Wavelet-based Approach Research Articles

About Verification of Correct Wavelet-Based Approach to Local Static Analysis of Bernoulli Beam

This paper is devoted to verification of correct and efficient wavelet-based method of local static analysis of Bernoulli beam on elastic foundation, proposed by authors. Corresponding results for sample problem have been compared with analytical solutions. Comparison shows that the localization of the problem with reducing its size by proposed method provide high-accuracy results for desired regions of the structure even in high level of reduction in wavelet coefficients. It should be noted that, the wavelet analysis can exactly decompose problem and the sources of the observed error between the analytical solution and numerical result, is based mainly on applied method for solving (in this case, finite difference method), and can be improved.

Theoretical Foundations of Correct Wavelet-Based Approach to Local Static Analysis of Bernoulli Beam

This paper is devoted to correct and efficient method of local static analysis of Bernoulli beam on elastic foundation. First of all, problem discretized by finite difference method, and then transformed to a localized one by using the Haar wavelets. Finally, imposing an optimal reduction in wavelet coefficients, the localized, reduced results can be obtained. It becomes clear after comparison with analytical solutions, that the localization of the problem by multiresolution wavelet approach gives exact solution in desired regions of beam even in high level of reduction in wavelet coefficients. This localization can be applied to any arbitrary region of the beam by choosing optimum reduction matrix and obtaining exact solutions with an acceptable reduced size of the problem.

A Wavelet-Statistical Features Approach for Nonconvulsive Seizure Detection.

The detection of nonconvulsive seizures (NCSz) is a challenge because of the lack of physical symptoms, which may delay the diagnosis of the disease. Many researchers have reported automatic detection of seizures. However, few investigators have concentrated on detection of NCSz. This article proposes a method for reliable detection of NCSz. The electroencephalography (EEG) signal is usually contaminated by various nonstationary noises. Signal denoising is an important preprocessing step in the analysis of such signals. In this study, a new wavelet-based denoising approach using cubical thresholding has been proposed to reduce noise from the EEG signal prior to analysis. Three statistical features were extracted from wavelet frequency bands, encompassing the frequency range of 0 to 8, 8 to 16, 16 to 32, and 0 to 32 Hz. Extracted features were used to train linear classifier to discriminate between normal and seizure EEGs. The performance of the method was tested on a database of nine patients with 24 seizures in 80 hours of EEG recording. All the seizures were successfully detected, and false positive rate was found to be 0.7 per hour.

REGULARIZED 3D FUNCTIONAL REGRESSION FOR BRAIN IMAGE DATA VIA HAAR WAVELETS.

The primary motivation and application in this article come from brain imaging studies on cognitive impairment in elderly subjects with brain disorders. We propose a regularized Haar wavelet-based approach for the analysis of three-dimensional brain image data in the framework of functional data analysis, which automatically takes into account the spatial information among neighboring voxels. We conduct extensive simulation studies to evaluate the prediction performance of the proposed approach and its ability to identify related regions to the outcome of interest, with the underlying assumption that only few relatively small subregions are truly predictive of the outcome of interest. We then apply the proposed approach to searching for brain subregions that are associated with cognition using PET images of patients with Alzheimer's disease, patients with mild cognitive impairment, and normal controls.

On the detection of extreme movements and persistent behaviour in Mediterranean stock markets: a wavelet-based approach

We combine the global Hurst exponent and Morlet wavelet multi-resolution analysis (MRA) to investigate the dynamic behaviour of six selected stock markets in the Mediterranean region. Specifically, we employ the resonance coefficients and their power spectra to identify potential extreme movements and long-term dependence in stock returns. Using weekly data for the period 2005 to 2010, our results reveal that the wavelet MRA is able to reconstruct the effects of major extreme shocks on stock returns of studied markets, such as the Asian financial crisis, the 9/11 terrorist attacks and the 2007–2009 financial crisis. Moreover, the wavelet-based global Hurst exponent indicates the presence of long-term dependencies in stock returns of all the considered markets, except for France where the anti-persistent behaviour is detected. Overall, our findings are useful to assess the stock market efficiency and provide new insights into stock market dynamics over different time scales.

Simulating Bivariate Stationary Processes with Scale-Specific Characteristics

By modifying and generalizing the wavelet-based approach of approximately simulating univariate long-memory processes that is available in the literature, we propose a methodology for simulating a bivariate stationary process, whose components exhibit different relationships at different scales. We derive the formulas for the autocovariance and cross-covariance sequences of the simulated bivariate process. We provide a setting for the parameters of the simulation which might generate a bivariate time series resembling that of stock log returns. Using this setting, we study the properties of our methodology via Monte Carlo simulation.

