novel FSTCKF improves the robustness of traditional CKF while minimizing the algorithm time complexity under various conditions.

Remote Sensing Image Registration Based on Improved KAZE and BRIEF Descriptor

Remote sensing image registration is still a challenging task owing to the significant influence of nonlinear differences between remote sensing images.To solve this problem,this paper proposes a novel approach with regard to feature-based remote sensing image registration.There are two key contributions:1)we bring forward an improved strategy of composite nonlinear diffusion filtering according to the scale factors in multi-scale space and 2)we design a gradually decreasing resolution of multi-scale pyramid space.And a binary code string is served as feature descriptors to improve matching efficiency.Extensive experiments of different categories of remote image datasets on feature extraction and feature registration are performed.The experimental results demonstrate the superiority of our proposed scheme compared with other classical algorithms in terms of correct matching ratio,accuracy and computation efficiency.

Properties of a general quaternion-valued gradient operator and its applications to signal processing

The gradients of a quaternion-valued function are often required for quaternionic signal processing algorithms.The HR gradient operator provides a viable framework and has found a number of applications.However,the applications so far have been limited to mainly real-valued quaternion functions and linear quaternionvalued functions.To generalize the operator to nonlinear quaternion functions,we define a restricted version of the HR operator,which comes in two versions,the left and the right ones.We then present a detailed analysis of the properties of the operators,including several different product rules and chain rules.Using the new rules,we derive explicit expressions for the derivatives of a class of regular nonlinear quaternion-valued functions,and prove that the restricted HR gradients are consistent with the gradients in the real domain.As an application,the derivation of the least mean square algorithm and a nonlinear adaptive algorithm is provided.Simulation results based on vector sensor arrays are presented as an example to demonstrate the effectiveness of the quaternion-valued signal model and the derived signal processing algorithm.

Target tracking methods based on a signal-to-noise ratio model

In traditional target tracking methods,the angle error and range error are often measured by the empirical value,while observation noise is a constant.In this paper,the angle error and range error are analyzed.They are influenced by the signalto-noise ratio(SNR).Therefore,a model related to SNR has been established,in which the SNR information is applied for target tracking.Combined with an advanced nonlinear filter method,the extended Kalman filter method based on the SNR model(SNR-EKF)and the unscented Kalman filter method based on the SNR model(SNR-UKF)are proposed.There is little difference between the SNR-EKF and SNR-UKF methods in position precision,but the SNR-EKF method has advantages in computation time and the SNR-UKF method has advantages in velocity precision.Simulation results show that target tracking methods based on the SNR model can greatly improve the tracking performance compared with traditional tracking methods.The target tracking accuracy and convergence speed of the proposed methods have significant improvements.

Variational Bayesian Kalman filter using natural gradient

We propose a technique based on the natural gradient method for variational lower bound maximization for a variational Bayesian Kalman filter.The natural gradient approach is applied to the Kullback-Leibler divergence between the parameterized variational distribution and the posterior density of interest.Using a Gaussian assumption for the parametrized variational distribution,we obtain a closed-form iterative procedure for the Kullback-Leibler divergence minimization,producing estimates of the variational hyper-parameters of state estimation and the associated error covariance.Simulation results in both a Doppler radar tracking scenario and a bearing-only tracking scenario are presented,showing that the proposed natural gradient method outperforms existing methods which are based on other linearization techniques in terms of tracking accuracy.