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Consider the nonparametric curve estimation problem. Wavelet shrinkage methods are applied to the data in the wavelet domain for noise reduction. After denoising, the function can be estimated by w...

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.

[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.

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

У роботі запропоновано ефективний метод відновлення сигналів SIMS від сильно розмитих дискретних піків. Ця методика грунтується на регуляризації Тихонова-Міллера, де включена апріорна модель розв’язку. Останній – це шумопригнічуючий сигнал, отриманий при використанні фільтра Калмана. Це цікавий методом оцінки, але він може бути використаний тільки тоді, коли ми можемо точно описати наш зразок. Порівнюючи результати запропонованої методики з результатами літератури, наш алгоритм дає найкращі результати без артефактів і коливань, пов'язаних з шумом, і значного поліпшення глибинного аналізу, у той час як коефіцієнт підсилення менш поліпшений, ніж коефіцієнт, отриманий методом вейвлетів. Таким чином, цей новий алгоритм може розширити межі вимірювань SIMS до граничної роздільної здатності. This paper presents an efficient method for recovery of SIMS signals from strongly noised blurred discrete data. This technique is based on Tikhonov-Miller regularization where a priori model of solution is included. The latter is a denoisy signal obtained using the Kalman filter. This is an interesting estimation method, but it can only be used when the system is described precisely. By comparing the results of the proposed technique with those of the literature, our algorithm gives the best results without artifacts and oscillations related to noise and significant improvement of the depth resolution. While, the gain in FWHM is less improved than those obtained by the wavelet technique. Therefore, this new algorithm can push the limits of SIMS measurements towards its ultimate resolution.

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.

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 view of the low signal to noise ration and the difficulty on de-noising for ECG signal collected under unconstrained environment, a GA(Generation Algorithm) based wavelet method of finger ECG de-noising is proposed after a systematic study of wavelet threshold de-noising and generation algorithm. This new algorithm can dynamically get the optimal solution to fit the threshold in accordance with the characteristic of finger ECG. Then the algorithm is verified by fitting ECG and finger ECG. Compared with other algorithm, results show that the proposed method get the better performance according to the performance index including the output SNR, correlation coefficient and root mean square. Keywords-finger ECG; generation algorithm; wavelet de-noising

In Medical diagnosis operations such as feature extraction and object recognition will play the key role. These tasks will become difficult if the images are corrupted with noise. So the development of effective algorithms for noise removal became an important research area in present days. Developing Image denoising algorithms is a difficult task since fine details in a medical image embedding diagnostic information should not be destroyed during noise removal. Many of the wavelet based denoising algorithms use DWT (Discrete Wavelet Transform) in the decomposition stage are suffering from shift variance and lack of directionality. To overcome this in this paper we are proposing the denoising method which uses dual tree complex wavelet transform to decompose the image and shrinkage operation to eliminate the noise from the noisy image. In the shrinkage step we used semi-soft and stein thresholding operators along with traditional hard and soft thresholding operators and verified the suitability of dual tree complex wavelet transform for the denoising of medical images. The results proved that the denoised image using DTCWT (Dual Tree Complex Wavelet Transform) have a better balance between smoothness and accuracy than the DWT and less redundant than UDWT (Undecimated Wavelet Transform). We used the SSIM (Structural similarity index measure) along with PSNR (Peak signal to noise ratio) to assess the quality of denoised images.

The field of terahertz (THz) science and technology has achieved significant progress over the last decades. Research interest focuses on THz spectroscopy and imaging. The signal-to-noise ratio (SNR) of the THz system is of great importance in the application of THz spectroscopy and imaging. In this letter, the wavelet de-noising technology is used to improve SNR and increase the speed of the THz time-domain spectroscopy system by reducing the repeating times.

While wireless sensors are increasingly adopted in various applications, the need of developing data reduction methods to alleviate data transmission rate issue between the sensors and the data interpretation unit becomes more urgent. This article presents a new data reduction method for sensors used in structural health monitoring application. Our goal is to achieve an effective data reduction capability while maintaining adequate power for damage detection. We propose to establish an explicit measure of damage detection capability for the features in the response signals and use this measure to select the subset of the features that balance between the degree of data reduction and the damage detection capability. We also explore a computationally efficient procedure searching for the best subset of the features. This new method is tested on experimentally obtained Lamb wave signals for beam damage detection. Performance comparisons with respect to the existing methods demonstrate the strength of the proposed method.

Cross-validation has been successfully used in various areas of statistics. However, it has not been used much in wavelet shrinkage estimation because fast wavelet methods cannot be applied to deleted data. In this paper, we show this problem can be avoided by using a fast imputation of data. This allows level-dependent cross- validation which is attractive to data with different sparseness. The proposed methods can be easily extended to higher dimensional problem such as image. Results from simulation and examples demonstrate the promising empirical properties of the procedure. In particular, the methods proposed in this work provide outstanding results for non-Gaussian noises because cross-validation is not based on normality assumptions.

The core of the wavelet approach to nonparametric regression is thresholding of wavelet coefficients. This paper reviews a cross-validation method for the selection of the thresholding value in wavelet shrinkage of Oh, Kim, and Lee (2006), and introduces the R package CVThresh implementing details of the calculations for the procedures. This procedure is implemented by coupling a conventional cross-validation with a fast imputation method, so that it overcomes a limitation of data length, a power of 2. It can be easily applied to the classical leave-one-out cross-validation and K-fold cross-validation. Since the procedure is computationally fast, a level-dependent cross-validation can be developed for wavelet shrinkage of data with various sparseness according to levels.

