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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. [ABSTRACT FROM AUTHOR]

Constant false alarm rate (CFAR) algorithms allow RADAR systems to set detection thresholds and isolated the target from noise or clutter to keeping the false alarm rate at certain level. In this paper a technique added to Improved Switching IS-CFAR system is used to reduce the non-homogenous effect and clutter wall, this technique is called wavelet de-noising. The detection performance of Improving IS-CFAR using wavelet de-noising (I2S-CFAR) processor is compared with the IS-CFAR detectors for homogeneous, non-homogenous and clutter wall. By using wavelet de-noising a gain in signal to noise ratio (SNR) about 2.6dB achieved for the same probability of detection.

Background Researches declared that the super-Gaussian property contributed to the success of some spatial independent component analysis (ICA) algorithms in brain fMRI source separation (e.g., Infomax and FastICA), which implied that sparse approximation transforming the sources (super-Gaussian or Gaussian-like) with stronger super-Gaussian feature would possibly improve the separation performance of these algorithms. New method This paper presented a novel wavelet-shrinkage based ICA (WASICA) model, an extension of our previous SACICA, for single-subject analysis. In contrast, two main aspects had been effectively enhanced: (1) sparse approximation coefficients set formation, made up of two sub-procedures: the wavelet-shrinkage of wavelet packet (WP) tree nodes, and the automatic nodes selection and integration based on the relative WP energy; (2) ICA-based decomposition and reconstruction, composed of temporal dynamics extraction using ICA, WP reconstruction based on the sparse approximation coefficients set and least-square-based functional networks reconstruction. Results The wavelet-shrinkage and the automatic nodes selection and integration simultaneously transformed both the mixtures and underlying sources into effective sparse approximation coefficients sets, exhibiting stronger super-Gaussian distribution; WP projected-back approximation with nuisance-exclusion contributed to networks reconstruction. Comparison with existing methods Simulation 1 revealed WASICA successfully recovered super-Gaussian and some Gaussian-like sources. Simulation 2 and hybrid data experiments showed that WASICA with good temporal performance had stronger source recovery ability and signal detection sensitivity spatially than FastICA, Infomax and SACICA did; the higher intra-consistency in task-related experiments denoted WASICA occupied stronger spatial robustness against smooth kernels. Conclusions WASICA was a promising brain signal separation model with charming spatial–temporal performance. [ABSTRACT FROM AUTHOR]

Wavelet shrinkage is a promising method in image denoising, the key factor of which lies in the threshold selection. A fast and effective wavelet denoising method, called Iterative Generalized Cross-Validation and Fast Translation Invariant (IGCV–FTI) is proposed, which reduces the computation cost of the standard Generalized Cross-Validation (GCV) method and efficiently suppresses the Pseudo-Gibbs phenomena with an extra gain of 1–1.87 dB in PSNR compared with GCV. In the proposed approach, we establish a novel functional relation between the GCV results of two neighboring thresholds based on integer wavelet transform, and combine it with threshold-search interval optimization. As a result, the proposed IGCV reduces the time complexity of original GCV algorithm by two orders of magnitude. In addition, a recursion strategy is applied to expedite the translation invariant. The high efficiency and proficient capacity to remove noise make IGCV–FTI a good choice for image denoising. [ABSTRACT FROM AUTHOR]

In this article, we propose a denoising methodology in the wavelet domain based on a Bayesian hierarchical model using Double Weibull prior. We propose two estimators, one based on posterior mean (Double Weibull Wavelet Shrinker, DWWS) and the other based on larger posterior mode (DWWS-LPM), and show how to calculate them efficiently. Traditionally, mixture priors have been used for modeling sparse wavelet coefficients. The interesting feature of this article is the use of non-mixture prior. We show that the methodology provides good denoising performance, comparable even to state-of-the-art methods that use mixture priors and empirical Bayes setting of hyperparameters, which is demonstrated by extensive simulations on standardly used test functions. An application to real-word dataset is also considered. [ABSTRACT FROM AUTHOR]

