Wavelet-based Denoising Research Articles

Denoising methods for thermomechanical decomposition for quasi-equilibrium molecular dynamics simulations

In this work, we applied robust denoising methods well established in the signal processing field for the thermomechanical decomposition of velocity data obtained from molecular dynamics (MD) simulations. In the decomposition, the atomic velocity was assumed to be the sum of the mechanical velocity and the thermal velocity, which can be linked to the stress and temperature field at the continuum scale, respectively. For the quasi-equilibrium process, with the thermal velocity treated as the Gaussian distributed stationary noise with zero mean and a positive variance that is linearly proportional to temperature and mechanical velocity as the clean signal, the velocity decomposition can be recasted into a denoising problem, for which powerful denoising methods have been developed to estimate a clean signal from noisy data. We investigated the widely-used linear parametric real-domain, linear nonparametric Fourier-based, and nonlinear nonparametric wavelet-based denoising methods, first on their theoretical properties and then made comparsion among them for denosing some synthetic noisy 1-dimensional (1D) data generated from MD simulations. The nonlinear wavelet-based thresholding estimator possessed better optimality properties than the other estimators, and also outperformed the other estimators in the synthetic data test. A further test comparing the various denoising methods for an adiabatic shear crack nucleation and propagation process simulated using MD simulations showed better performance by the wavelet-based denoisng method. Results from this work reveal good potential of applying wavelet-based denoising method to the study of thermomechanical processes simulated using MD simulations.

A Comparative Study on Thresholding Methods in Wavelet-based Image Denoising

Wavelet-based image denoising is an important technique in the area of image noise reduction. Wavelets have their natural ability to represent images in a very sparse form which is the foundation of wavelet-based denoising through thresholding. This paper explores properties of several representative thresholding techniques in wavelets denoising, such as VisuShrink, SureShrink, BayesShrink and Feature Adaptive Shrinkage. A quantitative comparison between these techniques through PSNR (Peak Signal-to-Noise Ratio) is also given.

A Novel Image Denoising using Matched Partial Biorthogonal Wavelets and Adaptive Thresholding

denoising of a natural image corrupted by Gaussian noise is a problem in signal or image processing Even though much work has been done in the field of wavelet thresholding, most of it was focused on statistical modeling of wavelet coefficients and the optimal choice of thresholds. This paper describes a new method for suppression of noise in image by fusing the wavelet Denoising technique with optimized thresholding function, improving the denoised results significantly by using partial biorthogonal wavelets. In today's scenario denoising techniques use the classical orthonormal wavelets for decomposition of an image corrupted with additive white Gaussian noise, upon which various thresholding strategies are built. We present a method to design partial biorthogonal wavelet bases and report on their potential for denoising. This paper describes a new method for suppression of noise in image by fusing the wavelet Denoising technique with optimized thresholding function, improving the denoised results significantly. Simulated noise images are used to evaluate the denoising performance of proposed algorithm along with another wavelet-based denoising algorithm. Experimental result shows that the proposed denoising method outperforms standard wavelet denoising techniques in terms of the PSNR and the preservation of edge information. The use of available biorthogonal wavelets in image denoising is less common because of their poor performance. But when we combine the approach of fusion with partial biorthogonal wavelets then the performance is increases in comparison of traditional methodology. This point to the importance of matching when using wavelet-based denoising.

A Wavelet-Based Mammographic Image Denoising and Enhancement with Homomorphic Filtering

Breast cancer continues to be a significant public health problem in the world. The diagnosing mammography method is the most effective technology for early detection of the breast cancer. However,...

Casein Aggregates Built Step-by-Step on Charged Polyelectrolyte Film Surfaces Are Calcium Phosphate-cemented

