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Highlights • A novel designed EEG-EOG signal contamination model to quantitatively validate artifact removal from EEGs. • A two-stage wavelet shrinkage method proposed for the quality of the reconstructed EEG signal and evaluated in the frequency spectrum, which represents how much the original specific brain-state characteristic can be reconstructed. • We checked the threshold multiplier at both stage-I, stage-II and L (decomposition level). • Westated the importance of the threshold multiplier and L in the proposed scheme. • We used the real EOG and EEG signal to demonstrate the effectiveness of proposed scheme. Abstract Electroencephalogram (EEG) data inevitably contain large amounts of noise, particularly from ocular potentials in tasks with eye movements, known as electro-oculography (EOG) artifact, which has been a crucial issue in brain–computer-interface studies. This time-frequency characteristic has been substantially dealt with in previous proposed denoising algorithms that relied on a consistent assumption based on the single-noise component model. However, the traditional model is not applicable for biomedical signals that consist of multiple signal components, such as weak EEG signals that are easily recognized as noise because of the signal amplitude with respect to the EOG signal. In consideration of the realistic signal contamination, we designed a novel EEG-EOG signal contamination model to quantitatively validate artifact removal from EEGs. We then proposed the two-stage wavelet shrinkage method with the decomposition of the undecimated wavelet transform (UDWT), which is suitable for signal structure. Open-source clinical intracranial EEGs with the hundred dataset in each behavioral condition were introduced to the validation as "true EEG" before the contamination of artificial EOGs. The quality of the reconstructed EEG signal has evaluated in the frequency spectrum, which represents how much the original specific brain-state characteristic can be reconstructed. Numerical analyses demonstrated that the first stage pursued abrupt changes with high amplitudes provided by assumed EOGs, and the second stage provided the EEG frequency spectrum as observed in the original signal. What the performance exceeded the conventional shrinkage suggests that threshold values is required to be set properly depending on individual amplitudes of contaminated bio-signal sources as our proposed method demonstrated. This result focused on the actual amplitude-frequency structure in the polygenetic signal. It not only provided the decomposition performance, but also revealed how bio-signals are mixed together by using a new standard model for robust validation in the EEG-EOG signal contamination. [ABSTRACT FROM AUTHOR]

The X-ray angiogram image denoising is always one of the most popular research in the field of computer vision. While the methods removed the noise, the useful structure (such as peripheral vascular) had also been smoothed, the fundamental reason is that the denoising methods cannot efficiently distinguish structural areas from flat areas. In this paper, we have proposed a spatially adaptive image denoising (SAID) method which contains two steps: spatially adaptive gradient descent (SAGD) image denoising and dual-domain filter (DDF). The SAGD denoising method contains the following parts: first of all, the wavelet shrinkage method is used to estimate redundant information which is composed of the noise and useful structures; secondly, according to the characteristic of second order matrix, a spatially adaptive gradient factor (SAGF) has been constructed to distinguish the structure from flat areas; finally, the SAGF replaces the original gradient factor and then the SAGD image denoising method is formed. To further improve the quality of the SAGD image, the SAGD image is re-denoised by a modified DDF which is guided with a rotationally invariant non-local filter (RINLF) in spatial domain and gets structural details by wavelet shrinkage in frequency domain. The results of simulation experiments verify that the proposed SAID method can get well quantitative and qualitative results which are even superior to those using the state-of-the-art denoising methods. Even more, the fluctuation of peak signal-to-noise ratio (PSNR) value is very small with a small disturbance of SAGF, which illustrates that our algorithm is more robust than the prior progressive image denoising (PID) method. Moreover, the comparison results of the extensive experiments on clinical X-ray cardiovascular angiogram images further illustrate that our method can yield clearer cardiovascular images which can provide more useful vascular information for clinicians to analyze and diagnose the cardiovascular diseases. [ABSTRACT FROM AUTHOR]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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: Lateral correlation analyses are carried out in different scales for two sets of full-scale thunderstorm downburst full wind speed time series. These two sets of data were recorded at the TTU field site, Texas, USA, on June 4 and 15, 2002, respectively. The same data sets were also used in the authors’ previous paper [L. Chen, C.W. Letchford, Proper orthogonal decomposition of two vertical profiles of full-scale nonstationary correlated downburst wind speeds, J. Wind Eng. Ind. Aerodyn., 93(3)(2005) 187–266.], which presents a methodology to model downburst vertical profiles. The statistical procedures utilized in [7], such as the POD technique, the wavelet shrinkage for time-varying mean inference, the two-stage weighted moving-average method for time-varying variance inference and the Priestley''s EPSD estimator, are also employed in this paper and their details are thus omitted. While in [7] the authors employed the proper orthogonal decomposition (POD) to reduce the dimensions, POD in this article is employed to measure the degree of the correlation between two deterministic time series. Conventionally, wind speeds are decomposed to a time-varying mean speed and a nonstationary fluctuating speed by virtue of wavelet shrinkage [7]. Time-varying mean speeds are in the largest scale, which are essentially due to translations of storms and radial velocities of spreading flow. It was observed that the time-varying standard deviations [7] of fluctuating speeds are basically driven by time-varying mean speeds other than small-scale turbulence. Therefore, time-varying standard deviations are considered in the medium scale. Finally, the modulated fluctuating speeds are viewed in the smallest scale and due to small-scale turbulence. It is found that (1) the two lateral profiles are fully correlated and almost evenly spatially distributed in the largest and medium scales with more than 96% of the total energy; (2) they are uncorrelated in the smallest scale since the measurement locations are at least 263m apart. [Copyright &y& Elsevier]

