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Wavelet thresholding (or shrinkage) attempts to remove the noises existing in the signals while preserving inherent pattern characteristics in the reconstruction of true signals. For data-denoising purpose, we present a new wavelet thresholding procedure which employs the step-down testing idea of identifying active contrasts in unreplicated fractional factorial experiments. The proposed method employs bootstrapping methods to a step-down test for thresholding wavelet coefficients. By introducing the concept of a false discovery error rate in testing wavelet coefficients, we shrink the wavelet coefficients with $p$ -values higher than the error rate. The error rate controls the expected proportion of wrongly accepted coefficients among chosen wavelet coefficients. Bootstrap samples are used to approximate the $p$ -value for computational efficiency. We also present some guidelines for selecting the values of hyper-parameters which affect the performance in the step-down thresholding procedure. Based on some common testing signals and an air-conditioner sounds example, the comparison of our proposed procedure with other thresholding methods in the literature is performed. The analytical results show that the proposed procedure has a potential in data-denoising and data-reduction in a variety of signal reconstruction applications.

We describe the lifting dual tree complex wavelet transform (LDTCWT), a type of lifting wavelets remodeling that produce complex coefficients by employing a dual tree of lifting wavelets filters to get its real part and imaginary part. Permits the remodel to produce approximate shift invariance, directionally selective filters and reduces the computation time (properties lacking within the classical wavelets transform). We describe a way to estimate the accuracy of this approximation and style appropriate filters to attain this. These benefits are often exploited among applications like denoising, segmentation, image fusion and compression. The results of applications shrinkage denoising demonstrate objective and subjective enhancements over the dual tree complex wavelet transform (DTCWT). The results of the shrinkage denoising example application indicate empirical and subjective enhancements over the DTCWT. The new transform with the DTCWT provide a trade-off between denoising computational competence of performance, and memory necessities. We tend to use the PSNR (peak signal to noise ratio) alongside the structural similarity index measure (SSIM) and the SSIM map to estimate denoised image quality.

To remove the speckle noise of synthetic aperture radar (SAR) images, a novel denoising algorithm based on Bayes wavelet shrinkage and a fast guided filter is proposed. According to the statistical properties of SAR images, the noise-free signal and speckle noise in the wavelet domain are modeled as Laplace and Fisher-Tippett distributions respectively. Then a new wavelet shrinkage algorithm is obtained by adopting the Bayes maximum a posteriori estimation. Speckle noise in the high-frequency domain of SAR images is shrunk by this new wavelet shrinkage algorithm. As the wavelet coefficients of the low-frequency domain also contain some speckle noise, speckle noise in the low-frequency domain can be further filtered by the fast guided filter. The result of the denoising experiments of simulated SAR images and real SAR images demonstrate that the proposed algorithm has the ability to better denoise and preserve edge information.

In this paper, we revisit the effects of principal component analysis (PCA) on hyperspectral imagery denoising. Our previous work combined PCA with wavelet shrinkage and particularly good denoising results has been achieved. We debate that any denoising methods can be used to replace wavelet shrinkage in our PCA+wavelet shrinkage algorithm. The major difference between this work and our previous PCA-based denoising method is that we consider a mixture of Gaussian and shot noise in this work whereas our previous methods studied Gaussian white noise alone. In addition, we retain [Formula: see text] [Formula: see text] PCA output components in our forward PCA transform in this paper whereas we keep all PCA output components [Formula: see text] in our previous works. The [Formula: see text] above is the number of spectral bands in the original hyperspectral imagery data cube. In addition, PCA is much better than nonlinear PCA for hyperspectral imagery denoising when Gaussian white noise and shot noise are introduced as demonstrated in this paper. Extensive experiments demonstrate that the method proposed in this paper outperforms the existing methods significantly in terms of signal-to-noise ratio for two testing hyperspectral imagery data cubes.

Rapid switching of the power switches inside a grid-connected power converter causes a huge number of high-frequency spikes, which could degrade the power converters' functioning. The power spike smoothing algorithm is a digital solution to removing these switching spikes from the sensor measurement. It uses the wavelet decomposition to reveal the high-frequency components so that specific suppression policy could apply. Reconstruction from the original low-frequency components and reduced high-frequency components result in the smoothing effect in the output waveform, and the degree of the smoothing effect is adjustable depending on the variance of each power converter through the parameter shrinkage degree.

