Hard Thresholding Research Articles

Fiber Vector Eigenmode Multiplexing Based High Capacity Transmission Over 5-km FMF With Kramers-Kronig Receiver

Vector modes (VMs) with spatially nonhomogeneous polarization patterns, combining polarization and spatial-mode degrees of freedom together, are regarded as the eigenmodes of optical fiber. Such eigenmodes have potential to be used to implement the high capacity spatial division multiplexing (SDM)/mode division multiplexing (MDM) based optical fiber communication systems. Here, we respectively demonstrate 2 VMs of the same order (l = +2, EH11o and EH11e modes) and 2 VMs of different orders (l = 0, HE11o mode and l = +2, EH11e mode) multiplexing transmissions over 5-km few-mode fiber (FMF). The mode crosstalk after FMF transmission has been minimized to prepare high capacity signal transmission without multiple-input-multiple-output (MIMO) digital signal processing (DSP). To increase the transmission capacity and decrease the system cost, the Kramers-Kronig (KK) receiver has been employed and the single-wavelength two sets of eigenmodes multiplexed 360 Gbit/s and 400 Gbit/s signal transmissions over 5-km FMF link are realized, respectively. Then, to further burst the transmission capacity, 2 vector-mode-division-multiplexing channels (HE11o and EH11e modes) in combination of 5 wavelength-division-multiplexing (WDM) channels with a total of 10 parallel channels have been demonstrated. A total data rate of 1.12 Tbit/s with 28 GBaud 16-state quadrature amplitude modulation (QAM) signal has been realized over the 5-km FMF. In all data-carrying experimental demonstrations, the bit-error rate (BER) performance of each VM channel is below the 7% hard decision forward error correction threshold (FEC) at BER of 3.8 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> . The experimental results highlight that the VMDM-based optical transmission technology could find enormous potential in huge-capacity short-reach optical interconnects.

The Analytic of Image Processing Smoothing Spaces Using Wavelet

Image analysis took wide areas in many fields, including medicine, physics, and other areas where you need a tool to deal with it smoothly and softly without losing the original image information. Using an image of a sample of a physical atom that was analyzed and highlighting the compression and raising the noise, histogram and statistics the image statistics where the best results were recorded when using a specific threshold i.e. when pressing the methods were used the first has the threshold methods is Balance sparsity-norm, Remove near 0 and Bal-sparsity-norm(sqrt). As for the methods of raising the noise are fixed form thresholding method with soft threshold, penalize high with hard threshold, penalize medium with hard threshold, penalize low with hard threshold, Bal sparsity norm (sqrt) with soft threshold, where image parameters were divided into approximation coefficients and details coefficients. Through the analysis, a suitable threshold value was obtained, which helps to restore energy that leads to the fact that the compressed necessity did not lose much of its original information, which proves the new wavelets in the field of physical and medical imaging.

EFFECT OF WAVELET DE-NOISING ON THE CLASSIFICATION OF PIG BEHAVIOUR

To efficiently eliminate the noise generated by the triaxial accelerometer when collecting pigs’ behavioural data, this paper adopted SNR and MSE as the indexes to evaluate the de-noising effect of pigs’ acceleration signal under various combinations of wavelet basis, decomposition layer, threshold rule and threshold function. Based on the optimal wavelet parameter combinations, the de-noised data were divided into a training dataset and test dataset to conduct a 3-fold cross validation. The results showed that Db4 wavelet can achieve a satisfactory de-noising effect when used as a wavelet basis for 8 layers wavelet decomposition based on Rigrsure threshold rules and the new improved threshold function. As a result, compared with traditional wavelet hard threshold de-noising, soft threshold de-noising and EMD de-noising method, the improved threshold function improved the stability of signal filtering, which was shown to be more practical, effective and feasible. As such, wavelet de-noising was found to significantly improve the classification accuracy of all four behaviour classes (lying, standing, walking and exploring) considered for this study, and the overall major mean accuracy was improved from 0.680 to 0.826.