The NeighShrink and ModiNeighShrink areefficient image denoising algorithms that are based on universal threshold and discrete wavelet transform. The improved image denoising method based on wavelet thresholding (IIDMWT) method gives better results than the NeighShrink and ModiNeighShrink by using the modified universal threshold. These methods kill too many wavelet coefficients; some of them may contain useful image information. Thus, we may not get good quality of image using these methods. In this paper, we extend the idea of Cai and Silverman for developing a new image denoising method and determine the coefficients of neighboring window for every subband. The experimental results show that in most of the cases, our proposed method performs better than the NeighShrink, ModiNeighShrink, and IIDMWT in terms of peak signal- to-noise ratio and structural similarity index measure. [ABSTRACT FROM AUTHOR]

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 study, in order to verify the effectiveness of the variable filter band discrete wavelet transform (VFB-DWT) and construction method of the variable-band filter (VBF), a fetal ECG extraction has been carried out and the main results obtained are as follows. The approach to configuration VBF by selecting the frequency band only where the fetal ECG component is present was effective to configure the optimal base sensible signal. The extraction of the fetal ECG was successful by applying the wavelet shrinkage to VFB-DWT, which used the constructed VBF. The information entropy was selected as an evaluation index, and two kinds of ECG signals are used to evaluate the wavelet transform basis between the wavelet packet transform (WPT) and the VFB-DWT. One is a synthesized signal composed of white noise, the maternal ECG and the fetal ECG. The other signal is the real target signal separated by independent component analysis (ICA) and has the mother's body noise, the maternal ECG and the fetal ECG. The result shows that the basis by VBF of the VFB-DWT is better than the basis of the WPT that was chosen by the best basis algorithm (BBA). [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. Method 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. [ABSTRACT FROM AUTHOR]

A novel type of threshold functions with a variable parameter is proposed based on the wavelet shrinkage architecture presented by Donoho DL and Johnstone IM, and the effect of different parameter on signal shrinkage is also analyzed. This new type of threshold functions has many advantages over the soft and hard threshold functions. It is continuous and simple in expression, and has any order derivative which makes some kinds of mathematical processing very simple and convenient. It also overcomes the shortcomings of the soft threshold method where there is an invariable dispersion between the estimated wavelet coefficients and the decomposed wavelet coefficients. Further more, the new type of threshold functions is more flexible than the soft-threshold and hard-threshold functions and integrates their excellence features. All these advantages make it possible to construct an adaptive signal denoising algorithm. Comparative experiment results show that the wavelet shrinkage method adopting the new threshold function is more capable of eliminating the noise from the signal, and results in less MSE and higher SNR than the traditional method adopting hard and soft threshold function. [ABSTRACT FROM AUTHOR]

In this paper, the estimated linear models of Box-Jenkins has been compared from time series observations , before and after wavelet shrinkage filtering and then reducing the order of the estimated model from filtered observations (with preserving the accuracy and suitability of the estimated models) and re-compared with the estimated linear model of original observations, depending on some statistical criteria through taking a practical application of time series and using statistical programs such as Statgraphics, NCSS and MATLAB. The results of the paper showed the efficiency of wavelet shrinkage filters in solving the noise problem and obtaining the efficient estimated models , and specifically the wavelet shrinkage filter (dmey) with Soft threshold which estimated it's level using the Fixed Form method of filtered observations , and the possibility of obtaining linear models of the filterd observations with lower orders and higher efficiency compared with the corresponding estimated model of original observations [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we introduce a new Bayesian nonparametric model for estimating an unknown function in the presence of Gaussian noise. The proposed model involves a mixture of a point mass and an arbitrary (nonparametric) symmetric and unimodal distribution for modeling wavelet coefficients. Posterior simulation uses slice sampling ideas and the consistency under the proposed model is discussed. In particular, the method is shown to be computationally competitive with some of best Empirical wavelet estimation methods. [Copyright &y& Elsevier]