The possible mechanism of casein aggregation and micelle buildup was studied in a new approach by letting α-casein adsorb from low concentration (0.1 mg·ml(-1)) solutions onto the charged surfaces of polyelectrolyte films. It was found that α-casein could adsorb onto both positively and negatively charged surfaces. However, only when its negative phosphoseryl clusters remained free, i.e. when it adsorbed onto a negative surface, could calcium phosphate (CaP) nanoclusters bind to the casein molecules. Once the CaP clusters were in place, step-by-step building of multilayered casein architectures became possible. The presence of CaP was essential; neither Ca(2+) nor phosphate could alone facilitate casein aggregation. Thus, it seems that CaP is the organizing motive in the casein micelle formation. Atomic force microscopy revealed that even a single adsorbed casein layer was composed of very small (in the range of tens of nanometers) spherical forms. The stiffness of the adsorbed casein layer largely increased in the presence of CaP. On this basis, we can imagine that casein micelles emerge according to the following scheme. The amphipathic casein monomers aggregate into oligomers via hydrophobic interactions even in the absence of CaP. Full scale, CaP-carrying micelles could materialize by interlocking these casein oligomers with CaP nanoclusters. Such a mechanism would not contradict former experimental results and could offer a synthesis between the submicelle and the block copolymer models of casein micelles.

A Novel Intelligent Wavelet Domain Noise Filtration Technique:Application to Medical Images

Medical images, acquired with low exposure to radiation or after administering low-dose of imaging agents, often suffer due to noise arising from physiological sources and from acquisition hardware. The noise can be detrimental to the correct diagnosis as well for the computation of quantitative functional information. To overcome these deficiencies, this paper presents a genetic algorithm-based wavelet domain denoising technique. The proposed technique incorporates genetic algorithm within wavelet denoising framework for threshold optimization. The main purposes of the new technique are twofold: first, it intelligently adapts itself to various types of image noise without any prior knowledge of imaging process; secondly, it balances the preservation of diagnostic relevant details against the degree of noise reduction by optimizing the SNR and Liu’s error factor as the basis of objective function. The application of the new method on ultrasound and MR images of brain has shown a superior performance over the state-of-art wavelet-based denoising methods in terms of visual quality as well as quantitative metrics such as PSNR, RMSE and Liu’s error factor.

A wavelet‐based SPECT reconstruction algorithm for nonuniformly attenuated Radon transform

Single photon emission computed tomography (SPECT) is a tomography technique that can greatly show information about the metabolic activity in the body and improve the clinical diagnosis. In SPECT, because of photoelectric absorption and Compton scattering, the emitted gamma photons are attenuated inside the body before arriving at the detector. The goal of quantitative SPECT reconstruction is to obtain an accurate image of the radioactivity distribution in the interested area of a human body, so the compensation for nonuniform attenuation and the treatment of Poisson noise are necessary in the quantitative SPECT reconstruction. The authors know that the wavelet transform has characteristics of multiresolution and localized nature, and these characteristics can be applied for denoising and localized reconstruction. Based on the explicit inversion formula for the attenuated Radon transform, the authors present a wavelet-based SPECT reconstruction algorithm with compensation for nonuniform attenuation. The wavelet-based SPECT reconstruction algorithm offers the ability for denoising in the reconstruction processing. In simulation, 128 projections were simulated evenly spaced over 360 degrees by a circular orbit, each with 128 bins. Simulation results show that the wavelet-based denoising is effective in SPECT reconstruction. The authors present a wavelet-based SPECT reconstruction algorithm with compensation for nonuniform attenuation. The reconstruction results from computer simulations show that the wavelet-based SPECT reconstruction algorithm is accurate.

Wavelet-Based Denoising for Traffic Volume Time Series Forecasting with Self-Organizing Neural Networks

Abstract: In their goal to effectively manage the use of existing infrastructures, intelligent transportation systems require precise forecasting of near-term traffic volumes to feed real-time analytical models and traffic surveillance tools that alert of network links reaching their capacity. This article proposes a new methodological approach for short-term predictions of time series of volume data at isolated cross sections. The originality in the computational modeling stems from the fit of threshold values used in the stationary wavelet-based denoising process applied on the time series, and from the determination of patterns that characterize the evolution of its samples over a fixed prediction horizon. A self-organizing fuzzy neural network is optimized in its configuration parameters for learning and recognition of these patterns. Four real-world data sets from three interstate roads are considered for evaluating the performance of the proposed model. A quantitative comparison made with the results obtained by four other relevant prediction models shows a favorable outcome.