Reliability modeling for multistage systems subject to competing failure processes

AbstractIn this paper, a novel multistage reliability model is provided as systems are often divided into many stages according to system degradation characteristics. Multistage hard failure (caused by random shock) process (MHFP) and multistage soft failure (caused by random shock and continuous degradation) process (MSFP) are introduced to describe the competing failure processes, where either the MSFP or MHFP would break down the system. The shock processes impact the system in three ways: (1) fatal load shocks cause hard failure immediately in the hard failure process; (2) time shocks cause a hard failure threshold changing; (3) damage load shocks cause degradation level increasing in the soft failure process. In this paper, a density function dispersion method is carried out to address the multistage reliability model, and the effectiveness of the proposed models is demonstrated by reliability analysis with the one‐stage model. Finally, the multistage model is applied to a case study, the degradation process is divided into three stages, and the hard failure threshold can be transmitted twice. The proposed model can be applied in other multistage situations, and the calculation method can satisfy the accuracy requirements.

Denoising of LCR Wave Signal of Residual Stress for Rail Surface Based on Lifting Scheme Wavelet Packet Transform

According to the acousto elastic effect, the residual stress on the surface of the rail can be evaluated by measuring the change in the propagation velocity of ultrasonic waves, such as longitudinal critically refracted (LCR) waves on the surface of the rail. The LCR wave signal is often polluted by a variety of noise sources, coupled with the influence of the poor surface condition of the inspected component, which greatly reduces the detectability and online measurement ability of the LCR wave signal. This paper proposes the application of the lifting scheme wavelet packet transform (LSWPT) denoising method to solve the noise suppression problem of LCR wave signal. The traditional wavelet transform (WT), wavelet packet transform (WPT), as well as the lifting scheme wavelet transform (LSWT) and lifting scheme wavelet packet transform are compared and analyzed in the soft thresholding and hard thresholding processing of denoising ability and efficiency of the noisy LCR wave signal. The experimental results show that the LSWPT method has the characteristics of fast calculation speed and a good denoising effect, and it is an efficient method of denoising signals for on-line ultrasonic measurement of residual stress on the rail surface.

An improved denoise method based on EEMD and optimal wavelet threshold for model building of OPAX

To improve the accuracy of Operational Path Analysis with Exogeneous Inputs (OPAX) model by excluding the noise interference sufficiently in the vehicle operating condition data (time-domain vibration signal), the combined noise reduction method of Ensemble Empirical Mode Decomposition (EEMD) and wavelet threshold was used. Since the noise content of each noisy intrinsic mode functions (IMFs) decomposed by EEMD is uncertain, the effective signal element in the less noisy IMFs affects the accuracy of the first-layer wavelet coefficients to estimate the noise variance, the EEMD and wavelet particle swarm optimization sample entropy threshold denoising (EEMD-WPSE) method is presented in terms of information entropy. In this method, the sample entropy of the eliminated noise is used as the information cost function, together with the particle swarm optimization algorithm to find the optimal wavelet threshold of each high-frequency noisy IMFs. After denoising the simulation signal, it is found that the combination of EEMD-WPSE threshold with hard threshold function, soft threshold function and half-soft threshold function identifying higher SNR and lower RMSE, are given to demonstrate the higher universality of the proposed method. The method is applied to the noise reduction processing of the automobile operating condition data for constructing the OPAX model, and the degree of similarity between the synthesized responses of the care-target point obtained by the OPAX model and the measured responses under the second order operational condition are observed, as it turned out, the calculation results of SNR and RMSE indicated that EEMD-WPSE can better promote the accuracy of OPAX model in terms of noise reduction.

Reliability analysis for systems subject to mutually dependent degradation and shock processes

This paper studies the reliability problem for systems subject to two types of dependent competing failure processes, that is, soft failure and hard failure processes. A soft failure happens when the total degradation of the system exceeds a given critical level, while a hard failure occurs when the accumulative shock load caused by shocks surpasses the hard failure threshold. These two failure processes are mutually dependent due to the fact that external shocks will bring sudden increments in the degradation of the system, and the total amount of degradation will decrease the hard failure threshold of the system. The system fails whenever either of these two failure modes happens. Assuming that the arrival of shocks follows a Poisson process, the reliability function of the system under cumulative shock model is derived by using some analytical techniques. Some important reliability indices, including the mean lifetime of the system, the expected number of shocks until system failure, the probabilities of soft and hard failures, are calculated explicitly. Moreover, a special case that the hard failure process and soft failure process are mutually independent is also discussed. Monte Carlo method is employed to calculate the multiple integrals existing in the expressions of reliability function and reliability indices. A numerical example of the Reinforced Concrete pier columns on sea bridge is presented to illustrate the proposed model.