We propose a new algorithm for denoising of multivariate function values given at scattered points in $${\mathbb{R}^{d}}$$ . The method is based on the one-dimensional wavelet transform that is applied along suitably chosen path vectors at each transform level. The idea can be seen as a generalization of the relaxed easy path wavelet transform by Plonka (Multiscale Model Simul 7:1474-1496, ) to the case of multivariate scattered data. The choice of the path vectors is crucial for the success of the algorithm. We propose two adaptive path constructions that take the distribution of the scattered points as well as the corresponding function values into account. Further, we present some theoretical results on the wavelet transform along path vectors in order to indicate that the wavelet shrinkage along path vectors can really remove noise. The numerical results show the efficiency of the proposed denoising method. [ABSTRACT FROM AUTHOR]

Abstract: Electrical load disaggregation for end-use recognition in the smart home has become an area of study of its own right. The most well-known examples are energy monitoring, health care applications, in-home activity modeling, and home automation. Real-time energy-use analysis for whole-home approaches needs to understand where and when the electrical loads are spent. Studies have shown that individual loads can be detected (and disaggregated) from sampling the power at one single point (e.g. the electric service entrance for the house) using a non-intrusive load monitoring (NILM) approach. In this paper, we focus on the feature extraction and pattern recognition tasks for non-intrusive residential electrical consumption traces. In particular, we develop an algorithm capable of determining the step-changes in signals that occur whenever a device is turned on or off, and which allows for the definition of a unique signature (ID) for each device. This algorithm makes use of features extracted from active and reactive powers and power factor. The classification task is carried out by Support Vector Machines and 5-Nearest Neighbors methods. The results illustrate the effectiveness of the proposed signature for distinguishing the different loads. [Copyright &y& Elsevier]

The rich information available in hyperspectral imagery has provided significant opportunities for material classification and identification. Due to the problem of the “curse of dimensionality” (called Hughes phenomenon) posed by the high number of spectral channels along with small amounts of labeled training samples, dimensionality reduction is a necessary preprocessing step for hyperspectral data. Generally, in order to improve the classification accuracy, noise bands generated by various sources (primarily the sensor and the atmosphere) are often manually removed in advance. However, the removal of these bands may discard some important discriminative information, eventually degrading the classification accuracy. In this paper, we propose a new strategy to automatically select bands without manual band removal. Firstly, wavelet shrinkage is applied to denoise the spatial images of the whole data cube. Then affinity propagation, which is a recently proposed feature selection approach, is used to choose representative bands from the noise-reduced data. Experimental results on three real hyperspectral data collected by two different sensors demonstrate that the bands selected by our approach on the whole data (containing noise bands) could achieve higher overall classification accuracies than those by other state-of-the-art feature selection techniques on the manual-band-removal (MBR) data, even better than the bands identified by the proposed approach on the MBR data, indicating that the removed “noise” bands are valuable for hyperspectral classification, which should not be eliminated. [ABSTRACT FROM PUBLISHER]

This paper reports on a new mechanism to decrease the number of averages and, consequently, the measurement time of Brillouin optical time-domain analysis (BOTDA) sensors using wavelet shrinkage techniques. Two different wavelet shrinkage techniques, VisuShrink and SureShrink, are applied to denoise signals acquired from measurements in BOTDA sensors. The conventional method to denoise signals in BOTDA sensors is ensemble averaging. Ensemble averaging is a time consuming technique, as it requires many acquisitions of signals to provide an acceptable SNR. To reduce the number of acquisitions, the setup of the BOTDA sensor is modified to denoise acquired signals using VisuShrink or SureShrink before applying ensemble averaging. Experimental results show a significant reduction in the number of averages required to provide an accurate measurement, and consequently, a substantial saving in the measurement time of the sensor. It has been shown that the combination of ensemble averaging with VisuShrink or SureShrink reduces the measurement time of the sensor up to 90%. This reduction in the measurement time enables the implementation of dynamic and fast measurements with BODTA sensors and opens opportunities to target a new range of applications. [ABSTRACT FROM PUBLISHER]

