Multiresolution Wavelet Research Articles

Multiframe Ultrasonic TOFD Weld Inspection Imaging Based on Wavelet Transform and Image Registration

TOFD (time of flight diffraction) is a kind of weld defect detection technology by using ultrasonic diffraction wave signal. Because the diffraction intensity is far less than ultrasonic echo wave intensity, thus, the noise contained in TOFD signal is fairly large, and the formed image is not clear enough. Therefore, it is difficult to determine the size of defects accurately. In this paper, a method of noise reduction of TOFD signal and improving the resolution of the image are discussed based on the combination of wavelet thresholding and image registration. Wavelet multiresolution analysis method is adopted and the A-scan signal is decomposed into different frequency components. We propose a new threshold function to process the wavelet coefficients, which guarantees to denoise while preserving the useful information as much as possible. Setting up the ultrasonic TOFD inspection system and the image data with randomly distributed noise can be obtained via fine shake of the probes during testing. Then, image registration based on maximum correlation and blending is adopted to eliminate the noise in further step. The result shows that the proposed method can achieve denoising, together with resolution enhancement.

STUDY ON DE-NOISING METHODS FOR SOIL COMPRESSIVE STRESS SIGNAL DURING VIBRATION COMPACTION

The compressive stress signal of soil during vibration compaction is an unstable and transient saltation signal accompanied by broadband noise, and the spectra of the signal and noise always overlap. To extract the ideal original signal from noisy data, this paper studies several signal de-noising methods such as low-pass filtering, multi-resolution wavelet transform, spectrum subtraction and independent component analysis. Experiments show that the traditional low-pass filter is only applicable when the spectra of the signal and noise can be separated in the frequency domain. The multi-resolution wavelet transform can decompose the signal into different frequency bands and remove the noise efficiently by extracting useful the frequency band of the signal, but this method is not reliable when the signal to noise ratio (SNR) is low. Spectrum subtraction can remove strong background noise with stationary statistical characteristics even if the noise level is high and the spectrum of the signal overlaps with that of the noise. Independent component analysis can extract weak signals which are combined with heavy noise and can separate the noise from signal effectively when the independent channel hypothesis holds. These de-noising methods are of great importance for further analysing vibration signals in engineering.

Recaptured Image Forensics Algorithm Based on Multi-Resolution Wavelet Transformation and Noise Analysis

With the rapid development of digital cameras and smart phones, the image identification system in current times will be of a great impact. This will cause the form of image information to increase serious security issues. Especially, the emergence of the recaptured image makes conventional digital image forensics algorithm invalid. Therefore, a new image forensics algorithm is urgently needed to identify the recaptured image. In this paper, a new recaptured image identifying algorithm is put forward based on wavelet transformation and noise analysis by analyzing the differences between the real and recaptured images generated in the imaging process. First, the proposed algorithm extracts mean value, variance and skewness as wavelet characteristic from the high-frequency images and low-frequency images by wavelet transformation. Meanwhile, the proposed algorithm analyzes the noise image by means of local binary pattern to extract noise characteristic. Finally, the support vector machine is applied to classify the recaptured image with wavelet characteristics and noise characteristics. The results show the presented method can not only identify the recaptured image obtained from different media but also have better identification rate, and the dimension of the characteristic vector is also lower than those obtained by other algorithms.

Bounds and Conditions for Compressive Digital Holography Using Wavelet Sparsifying Bases

Numerous experiments have been conducted with success in the field of compressive digital holography, but the theory to determine optimal measurement conditions is lagging behind. In contrast to a prior study that expects object wavefields to be sparse in the spatial domain, we investigate how the configuration of the interferometer influences the reconstruction of wavefields that are sparse in a multiresolution orthogonal wavelet basis. In particular, we derive expressions for the coherence between the free-space wave propagation operator and the basis functions of a Shannon multiresolution representation as a function of the wavelength, the propagation distance, the image sensor's pixel pitch, and the scale of the basis functions. These expressions reveal that the coherence as a function of the Fresnel number is subject to specific scaling and translating rules as the scale of the basis functions changes. For a multiresolution orthogonal wavelet representation and digital holograms that are recorded in the near field, we deduce subsequently the optimal configuration of the interferometer and we show by means of hypothesis testing that the associated phase transition bound coincides with the weak threshold for block-sparse compressive sensing with a block length of 2, which is an optimal bound for the class of complex-valued compressive sensing problems. By means of experiments with a USAF 1951 resolution target and an angle grid, we validate our findings and demonstrate that the reconstructed object wavefields are resilient to sparsity defects and additive noise.