Learning physically consistent differential equation models from data using group sparsity.

We propose a statistical learning framework based on group-sparse regression that can be used to (i) enforce conservation laws, (ii) ensure model equivalence, and (iii) guarantee symmetries when learning or inferring differential-equation models from data. Directly learning interpretable mathematical models from data has emerged as a valuable modeling approach. However, in areas such as biology, high noise levels, sensor-induced correlations, and strong intersystem variability can render data-driven models nonsensical or physically inconsistent without additional constraints on the model structure. Hence, it is important to leverage prior knowledge from physical principles to learn biologically plausible and physically consistent models rather than models that simply fit the data best. We present the group iterative hard thresholding algorithm and use stability selection to infer physically consistent models with minimal parameter tuning. We show several applications from systems biology that demonstrate the benefits of enforcing priors in data-driven modeling.

An Advanced Artificial Intelligence System for Investigating Tropical Cyclone Rapid Intensification with the SHIPS Database

Currently, most tropical cyclone (TC) rapid intensification (RI) prediction studies are conducted based on a subset of the SHIPS database using a relatively simple model structure. However, variables (features) in the SHIPS database are built upon human expertise in TC intensity studies based on hard and subjective thresholds, and they should be explored thoroughly to make full use of the expertise. Based on the complete SHIPS data, this study constructs a complicated artificial intelligence (AI) system that handles feature engineering and selection, imbalance, prediction, and hyper parameter-tuning, simultaneously. The complicated AI system is used to further improve the performance of the current studies in RI prediction, and to identify other essential SHIPS variables that are ignored by previous studies with variable importance scores. The results outperform most of the earlier studies by approximately 21–50% on POD (Probability Of Detection) with reduced FAR (False Alarm Rate). This study built a baseline for future work on new predictor identification with more complicated AI techniques.

Evaluation of fractured–vuggy reservoir by electrical imaging logging based on a de-noising method

The existence of fractures and vugs in igneous formation is a key factor to determine the productivity of oil and gas reservoirs. Fracture–vug plane porosity and porosity spectrum (fracture–vug parameters) are important parameters to evaluate the development of fractures and vugs. In the process of drilling, the bit forms shallow holes and scratches on the borehole wall which is characterized by pitting, strip and block noise in the electrical imaging logging static image. The background noise affects the identification of fractures and vugs and the extraction of parameters. It is found that the background noise mainly exists in the high-frequency conductivity data. In order to suppress the background noise, empirical mode decomposition is applied to conductivity data of electrical imaging logging, and the wavelet hard threshold de-noising is applied to high-frequency intrinsic mode function components. The de-noising fracture–vug parameters have a good correspondence with the electrical imaging logging static image, and have a better linear relationship with the core porosity. These illustrate that the application of the de-noising method in the electrical imaging logging is reasonable and effective. The de-noising porosity spectrum becomes narrower in the reservoir with poor fractures and vugs, which can reveal the development of secondary pores more clearly. In reservoir interpretation, the de-noising fracture–vug plane porosity and porosity spectrum have good consistency with conventional and acoustic logging data, which can effectively evaluate the fractures and vugs in reservoirs.

Iterative Hard Thresholding with Combined Variable Step Size &amp; Momentum-Based Estimator for Wireless Communication Systems with Dynamic Sparse Channels

The channel of the broadband wireless communications system can be modeled as a dynamic sparse channel. Such a channel is difficult to reconstruct by using linear channel estimators that are normally employed for dense channels’ estimation because of their lack of capacity to use the inherent channel’s sparsity. This paper focuses on reconstructing this type of time-varying sparse channel by extending a recently proposed dynamic channel estimator. Specifically, variable step size’s mechanism and variable momentum parameter are incorporated into traditional Iterative Hard Thresholding-based channel estimator to develop the proposed Iterative Hard Thresholding with Combined Variable Step Size and Momentum (IHT-wCVSSnM)-based estimator. Computer simulations carried out in the context of a wireless communication system operating in a dynamic sparse channel, show that the proposed IHT-wCVSSnM-based estimator performs better than all the other estimators significantly. However, the computational complexity cost of the proposed estimator is slightly higher than the closely performing channel estimator. Nevertheless, the inherent complexity cost of the proposed estimator could be compromised in a situation where the system’s performance is of higher priority when compared with the computational complexity cost.