Wavelet-Based Adaptive Denoising and Baseline Correction for MALDI TOF MS

Proteomic profiling by MALDI TOF mass spectrometry (MS) is an effective method for identifying biomarkers from human serum/plasma, but the process is complicated by the presence of noise in the spectra. In MALDI TOF MS, the major noise source is chemical noise, which is defined as the interference from matrix material and its clusters. Because chemical noise is nonstationary and nonwhite, wavelet-based denoising is more effective than conventional noise reduction schemes based on Fourier analysis. However, current wavelet-based denoising methods for mass spectrometry do not fully consider the characteristics of chemical noise. In this article, we propose new wavelet-based high-frequency noise reduction and baseline correction methods that were designed based on the discrete stationary wavelet transform. The high-frequency noise reduction algorithm adaptively estimates the time-varying threshold for each frequency subband from multiple realizations of chemical noise and removes noise from mass spectra of samples using the estimated thresholds. The baseline correction algorithm computes the monotonically decreasing baseline in the highest approximation of the wavelet domain. The experimental results demonstrate that our algorithms effectively remove artifacts in mass spectra that are due to chemical noise while preserving informative features as compared to commonly used denoising methods.

Semi-automatic algorithm for construction of the left ventricular area variation curve over a complete cardiac cycle

BackgroundTwo-dimensional echocardiography (2D-echo) allows the evaluation of cardiac structures and their movements. A wide range of clinical diagnoses are based on the performance of the left ventricle. The evaluation of myocardial function is typically performed by manual segmentation of the ventricular cavity in a series of dynamic images. This process is laborious and operator dependent. The automatic segmentation of the left ventricle in 4-chamber long-axis images during diastole is troublesome, because of the opening of the mitral valve.MethodsThis work presents a method for segmentation of the left ventricle in dynamic 2D-echo 4-chamber long-axis images over the complete cardiac cycle. The proposed algorithm is based on classic image processing techniques, including time-averaging and wavelet-based denoising, edge enhancement filtering, morphological operations, homotopy modification, and watershed segmentation. The proposed method is semi-automatic, requiring a single user intervention for identification of the position of the mitral valve in the first temporal frame of the video sequence. Image segmentation is performed on a set of dynamic 2D-echo images collected from an examination covering two consecutive cardiac cycles.ResultsThe proposed method is demonstrated and evaluated on twelve healthy volunteers. The results are quantitatively evaluated using four different metrics, in a comparison with contours manually segmented by a specialist, and with four alternative methods from the literature. The method's intra- and inter-operator variabilities are also evaluated.ConclusionsThe proposed method allows the automatic construction of the area variation curve of the left ventricle corresponding to a complete cardiac cycle. This may potentially be used for the identification of several clinical parameters, including the area variation fraction. This parameter could potentially be used for evaluating the global systolic function of the left ventricle.

Complex Domain Wavelet-Based Denoising of Measured UHF Wireless Channel Power Delay Profiles

This work extends the use of wavelet-based denoising as an alternative processing scheme to improve measured mobile-radio channel power delay profiles. It has already been reported that, when applied on real domain data (amplitude only), denoising provides mainly a qualitative improvement. Here, phase content was also considered, leading to significant qualitative and quantitative improvement of the processed profiles. Signal-to-noise ratios and dynamic ranges improvements as high as 50 dB have been observed.

Using diffusion equations for improving performance of wavelet-based image denoising techniques

A new method based on anisotropic diffusion and wavelet transform is presented for image noise reduction. In the existing wavelet thresholding methods, the final noise reduced image has limited improvement. It is due to keeping the approximate coefficients of the image unchanged. These coefficients have the main information of the image. Since noise affects both the approximate and detail coefficients, in this research, the anisotropic diffusion technique for noise reduction is applied on the approximation band to alleviate the deficiency of the existing wavelet thresholding methods. The proposed method was applied on several standard noisy images and the results indicate superiority of the proposed method over the existing wavelet-based image denoising, anisotropic diffusion, fourth-order anisotropic diffusion and median filtering techniques.

Wavelet-based denoising of fetal phonocardiographic signals

Auscultation is still one of the first basic analytical tools used to evaluate functional state of the fetal heart, as well as the first indicator of fetal well-being. Its modern form is called fetal phonocardiography (fPCG). The fPCG technique is passive and can be used for long-term monitoring. In order to improve the diagnostic capabilities of fPCG, robust signal processing techniques are needed for denoising of the signals. Traditional denoising techniques apply a linear filter to remove the noise and interference from the fPCG signals. These methods have certain limitations for the non-stationary random fPCG signals. In this paper, an improved technique for denoising of fPCG signals is presented. A highly sensitive data recording module is used to acquire the fPCG signals from the maternal abdominal surface. The acquired fPCG signals are decomposed, denoised and reconstructed by utilising Matlab wavelet transform toolbox. The proposed approach improves the signal to noise ratio (SNR) of these signals. The presented technique can be used in preprocessing stage of all fPCG-based fetal monitoring applications.