We develop a data-driven approach for signal denoising that utilizes variational mode decomposition (VMD) algorithm and Cramer Von Misses (CVM) statistic. In comparison with the classical empirical mode decomposition (EMD), VMD enjoys superior mathematical and theoretical framework that makes it robust to noise and mode mixing. These desirable properties of VMD materialize in segregation of a major part of noise into a few final modes while majority of the signal content is distributed among the earlier ones. To exploit this representation for denoising purpose, we propose to estimate the distribution of noise from the predominantly noisy modes and then use it to detect and reject noise from the remaining modes. The proposed approach first selects the predominantly noisy modes using the CVM measure of statistical distance. Next, CVM statistic is used locally on the remaining modes to test how closely the modes fit the estimated noise distribution; the modes that yield closer fit to the noise distribution are rejected (set to zero). Extensive experiments demonstrate the superiority of the proposed method as compared to the state of the art in signal denoising and underscore its utility in practical applications where noise distribution is not known a priori. (C) 2020 Elsevier Inc. All rights reserved.

The present work aims at developing a new approach towards the analysis of the crack path through the access to the information from the infrared (IR) video imaging of the steady fatigue crack growth. We first test some commonly available infrared image filtering techniques, and then we introduce a new robust algorithm to identify the position of the dynamic crack. The proposed procedure performs the local analysis of the temperature distribution around the fatigue crack tip in the 316L stainless steel. The developed MATLAB framework simplifies the routine processing and permits analyzing multiple experiments reasonably easily. Two filtering procedures - Gaussian and wavelet shrinkage - were implemented and applied successively to denoise the IR images. Both filters produce comparable and good quality results. The new algorithm capable of automatically locating the crack tip position from consecutive filtered IR images is proposed. Remarkably successful results are demonstrated with only small errors caused by materials distortion. © 2019 This is an open access article under the terms of the CC-BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

[EN] Objective :The most relevant source of signal contamination in the cardiac electrophysiology (EP) laboratory is the ubiquitous powerline interference (PLI). To reduce this perturbation, algorithms including common fixed-bandwidth and adaptive-notch filters have been proposed. Although such methods have proven to add artificial fractionation to intra-atrial electrograms (EGMs), they are still frequently used. However, such morphological alteration can conceal the accurate interpretation of EGMs, specially to evaluate the mechanisms supporting atrial fibrillation (AF), which is the most common cardiac arrhythmia. Given the clinical relevance of AF, a novel algorithm aimed at reducing PLI on highly contaminated bipolar EGMs and, simultaneously, preserving their morphology is proposed. Approach: The method is based on the wavelet shrinkage and has been validated through customized indices on a set of synthesized EGMs to accurately quantify the achieved level of PLI reduction and signal morphology alteration. Visual validation of the algorithm¿s performance has also been included for some real EGM excerpts. Main results: The method has outperformed common filtering-based and wavelet-based strategies in the analyzed scenario. Moreover, it possesses advantages such as insensitivity to amplitude and frequency variations in the PLI, and the capability of joint removal of several interferences. Significance: The use of this algorithm in routine cardiac EP studies may enable improved and truthful evaluation of AF mechanisms., Research supported by grants DPI2017-83952-C3 MINECO/AEI/FEDER, UE and SBPLY/17/180501/000411 from Junta de Comunidades de Castilla-La Mancha.

Partial Discharge (PD) measurements of large generators are extremely affected and hampered by noise, making the denoising of PD signal an inevitable issue. Wavelet shrinkage is the most commonly employed method for PD signal denoising. The appropriate mother wavelet and decomposition level are critically important for the denoising performance. In consideration of the PD signal characteristics of large generators, a novel wavelet shrinkage scheme for PD signal denoising is presented. In the scheme, a scale dependent wavelet selection method is proposed, the core idea is that the optimum wavelet at each scale is selected as the one maximizing the energy ratio of coefficients beside and inside the range formed by the threshold, which correspond to the signal to be reserved and noise to be removed, respectively. In addition, taking into account the influence of mother wavelet at each scale on the decomposition level, an approach for decomposition level determination is put forward based on the energy composition after decomposition at each scale. The application results on the simulated signals with different SNR obtained by combining the various pulses and measured signal on-site show the effectiveness of the proposed scheme. Besides, the denoising results are compared with that of the existing wavelet selection methods and the proposed wavelet selection method shows an obvious advantage.