On the feasibility of using satellite gravity observations for detecting large-scale solid mass transfer events

The main focus of this paper is to assess the feasibility of utilizing dedicated satellite gravity missions in order to detect large-scale solid mass transfer events (e.g. landslides). Specifically, a sensitivity analysis of Gravity Recovery and Climate Experiment (GRACE) gravity field solutions in conjunction with simulated case studies is employed to predict gravity changes due to past subaerial and submarine mass transfer events, namely the Agulhas slump in southeastern Africa and the Heart Mountain Landslide in northwestern Wyoming. The detectability of these events is evaluated by taking into account the expected noise level in the GRACE gravity field solutions and simulating their impact on the gravity field through forward modelling of the mass transfer. The spectral content of the estimated gravity changes induced by a simulated large-scale landslide event is estimated for the known spatial resolution of the GRACE observations using wavelet multiresolution analysis. The results indicate that both the Agulhas slump and the Heart Mountain Landslide could have been detected by GRACE, resulting in $${\vert }0.4{\vert }$$ and $${\vert }0.18{\vert }$$ mGal change on GRACE solutions, respectively. The suggested methodology is further extended to the case studies of the submarine landslide in Tohoku, Japan, and the Grand Banks landslide in Newfoundland, Canada. The detectability of these events using GRACE solutions is assessed through their impact on the gravity field.

A hybrid solar radiation modeling approach using wavelet multiresolution analysis and artificial neural networks

Assessment of solar potential over a location of interest is an important step towards the successful planning of renewable energy projects. However, solar data are not available for every point of interest due to the absence of meteorological stations and sophisticated solar sensors, so solar radiation has to be estimated using models. This paper presents a hybrid technique to improve the performance of a widely used modeling technique i.e. artificial neural network (ANN). Four different architectures of ANN, namely: multilayer perceptron (MLP), Adaptive neuro-fuzzy inference system (ANFIS), Nonlinear autoregressive recurrent exogenous neural network (NARX), and generalized regression neural networks (GRNN), are used in this study. A wavelet multiresolution analysis is applied to decompose the complex meteorological signals into relatively simple parts, wavelet sub-series, using discrete wavelet transformation (DWT) algorithm. The wavelet sub-series are modeled by the ANN models and reconstructed to estimate the original signal. Hence, enhancing the learning process of these models. Four meteorological parameters, namely: temperature (T), relative humidity (RH), wind speed (WS), and sunshine duration (SSD), are used to mode the global horizontal irradiation (GHI) over Abu Dhabi, the United Arab Emirates. The proposed approach is compared to standalone ANN models and validated using well-known statistical validation metrics including coefficient of determination (R2), root mean square error (RMSE), mean bias error (MBE), mean absolute percentage error (MAPE), and t-statistics. In addition, wavelet cross spectrum (WCS) is used as a visual indicator of the model performance in time, frequency, and phase domains. The results show that using the proposed strategy considerably improves the modeling performance of the ANN with a maximum improvement of 6.84% in R2 for MLP. In addition, minimum RMSE of 2.78% is observed for GRNN.

CEEMDAN and OWMRA as a hybrid method for rolling bearing fault diagnosis under variable speed

The diagnosis of bearing faults in rotating machines working with variable speed, such as wind turbines, gearboxes, and mine excavators, represents a challenge when using vibration analysis. In this paper, the feasibility of an optimized hybrid method based on Empirical Mode Decomposition (EMD) and Wavelet Multi-Resolution Analysis (WMRA) is checked for rolling bearing fault diagnostic by analyzing non-stationary vibration signals obtained from a variable speed rotating machine. An optimized EMD analysis called Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) is first used to decompose bearing signals. Amongst obtained Intrinsic Mode Functions (IMF), the one that has the highest kurtosis and covers the bearing natural frequency is chosen to be used for the next step which, given a signal, calculates its envelope by applying Hilbert Transform and then produces a new reconstructed signal using an Optimized WMRA. An Order Tracking (OT) algorithm is then applied on the envelope of the reconstructed signal to remove the effects of speed variation. An envelope order spectrum is finally calculated to bring out the fault characteristic order. The results show that the proposed hybrid approach have successfully highlighted the bearing faults in the non-stationary conditions, with both simulated and experimental signals.