The image de-noising is the process to remove the noise from the image naturally corrupted by the noise. The wavelet method is one among the various methods for recovering infinite dimensional objects like curves, densities, images etc. The wavelet techniques are very effective to remove the noise because of its ability to capture the energy of a signal in few energy transform values. The wavelet methods are based on shrinking the wavelet coefficients in the wavelet domain. This paper concentrates on selecting a threshold for wavelet function estimation. A new threshold value is pro-posed to shrink the wavelet coefficients obtained by wavelet decomposition of a noisy image by considering that the sub band coefficients have a gener-alized Gaussian distribution. The proposed threshold value is based on the power of 2 in the size 2J x 2J of the data that can be computed efficiently. The experiment has been conducted on various test images to compare with the established threshold parameters. The result shows that the proposed threshold value removes the noise significantly. [ABSTRACT FROM AUTHOR]

Abstract: 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. [Copyright &y& Elsevier]

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. [ABSTRACT FROM AUTHOR]

Abstract: 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. [Copyright &y& Elsevier]

Abstract: Objective: We propose a method for preprocessing event-related functional magnetic resonance imaging (fMRI) data that can lead to enhancement of template-free activation detection. The method is based on using a figure of merit to guide the wavelet shrinkage of a given fMRI data set. Background: Several previous studies have demonstrated that in the root-mean-square error setting, wavelet shrinkage can improve the signal-to-noise ratio of fMRI time courses. However, preprocessing fMRI data in the root-mean-square error setting does not necessarily lead to enhancement of template-free activation detection. Motivated by this observation, in this paper, we move to the detection setting and investigate the possibility of using wavelet shrinkage to enhance template-free activation detection of fMRI data. Methodology: The main ingredients of our method are (i) forward wavelet transform of the voxel time courses, (ii) shrinking the resulting wavelet coefficients as directed by an appropriate figure of merit, (iii) inverse wavelet transform of the shrunk data, and (iv) submitting these preprocessed time courses to a given activation detection algorithm. Two figures of merit are developed in the paper, and two other figures of merit adapted from the literature are described. Results: Receiver-operating characteristic analyses with simulated fMRI data showed quantitative evidence that data preprocessing as guided by the figures of merit developed in the paper can yield improved detectability of the template-free measures. We also demonstrate the application of our methodology on an experimental fMRI data set. Conclusions: The proposed method is useful for enhancing template-free activation detection in event-related fMRI data. It is of significant interest to extend the present framework to produce comprehensive, adaptive and fully automated preprocessing of fMRI data optimally suited for subsequent data analysis steps. [Copyright &y& Elsevier]

In this paper, a new denoising method is proposed for hyperspectral data cubes that already have a reasonably good signal-to-noise ratio (SNR) (such as 600 : 1). Given this level of the SNR, the noise level of the data cubes is relatively low. The conventional image denoising methods are likely to remove the fine features of the data cubes during the denoising process. We propose to decorrelate the image information of hyperspectral data cubes from the noise by using principal component analysis (PCA) and removing the noise in the low-energy PCA output channels. The first PCA output channels contain a majority of the total energy of a data cube, and the rest PCA output channels contain a small amount of energy. It is believed that the low-energy channels also contain a large amount of noise. Removing noise in the low-energy PCA output channels will not harm the fine features of the data cubes. A 2-D bivariate wavelet thresholding method is used to remove the noise for low-energy PCA channels, and a 1-D dual-tree complex wavelet transform denoising method is used to remove the noise of the spectrum of each pixel of the data cube. Experimental results demonstrated that the proposed denoising method produces better denoising results than other denoising methods published in the literature. [ABSTRACT FROM AUTHOR]

