A wavelet denoising method of new adjustable threshold

In order to improve the effects of denoising, this paper introduces the basic principles of wavelet threshold denoising and traditional structures threshold functions. Meanwhile, it proposes wavelet threshold function and fixed threshold formula which are both improved here. First, this paper studies the problems existing in the traditional wavelet threshold functions and introduces the adjustment factors to construct the new threshold function basis on soft threshold function. Then, it studies the fixed threshold and introduces the logarithmic function of layer number of wavelet decomposition to design the new fixed threshold formula. Finally, this paper uses hard threshold, soft threshold, Garrote threshold, and improved threshold function to denoise different signals. And the paper also calculates signal-to-noise (SNR) and mean square errors (MSE) of the hard threshold functions, soft thresholding functions, Garrote threshold functions, and the improved threshold function after denoising. Theoretical analysis and experimental results showed that the proposed approach could improve soft threshold functions with constant deviation and hard threshold with discontinuous function problems. The proposed approach could improve the different decomposition scales that adopt the same threshold value to deal with the noise problems, also effectively filter the noise in the signals, and improve the SNR and reduce the MSE of output signals.

Wavelet de-noising method is often used in the processing of magnetotelluric (MT) signal, and the wavelet hard and soft threshold de-noising method are the most popular although there is much room for improvement in the threshold function selection and threshold determination. A new adaptive wavelet threshold de-noising method was proposed by selecting a new threshold function and presenting an adaptive method for obtaining optimal threshold based on the multi-resolution Stein unbiased risk estimation. New threshold function and an adaptive method to determine threshold were discussed, and the principle and implementation of the algorithm were given. The simulated signal and the measured MT data contaminated by impulse interference were analyzed, and the obtained results were compared with those of the conventional wavelet hard and soft threshold de-noising methods. The results show that the proposed method overcomes the defects of the traditional wavelet soft and hard threshold due to a new threshold function, and a new method to determine the threshold of each layer is applied and provides an adaptive method for filtering MT data in the wavelet domain that requires a minimum of human intervention. The presented de-noising method is very suitable for suppressing the impulse interference for MT data and can get higher signal-to-noise ratio than the traditional wavelet threshold de-noising methods. After de-noising, the accurate data is loaded for further impedance estimation and geological interpretation.

Acoustic emission (AE) detection, as a non-electrical detection method, is very suitable for effective fault detection of power equipment with a strong electromagnetic field. However, the AE signal collected at industrial sites often contains a lot of interference noise, affecting the analysis and prediction of faults. In this study, a wavelet denoising method based on a new threshold function is proposed, to achieve a noise reduction in the low signal-to-noise ratio (SNR) signals. Simulation experiment results show that the proposed threshold function not only overcomes the shortcomings of the discontinuous hard threshold function, but also solves the constant deviation of the soft threshold function. What’s more, the proposed function achieves a good adaptability. When SNR = 10 dB: The SNR of the new threshold is 20.6622, and the RMSE is 0.0026. The SNR of the hard threshold is 20.2246 and the RMSE is 0.0027, compared with the traditional hard threshold method, the SNR of the new threshold is increased by 2.16% and the root mean square error (RMSE) is reduced by 3.7%; the SNR of the soft threshold is 15.5656, and the RMSE is 0.0047, compared with the traditional soft threshold method, the new threshold has a 32.74% increase in SNR and a 40.43% reduction in RMSE. When SNR = -10 dB: The SNR of the new threshold is 4.2602, and the RMSE is 0.0172. The SNR of the hard threshold is 3.8558 and the RMSE is 0.0182, compared with the traditional hard threshold method, the SNR of the new threshold is increased by 10.49% and the RMSE is reduced by 5.49%; the SNR of the soft threshold is 2.1625, and the RMSE is 0.0212, compared with the soft threshold method, SNR is improved by 97% and RMSE is reduced by 18.87%. Performance analyses have proved that the improved wavelet denoising method can obtain a good noise reduction effect. It is very helpful for AE signal analysis with the generally low SNR, which can improve the accuracy of failure identification in subsequent acts.

Stock is one type of long-term investment in the capital market. The stock movement indicator that is most often used in analysis by investors is the Indonesia Composite Index (ICI). ICI data is a variety of time series data, so it can be analyzed using forecasting. One forecasting method that can be used is the wavelet thresholding method. The wavelet threshold can analyze stationary, non-stationary, and nonlinear time series data by producing smooth estimates. The wavelet threshold has a wavelet filter and threshold parameters and threshold functions that can be used in analyzing. In this study MSE was assessed from several wavelet filters namely haar, daubechies, and coiflets filters at levels 1 to 7 with the thresholding function namely soft thresholding and thresholding parameters, namely minimax thresholding and sure thresholding. The data used is IHGS data in 2018 totaling 240 data. Based on the data analysis performed, MSE was obtained which means that the best filter provided in order 2 wavelet coiflet filter at level 2 and thresholding parameter is sure of thresholding with MSE value of 0.0094