On-line partial discharge monitoring in medium voltage underground cables

For many years incipient partial discharge (PD) faults in power cables have been identified through off-line investigation techniques. More recently, in an effort to allow pro-active asset management of the medium-voltage (MV) cable network to be carried out, continuous on-line monitoring systems are being installed with the aim of reducing unexpected failures. This study presents work on the analysis and handling of acquired data, from the point of view of asset management and the PD activities observed in an on-line cable monitoring systems. Initially, a review of on-line against off-line cable PD monitoring is presented, in terms of their setups and their respective advantages and disadvantages. The study then presents the authors’ experience of applying wavelet-based denoising techniques [both the discrete wavelet transform (DWT) and the second generation wavelet transform (SGWT)] to PD data denoising. Results of a study on the on-line PD-based monitoring of MV underground cables that are presented in the following section demonstrate that PD activity which is observed in on-line monitoring also has an associated high level of electrical noise that must be removed to allow proper identification of the PD signals and the denoised PD activity is seen to vary with time. Finally, the necessity of developing a means by which knowledge rules can automatically be acquired from on-line condition monitoring data, to reduce reliance on human expertise, is discussed.

Parallel implementation of wavelet-based image denoising on programmable PC-grade graphics hardware

The discrete wavelet transform (DWT) has been extensively used for image compression and denoising in the areas of image processing and computer vision. However, the intensive computation of DWT due to its inherent multilevel data decomposition and reconstruction operations brings a bottleneck that drastically reduces its performance and implementations for real-time applications when facing large size digital images and/or high-definition videos. Although various software-based acceleration solutions, such as the lifting scheme, have been devised and achieved a higher performance in general, the pure software accelerated DWT still struggle to cope with the demands from real-time and interactive applications. With the growing capacity and popularity of graphics hardware, personal computers (PCs) nowadays are often equipped with programmable graphics processing units (GPUs) for graphics acceleration. The GPU offers a cost-effective parallel data processing mechanism for operations on large amount of data, even for applications beyond graphics. This practice is commonly referred as general-purpose computing on GPU (GPGPU). This paper presented a GPGPU framework with the corresponding parallel computing solution for wavelet-based image denoising by using off-the-shelf consumer-grade programmable GPUs. This framework can be readily incorporated with different forms of DWT by customizing the parameter of the wavelet kernel. Experiment results show that the framework gains applicability in data parallelism and satisfaction performance in accelerating computations for wavelet-based denoising.

A Wavelet-Based Mammographic Image Denoising and Enhancement with Homomorphic Filtering

Breast cancer continues to be a significant public health problem in the world. The diagnosing mammography method is the most effective technology for early detection of the breast cancer. However, in some cases, it is difficult for radiologists to detect the typical diagnostic signs, such as masses and microcalcifications on the mammograms. This paper describes a new method for mammographic image enhancement and denoising based on wavelet transform and homomorphic filtering. The mammograms are acquired from the Faculty of Medicine of the University of Akdeniz and the University of Istanbul in Turkey. Firstly wavelet transform of the mammograms is obtained and the approximation coefficients are filtered by homomorphic filter. Then the detail coefficients of the wavelet associated with noise and edges are modeled by Gaussian and Laplacian variables, respectively. The considered coefficients are compressed and enhanced using these variables with a shrinkage function. Finally using a proposed adaptive thresholding the fine details of the mammograms are retained and the noise is suppressed. The preliminary results of our work indicate that this method provides much more visibility for the suspicious regions.