Magnetocardiograms recorded in unshielded environments avoid the necessity of especially designed chambers, but are more sensitive to external interferences. Reliable denoising techniques have to be developed, which should not distort the clinical measurements. In the present paper, two filtering algorithms based on wavelet shrinkage, using intrinsic properties of the signal, have been developed and compared. The algorithm is fast computing and displays good results, enabling further improvements of the magnetocardiogram tehnique.

The extraction of Fetal ECG (FECG) is still a difficult task in non-invasive approach since the frequency components of dominant maternal ECG and fetal ECG signals are generally overlapped. Besides, the baseline wander and high-frequency noise make the clear FECG difficult to be extracted. In this paper, we proposed a new combination of independent component analysis (ICA), improved complete ensemble empirical mode decomposition (ICEEMDAN), and wavelet shrinkage (WS) de-noising (ICA-ICEEMDAN-WS) to extract FECG while reducing the noise. ICA algorithm as the first step of our proposed method separated the mixed abdominal ECG signal to obtain the noisy FECG. Then for further denoisng and obtain higher SNR, noisy FECG was decomposed by the newly proposed ICEEMDAN that is more accurate for non-linear and non-stationary bio-signal processing. The informative extracted components were then determined based on the statistical significance test. WS de-noising removed the remained noisy subcomponents and finally the baseline wander was reduced by partial reconstruction. The performance of ICA-ICEEMDAN-WS method was evaluated using simulated and real data sets. Our results showed that our proposed method outperformed ICA-EEMD-WS, the recently proposed algorithm based on ensemble empirical mode decomposition

An interferometric synthetic aperture radar (InSAR) phase denoising algorithm using the local sparsity of wavelet coefficients and nonlocal similarity of grouped blocks was developed. From the Bayesian perspective, the double- l 1 norm regularization model that enforces the local and nonlocal sparsity constraints was used. Taking advantages of coefficients of the nonlocal similarity between group blocks for the wavelet shrinkage, the proposed algorithm effectively filtered the phase noise. Applying the method to simulated and acquired InSAR data, we obtained satisfactory results. In comparison, the algorithm outperformed several widely-used InSAR phase denoising approaches in terms of the number of residues, root-mean-square errors and other edge preservation indexes.

International audience; Electro optical techniques are efficient backside contactless techniques usually used for design debug and defect location in modern VLSI. Unfortunately, the signal to noise ratio is quite low and depends on laser power with potential device stress due to long acquisition time or high laser power, especially in up to date technologies. Under these conditions, to maintain a good signal or image quality, specific signal or image processing techniques can be implemented. In this paper, we proposed a new spatial filtering by stationary wavelets and contrast enhancement which allows the use of low laser power and short acquisition time in image mode.

Background subtraction without a separate training phase has become a critical task, because a sufficiently long and clean training sequence is usually unavailable, and people generally thirst for immediate detection results from the first frame of a video. Without a training phase, we propose a background subtraction method based on three-dimensional (3D) discrete wavelet transform (DWT). Static backgrounds with few variations along the time axis are characterized by intensity temporal consistency in the 3D space-time domain and, hence, correspond to low-frequency components in the 3D frequency domain. Enlightened by this, we eliminate low-frequency components that correspond to static backgrounds using the 3D DWT in order to extract moving objects. Owing to the multiscale analysis property of the 3D DWT, the elimination of low-frequency components in sub-bands of the 3D DWT is equivalent to performing a pyramidal 3D filter. This 3D filter brings advantages to our method in reserving the inner parts of detected objects and reducing the ringing around object boundaries. Moreover, we make use of wavelet shrinkage to remove disturbance of intensity temporal consistency and introduce an adaptive threshold based on the entropy of the histogram to obtain optimal detection results. Experimental results show that our method works effectively in situations lacking training opportunities and outperforms several popular techniques.

In our previous work, we proposed wavelet shrinkage estimation (WSE) for nonhomogeneous Poisson process (NHPP)-based software reliability models (SRMs), where WSE is a data-transform-based nonparametric estimation method. Among many variance-stabilizing data transformations, the Anscombe transform and the Fisz transform were employed. We have shown that it could provide higher goodness-of-fit performance than the conventional maximum likelihood estimation (MLE) and the least squares estimation (LSE) in many cases, in spite of its non-parametric nature, through numerical experiments with real software-fault count data. With the aim of improving the estimation accuracy of WSE, in this paper we introduce other three data transformations to preprocess the software-fault count data and investigate the influence of different data transformations to the estimation accuracy of WSE through goodness-of-fit test.

