Proposed Thresholding Function Research Articles

A New Denoising Method for Belt Conveyor Roller Fault Signals.

In the process of the intelligent inspection of belt conveyor systems, due to problems such as its long duration, the large number of rollers, and the complex working environment, fault diagnosis by acoustic signals is easily affected by signal coupling interference, which poses a great challenge to selecting denoising methods of signal preprocessing. This paper proposes a novel wavelet threshold denoising algorithm by integrating a new biparameter and trisegment threshold function. Firstly, we elaborate on the mutual influence and optimization process of two adjustment parameters and three wavelet coefficient processing intervals in the BT-WTD (the biparameter and trisegment of wavelet threshold denoising, BT-WTD) denoising model. Subsequently, the advantages of the proposed threshold function are theoretically demonstrated. Finally, the BT-WTD algorithm is applied to denoise the simulation signals and the vibration and acoustic signals collected from the belt conveyor experimental platform. The experimental results indicate that this method's denoising effectiveness surpasses that of traditional threshold function denoising algorithms, effectively addressing the denoising preprocessing of idler roller fault signals under strong noise backgrounds while preserving useful signal features and avoiding signal distortion problems. This research lays the theoretical foundation for the non-contact intelligent fault diagnosis of future inspection robots based on acoustic signals.

AN ENHANCED SHRINKAGE FUNCTION FOR DENOISING ECONOMIC TIME SERIES DATA USING WAVELET ANALYSIS

In the realm of economic (financial) time series analysis, accurate prediction holds paramount importance. However, these data often suffer from the presence of noise, particularly in highly random and non-stationary datasets like stock market data. Dealing with noisy data makes predicting noise-free economic models exceedingly challenging. This research paper introduces an innovative shrinkage (thresholding) function designed to improve the efficiency of wavelet shrinkage denoising in the context of financial time series data. The proposed function is constructed based on an arctangent model with adjustable parameters meticulously chosen to ensure the function maintains continuous differentiability. The application of this novel shrinkage function effectively reduces noise in stock data. Employing R program for data analysis and figure plotting, the performance of this approach is rigorously validated using closing price data from the Shanghai Composite Index, spanning the period from January 4, 2000 to August 28, 2023. The experimental results demonstrate that the proposed thresholding function outperforms classical shrinkage functions (hard, soft, and nonnegative garrote) in both continuous derivative property and denoising efficacy.

Dynamics of a nonlocal SIR epidemic model with free boundaries

This paper is devoted to a nonlocal SIR type epidemic model, with free boundary denoting the expanding front. We aim to examine the full information about the dynamical behaviors of the involved disease that caused by the nonlocal diffusion and growing habitat. We obtain a classification for the spreading and vanishing cases, and show that those are determined by the new proposed threshold function R0F(t) and especially the corresponding initial data R0F(0). We prove that R0F(t)≤R0 and R0F(t)→R0 as t tends to ∞, R0 here representing the basic reproductive number of the associated ordinary differential equation. Also, the result show that the introduce of the nonlocal diffusion makes the disease becomes more easier to spread. In addition, we present some numerical simulations to confirm the theoretical results, as well as the impacts of R0 and the expanding capability.

Combined EEMD with a Novel Flexible Wavelet Threshold Function for Weighing Signal Denoising Approach

This paper proposes a method of combining ensemble empirical mode decomposition (EEMD) with a novel flexible wavelet threshold function to reduce the random error in the weighing result that caused by the nonstationary and nonlinear noise in quality characteristic parameter measurement equipment. The original signal is first processed by EEMD, and then, all intrinsic mode functions (IMFs) are processed by a novel flexible threshold function proposed by this paper. Finally, the denoised signal is obtained by adding reconstructed IMFs and residual. Through theoretical analysis, the proposed threshold function can retain more useful information and have continuity at the segmentation point. Moreover, the addition of adjustable parameters makes it more adaptable. Its advantages are verified by comparing the denoised results with other threshold functions in the simulation model. In weighing experiment, the validity of the novel flexible threshold function in weighing signal denoising is verified, and the effectiveness of the proposed method is also quantitatively confirmed by comparing the random errors of the original signal and the denoised signal.

