Search

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...

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.

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.

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 paper is devoted to the new model for image decomposition, that splits an image f into three components u+v+w, where u a piecewise-smooth or the "cartoon" component, v a texture component and w the noise part in variational approach. This decomposition model in fact incorporates the advantages of two preceding models: the second-order total variation minimization of Rudin-Osher-Fatemi (ROF2), and wavelet shrinkage for oscillatory functions. This decomposition model is presented as an extension of the three components decomposition algorithm of Aujol et al. in [Dual norms and image decomposition models, Int. J. Comput. Vis. 63(1)(2005) 85–104]. It also continues the idea introduced previously by authors in [Denoising 3D medical images using a second order variational model and wavelet shrinkage, Imag. Anal. and Rec., Lecture Notes in Computer Science, 7325(2012), 138-145], for two components decomposition model. The ROF2 model was first proposed by Bergounioux et al. in [A second-order model for image denoising, Set-Valued Anal. and Var. Anal., 18(2010), 277-306], it is an improved regularization method to overcome the undesirable staircasing effect. The wavelet shrinkage is well combined to separate the oscillating part due to texture from that due to noise. Experimental results validate the proposed algorithm and demonstrate that the image decomposition model presents effective and comparable performance to other previous models.

In this paper, a novel algorithm based on the local projection noise reduction approach is applied to smooth noise for strongly contaminated chaotic oscillators. Specifically, one-dimensional time series are embedded into a high dimensional phase space and the noise level is defined through orthogonal projections of the data points within the neighbourhood of the reference point onto linear subspaces. The current vector of the phase space is denoised by performing two-dimensional discrete stationary wavelet transform (SWT)-based filtering in the neighbourhood of the phase point. Numerical results show that our algorithm effectively recovers continuous-time chaotic signals in heavy-noise environments and outperforms the classical local projection noise reduction approach for simulated data from the Rössler system and Duffing oscillator at signal-to-noise ratios (SNRs) from 15 to 0 dB, either for the real world data – human breath time series.

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.

In this paper, we present a new class of iterative regularization methods in the setting of Besov spaces, which can be seen as generalizations of J. Xu's method. By incorporating translation invariant wavelet transform, minimizers of the new methods can be understood as the alternative to translation invariant wavelet shrinkage with weight that is dependent on the wavelet decomposition scale and the Besov smooth order. And we generalize the iterative regularization methods to a new class of nonlinear inverse scale spaces with scale and Besov smooth order dependent weight. The numerical results show an excellent denoising effect and improvement over J. Xu's method.

We consider the denoising of a function (an image or a signal) containing smooth regions and edges. Classical ways to solve this problem are variational methods and shrinkage of a representation of the data in a basis or a frame. We propose a method which combines the advantages of both approaches. Following the wavelet shrinkage method of Donoho and Johnstone, we set to zero all frame coefficients with respect to a reasonable threshold. The shrunk frame representation involves both large coefficients corresponding to noise (outliers) and some coefficients, erroneously set to zero, leading to Gibbs-like oscillations in the estimate. We design a specialized (nonsmooth) objective function allowing all these coefficients to be selectively restored, without modifying the other coefficients which are nearly faithful, using regularization in the domain of the restored function. We analyze the well-posedness and the main properties of this objective function. We also propose an approximation of this method which...

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.

Total variation (TV) is a powerful method that brings great benefit for edge-preserving regularization. Despite being widely employed in image processing, it has restricted applicability for 1-D signal processing since piecewise-constant signals form a rather limited model for many applications. Here we generalize conventional TV in 1-D by extending the derivative operator, which is within the regularization term, to any linear differential operator. This provides flexibility for tailoring the approach to the presence of nontrivial linear systems and for different types of driving signals such as spike-like, piecewise-constant, and so on. Conventional TV remains a special case of this general framework. We illustrate the feasibility of the method by considering a nontrivial linear system and different types of driving signals.

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.

The measure technology of low-field pulsed NMR (nuclear magnetic resonance) is a new technology, which has great potential development. It can be widely used in industry and agriculture for product detection as a lossless method. The most important work of NMR measurement is the multi-exponential inversion of NMR signal based on the peak information. But the signal is interfused by noise during the measurement. It is important to reduce the noise while keeping the peaks well. The effective wavelet shrinkage method based on SWT (Stationary Wavelet Transform) is firstly introduced in this paper. All wavelet coefficients at the same scale are shrinked with the same threshold in the traditional algorithm, which is not appropriate for NMR signal because the SNR of NMR signal varies in different position. In view of this, the adaptive thresholds are introduced for NMR signal denoising. Different coefficients at the same wavelet scale are shrinked with different thresholds which are self-adaptive to SNR in our algorithm. The novel method is applied to the low-field pulsed NMR experimental equipment developed by ourselves. The experimental results indicate that our method can keep the peaks and edges while restraining noise well.

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.

MODIS measurements contain the striping signals in the longwave infrared bands because MODIS is a multi-detector sensor. We describe a wavelet method for recovery of MODIS data from its stripe signals. Our work is organized into four broad sections. Section 1 will introduce wavelet shrinkage method for de-noising noisy data, compare the character of the wavelet method and the FFT method in de-noising processing. The objective of section 2 is to find out the scale of MODIS stripe by the wavelet analysis for MODIS stripe data using continuous wavelet transforms. Section 3 analyses Stripe data pattern for the MODIS level 1B stripe data, present the wavelet shrinkage method for MODIS level 1B data. Section 4 will provide a comparing for MODIS cloud product and atmospheric profile product between the original data and de-striped data. We can find that there’s been an improvement in MODIS cloud product and atmospheric profile product after de-striping. And we can get more understanding for the stripe regular pattern.

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.

Most two-dimensional methods for wavelet shrinkage are efficient for edge-preserving image denoising, but they suffer from poor rotation invariance. We address this problem by designing novel shrinkage rules that are derived from rotationally invariant nonlinear diffusion filters. The resulting Haar wavelet shrinkage methods are computationally inexpensive and they offer substantially improved rotation invariance.

We study the connections between discrete one-dimensional schemes for nonlinear diffusion and shift-invariant Haar wavelet shrinkage. We show that one step of (stabilised) explicit discretisation of nonlinear diffusion can be expressed in terms of wavelet shrinkage on a single spatial level. This equivalence allows a fruitful exchange of ideas between the two fields. In this paper we derive new wavelet shrinkage functions from existing diffusivity functions, and identify some previously used shrinkage functions as corresponding to well known diffusivities. We demonstrate experimentally that some of the diffusion-inspired shrinkage functions are among the best for translation-invariant multiscale wavelet shrinkage denoising.

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)

Nonlinear diffusion and wavelet shrinkage are two successfully applied methods for discontinuity preserving denoising of signals and images. Recently, relations between both methods have been established taking into account wavelet shrinkage at one or multiscale. In this paper we show that one step of (stabilized) explicit discretization of nonlinear diffusion can be expressed in terms of tight frame shrinkage on a single spatial level or multiscale. We prove that our scheme permits larger steps while having more choices of shrinkage functions. Numerical examples demonstrate the behavior of our scheme for one or two scales.

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.