Summary: Ordered subset expectation–maximization (OSEM) method in positron emission tomography (PET) has been very popular recently. It is an iterative algorithm and provides images with superior noise characteristics compared to conventional filtered backprojection (FBP) algorithms. Due to the lack of smoothness in images in OSEM iterations, however, some type of inter-smoothing is required. For this purpose, the smoothing based on the convolution with the Gaussian kernel has been used in clinical PET practices. In this paper, we incorporated a robust wavelet de-noising method into OSEM iterations as an inter-smoothing tool. The proposed wavelet method is based on a hybrid use of the standard wavelet shrinkage and the robust wavelet shrinkage to have edge preserving and robust de-noising simultaneously. The performances of the proposed method were compared with those of the smoothing methods based on the convolution with Gaussian kernel using software phantoms, physical phantoms, and human PET studies. The results demonstrated that the proposed wavelet method provided better spatial resolution characteristic than the smoothing methods based on the Gaussian convolution, while having comparable performance in noise removal. [Copyright &y& Elsevier]

Abstract: This paper describes a technique for inverse halftoning based on the wavelet domain deconvolution that comprises Fourier-domain followed by wavelet-domain noise suppression, in order to benefit from the advantages of each of them. The proposed algorithm can be formulated as a linear deconvolution problem. In fact, we model such a gray-scale image to be the result of a convolution of the original image with a point spread function (PSF) and a colored noise. Our method performs inverse halftoning by first inverting the model specified convolution operator and then attenuating the residual noise using scalar wavelet-domain shrinkage. Using simulations, we verify that the proposed method is competitive with state-of-the-art inverse halftoning techniques in the mean-square-sense and that has also good visual performance. We illustrate the results with simulations on some examples. [Copyright &y& Elsevier]