Wavelet-based multifractal analysis of earthquakes temporal distribution in Mammoth Mountain volcano, Mono County, Eastern California

This paper presents a wavelet-based multifractal approach to characterize the statistical properties of temporal distribution of the 1982–2012 seismic activity in Mammoth Mountain volcano. The fractal analysis of time-occurrence series of seismicity has been carried out in relation to seismic swarm in association with magmatic intrusion happening beneath the volcano on 4 May 1989. We used the wavelet transform modulus maxima based multifractal formalism to get the multifractal characteristics of seismicity before, during, and after the unrest. The results revealed that the earthquake sequences across the study area show time-scaling features. It is clearly perceived that the multifractal characteristics are not constant in different periods and there are differences among the seismicity sequences. The attributes of singularity spectrum have been utilized to determine the complexity of seismicity for each period. Findings show that the temporal distribution of earthquakes for swarm period was simpler with respect to pre- and post-swarm periods.

A wavelet melt detection algorithm applied to enhanced-resolution scatterometer data over Antarctica (2000–2009)

Abstract. Melting is mapped over Antarctica at a high spatial resolution using a novel melt detection algorithm based on wavelets and multiscale analysis. The method is applied to Ku-band (13.4 GHz) normalized backscattering measured by SeaWinds onboard the satellite QuikSCAT and spatially enhanced on a 5 km grid over the operational life of the sensor (1999–2009). Wavelet-based estimates of melt spatial extent and duration are compared with those obtained by means of threshold-based detection methods, where melting is detected when the measured backscattering is 3 dB below the preceding winter mean value. Results from both methods are assessed by means of automatic weather station (AWS) air surface temperature records. The yearly melting index, the product of melted area and melting duration, found using a fixed threshold and wavelet-based melt algorithm are found to have a relative difference within 7% for all years. Most of the difference between melting records determined from QuikSCAT is related to short-duration backscatter changes identified as melting using the threshold methodology but not the wavelet-based method. The ability to classify melting based on relative persistence is a critical aspect of the wavelet-based algorithm. Compared with AWS air-temperature records, both methods show a relative agreement to within 10% based on estimated melt conditions, although the fixed threshold generally finds a greater agreement with AWS. Melting maps obtained with the wavelet-based approach are also compared with those obtained from spaceborne brightness temperatures recorded by the Special Sensor Microwave/Image (SSM/I). With respect to passive microwave records, we find a higher degree of agreement (9% relative difference) for the melting index using the wavelet-based approach than threshold-based methods (11% relative difference).

Interval Estimation Method for Decision Making in Wavelet-Based Software Reliability Assessment

Recently, the wavelet-based estimation method has gradually been becoming popular as a new tool for software reliability assessment. The wavelet transform possesses both spatial and temporal resolution which makes the wavelet-based estimation method powerful in extracting necessary information from observed software fault data, in global and local points of view at the same time. This enables us to estimate the software reliability measures in higher accuracy. However, in the existing works, only the point estimation of the wavelet-based approach was focused, where the underlying stochastic process to describe the software-fault detection phenomena was modeled by a non-homogeneous Poisson process. In this paper, we propose an interval estimation method for the wavelet-based approach, aiming at taking account of uncertainty which was left out of consideration in point estimation. More specifically, we employ the simulation-based bootstrap method, and derive the confidence intervals of software reliability measures such as the software intensity function and the expected cumulative number of software faults. To this end, we extend the well-known thinning algorithm for the purpose of generating multiple sample data from one set of software-fault count data. The results of numerical analysis with real software fault data make it clear that, our proposal is a decision support method which enables the practitioners to do flexible decision making in software development project management.

WAVELET-BASED ANALYSIS OF CEREBROVASCULAR DYNAMICS IN NEWBORN RATS WITH INTRACRANIAL HEMORRHAGES

Intracranial hemorrhage (IH) is a major problem of neonatal intensive care. The incidence of IH is typically asymptomatic and cannot be effectively detected by standard diagnostic methods. The mechanisms underlying IH are unknown but there is evidence that stress-induced disorders in adrenergic regulation of cerebral venous blood flow (CVBF) are among the main reasons. Quantitative and qualitative assessment of CVBF could significantly advance understanding of the nature of IH in newborns. In this work, we analyze variations of CVBF in newborn rats with an experimental model of stress-induced IH and adrenaline injection. Our analysis is based on the Doppler optical coherence tomography (DOCT) and a proposed adaptive wavelet-based approach that provides sensitive markers of abnormal reactions of the sagittal vein to external factors. The obtained results demonstrate that the incidence of IH in newborn rats is accompanied by a suppression of CVBF with the development of venous insufficiency and areactivity to adrenaline. We introduce a numerical measure θ, quantifying reactions of CVBF and show that the values θ < 1.23 estimated in the low-frequency (LF) spectral range corresponding to the sympathicus indicate abnormal reactions associated with the development of IH. We conclude that the revealed areactivity of the cerebral veins to adrenaline represents a possible mechanism responsible for pathological changes in CVBF.