Abstract: Noise reduction without any prior knowledge of noise or signals is addressed in this study. Compared with conventional filters, wavelet shrinkage can respect this requirement to reduce noise from received signal in wavelet coefficients. However, wavelet threshold depends on an estimate of noise deviation and a weight relating signal''s length cannot be applied in every case. This paper uses particle swarm optimization (PSO) to explore a suitable threshold in a complete solution space, named PSOShrink. A general-purpose objective function which is derived from blind signal separation (BSS) theory is further proposed. In simulation, four benchmarks signals and three degrading degrees are testing; meanwhile, three existing algorithm with state-of-the-art are performed for comparison. PSOShrink can not only recovers source signals from a heavy blurred signal but also remains details of a source signal from a light blurred signal; moreover, it performs outstanding denoising in every simulation case. [Copyright &y& Elsevier]

In this paper, we have proposed a multilevel soft thresholding technique for noise removal in Daubechies complex wavelet transform domain. Two useful properties of Daubechies complex wavelet transform, approximate shift invariance and strong edge representation, have been explored. Most of the uncorrelated noise gets removed by shrinking complex wavelet coefficients at the lowest level, while correlated noise gets removed by only a fraction at lower levels, so we used multilevel thresholding and shrinkage on complex wavelet coefficients. The proposed method firstly detects strong edges using imaginary components of complex coefficients and then applies multilevel thresholding and shrinkage on complex wavelet coefficients in the wavelet domain at non-edge points. The proposed threshold depends on the variance of wavelet coefficients, the mean and the median of absolute wavelet coefficients at a particular level. Dependence of these parameters makes this method adaptive in nature. Results obtained for one-dimensional signals and two-dimensional images demonstrate an improved denoising performance over other related methods available in the literature. [ABSTRACT FROM AUTHOR]

This paper presents a non-linear filtering method based on the multiresolution analysis of the Discrete Wavelet Transform (DWT). The main idea is to use the time-frequency localization properties of the wavelet decomposition. The proposed algorithm is using an extra decomposition of the identified noise in order to reduce the correlation between the electrocardiogram (ECG) signal and noise. The linear denoising approach assumes that the noise can be found within certain scales, for example, at the finest scales when the coarsest scales are assumed to be noise-free. The non-linear thresholding approach involves discarding the details exceeding a certain limit. This approach assumes that every wavelet coefficient contains noise which is distributed over all scales. The non-linear filter thresholds the wavelet coefficients and subtracts the correlated noise. The used threshold depends on the noise level in each of the frequency bands associated to the wavelet decomposition. The proposed non-linear filter acts by thresholding the detail coefficients in a particular way, in order to eliminate the correlation between the noise and the signal. In this paper, in order to evaluate the proposed filtering method, signals from the MIT-BIH database have been used, and the filtering procedure was performed with added Gaussian noise. The proposed procedure was compared with ordinary wavelet transform and wavelet packet transform based denoising procedures, the followed parameters are the signal to noise ratio and the denoising error. [ABSTRACT FROM AUTHOR]

Abstract: The paper presents a novel despeckling method, based on Daubechies complex wavelet transform, for medical ultrasound images. Daubechies complex wavelet transform is used due to its approximate shift invariance property and extra information in imaginary plane of complex wavelet domain when compared to real wavelet domain. A wavelet shrinkage factor has been derived to estimate the noise-free wavelet coefficients. The proposed method firstly detects strong edges using imaginary component of complex scaling coefficients and then applies shrinkage on magnitude of complex wavelet coefficients in the wavelet domain at non-edge points. The proposed shrinkage depends on the statistical parameters of complex wavelet coefficients of noisy image which makes it adaptive in nature. Effectiveness of the proposed method is compared on the basis of signal to mean square error (SMSE) and signal to noise ratio (SNR). The experimental results demonstrate that the proposed method outperforms other conventional despeckling methods as well as wavelet based log transformed and non-log transformed methods on test images. Application of the proposed method on real diagnostic ultrasound images has shown a clear improvement over other methods. [Copyright &y& Elsevier]

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. [ABSTRACT FROM AUTHOR]

Abstract: 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%. [Copyright &y& Elsevier]

