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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.

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 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.

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.

Wavelet transform-based filters are widely adopted for noise removal from grayscale digital images because these techniques can effectively combine cancellation of noise and preservation of image details. The aim of this paper is to provide accurate quantitative evaluations of these key filtering features without the limitations (and the errors) of current metrics. For the first time, the exact amounts of filtering distortion and unfiltered noise produced by a wavelet-based denoising filter are formally computed resorting to the filter theory only. Computer simulations are reported in the paper in order to show how residual noise and filtering distortion affect the results at the pixel level. Comparisons with current metrics are also provided.

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.

The method of detrended fluctuation analysis (DFA) is useful in revealing the extent of long-range dependence, it has successfully been applied to different fields of interest. In this paper we proposed a smoothed detrended fluctuation analysis method based on the principle of wavelet shrinkage. The procedure is illustrated and compared with the DFA method by Monte Carlo simulations on fractional Gaussian noise models.

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

A previsao de series temporais e largamente utilizada nas diversas areas do conhecimento humano, principalmente no planejamento e direcionamento estrategico das empresas. O sucesso desta tarefa depende das tecnicas de previsoes aplicadas. Neste artigo, e proposta uma metodologia hibrida para se projetar series temporais. Para a validacao da metodologia foi escolhida uma serie de tempo ja modelada por outros autores, possibilitando a comparacao dos resultados. A metodologia proposta integra as seguintes tecnicas: encolhimento wavelet, decomposicao wavelet de nivel r e redes neurais artificiais (RNAs). Primeiramente, uma serie temporal a ser prevista e submetida ao metodo de filtragem wavelet proposto, o qual a decompoe em componentes de tendencia e de residuo linear. Em seguida, ambas sao decompostas via decomposicao de nivel r, gerando, para cada uma, r+1 componentes wavelet (CWs); e, em seguida, cada CW e individualmente modelada por uma RNA. Finalmente, as previsoes para todas as CWs sao linearmente combinadas, produzindo as previsoes para a serie temporal supracitada. Para avalia-lo, a serie temporal de Canadian Lynx foi usada e todos os resultados alcancados pelo metodo proposto foram melhores do que outros existentes na literatura.

Wavelet shrinkage is a strategy to obtain a nonlinear approximation to a given function f and is widely used in data compression, signal processing and statistics, etc. For Calderon-Zygmund operators T, it is interesting to construct estimator of Tf, based on wavelet shrinkage estimator of f. With the help of a representation of operators on wavelets, due to Beylkin et al., an estimator of Tf is presented in this paper. The almost everywhere convergence and norm convergence of the proposed estimators are established.

In this paper, the generalized Bayes estimator of elliptical distribution parameter’s under asymmetric Linex error loss function is considered. The new shrinkage generalized Bayes estimator by applying wavelet transformation is investigated. We develop admissibility and minimaxity of shrinkage estimator on multivariate normal distribution.We present the simulation in order to test validity of purpose estimator.

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.

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 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 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.

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.

By substituting an anisotropic diffusion operator for the isotropic Laplace operator in the directed diffusion equation, adding two different coefficients in the two diffusion terms, and choosing the image denoised by soft wavelet shrinkage as the initial approximate image, an improved directed diffusion equation model is proposed. Experiments show that the new model can solve the problem that edges and details will be rapidly blurred during the diffusion process in the directed diffusion equation.

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.

In this paper, we introduce a novel hybrid variational model which gen- eralizes the classical total variation method and the wavelet shrinkage method. An alternating minimization direction algorithm is then employed. We also prove that it converges strongly to the minimizer of the proposed hybrid model. Finally, some nu- merical examples illustrate clearly that the new model outperforms the standard total variation method and wavelet shrinkage method as it recovers better image details and avoids the Gibbs oscillations. AMS subject classifications: 90C25, 52A41, 28E99, 62P35

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.

This paper considers the problem of selecting a robust threshold of wavelet shrinkage. Previous approaches reported in literature to handle the presence of outliers mainly focus on developing a robust procedure for a given threshold; this is related to solving a nontrivial optimization problem. The drawback of this approach is that the selection of a robust threshold, which is crucial for the resulting fit is ignored. This paper points out that the best fit can be achieved by a robust wavelet shrinkage with a robust threshold. We propose data-driven selection methods for a robust threshold. These approaches are based on a coupling of classical wavelet thresholding rules with pseudo data. The concept of pseudo data has influenced the implementation of the proposed methods, and provides a fast and efficient algorithm. Results from a simulation study and a real example demonstrate the promising empirical properties of the proposed approaches.

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.