Mango maturity classification instead of maturity index estimation: A new approach towards handheld NIR spectroscopy

Estimation of on-tree mango maturity is essential for the prediction of harvest time. Dry matter (DM) is a useful index in deciding mango maturity, and post-harvest quality. Existing NIR based maturity meters employ machine learning regressors to predict a maturity index value (such as DM, oBrix, or etc.) and then impose a hard threshold on predicted value to estimate maturity state of the fruit. In this paper, a new approach for non-destructive hand-held fruit maturity meter is investigated. The developed approach directly classifies the maturity state (mature/immature) using a classifier trained on maturity labels assigned through standard DM thresholds for investigated mango varieties. To develop the hardware of the device, a commercial-off-the-shelf development kit of NIR micro-spectrometer in the spectral range of 400–1100 nm was used with an embedded computational hardware, a micro-halogen lamp, a lithium battery, and a display. The application software (developed in C++) is designed to collect interactance spectra, remove noise, reduce dimensionality, and classify maturity state. Performance of the developed approach is evaluated by on-tree test samples of mango fruit of different season. Comparison of both the literature reported indirect maturity estimation and proposed direct maturity classification is conducted. The test results show that the maximum accuracy achieved using indirect maturity estimation using hard thresholds is 55.9%. Whereas direct maturity classification using KNN achieved 88.2% accuracy in predicting the maturity state (mature/immature) of the test mangoes. Overall results show that the developed DM mango maturity method has considerable potential to detect maturity state of mangoes in practical situations.

Convolutional long short-term memory neural network equalizer for nonlinear Fourier transform-based optical transmission systems

We evaluate improvement in the performance of the optical transmission systems operating with the continuous nonlinear Fourier spectrum by the artificial neural network equalisers installed at the receiver end. We propose here a novel equaliser designs based on bidirectional long short-term memory (BLSTM) gated recurrent neural network and compare their performance with the equaliser based on several fully connected layers. The proposed approach accounts for the correlations between different nonlinear spectral components. The application of BLSTM equaliser leads to a 16x improvement in terms of bit-error rate (BER) compared to the non-equalised case. The proposed equaliser makes it possible to reach the data rate of 170 Gbit/s for one polarisation conventional nonlinear Fourier transform (NFT) based system at 1000 km distance. We show that our new BLSTM equalisers significantly outperform the previously proposed scheme based on a feed-forward fully connected neural network. Moreover, we demonstrate that by adding a 1D convolutional layer for the data pre-processing before BLSTM recurrent layers, we can further enhance the performance of the BLSTM equaliser, reaching 23x BER improvement for the 170 Gbit/s system over 1000 km, staying below the 7% forward error correction hard decision threshold (HD-FEC).

Co-movement selective detection filter to identify time series co-movement indicator or to filter out symmetric economic shocks

The paper deals with designing a mask suitable for a selective filtering of data. The design of the mask is performed in the time-frequency domain and the selection is based on the co-movement measure of time series. We propose two approaches for the mask construction: i) hard thresholding based on χ2 testing; ii) adaptive based thresholding. The proposed mask can be used for time series filtering in which we obtain either the adjusted time series or the construction of the time series containing only the co-moved parts. Further, after computing an inverse transform we can obtain time series with/without the co-moved area applicable for consequent econometric analyses. The paper provides recommendations concerning the selection of a particular approach in a given situation. The proposed methodology is demonstrated on the adjustment of industrial production index of Euro Area and selected G8 countries about co-movement with the US.

Nonparametric regression with warped wavelets and strong mixing processes

We consider the situation of a univariate nonparametric regression where either the Gaussian error or the predictor follows a stationary strong mixing stochastic process and the other term follows an independent and identically distributed sequence. Also, we estimate the regression function by expanding it in a wavelet basis and applying a hard threshold to the coefficients. Since the observations of the predictor are unequally distant from each other, we work with wavelets warped by the density of the predictor variable. This choice enables us to retain some theoretical and computational properties of wavelets. We propose a unique estimator and show that some of its properties are the same for both model specifications. Specifically, in both cases the coefficients are unbiased and their variances decay at the same rate. Also the risk of the estimator, measured by the mean integrated square error is almost minimax and its maxiset remains unaltered. Simulations and an application illustrate the similarities and differences of the proposed estimator in both situations.