On the basis of wavelet theory, we propose an outlier-detection algorithm for satellite gravity gradiometry by applying a wavelet-shrinkage-de-noising method to some simulation data with white noise and outliers. The result shows that this novel algorithm has a 97% success rate in outlier identification and that it can be efficiently used for pre-processing real satellite gravity gradiometry data.

Computer signal processing is used for quantitative data analysis (QDA) in magnetic resonance spectroscopy (MRS). The main difficulty in QDA is that MRS signals appear to be contaminated with random noise. Noise reduction can be achieved by coherent averaging, but it is not always possible to average many MRS waveforms. Wavelet shrinkage de-noising (WSD) is a technique that can be employed in this case. The potentialities of WSD in MRS, alone and combined with the Cadzow algorithm, are analyzed through computer simulations. The results can facilitate an appropriate application of WSD, as well as a deeper understanding of this technique. © 2002 Wiley Periodicals, Inc. Concepts Magn Reson 14: 388–401, 2002

Filtering time series is an important task in many domains as biomedical signal processing. The Heart Rate Variability (HRV) is the analysis of the RR time series obtained as intervals between heart beats. Usually the RR time series obtained are non-stationary and are present ectopic beats, which prevents extraction of useful information, therefore must often be filtered in order to emphasize different characteristics or properties. This paper presents a method to filter R-R time series, using wavelet shrinkage techniquein order to have a new and more adapted visualization of the HRV’s graphical interpretation as Lorenz plot.

Wavelet shrinkage has been proposed as a highly adaptable approach to signal smoothing, which can produce optimum results in some senses. This paper examines the performance of the method as a function of its parameters, by simulation for time series showing gradual, rapid and discontinuous variations, for a range of signal-to-noise ratios. Some general conclusions are drawn. The effects of the choice of wavelet, choice of threshold and choice of resolution cut-off are considered. The use of the residual autocorrelation as a diagnostic tool is suggested.

In many situations where ambulatory monitoring is needed, the electroencephalogram (EEG) and the electrocardiogram (ECG) are desired to be simultaneously used. Therefore, it would be desirable if one can acquire both EEG and ECG signals with a single measurement. One of the key techniques in such kind of application is to separate EEG and ECG using signal processing techniques. In our study, we have confirmed that by applying non-cephalic reference electrode in the EEG recording, it is possible to obtain ECG signals available for signal processing. We also improved the wavelet shrinkage algorithm by performing window operations in approximation level five of wavelet components to successfully separate the EEG components from the ECG signal. Our results showed that the improved normalized power spectrum were accurate in all frequency bands for the EEG components, while the R peak detection for the ECG were 100 % successful in this study.

The advantage of using DNA microarray data when investigating human cancer gene expressions is its ability to generate enormous amount of information from a single assay in order to speed up the scientific evaluation process. The number of variables from the gene expression data coupled with comparably much less number of samples creates new challenges to scientists and statisticians. In particular, the problems include enormous degree of collinearity among genes expressions, likely violation of model assumptions as well as high level of noise with potential outliers. To deal with these problems, we propose a block wavelet shrinkage principal component (BWSPCA) analysis method to optimize the information during the noise reduction process. This paper firstly uses the National Cancer Institute database (NC160) as an illustration and shows a significant improvement in dimension reduction. Secondly we combine BWSPCA with an artificial neural network-based gene minimization strategy to establish a Block Wavelet-based Neural Network model in a robust and accurate cancer classification process (BWNN). Our extensive experiments on six public cancer datasets have shown that the method of BWNN for tumor classification performed well, especially on some difficult instances with large-class (more than two) expression data. This proposed method is extremely useful for data denoising and is competitiveness with respect to other methods such as BagBoost, RandomForest (RanFor), Support Vector Machines (SVM), K-Nearest Neighbor (KNN) and Artificial Neural Network (ANN).