Abstract: The paper proposes a novel analysis framework for nonstationary wind speeds, from which accumulated results can potentially lead to or enhance empirical nonstationary wind speed models such as the hybrid one for downbursts in (Eng. Struct. 26 (2004) 619). This framework is motivated by the proper orthogonal decomposition (POD) technique and consists of four major steps: separation, POD, approximation and property inference. In the first step, the original wind speed time histories are separated into their time-varying mean speeds and fluctuating speeds through wavelet shrinkage, which is a promising new tool for smoothing; fluctuating speeds are further expressed as the product of their time-varying standard deviations and normalized fluctuating speeds with unit variance. In the second step, the POD is applied to the time-varying means, standard deviations and normalized fluctuation. In the third step, by properly selecting the number of retained modes, the original time series can be approximated to a numerical model. Finally, wind properties such as velocity vertical profiles and turbulence vertical profiles can be calculated from the model. The POD employed herein is a specific POD for arbitrary multivariate data representation. The normalized fluctuations are characterized by both their power spectral densities (PSD) and evolutionary power spectral densities (EPSD). The concept of EPSD for nonstationary processes is briefly presented and one EPSD estimator is given. Specifically, the PSD/EPSD of an original process is related to the PSD/EPSD of the principal coordinate process obtained by the POD. This framework is applied to two sets of nonstationary full-scale thunderstorm downburst wind speed time series. Many appealing downburst properties are obtained and the benefit of the POD is demonstrated. [Copyright &y& Elsevier]

Wavelet shrinkage denoising of the displacement estimates to reduce noise artefacts, especially at high overlaps in elastography, is presented in this paper. Correlated errors in the displacement estimates increase dramatically with an increase in the overlap between the data segments. These increased correlated errors (due to the increased correlation or similarity between consecutive displacement estimates) generate the so-called “worm” artefact in elastography. However, increases in overlap on the order of 90% or higher are essential to improve axial resolution in elastography. The use of wavelet denoising significantly reduces errors in the displacement estimates, thereby reducing the worm artefacts, without compromising on edge (high-frequency or detail) information in the elastogram. Wavelet denoising is a term used to characterize noise rejection by thresholding the wavelet coefficients. Worm artefacts can also be reduced using a low-pass filter; however, low-pass filtering of the displacement estimates does not preserve local information such as abrupt change in slopes, causing the smoothing of edges in the elastograms. Simulation results using the analytic 2-D model of a single inclusion phantom illustrate that wavelet denoising produces elastograms with the closest correspondence to the ideal mechanical strain image. Wavelet denoising applied to experimental data obtained from an in vitro thermal lesion phantom generated using radiofrequency (RF) ablation also illustrates the improvement in the elastogram noise characteristics. (E-mail: tvarghese@wisc.edu) [Copyright &y& Elsevier]

This paper proposes a new method for image denoising with edge preservation and enhancement, based on image multi-resolution decomposition by a redundant wavelet transform. At each resolution, the coefficients associated with noise and the coefficients associated with edges are modeled by Gaussians, and a shrinkage function is assembled. The shrinkage functions are combined in consecutive resolutions, and geometric constraints are applied to preserve edges that are not isolated. Within the proposed framework, edge related coefficients may be enhanced and denoised simultaneously. Finally, the inverse wavelet transform is applied to the modified coefficients. This method is adaptive, and performs well for images contaminated by natural and artificial noise. [Copyright &y& Elsevier]

The modeling of biological systems has now become an essential prerequisite for effective bioprocess design, optimization and analysis. The difficulties present in using conventional techniques to model such a complex system make the application of artificial neural networks (ANNs) to these problems particularly attractive because of their capability for nonlinear mapping and lack of necessity for detailed mechanistic knowledge. However, building a reliable ANN model requires sufficient training data, which may be difficult when data are collected from litre-scale experiments. In this work, a bioconversion (with only limited experimental data) was firstly modeled by a radial basis function (RBF) neural network. Although the model provided a very low variance between experiment and simulation, it tended to result in oscillatory behaviour, which clearly does not reflect the accurate profile of the reaction. In order to overcome this drawback, wavelet shrinkage with biorthogonal filters was used to generate a reconstructed function using the RBF model as a base. The synthesis of N-acetyl-d-neuraminic acid by the enzymatic condensation of pyruvate with N-acetyl-d-mannosamine was used as a case study to show the effectiveness of the approach. The effects of alternative filters and border distortion are also discussed. [Copyright &y& Elsevier]