Electric energy signals are often contaminated by noise during the collection process, which affects the accurate positioning of disturbances. The discontinuity of traditional hard threshold functions can lead to oscillations, while excessive smoothness of soft threshold functions can lead to signal distortion. The optimized threshold function and scale adaptive processing on the selection of the threshold are proposed. The wavelet thresholding method is used to process voltage sag, rise, and interrupt signals containing noise. The denoised signal is decomposed into five scale wavelets using db7 wavelet and detected by using wavelet transform modulus maximum and signal singularity principle. Experiments have shown that optimized threshold and threshold function not only effectively denoise but also retain the effective mutation point information in the original signal, and the new method is reliable in detection.

This paper introduces the theory and method of image de-noising on wavelet threshold. On the basis of the traditional threshold algorithm, a new improved algorithm which changes the threshold is put forward. And use the MATLAB to achieve the remote sensing image de-noising. Experimental results show that the peak signal noise ratio (PSNR) of the new threshold algorithm has improved significantly than the traditional threshold algorithm and lower mean square error (MSE) significantly in Gaussian noise of remote sensing image de-noising. The de-noising effect is better.

Electrocardiogram (ECG) signal is the most direct means of detecting human health condition. In the process of acquisition, ECG will be contaminated by all kinds of noises and interferences, while the effects of traditional wavelet denoising algorithms are not very satisfying. This paper presented a novel thresholding method based on Discrete Wavelet Transform (DWT). Compared with the traditional hard thresholding and soft thresholding, it can effectively suppress all kinds of high-frequency and lowfrequency noises. To a certain extent, the novel thresholding method protects the characteristics and amplitude of ECG signal perfectly. Finally, MIT-BIH arrhythmia database was used to verify this novel thresholding method; the experimental results showed that the performance of the proposed algorithm is better than the traditional wavelet thresholding algorithms. This proposed new thresholding algorithm can maintain the geometrical characteristics of ECG signal much better, and it also has higher Signal Noise Ratio (SNR).

Based on multi-resolution analysis of wavelet, this article is aimed at building a new soft threshold function for wavelet de-noising, to overcome the discontinuous disadvantage of the hard threshold function. In the area adjacent to the threshold, continuously adjustable nonlinear functions are introduced in piecewise to process the wavelet coefficients more carefully in this area. Consequently, large deviation caused by super-compression of wavelet coefficients when using traditional soft threshold could be avoided, and the nonlinearity of the system is able to be effectively kept. Using both signal to noise ratio (SNR) and mean square error (MSE) as the evaluation indicators, simulation results show that the improved method is more effective than the method based on traditional hard and soft threshold.

Digital signals are often contaminated by noise during signal acquisition and transmission for sewage sensing signal treatment such as aeration volume, oxygen content and water transparency etc. Sometimes, noise is a mixed one of gaussian noise and impulse noise. Unfortunately, existing denoising algorithms are often designed for removing single gaussian noise or impulse noise. In this paper, an efficient algorithm for mixed noise removal in signal is proposed, including space impulse noise removal and wavelet Gaussian noise removal. An impulse noise detection algorithm based on median filter is given to filter impulse signal, also a lifting wavelet was constructed by lifting original wavelet. The threshold based on lifting wavelet transform for signal was applied to denoising gaussian noise. Simulations are conducted on the presented algorithm, and the simulation result shows that this algorithm can remove mixed Gaussian and impulse noise in signal efficiently.

Denoising computed tomography (CT) medical images is crucial in preserving information and restoring images contaminated with noise. Standard filters have extensively been used for noise removal and fine details’ preservation. During the transmission of medical images, noise degrades the visibility of anatomical structures and subtle abnormalities, making it difficult for radiologists to accurately diagnose and interpret medical conditions. In recent studies, an optimum denoising filter using the wavelet threshold and deep-CNN was used to eliminate Gaussian noise in CT images using the image quality index (IQI) and peak signal-to-noise ratio (PSNR). Although the results were better than those with traditional techniques, the performance resulted in a loss of clarity and fine details’ preservation that rendered the CT images unsuitable. To address these challenges, this paper focuses on eliminating noise in CT scan images corrupted with additive Gaussian blur noise (AGBN) using an ensemble approach that integrates anisotropic Gaussian filter (AGF) and wavelet transform with a deep learning denoising convolutional neural network (DnCNN). First, the noisy image is denoised by AGF and Haar wavelet transform as preprocessing operations to eliminate AGBN. The DnCNN is then combined with AGF and wavelet for post-processing operation to eliminate the rest of the noises. Specifically, we used AGF due to its adaptability to edge orientation and directional information, which prevents blurring along edges for non-uniform noise distribution. Denoised images are evaluated using PSNR, mean squared error (MSE), and the structural similarity index measure (SSIM). Results revealed that the average PSNR value of the proposed ensemble approach is 28.28, and the average computational time is 0.01666 s. The implication is that the MSE between the original and reconstructed images is very low, implying that the image is restored correctly. Since the SSIM values are between 0 and 1.0, 1.0 perfectly matches the reconstructed image with the original image. In addition, the SSIM values at 1.0 or near 1.0 implicitly reveal a remarkable structural similarity between the denoised CT image and the original image. Compared to other techniques, the proposed ensemble approach has demonstrated exceptional performance in maintaining the quality of the image and fine details’ preservation.