Removing the singularity of a penalty via thresholding function matching

By introducing the idea of thresholding function matching, it is illustrated that both bridge penalty and log penalty can be transformed so as to circumvent certain difficulties in numerical computation and the definition of local minimality. The fact that both bridge penalty and log penalty have derivatives going to infinity at zero. This hinders their applications in statistics although it is reported in the literature that they allow recovery of sparse structure in the data under some conditions. It is illustrated in the simulation studies that in the variable selection problems, penalized likelihood estimation based on the transformed penalty obtained by the proposed thresholding function matching method outperform those based on many other state-of-art penalties, particularly when the covariates are strongly correlated. The one-to-one correspondence between the transformed penalties and their thresholding functions are also established.

A Continuous Differentiable Wavelet Shrinkage Function for Economic Data Denoising

In economic (financial) time series analysis, prediction plays an important role and the inclusion of noise in the time series data is also a common phenomenon. In particular, stock market data are highly random and non-stationary, thus they contain much noise. Prediction of the noise-free data is quite difficult when noise is present. Therefore, removal of such noise before predicting can significantly improve the prediction accuracy of economic models. Based on this consideration, this paper proposes a new shrinkage (thresholding) function to improve the performance of wavelet shrinkage denoising. The proposed thresholding function is an arctangent function with several parameters to be determined and the optimal parameters are determined by ensuring that the thresholding function satisfies the condition of continuously differentiable. The closing price data with the Shanghai Composite Index from January 1991 to December 2014 are used to illustrate the application of the proposed shrinkage function in denoising the stock data. The experimental results show that compared with the classical shrinkage (hard, soft, and nonnegative garrote) functions, the proposed thresholding function not only has the advantage of continuous derivative, but also has a very competitive denoising performance.

Application of improved wavelet adaptive threshold de-noising algorithm in FBG demodulation

A novel wavelet adaptive threshold algorithm is proposed in this paper, which is used to process the noisy spectral signal of the fiber Bragg grating (FBG) sensor system. The optimum wavelet basis and decomposition layer are selected by experimental simulation, and the noisy FBG signal is processed via proposed threshold function. The experiments and simulation results show that the proposed algorithm performs better than the traditional algorithms in de-noising ability for the noisy spectral signal. In this paper, SNR and GSNR are higher as well as RMSE is lower. This implies that the proposed algorithm provides a precise demodulation algorithm for the FBG sensing signal.

Moving object detection using a background modeling based on entropy theory and quad-tree decomposition

A particular algorithm for moving object detection using a background subtraction approach is proposed. We generate the background model by combining quad-tree decomposition with entropy theory. In general, many background subtraction approaches are sensitive to sudden illumination change in the scene and cannot update the background image in scenes. The proposed background modeling approach analyzes the illumination change problem. After performing the background subtraction based on the proposed background model, the moving targets can be accurately detected at each frame of the image sequence. In order to produce high accuracy for the motion detection, the binary motion mask can be computed by the proposed threshold function. The experimental analysis based on statistical measurements proves the efficiency of our proposed method in terms of quality and quantity. And it even outperforms substantially existing methods by perceptional evaluation.

Classical Tamil Speech Enhancement with Modified Threshold Function using Wavelets

Speech enhancement is a challenging problem due to the diversity of noise sources and their effects in different applications. The goal of speech enhancement is to improve the quality and intelligibility of speech by reducing noise. Many research works in speech enhancement have been accomplished in English and other European Languages. There has been limited or no such works or efforts in the past in the context of Tamil speech enhancement in the literature. The aim of the proposed method is to reduce the background noise present in the Tamil speech signal by using wavelets. New modified thresholding function is introduced. The proposed method is evaluated on several speakers and under various noise conditions including White Gaussian noise, Babble noise and Car noise. The Signal to Noise Ratio (SNR), Mean Square Error (MSE) and Mean Opinion Score (MOS) results show that the proposed thresholding function improves the speech enhancement compared to the conventional hard and soft thresholding methods.