Wavelet-Based Response Computation for Base-Isolated Structure under Seismic Excitation

This paper presents a wavelet-based approach for estimating the response of the base-isolated structure under seismic ground motions. The seismic ground motion record is expressed as the multi-scale wavelet coefficients which presents the time frequency characteristics of the seismic excitation. The wavelet domain governing differential equation between the wavelet coefficients of the excitation and response is derived. Numerical study on a one-storey base isolated structure is performed. The result shows that the wavelet based response computation method is of high precision.

A Wavelet-based Approach to Improve Foggy Image Clarity

Under foggy viewing conditions, image contrast is often significantly degraded by atmospheric aerosols, which makes it difficult to quickly detect and track moving objects in intelligent transportation systems (ITS). A foggy image visibility enhancing algorithm based on an imaging model and wavelet transform technique is proposed in this paper. An optical imaging model in foggy weather conditions is established to determine the image degradation factors and compensation strategies. Based on this, the original image is firstly transferred into YUV color space of a luminance and two chrominance components. Then the luminance component is decomposed through wavelet transform into low- and high-frequency subbands. In the low-frequency subband, the medium scattered light component is estimated using Gaussian blur and removed from the image. Nonlinear transform for enhancement of foggy images is applied to high-frequency subbands. In the end, a new image is recovered by combining the chrominance components and the corrected luminance component altogether. Experimental results demonstrate that this algorithm can handle the problem of image blurring caused by atmospheric scattering effectively, and has a better real-time performance compared with a standard model-based procedure.

Estimating Software Intensity Function Based on Translation-Invariant Poisson Smoothing Approach

Because the software failure occurrence process is well-modeled by a non-homogeneous Poisson process, it is of great interest to estimate accurately the software intensity function of Non-Homogeneous Poisson Process (NHPP)-based software reliability models (SRM) from observed software-fault count data. In recent years, wavelet-based techniques have been well established in Poisson intensity estimation because of their technical advantages of computational cost and accuracy. The approach enables us to carry out the analysis of a software debugging process in a nonparametric way. In this paper, we propose an applied Haar wavelet-based approach which is without an approximate data transformation, for software reliability assessment. In a numerical study with real software-fault count data, we compare the proposed estimation method with the previously used data transformation-based estimation method, as well as conventional maximum likelihood estimation and least squares estimation methods. Furthermore, we conduct sensitivity analysis of the resolution level, which affects the estimation accuracy of the proposed method. We also estimate some predictive measures such as software reliability.

A Combined Wavelet-Based Mesh-Free Method for Solving the Forward Problem in Electrical Impedance Tomography

In this paper, a combined wavelet-based mesh-free method is suggested to solve the forward problem in electrical impedance tomography (EIT). EIT is a noninvasive imaging modality based on the reconstruction of the conductivity profile inside a solution domain. The forward problem simulates measurement data for comparing with experimental data in the inverse problem. The forward problem can be solved by the finite element method (FEM) or the mesh-free method. Since the solution of the FEM depends on the mesh shape and boundary condition constraints are difficult to be applied to the mesh-free method, the combined wavelet-based mesh-free approach can resolve the disadvantages of both methods in the EIT forward problem. In order to apply interface conditions between different regions, slope jump functions are entered to the set of basis functions. Two different 2-D EIT problems are modeled. The simulation results obtained by the combined wavelet-based mesh-free method are compared with the FEM in terms of accuracy and computational cost. Moreover, the effects of object movement and deformation are investigated on the accuracy of the simulated electrode voltages using the standard FEM and combined wavelet-based mesh-free method.

Wavelet-Based Approach to Evaluation of Signal Integrity

In this paper, we present a new approach to evaluation of signal integrity that is based on signal energy density as a function of time and frequency, represented by its wavelet scalogram. Using signal integrity ratio and cumulative energy ratio, we illustrate signal integrity analysis with simulated examples, followed by the demonstration of their usefulness through analysis of experimental data of a real audio amplifier. These figures of merit represent the extent to which the integrity of a signal is diminished by the electromagnetic interference effects and/or nonlinear processes.