Watermelon ripeness detection by wavelet multiresolution decomposition of acoustic impulse response signals

Ripeness is an important index for evaluating the quality of watermelons. This paper presents a simple, effective, and inexpensive approach to detecting watermelon ripeness based on wavelet multi-resolution decomposition (WMRD) and a statistical hypothesis test. The key idea in the proposed method is to model each WMRD coefficient as a random variable. For a specific coefficient, two samples are obtained by the multi-scale decomposition of watermelon acoustic signals, where one is for ripe watermelons and the other is for unripe ones. It is found that that many coefficients can be regarded as normal random variables, both for ripe and unripe watermelons. A discrimination index is proposed to estimate the separation degree of two samples, in order to determine the best WMRD coefficient. The probability density functions for ripe and unripe watermelons are obtained using the samples with the best coefficient. As a result, an inequality based on the hypothesis test at a 5% significant level is established for detecting watermelon ripeness. Using the proposed method, the training and test accuracies can reach 91.67% and 91.76%, respectively.

Classification of User Trajectories in LTE HetNets Using Unsupervised Shapelets and Multiresolution Wavelet Decomposition

The classification of user trajectories in Long-Term Evolution (LTE) heterogeneous networks (HetNets) is investigated in this paper. We propose a methodology to classify user trajectories based on the measurement reports submitted to the serving base station as part of the handover process; we propose to consider each measurement report as a time series. This methodology allows base stations to automatically and autonomously discover the radio-frequency (RF) conditions of their cell edge (e.g., signal strength degradation and interference levels). We propose the application of machine learning and data mining techniques to identify patterns in the reference signal received power measurement reports submitted by users as they approach the edge of the service area. Our time-series clustering algorithm based on unsupervised shapelets and multiresolution wavelet decomposition provided superior performance compared to a discrete Fourier transform (DFT)-based clustering algorithm. Our algorithm was able to provide clustering results with an average accuracy of 95%. Furthermore, the quality measure of the resulting clusters was up to 75% better, compared to the clustering results provided by the DFT-based algorithm. We also proposed a novel methodology to calculate a suitable number of clusters with no prior knowledge regarding the data; an average accuracy close to 90% was achieved.

Wavelet multiresolution analysis and dyadic scalogram for detection of epileptiform paroxysms in electroencephalographic signals

Abstract Introduction Early detection of epilepsy by the review of large electroencephalographic (EEG) recordings is very stressful, time-consuming, and subjective for neurologists. Several automatic seizure detection systems have been proposed in the literature to solve this problem. Methods This study proposes two complementary wavelet-based approaches for detecting epileptiform paroxysms in EEG signals. First methodology applied the wavelet multiresolution analysis (MRA) to filter non-epileptiform activity in long-term EEG. Second methodology used the wavelet dyadic scalogram to analyze which scales were related to the epileptiform paroxysms. For tests, 65 wavelet functions were selected between daubechies, biorthogonal, symlets, reverse biorthogonal and coiflet wavelet families in order to evaluate their performance. Results For MRA, it was noted a better performance by using the db4 function, by reaching 48.30% of energy with 8 wavelet coefficients, 0.717658 of correlation and 36.799 of root mean square error (RMSE). For wavelet dyadic scalograms, were chosen bior3.9 and rbio1.5 functions, by reaching 77.98% of sensitivity, 94.08% of specificity, 87.87% of efficiency and 0.9613 of area under the curve (AUC value) by using bior3.9. Conclusion The presented approaches are highly complementary for a whole automatic seizure detection system by using the MRA as pre-processing stage to filter non-epileptiform activity, and wavelet dyadic scalogram for extracting desired features from filtered EEG signals.

Analysis of non-stationary wind characteristics at an arch bridge using structural health monitoring data

The accurate characterization of the wind characteristics of extreme wind events is crucial to the structural design and safety evaluation. However, the field-measured wind data during typhoons exhibit a strong non-stationary feature with an inherent time-varying trend which deviates from the traditional stationary assumption. This paper presents the study of non-stationary wind characteristics of Typhoon Soudelor at the Jiubao Bridge located in Hangzhou, China, which has been instrumented with a structural health monitoring system. After data classification by the stationary test, the non-stationary wind data are analyzed by both traditional stationary wind model and non-stationary wind model which considers the inherent time–varying mean wind speed. The empirical mode decomposition (EMD) and wavelet multiresolution analysis (MRA) are employed to extract the underlying trend from the original wind data as the time-varying mean wind speed for the non-stationary wind model. Based on two categories of fluctuating wind speeds obtained by removing the constant and time-varying mean wind speed, the wind characteristics including the mean wind speed, turbulence intensity, gust factor, probability distribution and power spectral density are comparatively analyzed. The results indicate that the time-varying mean wind speed can be effectively identified and extracted by the EMD and MRA. The non-stationary wind model is more appropriate than the traditional stationary wind model in the analysis of non-stationary wind speed data during a typhoon.