Energy conservation‐based thresholding for effective wavelet denoising of partial discharge signals

Recent studies have shown that wavelet transform can effectively be used for noise reduction in the context of partial discharge (PD) signal detection and classification. Several thresholding approaches for wavelet denoising have been reported in the literature. In this study, a novel wavelet threshold estimation method, named energy conservation-based thresholding (ECBT), is introduced. The proposed thresholding function is capable of conserving a significant portion of the original signal energy, while the threshold value is determined based on the relative difference between the original and noisy signal energies. The proposed method is first applied to PD signals contaminated with different levels of simulated noise. Results show that ECBT produces a denoised PD signal with higher signal-to-noise ratio (SNR) and less distortion than PDs produced by the existing wavelet methods. Then, ECBT is modified to address actual PD signals corrupted with real noise, where a robust SNR estimation method is derived to estimate the noise level embedded in the measured PD signals. The denoised PD signals indicate that the proposed method yields higher reduction in noise levels than other methods.

Compressively Sampled MR Image Reconstruction Using Hyperbolic Tangent-Based Soft-Thresholding

The application of compressed sensing (CS) to magnetic resonance (MR) images utilizes the transformed domain sparsity to enable the reconstruction from an under-sampled k-space (Fourier) data using a non-linear recovery algorithm. In order to estimate the missing k-space data from the partial Fourier samples, the reconstruction algorithms minimize an objective function based on mixed l1 − l2 norms. Iterative-shrinkage algorithms, such as parallel coordinate descent (PCD) and separable surrogate functional, provide an efficient numerical technique to minimize the l1-regularized least square optimization problem. These algorithms require a thresholding step to induce sparsity in the solution, which is an essential requirement of the CS recovery. This paper introduces a novel soft-thresholding method based on the hyperbolic tangent function. It has been shown that by using the proposed thresholding function in the sparsifying domain and a data consistency step in the k-space, the iterative-shrinkage algorithms can be used effectively to recover the under-sampled MR images. For the purpose of demonstration, we use the proposed soft-thresholding and data consistency with the PCD algorithm and compare its performance with the conventional PCD, projection onto convex sets and low-resolution reconstruction methods. The metrics used to compare the various algorithms are the artifact power, the peak signal-to-noise ratio, the correlation and the structural similarity index. The experimental results are validated using Shepp–Logan phantom image as well as real human head MR images taken from the MRI scanner at St. Mary’s Hospital, London.

A novel curvelet thresholding denoising method based on chi-squared distribution

In this paper, we first explored the advantages and disadvantages of the classical curvelet thresholding functions. To circumvent the inherent drawbacks of them, we introduced the chi-squared cumulative distribution to develop a novel thresholding function. The theoretical analysis and mathematical proofs show that the proposed thresholding function represents a compromise between soft and hard thresholding function and offers potential advantages of generally less sensitivity to small perturbations in the data over hard thresholding function and smaller bias and overall reconstruction error over soft thresholding function. Additionally, the proposed function is comparable to the semisoft thresholding function, while the latter requires two thresholds. Moreover, our proposed function can adjust flexibly between the hard and soft thresholding function through the parameter \(n\), providing a better balance between noise removal and detail preservation. Numerical experiments also demonstrate that the proposed thresholding function outperforms the three classical ones in terms of PSNR and visual quality.

An improved adaptive wavelet shrinkage for ultrasound despeckling

Ultrasound imaging is the most widely used medical diagnostic technique for clinical decision making, due to its ability to make real time imaging for moving structures, low cost and safety. However, its usefulness is degraded by the presence of signal dependent speckle noise. Several wavelet-based denoising schemes have been reported in the literature for the removal of speckle noise. This study proposes a new and improved adaptive wavelet shrinkage in the translational invariant domain. It exploits the knowledge of the correlation of the wavelet coefficients within and across the resolution scales. A preliminary coefficient classification representing useful image information and noise is performed with a novel inter-scale dependency measure. The spatial context adaptation of the wavelet coefficients within a subband is achieved by a local spatial adaptivity indicator, determined by using a truncation threshold. A weighted signal variance is estimated based on this measure and used in the determination of a subband adaptive threshold. The proposed thresholding function aims to reduce the fixed bias of the soft thresholding approach. Experiments conducted with the proposed filter are compared with the existing filtering algorithms in terms of Peak-Signal to Noise Ratio (PSNR), Mean Square Error (MSE), Structural Similarity Index Measure (SSIM), Equivalent Number of Looks (ENL) and Edge Preservation Index (EPI). A comparison of the results shows that the proposed filter achieves an improvement in terms of quantitative measures and in terms of visual quality of the images.