Dynamic optimization using adaptive direct multiple shooting

We present a wavelet-based grid refinement approach for direct multiple shooting applied to dynamic optimization problems. The algorithm, named adaptive multiple shooting, automatically generates a problem-dependent parameterization of the control profiles: Starting from an initially coarse parameterization, the control grid is refined iteratively using a wavelet analysis of the previously obtained optimal solution. Additional grid points are only inserted where required and redundant grid points are eliminated. Hence, the algorithm minimizes the number of grid points required to obtain accurate optimal control trajectories.First, we demonstrate the superiority of adaptive grid refinement over an equidistant discretization for the Williams–Otto semi-batch reactor employing multiple and single shooting. Here, the accuracy is checked using an optimal solution obtained by an indirect optimization approach. Second, we successfully demonstrate the efficiency of adaptive grid refinement compared to an equidistant discretization employing multiple shooting to a dynamically unstable HIPS (high impact polystyrene) polymerization reactor.

Multiresolution analysis of linearly oriented spatial point patterns

The assumption of direction invariance, i.e. isotropy, is often made in the practical analysis of spatial point patterns due to simpler interpretation and ease of analysis. However, this assumption is many times hard to find in real applications. We propose a wavelet-based approach to test for isotropy in spatial patterns based on the logarithm of the directional scalogram. Under the null hypothesis of isotropy, a random isotropic point pattern should be expected to have the same value of the directional scalogram for any possible direction. Monte Carlo simulations of the logarithm of the directional scalogram over all directions are used to approximate the test distribution and the critical values. We demonstrate the efficacy of the approach through simulation studies and an application to a desert plant data set, where our approach confirms suspected directional effects in the spatial distribution of the desert plant species.

Online sensors and wavelet-based filter approach for tsunami case study

The Tsunami classification model with real-time sensors placed at different locations and at different depths is proposed. To exclude the artifact effects in the sensor values, a wavelet-based denoising scheme is integrated in the model. In addition, a downsampling approach has been proposed to achieve maximum flat delay response, and the present results are compared with the Pc McClellan method. Various parameters such as conductivity, salinity, pressure, temperature, and dissolved oxygen are measured and sensed using multisensor grid architecture. Our results show that by sensing the above parameters and subject them online, it is possible to clearly distinguish the pre- and post-tsunami behaviors.

A wavelet-based approach for vibration analysis of framed structures

In this paper, an explicit time integration scheme is proposed for structural vibration analysis by using wavelet functions. Initially, the differential equation of vibration governing SDOF (single-degree of freedom) systems has been solved by wavelet operators, and later the proposed approach has been generalized for MDOF (multi-degrees of freedom) systems. For this purpose, two different types of wavelet functions have been exemplified including, complex Chebyshev wavelet functions and simple Haar wavelet functions. In the proposed approach, a straightforward formulation has been derived from the numerical approximation of response through the wavelet definition. Emphasizing on frequency-domain approximation, a simple step-by-step algorithm has been implemented and improved to calculate the response of MDOF systems. Moreover, stability and accuracy of results have been evaluated. The effectiveness of the proposed approach is demonstrated using three examples compared with some of the existing numerical integration schemes such as family of Newmark-β, Wilson-θ and central difference method. In all the procedures, computation time involved has also been considered. Finally, it is concluded that the vibration analysis of structures is improved by lesser computation time and high accuracy of proposed approach, particularly, in large-scaled systems.

Glacier surface velocity estimation using repeat TerraSAR-X images: Wavelet- vs. correlation-based image matching

For the observation and monitoring of glacier surface velocity (GSV), remote sensing is an increasingly suitable tool thanks to the high temporal and spatial resolution of the data. Radar sensors have the specific advantage over optical sensors of being nearly weather and time-independent.Two image pairs separated by 11days, acquired with the high-resolution spotlight (HS) and stripmap (SM) modes of the German sensor TerraSAR-X, were used to estimate GSV over Switzerland’s Aletsch Glacier. The SM mode covers larger ground swaths, making it more suitable for glacier-wide observations, while the HS images cover less area but offer the highest-possible spatial resolution, approximately 1×1m on the ground. The images were acquired during the summer to maximise feature visibility by minimal snow cover.GSV estimation was performed using two methods, the comparison of which was a major goal of this study: traditional cross-correlation optimisation and a dense image matching algorithm based on complex wavelet decomposition. Each method was found to have unique advantages and disadvantages, but it was concluded that for GSV monitoring, cross-correlation is probably preferable to the wavelet-based approach. While it generates fewer estimates per unit area, this is not necessarily a critical requirement for all glaciological applications, and the method requires less initial “tuning” (calibration) than the wavelet algorithm, making it a slightly better tool in operational contexts. Also, the use of the highest-resolution spotlight datasets is recommended over stripmap mode images when large-area coverage is less critical. The comparative lack of visible features at the resolution of the stripmap images made reliable GSV estimation difficult, with the exception of several small areas dominated by large crevasses.