Many shrinkage functions have been introduced and applied for the wavelet shrinkage denoising of computed tomography (CT) images. However, these functions have problems in continuity of functions and cause “shrinkage artifacts”. Therefore, we designed a new and smooth shrinkage function using noise distribution. The proposed shrinkage function was designed under the following four conditions: (1) use of noise distribution, (2) shrunk coefficients having all ranges of amplitude, (3) function continuity, and (4) property of a function that is controllable by two parameters. The designed function was applied to phantom and chest CT images and denoising performance was compared with other functions. In the proposed method, edge and pixel values were maintained when compared with previous functions, the occurrence of shrinkage artifacts was smaller, and high- quality denoised images were obtained. The proposed shrinkage function is effective for low-dose noisy CT images when using accurately selected parameters. [ABSTRACT FROM AUTHOR]

Abstract: This paper compares classical filtering techniques (Savitzky–Golay, Adaptive Degree Polynomial Filter, Fourier denoising, Butterworth and Chebyshev IIR filters) and the wavelet shrinkage (31 mother wavelets, 3 thresholding techniques and 11 decomposition levels). These techniques were compared with the original noisy signal and the reference signal, denoised experimentally by the averaging of 64 measurements. The best similarity to reference signal was observed in the case of filters, but they slightly oversmoothed the signal. The wavelet shrinkage gave less denoised signals. The significant influence of the thresholding technique and decomposition level was observed (the best conditions—the level 2 or 3 and soft thresholding). Changing of the mother wavelet almost does not change the result, which is similar to the earlier literature findings. The presented results can be used as general recommendations for denoising of the densitometric fingerprints before applying further chemometric algorithms. The best choices are: Savitzky–Golay filter of appropriate (optimized against the autocorrelation) window width or wavelet shrinkage with Haar wavelet, soft thresholding and high decomposition level. [Copyright &y& Elsevier]

Since Donoho et al. proposed the wavelet thresholding method for signal denoising, many different denoising approaches have been suggested. In this paper, we present three different wavelet shrinkage methods, namely NeighShrink, NeighSure and NeighLevel. NeighShrink thresholds the wavelet coefficients based on Donoho's universal threshold and the sum of the squares of all the wavelet coefficients within a neighborhood window. NeighSure adopts Stein's unbiased risk estimator (SURE) instead of the universal threshold of NeighShrink so as to obtain the optimal threshold with minimum risk for each subband. NeighLevel uses parent coefficients in a coarser level as well as neighbors in the same subband. We also apply a multiplying factor for the optimal universal threshold in order to get better denoising results. We found that the value of the constant is about the same for different kinds and sizes of images. Experimental results show that our methods give comparatively higher peak signal to noise ratio (PSNR), are much more efficient and have less visual artifacts compared to other methods. [ABSTRACT FROM AUTHOR]

Abstract: The digital processing of chromatographic thin-layer plate images has increasing popularity among last years. When using a camera instead of flatbed scanner, the charged coupled device (CCD) noise is a well-known problem—especially when scanning dark plates with weakly fluorescing spots. Various techniques are proposed to denoise (smooth) univariate signals in chemometric processing, but the choice could be difficult. In the current paper the classical filters (Savitzky–Golay, adaptive degree polynomial filter, Fourier denoising, Butterworth and Chebyshev infinite impulse response filters) were compared with the wavelet shrinkage (31 mother wavelets, 3 thresholding techniques and 8 decomposition levels). The signal obtained from 256 averaged videoscans was treated as the reference signal (with noise naturally suppressed, which was found to be almost white one). The best choice for denoising was the Haar mother wavelet with soft denoising and any decomposition level larger than 1. Satisfying similarity to reference signal was also observed in the case of Butterworth filter, Savitzky–Golay smoothing, ADPF filter, Fourier denoising and soft-thresholded wavelet shrinkage with any mother wavelet and middle to high decomposition level. The Chebyshev filters, Whittaker smoother and wavelet shrinkage with hard thresholding were found to be less efficient. The results obtained can be used as general recommendations for univariate denoising of such signals. [Copyright &y& Elsevier]