Motion detection with pyramid structure of background model for intelligent surveillance systems

This paper proposes a pyramidal background matching structure for motion detection. The proposed method utilizes spectral, spatial, and temporal features to generate a pyramidal structure of the background model. After performing the background subtraction based on the proposed background model, the moving targets can be accurately detected at each frame of the video sequence. In order to produce high accuracy for the motion detection, the proposed method also further includes a noise filter based on Bezier curve to smooth noise pixels, after which the binary motion mask can be computed by the proposed threshold function. Experimental results demonstrate that the proposed method substantially outperforms existing methods by perceptional evaluation.

Illumination-Sensitive Background Modeling Approach for Accurate Moving Object Detection

Background subtraction involves generating the background model from the video sequence to detect the foreground and object for many computer vision applications, including traffic security, human-machine interaction, object recognition, and so on. In general, many background subtraction approaches cannot update the current status of the background image in scenes with sudden illumination change. This is especially true in regard to motion detection when light is suddenly switched on or off. This paper proposes an illumination-sensitive background modeling approach to analyze the illumination change and detect moving objects. For the sudden illumination change, an illumination evaluation is used to determine two background candidates, including a light background image and a dark background image. Based on the background model and illumination evaluation, the binary mask of moving objects can be generated by the proposed thresholding function. Experimental results demonstrate the effectiveness of the proposed approach in providing a promising detection outcome and low computational cost.

Despeckling of medical ultrasound images based on quantum-inspired adaptive threshold

A speckle suppression method for medical ultrasound images is proposed by combining the dual-tree complex wavelet transform (DTCWT) with a new quantum-inspired adaptive threshold function. An adaptive non-Gaussian statistical model is proposed for the complex wavelet coefficients. According to products of the coefficients and their parents in multi-scale subbands, the quantum-inspired probability of noise is considered in the proposed threshold function. Experiments demonstrate the effectiveness of the proposed method.

Image denoising in the wavelet domain using a new adaptive thresholding function

In this paper, a new thresholding function is proposed for image denoising in the wavelet domain. The proposed function is further used in a new subband-adaptive thresholding neural network to improve the efficiency of the denoising procedure. Some new adaptive learning types are also proposed. In these learning methods, the threshold and the thresholding function effects are considered simultaneously. These methods are used to suppress two types of important noises, Gaussian and speckle, ranging from natural images to ultrasound and SAR pictures. The simulation results show that the proposed thresholding function has superior features compared to conventional methods when used with the proposed adaptive learning types. This makes it an efficient method in image denoising applications.

A study of modifying pruning strategies for dp beam search at a preset input frame

AbstractIn a conventional dynamic programming beam search, the parameters of the threshold function for pruning grid points in the dynamic programming region are assumed to be set to the same values throughout the speech input. In this paper, I describe a method designed to improve the effectiveness of decreasing the computation amount in the dynamic programming beam search by changing the parameters during speech input. An accumulated distance is defined that is not easily influenced by the quality of matching at the beginning of speech input. When this accumulated distance is used in the grid point pruning decision, the parameters of the threshold function can be changed to smaller values, at an early point in time of several frames from the beginning of the speech input, without missing grid points on the optimum dynamic programming path for the reference pattern. It was demonstrated through word recognition tests that the computation amount when the proposed threshold function is used can be decreased to about 1/5 of that in the conventional, simple grid point pruning method, and decreased by at least 1/2 compared to the threshold function of [11] because of the effectiveness of changing the threshold function's parameters at an early point during speech input.