Wavelet-enriched adaptive crystal plasticity finite element model for polycrystalline microstructures

Micromechanical analysis of polycrystalline microstructures of metals and alloys, using crystal plasticity finite element (CPFE) models is extensively used for predicting deformation and failure under various conditions of strain-rates, creep and fatigue loading. Many CPFE models involve a large number of degrees of freedom for accurate representation of realistic polycrystalline microstructures. This can lead to prohibitively high computational costs to conduct meaningful analyses of phenomena of interest. To overcome this limitation, the authors have recently developed a wavelet enrichment adapted finite element model in Azdoud and Ghosh (2017) for elastic materials. The method adaptively creates an optimal discretization space conforming to the solution profile by projecting the solution field onto a set of scaling and multi-resolution wavelet basis functions. This paper extends this wavelet adapted FE model to finite deformation, crystal plasticity analysis of polycrystalline microstructures. After presenting the formulations, various validation tests are conducted to examine the convergence rates and computational efficiency of this method.

Wavelet Multiresolution Analysis of the Liquidity Effect and Monetary Neutrality

This paper employs the maximum overlap discrete wavelet transform to obtain timescale decompositions of monetary aggregates, short-term interest rates and output to investigate two propositions in monetary economics: the liquidity effect and the long-run neutrality of money. Evidence from correlation and Granger causality over five timescales suggests that the liquidity effect is statistically significant in both the US and Sweden’s economies, with a shorter time horizon in the US than in Sweden. There is no evidence of monetary neutrality in both economies; at finest timescales, output Granger causes money in Sweden, whereas it is the other way around in the US. At long time horizons, there is a feedback between money and output in both economies. Key to our findings is that monetary disturbances have significant real effects and these effects last longer than it is assumed in real business cycle models.

3D multi-resolution wavelet convolutional neural networks for hyperspectral image classification

Hyperspectral images contain abundant spectral information, and three-dimensional (3D) feature extraction methods have been shown to be effective for classification. In this paper, we propose a hyperspectral image classification method that uses 3D multi-resolution wavelet convolutional network (3D MWCNNs) in which wavelets are first characterized by their time-frequency and multi-resolution. Then, the 3D-MWCNNs extract features from coarse to fine scales. In addition, 3D-MWCNNs work stably and effectively for approximation. In the conventional implementation of wavelets, empirical parameters must be determined in advance and the feature extraction process is not adaptive. Convolutional neural networks (CNNs) have strong adaptive learning capabilities and can extract features from low to high levels; however, they lack the theoretical underpinnings to perform multi-resolution approximation for filter learning. Therefore, by combining the CNNs framework with multi-resolution analysis theory, a model called 3D MWCNNs is proposed to extract the 3D features from different scales and different depths adaptively. 3D MWCNNs model is better at feature representation and approximation from 3D cube data; therefore, they capture the spatial and spectral features more discriminatively to improve the classification accuracy. Experimental results on three well-known hyperspectral images demonstrate that the proposed framework achieves considerably higher classification accuracy than do several state-of-the-art algorithms.

Multiscale wavelet-based analysis to detect hidden geodiversity

Geodiversity, a relatively new concept in earth sciences, synthesizes information related to abiotic layers and indicates their spatial interactions and interrelations. Geodiversity has been used in mountainous areas to assess both their ecological and economic potential. In this paper, we link geodiversity analysis with a multi-resolution wavelet transform to parse the hidden patterns of geodiversity of a plateau area from the Swiss Jura Mountains. We decomposed a high-resolution digital terrain model using a fractional spline wavelet transform method into four coarser resolution images, ranging from 4 to 32 m, to detect image discontinuities. This generated directional high-pass coefficients, which accumulated in a bottom-up approach to determine the terrain roughness and extract obvious topographical features. In addition, we mapped and quantified total geodiversity using available geological, tectonical and topographical elements on a 32-m square grid. The geodiversity index of the area was computed by adding the terrain roughness derived from a wavelet transform to the traditional formula. The correlation among the geodiversity index, terrain roughness, elevation and slope data was tested with exploratory regression and Spatial Lag regression models. We obtained four images that represent the wavelet-detected terrain roughness at four levels of decomposition, ranging from 4 to 32 m. The geodiversity index, computed based on the wavelet-detected roughness, accurately refined the results obtained with the total geodiversity traditional formula. The distribution of the wavelet-detected topographical features was more heterogenic, with a coarser map resolution and forming areas that correspond to the mapped areas with the most obvious geodiversity patterns. Our findings provide a tool for detecting hidden geodiversity patterns within areas that lack apparent landscape variability, as well as for overcoming traditional methods for assessing geodiversity by introducing the multiscale fractional spline wavelet transform with accurate mapping of the terrain roughness.