Wavelet-Based Noise Reduction by Joint Statistical Modeling of cDNA Microarray Images

Abstract Complementary DNA (cDNA) microarray experiments involve a large number of error-prone steps, which result in a high level of noise in the resulting red and green channel images. Removal of noise is a crucial step, since it makes further image processing easier and results in accurate gene expression measurements. The wavelet transform has shown significant success in the denoising of images including cDNA microarrays. Existing wavelet-based denoising methods process each image individually ignoring the information in the other channel. In this paper, a noise reduction technique is proposed that exploits the dependency between the wavelet transform coefficients of the two channels by using a locally-adaptive joint statistical model. The maximum a posteriori criterion is used to derive a joint estimator for the noise-free coefficients assuming suitable priors for the local variances. Significance of the proposed method is assessed by examining its effect on estimation of the log-intensity ratio. Ex...

Incorporation of wavelet-based denoising in iterative deconvolution for partial volume correction in whole-body PET imaging

Partial volume effects (PVEs) are consequences of the limited resolution of emission tomography. The aim of the present study was to compare two new voxel-wise PVE correction algorithms based on deconvolution and wavelet-based denoising. Deconvolution was performed using the Lucy-Richardson and the Van-Cittert algorithms. Both of these methods were tested using simulated and real FDG PET images. Wavelet-based denoising was incorporated into the process in order to eliminate the noise observed in classical deconvolution methods. Both deconvolution approaches led to significant intensity recovery, but the Van-Cittert algorithm provided images of inferior qualitative appearance. Furthermore, this method added massive levels of noise, even with the associated use of wavelet-denoising. On the other hand, the Lucy-Richardson algorithm combined with the same denoising process gave the best compromise between intensity recovery, noise attenuation and qualitative aspect of the images. The appropriate combination of deconvolution and wavelet-based denoising is an efficient method for reducing PVEs in emission tomography.

A Texture-Based Classification of Crackles and Squawks Using Lacunarity

An automatic classification method to efficiently discriminate the types of discontinuous breath sounds (DBSs), i.e., fine crackles (FCs), coarse crackles (CC), and squawks (SQ), is presented in this paper. Using the lacunarity of the acquired DBS, the proposed classification method, namely LAC, introduces a texture-based approach that captures the differences in the distribution of FC, CC, and SQ across the breathing cycle, which may lead to more accurate characterization of the pulmonary acoustical changes due to the related pathology. Prior to the lacunarity analysis, wavelet-based denoising of DBS is employed to eliminate effects of the vesicular sound (background noise) to DBS oscillatory pattern. LAC analysis builds its classification power both upon the use of lacunarity at an optimum scale and the approximation of its trajectory across an optimum range of scales using a three-parameter hyperbola model. LAC is applied to 363 DBS corresponding to 25 cases included in four lung sound databases. Results show that LAC efficiently classifies the three DBS categories in the comparison groups of FC-CC, FC-SQ (both with mean accuracy of 100%), CC-SQ (mean accuracy of 99.62%-100%), and FC-CC-SQ (mean accuracy of 99.75%-100%). When compared to other classification tools, LAC seems quite attractive, since, without employing high computational complexity, it results in high classification accuracy. Moreover, LAC introduces a "texture" concept in the analysis of breath sounds, something that strongly relates to the perception of the bioacoustic signals by the physician. Due to its simplicity, LAC could be implemented in a real-time context and be used in clinical medicine as a module of an integrated intelligent patient evaluation system.

The Estimation of Radial Exponential Random Vectors in Additive White Gaussian Noise

Image signals are always disturbed by noise during their transmission, such as in mobile or network communication. The received image quality is significantly influenced by noise. Thus, image signal denoising is an indispensable step during image processing. As we all know, most commonly used methods of image denoising is Bayesian wavelet transform estimators. The Performance of various estimators, such as maximum a posteriori (MAP), or minimum mean square error (MMSE) is strongly dependent on correctness of the proposed model for original data distribution. Therefore, the selection of a proper model for distribution of wavelet coefficients is important in wavelet-based image denoising. This paper presents a new image denoising algorithm based on the modeling of wavelet coefficients in each subband with multivariate Radial Exponential probability density function (PDF) with local variances. Generally these multivariate extensions do not result in a closed form expression, and the solution requires numerical solutions. However, we drive a closed form MMSE shrinkage functions for a Radial Exponential random vectors in additive white Gaussian noise (AWGN). The estimator is motivated and tested on the problem of wavelet-based image denoising. In the last, proposed, the same idea is applied to the dual-tree complex wavelet transform (DT-CWT), This Transform is an over-complete wavelet transform.