We propose in this paper an image noise severity measurement method that correlates well with human's quality perception on the presence of noise in images. In our approach, a 32x32 pixels mask is used to compute the differences between the original and noise-degraded images in terms of the statistical means and outlier values. These differences are formulated and then compared to the quality scores from the subjective evaluations. The degraded images were distorted by two common types of random noise for images - Gaussian white noise and impulse noise. Experiment results showed that this approach obtained higher correlation compare to classical Peak Signal to Noise Ratio (PSNR) method.

A large amount of noise is mixed in the actual process industrial data, which leads to a decline in data quality, which in turn affects the diagnosis results. In reality, the wavelet threshold method is generally used to remove noise. However, the hard threshold method which is in the wavelet threshold method has the disadvantages of poor signal continuity and signal oscillating. The soft threshold method has the disadvantages of constant deviation and large error of reconstructed signal. To this end, we propose a random soft-hard threshold algorithm which can combine hard and soft thresholds. Then the new algorithm is combined with the principal component analysis for fault diagnosis of the TE (Tennessee Eastman) process. The MATLAB simulation results show that the above method can effectively denoise, identify and detect faults more accurately, and can better find the variables that have the greatest impact on the fault.

In view of the wheel state monitoring, the wheel vibration signal is often used to reflect the wheel state information, but the original vibration signal contains a lot of noise. In order to extract the effective wheel information, it is necessary to reduce the noise of the original vibration signal. The problems existing in the traditional wavelet threshold denoising method include unreasonable threshold setting, lack of continuity of hard threshold function and fixed deviation of wavelet coefficients processed by soft threshold function. In this paper, the traditional wavelet threshold denoising method is improved from threshold selection and threshold function, and an improved wavelet threshold denoising method is proposed. This method is used to reduce the noise of the measured wheelset vibration signal and compared with the traditional wavelet denoising method from evaluation indexes and graphical results. The results show that the improved wavelet threshold denoising method has better noise reduction effect.

Quality is a very important parameter for all objects and their functionalities. In image-based object recognition, image quality is a prime criterion. For authentic image quality evaluation, ground truth is required. But in practice, it is very difficult to find the ground truth. Usually, image quality is being assessed by full reference metrics, like MSE (Mean Square Error) and PSNR (Peak Signal to Noise Ratio). In contrast to MSE and PSNR, recently, two more full reference metrics SSIM (Structured Similarity Indexing Method) and FSIM (Feature Similarity Indexing Method) are developed with a view to compare the structural and feature similarity measures between restored and original objects on the basis of perception. This paper is mainly stressed on comparing different image quality metrics to give a comprehensive view. Experimentation with these metrics using benchmark images is performed through denoising for different noise concentrations. All metrics have given consistent results. However, from representation perspective, SSIM and FSIM are normalized, but MSE and PSNR are not; and from semantic perspective, MSE and PSNR are giving only absolute error; on the other hand, SSIM and PSNR are giving perception and saliency-based error. So, SSIM and FSIM can be treated more understandable than the MSE and PSNR.

Wide variety of medical images are degraded by different types of noise such as Impulse noise, Gaussian noise, Poisson or a mixed of all. These noise disruptions typically result from sensor malfunctions, transmission issues, or environmental factors [1]. They provide an essential basis for clinical diagnosis and treatment. Unlike natural photographs, medical images often contain significant signal-related noise during their creation, resulting in lower contrast and more visible noise [3].No single method or procedure is effective for noise removal hence care should be taken before cleaning noisy area of image. Factors such as type of image (CT scan, Ultrasound, MRI etc) and type of noise such as (Gaussian, the impulsive and speckle noise etc) should be identified and based on the type of input, an appropriate method should be selected. For accurate segmentation of medical images through the automatic means,it is necessary to remove the noise from the images. There are many methods such as learning based (traditional methods) and non-learning based methods(using various types neural networks).To measure the denoising accuracy, parameters like Signal-to-Noise Ratio (SNR), Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index Measure (SSIM) are used. This paper discusses the results obtained through the various methods and their comparison in terms of PSNR,SSIM. Removing noise is crucial for accurate segmentation of medical images. These noise-less images are to be treated as pre-processed images for the segmentation task.