A new approach for flicker analysis using information‐theory‐based wavelet energy entropy

Flicker is one of the critical power quality disturbances seen in power distribution networks nowadays. Besides its effects on the human life, it causes malfunctioning and misoperation of sensitive electrical equipment. The measurement of the flicker level is defined in IEC 61000‐4‐15 standard by a flicker meter, which deals only with voltage signals and is not sufficient to understand the contribution of the load and background power systems separately. Therefore, in this letter we present a new approach to the evaluation of flicker characteristics in the light of multiresolution wavelet analysis and information‐theory‐based wavelet energy entropy analysis together. © 2017 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Wavelet Multiresolution Complex Network for Analyzing Multivariate Nonlinear Time Series

Characterizing complicated behavior from time series constitutes a fundamental problem of continuing interest and it has attracted a great deal of attention from a wide variety of fields on account of its significant importance. We in this paper propose a novel wavelet multiresolution complex network (WMCN) for analyzing multivariate nonlinear time series. In particular, we first employ wavelet multiresolution decomposition to obtain the wavelet coefficients series at different resolutions for each time series. We then infer the complex network by regarding each time series as a node and determining the connections in terms of the distance among the feature vectors extracted from wavelet coefficients series. We apply our method to analyze the multivariate nonlinear time series from our oil–water two-phase flow experiment. We construct various wavelet multiresolution complex networks and use the weighted average clustering coefficient and the weighted average shortest path length to characterize the nonlinear dynamical behavior underlying the derived networks. In addition, we calculate the permutation entropy to support the findings from our network analysis. Our results suggest that our method allows characterizing the nonlinear flow behavior underlying the transitions of oil–water flows.

A multiresolution wavelet networks architecture and its application to pattern recognition

This paper aims at addressing a challenging research in both fields of the wavelet neural network theory and the pattern recognition. A novel architecture of the wavelet network based on the multiresolution analysis (MRWN) and a novel learning algorithm founded on the Fast Wavelet Transform (FWTLA) are proposed. FWTLA has numerous positive sides compared to the already existing algorithms. By exploiting this algorithm to learn the MRWN, we suggest a pattern recognition system (FWNPR). We show firstly its classification efficiency on many known benchmarks and then in many applications in the field of the pattern recognition. Extensive empirical experiments are performed to compare the proposed methods with other approaches.

Multiresolution Monogenic Wavelet Transform Combined with Bivariate Shrinkage Functions for Color Image Denoising

This paper studies and gives a new algorithm for vector-valued signal processing based on multiresolution monogenic wavelet transform (MMWT). The Riesz transform is employed in the synthesis part of the MMWT. The MMWT coefficients can provide comprehensive analysis of amplitude, phase and orientation for image processing. To demonstrate the properties of MMWT, new color image denoising algorithm is proposed by using MMWT and bivariate shrinkage function. The performance of the proposed algorithm is experimentally verified by using different test color images and noise levels in terms of peak signal-to-noise ratio value and visual quality. Extensive comparisons with the state-of-the-art multiresolution image denoising algorithms indicate that the proposed algorithm can obtain better denoising performance in both visual and quantitative performances. Computation time of the proposed method is analyzed and compared with existing approaches.

Assessing slagging propensity of coal from their slagging indices

Energy production by coal combustion is the most commonly used energy technology. At this time, the correlation between the existing coal slagging indices and the actual observations made in most conventional boilers is poor. Some of the conventional test results and empirical ratios frequently offer misleading information, especially, when their use is extended to other coals or blends. For better understanding of the coal properties related to slagging problems, here a multi-variable regression (MR) analysis equation to predict slagging propensity and new models based on multi-resolution wavelet neural network (MWNN) and vague sets are proposed. Coal samples collected from a wide range of Chinese power plants are evaluated. The results of predictions correlate well with the reported field performance of the coals and the new models offer better predictive capability for understanding the field slagging observations than the conventional indices. The methods proposed here provide an encouraging development towards the search for a generic technique of assessing the slagging potential of pulverized coals/blends in boilers.