Single image restoration through [formula omitted]-relaxed truncated [formula omitted] analysis-based sparse optimization in tight frames

Image restoration problems, i.e., recovery of an original high-quality image from the degraded observation, arise in various science and engineer areas. Over the past decades, the framelet-based methods are particularly investigated and adopted, owing to the excellent ability of sparse approximating the piecewise-smooth functions such as natural images. In this paper, we propose a novel tight frame-based ℓ2-relaxed truncated ℓ0 analysis-sparsity model that simultaneously exploiting the sparsity and support priors. The resulting nonconvex nonsmooth optimization problem is addressed by using the proposed proximal alternating adaptive hard thresholding (PAAHT) method. We also proved that the sequence generated by the proposed algorithm sublinearly converges. Numerical experiments on several typical image restoration problems demonstrate that the proposed method is more effective than the standard sparsity-inducing algorithms and outperforms several state-of-the-art methods in both objective and perceptual quality.

Joint Bilateral Filter for Signal Recovery from Phase Preserved Curvelet Coefficients for Image Denoising

Thresholding of Curvelet Coefficients, for image denoising, drains out subtle signal component in noise subspace. In effect, it also produces ringing artifacts near edges. We found that the noise sensitivity of Curvelet phases — in contrast to their magnitude — reduces with higher noise level. Thus, we preserved the phase of the coefficients below threshold at coarser scale and estimated the corresponding magnitude by Joint Bilateral Filtering (JBF) technique. In contrast to the traditional hard thresholding, the coefficients in the finest scale is estimated using Bilateral Filtering (BF). The proposed filtering approach in the finest scale exhibits better connectedness among the edges, while removing the granular artifacts in the denoised image due to hard thresholding. Finally, the use of Guided Image Filter (GIF) on the Curvelet-based reconstructed image (initial denoised image in spatial domain) ensures the preservation of small image information with sharper edges and textures detail in the final denoised image. The lower noise sensitivity of Curvelet phase at higher noise strength accelerates the performance of proposed method over several state-of-the-art techniques and provides comparable outcome at lower noise levels.

Reconstruction of Level Cross Sampled Signals Using Sparse Signals &amp; Backtracking Iterative Hard Thresholding

Industry 4.0 applications involve more number of sensors or Internet of Things (IoT) devices to support automation in the industry. It involves more number of computations to analyze the sensor data collected from several critical parts of the processing units. Sparse signal processing is one which has numerous applications in area od communication and signal processing. This paper presents a new approach to reduce the computations with the help of level cross sampling (LCS) and a backtracking based iterative hard thresholding (BIHT) algorithm for reconstruction. The process involve, an information signal is converted to a random sparse signal using non-uniform sampling at the transmitter side and then it can be reconstructed back using BIHT algorithm at receiver side. Simulation results exhibit the superior performance of the proposed BIHT reconstruction in comparison with the literature

Application of Improved Wavelet Threshold in Denoising of ECG Signals

The ECG signal is susceptible to interference from the external environment during the acquisition process, affecting the analysis and processing of the ECG signal. After the traditional soft-hard threshold function is processed, there is a defect that the signal quality is not high and the continuity at the threshold is poor. An improved threshold function wavelet denoising is proposed, which has better regulation and continuity, and effectively solves the shortcomings of traditional soft and hard threshold functions. The Matlab simulation is carried out through a large amount of data, and various processing methods are compared. The results show that the improved threshold function can improve the denoising effect and is superior to the traditional soft and hard threshold denoising.

A new face detection method based on Faster RCNN

The Non-Maximum Suppression (NMS) method based on Faster RCNN uses hard threshold to identify candidate face frames which to be detected. In complex scenes with partial occlusion of the face and uneven lighting, the phenomenon of missing and false detection of the face is prone to occur. Aiming at this problem, this paper proposes a new face detection method to extract face features through CNN, and generates a large number of face candidate frames which to be detected by the Region Proposal Network (RPN); the hard threshold of NMS is improved by linear weighting method, and the face candidate frame is screened by the linearly weighted NMS. Comparison experiment results show that on the FDDB dataset, the new face detection method in this paper can effectively avoid the false detection and missed detection of multiple faces under partial occlusion and uneven illumination, also has high detection accuracy and robustness.