The authors propose here a new method for reducing both impulsive noise and white noise by use of M-transform and wavelet shrinkage. M-transform is a new signal transformation proposed by the authors, and any periodic time signal can be considered as the output of a filter whose input is an M-sequence. By using the properties of M-transform, it is shown that both impulsive noise and white noise can be eliminated by use of first M-transform and then wavelet shrinkage. This method is applied well to the signal obtained in Atomic Force Microscope (AFM) signal which sometimes contains many impulsive noise and white noise. From the results of the experiment, it is shown that the proposed method is very efficient for impulsive noise reduction.

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...

In this paper, the improvement by deconvolution of the depth resolution in Secondary Ion Mass Spectrometry (SIMS) analysis is considered. Indeed, we have developed a new Tikhonov- Miller deconvolution algorithm where a priori model of the solution is included. This is a denoisy and pre-deconvoluted signal obtained from: firstly, by the application of wavelet shrinkage algorithm, secondly by the introduction of the obtained denoisy signal in an iterative deconvolution algorithm. In particular, we have focused the light on the effect of the iterations number on the evolution of the deconvoluted signals. The SIMS profiles are multilayers of Boron in Silicon matrix., {"references":["M. Boulakroune and D. Benatia, \"MultiscaleDeconvolution of Mass\nSpectrometry Signals,\" inAdvanced in Wavelet Theory and Their\nApplications in Engineering, Physics and Technology, In-Tech, 2012,\nch. 7, pp. 125-152.","Yu.N.Drozdov, M. N. Drozdov, A.V. Novikov, P. A. Yunin,and D. V.\nYurasov, \"Layer-by-layerAanalysis ofStructures Containing delta-layers\nby Secondary Ion Mass Spectrometry Taking into Account the TOF-5\nDepth Resolution Function,\"Journal of Surface Investigation, Russian,\nJuly 2012,Vol.6,pp. 574-577.","M. Boulakroune and D. Benatia, \"Improvement of SIMS Multilayer\nProfile Analysis,\" in 6th International Conference on Sciences of\nElectronics, Technologies of Information and Telecommunications\n(SETIT), Sousse 2012, IEEExplore, pp. 716-720.","N. Dahraoui, M. Boulakroune and D. Benatia, \"Traitements numériques\ndes measures par Spectrométrie de masse des Ions Secondaires.\nQuantification des profils en profondeur, Nouvel Algorithme de\nDéconvolution Multi-Résolution,\" in International Congress on\nTelecommunication and Application ICTA'2014, Bejaia- Algeria, 2014,\npp. 325-330.","V. V. Makarov, \"Deconvolution of high dynamic range depth profiling\ndata using the Tikhonov method,\" J. Surf. Interface. Anal. Vol. 27, 1999,\npp. 801-816.","B. Gautier, J. C. Dupuy, R. Prost and G. Prudon, \"Effectiveness and\nlimits of the deconvolution of SIMS depth profiles of boron in\nsilicon,\"Journal of Surface and Interface Analysis, Vol.25, 1997. pp.\n464-477.","B. Gautier, G. Prudon and J. C. Dupuy, \"Toward a better reliability in\nthe deconvolution of SIMS depth profiles,\"Surface and Interface\nAnalysis, 1998, Vol.26, pp. 974-983.","R. Collins, M. G. Dowsett and A. Allen, \"Deconvolution of\nconcentration profiles from SIMS data using measured response\nfunction,\" In International Conference on SIMS, Amesterdam, 1991, pp.\n111-114.","P.N. Allen and M.G. Dowsett, \"Maximum entropy quantification of\nSIMS depth profiles. Behavior as a function of primary ion energy,\"\nSurf. Interface Anal., Vol. 21, 1994, pp. 206-209.\n[10] V. Barakat, B. Guilpart R. Goutte and R. Prost, \"Model-based\nTikhonov- Miller image restoration, \"in International Conference on\nImage Processing (ICIP'97), Washington,IEEExplore,DC, USA,\n1997.Vol. 1, pp. 310-313.\n[11] G. Mancina, R. Prost, G. Prudon, B. Gautier and J. C. Dupuy,\n\"Deconvolution SIMS depth profiles: toward the limits of the resolution\nby self-deconvolution test,\" in SIMS Proceedings papers, the 12th SIMS\nInternational Conference, Elsevier, Brussels, Belgium, 1999. pp. 5-11\n[12] J. Bennett and A. Diebold, \"Round robin study of ultra-shallow B depth\nprofiling experimental conditions,\" In International Conference on\nSecondary Ion Mass Spectrometry1999: Brussels, Belgium ( SIMS XII),\nA. Benninghoven ed. Amesterdam: Elsevier, 2000. pp. 541-548."]}