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

The current work addresses topics related to signal filtering via wavelet shrinkage. Wavelets techniques applied to signal filtering go back to the 80’s and an overview about the main results in the area are presented, as well as the most recent contributions, concerning applications and methodological aspects involved. A short discussion about wavelets and a detailed presentation about the threshold operation are given. The main methods to define the threshold values are also described and their performances are tested through numerical simulations for 1D and 2D data. The presented results highlight the potential of associating wavelet methods to signal denoising techniques.

In this paper, we propose a new patch-based image denoising algorithm using graph signal processing. The concept of this algorithm is to take advantage of the redundancy of the BM3D transform and the edge preservation property of graph-based image processing. More specifically, we collect similar patches in the image, and construct a graph by connecting obtained patches. Then we apply a graph wavelet filter bank on graph signals to attenuate additive white gaussian noise by shrinking derived coefficients. We apply our proposed algorithm to depth map denoising. The experimental results demonstrate significant performance gains for the edge preservation and the noise reduction.

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.

Two-dimensional element distributions generated by scanning secondary ion mass spectrometry (SIMS) are characterised by Poisson statistics of small integer values, specially when the concentration of the measured element is in the sub-ppm range. To achieve high signal-to-noise ratios extremely long measurement time is needed. Because of the signal fluctuations from one measurement point to the next, structures even larger than the resolution of the instrument may not be detectable if the differences in concentration are small. This paper reports the application of a wavelet shrinkage algorithm for de-noising of images following Poisson distribution. In reconstructions of SIMS images resulting from this algorithm the noise is significantly suppressed without great loss of lateral resolution.

During ambulatory monitoring, it is sometimes required to record an electroencephalogram (EEG) and an electrocardiogram (ECG) simultaneously. It would be ideal if both EEG and ECG could be obtained with one measurement. Here, we introduce an algorithm that combines the wavelet shrinkage and variable cosine window operation to separate the EEG and ECG components from an EEG signal recorded with a noncephalic reference (NCR). Evaluation using simulated data and actual measured data showed that accurate frequency analysis of EEG and an R-R detection-based heart rate analysis were feasible with our proposed algorithm, which improved the signal-averaging based algorithm so that ECG components containing ectopic beats can be applied.

This paper proposes Empirical Mode Decomposition (EMD) followed by wavelet shrinkage denoising in hyperspectral image classification to improve classification accuracy. EMD decomposes signals into several Intrinsic Mode Functions (IMFs) and a final residue. In this paper, firstly, EMD is applied to each hyperspectral image band separately to obtain the IMFs of all image bands. Then, the first IMF of each band is applied to wavelet shrinkage denoising, as this IMF includes all local high spatial frequency components. The sums of lower order IMFs are then used to reconstruct hyperspectral image bands that are used as new features for classification. Support Vector Machine (SVM) based classification is used as classification approach in this paper. Experimental results show the effectiveness of the proposed approach.

Wavelet shrinkage methods have been very successful in denoising of biological signals. A New wavelet shrinkage method for denoising of biological signals is proposed in this paper. This method is applied to denoise ECG signal corrupted with additive Gaussian noise. We compared the performance of this new method with that of popular shrinkage methods based on hard and soft filters. Simulation results showed that this new method is superior to hard and soft shrinkage methods.

During ambulatory monitoring, it is often required to record the electroencephalogram (EEG) and the electrocardiogram (ECG) simultaneously. It would be ideal if both EEG and ECG can be obtained with one measurement. We introduce an algorithm combining the wavelet shrinkage and signal averaging techniques to extract the EEG and ECG components from an EEG lead signal to a noncephalic reference (NCR). The evaluation using simulation data and measured data showed that the normalized power spectrum unvaried in all frequency bands for the EEG components, and the sensitivity and specificity of R-wave detection for the ECG component were nearly 100%.

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.

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.

Digital radiography is a popular diagnostic imaging method. Denoising and enhancement have an important potential in obtaining as much easily interpretable diagnostic information as possible with reasonable absorbed doses of ionising radiation. Due to the increasing usage of high resolution and high precision images with a limited number of human experts, the computational efficiency of the denoising and enhancement becomes important. In this paper, a local adaptive image enhancement and simultaneous denoising algorithm for fulfilling the requirements of digital X-ray image enhancement is introduced. The algorithm is based on modification of the wavelet transform coefficients by a pointwise nonlinear transformation and reconstructing the enhanced image from the modified wavelet transform coefficients. The implementation of algorithm in software is simple, quick, and universal.

Wavelet shrinkage de-noising is applied to electrophoretic nuclear magnetic resonance (ENMR) data. Both threshold rules for removing noise, namely soft and hard, proposed in Donoho's (1993) VisuShrink, are used simultaneously. Soft thresholding is applied to fine levels of wavelet decomposition coefficients and hard thresholding is applied to coarse levels. This implementation is coordinated by visualizing the features presented in ENMR spectra.

We propose a visual inspection method of defect detection on textile surfaces; selectively removing the textural information from textile surfaces. For this purpose we use wavelet shrinkage, which was originally proposed by Donoho and Johnstone as a method to remove Gaussian white noise (1994, 1995). We also propose a modification of wavelet shrinkage to selectively remove textural information as noise. Once the textural information, is removed from textile surfaces, the remaining inspection processes can be conducted in the image domain. In this way, we can utilize the image processing methods and techniques developed so far for the visual inspection of other industrial products.

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)