For regularly spaced one-dimensional data, wavelet shrinkage has proven to be a compelling method for non-parametric function estimation. We create three new multiscale methods that provide wavelet-like transforms both for data arising on graphs and for irregularly spaced spatial data in more than one dimension. The concept of scale still exists within these transforms, but as a continuous quantity rather than dyadic levels. Further, we adapt recent empirical Bayesian shrinkage techniques to enable us to perform multiscale shrinkage for function estimation both on graphs and for irregular spatial data. We demonstrate that our methods perform very well when compared with several other methods for spatial regression for both real and simulated data. Although we concentrate on multiscale shrinkage (regression) we present our new ‘wavelet transforms’ as generic tools intended to be the basis of methods that might benefit from a multiscale representation of data either on graphs or for irregular spatial data. [ABSTRACT FROM AUTHOR]

We present novel wavelet-based inpainting algorithms. Applying ideas from anisotropic regularization and diffusion, our models can better handle degraded pixels at edges. We interpret our algorithms within the framework of forward-backward splitting methods in convex analysis and prove that the conditions for ensuring their convergence are fulfilled. Numerical examples illustrate the good performance of our algorithms. [ABSTRACT FROM AUTHOR]

A wavelet method is proposed for recovering damaged images. The proposed method combines wavelet shrinkage with preprocessing based on a binning process and an imputation procedure that is designed to extend the scope of wavelet shrinkage to data with missing values and perturbed locations. The proposed algorithm, termed as the BTW algorithm is simple to implement and efficient for recovering an image. Furthermore, this algorithm can be easily applied to wavelet regression for one-dimensional (1-D) signal estimation with irregularly spaced data. Simulation studies and real examples show that the proposed method can produce substantially effective results. [ABSTRACT FROM AUTHOR]

Abstract: We first generalize the wavelet-based iterative regularization method and the wavelet-based inverse scale space to shift invariant wavelet-based cases for image restoration. Then, a method to estimate the scale parameter is proposed from wavelet-based iterative regularization; different parameters with different iterations are obtained. The wavelet-based iterative regularization with the new parameter, which controls the extent of denoising more precisely in the wavelet domain, leads to iterative global wavelet shrinkage. We also obtain a time adaptive wavelet-based inverse scale space from the iterative procedure with the proposed parameter. We provide a proof of the convergence and obtain a stopping criterion for the iterative procedure with the new scale parameter based on wavelet transform. The proposed iterative regularized method obtains quite accurate results on a variety of images. Numerical experiments show that the proposed methods can efficiently remove noise and well preserve the details of images. [Copyright &y& Elsevier]

Abstract: We study a class of numerical schemes for nonlinear diffusion filtering that offers insights on the design of novel wavelet shrinkage rules for isotropic and anisotropic image enhancement. These schemes utilise analytical or semi-analytical solutions to dynamical systems that result from space-discrete nonlinear diffusion filtering on minimalistic images with pixels. We call them locally analytic schemes (LAS) and locally semi-analytic schemes (LSAS), respectively. They can be motivated from discrete energy functionals, offer sharp edges due to their locality, are very simple to implement because of their explicit nature, and enjoy unconditional absolute stability. They are applicable to singular nonlinear diffusion filters such as TV flow, to bounded nonlinear diffusion filters of Perona–Malik type, and to tensor-driven anisotropic methods such as edge-enhancing or coherence-enhancing diffusion filtering. The fact that these schemes use processes within -pixel blocks allows to connect them to shift-invariant Haar wavelet shrinkage on a single scale. This interpretation leads to novel shrinkage rules for two- and higher-dimensional images that are scalar-, vector- or tensor-valued. Unlike classical shrinkage strategies they employ a diffusion-inspired coupling of the wavelet channels that guarantees an approximation with an excellent degree of rotation invariance. By extending these schemes from a single scale to a multi-scale setting, we end up at hybrid methods that demonstrate the possibility to realise the effects of the most sophisticated diffusion filters within a fairly simplistic wavelet setting that requires only Haar wavelets in conjunction with coupled shrinkage rules. [Copyright &y& Elsevier]