Noise removal of electrocardiogram (ECG) signal has always been a subject of great study. A novel sparse wavelet shrinkage method is proposed based on maximum likelihood estimation for ECG signal corrupted with Gaussian noise. The method utilizes the prior information on the probability density of the data. The features and shrinkage parameters are estimated directly from the data. Noisy ECG signal collected from clinic recording is processed using the method. The results show that on contrast with traditional methods, the novel wavelet shrinkage method can achieve the optimal denoising of the ECG signal.

In this paper we present methods for removing the noise from a time sequence of digitally subtracted x-ray angiographic images. By observing the contrast agent propagation profile in a region of the angiogram one can estimate the time of arrival of that agent. Due to the large level of noise, it is difficult to detect the moment of the contrast agent arrival accurately. Hence denoising is required. Two methods are presented. The first one is based on 1D Wiener filtering of the time data. Wiener filter was chosen because it presents the optimal linear filter in the least-squares sense. The other method is based on 3D wavelet denoising via wavelet shrinkage technique, which is a nonlinear method. Since it is based on 3D wavelet basis it can perform denoising simultaneously in the spatial as well as in the time dimension of the image sequence. Wavelet based denoising proved to be superior but computationally more demanding. The experiments were performed on a sequence of cerebral angiograms.

Publisher Summary This chapter focuses on wavelet modeling and processing of nasal airflow traces. The study involved a careful review of the tracings extracted from sleep studies conducted on a group of 20 patients who were referred to the Sleep Disorders Laboratory of the University of Virginia Medical Center for evaluation of possible sleep apnea. The fundamental observation that nasal airflow varies continuously was made, so that the usual classification of breathing abnormalities into a finite number of categories is unnecessarily restrictive. Aspects of the signal that can be measured on a continuous scale were determined. The algorithm based on wavelet shrinkage estimation that was developed allowed obtaining precise measurements of the duration of the I/E/NF periods. On the basis of these durations derived measures of breathing that vary on a continuous scale and appear to be related to the characteristics and degree of severity of sleep-disordered breathing among subjects can be constructed. The results were obtained with simulation studies to assess how sensitive the performance of the algorithm is to varying input conditions and to the values of several tuning parameters.

Background: The signals acquired in brain-computer interface (BCI) experiments usually involve several complicated sampling, artifact and noise conditions. This mandated the use of several strategies as preprocessing to allow the extraction of meaningful components of the measured signals to be passed along to further processing steps. In spite of the success present preprocessing methods have to improve the reliability of BCI, there is still room for further improvement to boost the performance even more. Methods: A new preprocessing method for denoising P300-based brain-computer interface data that allows better performance with lower number of channels and blocks is presented. The new denoising technique is based on a modified version of the spectral subtraction denoising and works on each temporal signal channel independently thus offering seamless integration with existing preprocessing and allowing low channel counts to be used. Results: The new method is verified using experimental data and compared to the classification results of the same data without denoising and with denoising using present wavelet shrinkage based technique. Enhanced performance in different experiments as quantitatively assessed using classification block accuracy as well as bit rate estimates was confirmed. Conclusion: The new preprocessing method based on spectral subtraction denoising offer superior performance to existing methods and has potential for practical utility as a new standard preprocessing block in BCI signal processing.

One of many method for noise reduction in measured data is the wavelet-based Wavelet Shrinkage propagated by D. L. Donoho, I. M. Johnstone et al. since about 1990. A crucial step within this approach is the setting of the treshold which decides whether a wavelet coefficient is considered as noise or as data. We propose an one-paramerter family of thresholds. The parameter is the probability of making a false decision. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Wavelab is a library of wavelet-packet analysis, cosine-packet analysis and matching pursuit. The library is available free of charge over the Internet. Versions are provided for Macintosh, UNIX and Windows machines.

A new wavelet shrinkage denoising algorithm for an image is presented, which is based on the local characteristic of an image. The proposed algorithm efficiently reduces noise and achieves better peak signal-to-noise ratio than in previous work. It is shown that this method can reduce noise for low SNR images.

Classification is a powerful tool for the extraction of chemical information from analytical images. However, classification may sometimes not be applicable, when the clusters corresponding to single phases overlap due to high noise levels, such that they are not significantly distinguishable. We investigate the effect of the wavelet shrinkage de-noising algorithm on the subsequent classification of analytical images. By application of wavelet de-noising the distinction of phases in classification can be significantly improved.