Wavelet Theory Research Articles

Wavelet-Based Visual Analysis of Dynamic Networks.

Dynamic networks naturally appear in a multitude of applications from different fields. Analyzing and exploring dynamic networks in order to understand and detect patterns and phenomena is challenging, fostering the development of new methodologies, particularly in the field of visual analytics. In this work, we propose a novel visual analytics methodology for dynamic networks, which relies on the spectral graph wavelet theory. We enable the automatic analysis of a signal defined on the nodes of the network, making viable the robust detection of network properties. Specifically, we use a fast approximation of a graph wavelet transform to derive a set of wavelet coefficients, which are then used to identify activity patterns on large networks, including their temporal recurrence. The coefficients naturally encode the spatial and temporal variations of the signal, leading to an efficient and meaningful representation. This methodology allows for the exploration of the structural evolution of the network and their patterns over time. The effectiveness of our approach is demonstrated using usage scenarios and comparisons involving real dynamic networks.

Research on Marine Photovoltaic Power Forecasting Based on Wavelet Transform and Echo State Network

Abstract With the rapid development of photovoltaic power generation technology, photovoltaic power generation system has gradually become an important component of the integrated energy system of marine. High precision short-term photovoltaic power generation forecasting is becoming one of the key technologies in ship energy saving and ship energy efficiency improving. Aiming at the characteristics of marine photovoltaic power generation system, we designed a highprecision power forecasting model (WT+ESN) for marine photovoltaic power generation system with anti-marine environmental interference. In this model, the information mining of the photovoltaic system in marine environment is carried out based on wavelet theory, then the forecasting model basing on echo state network is construct ed. Lastly, three kinds of error metrics are compared with the three traditional models by Matlab, the result shows that the model has high forecasting accuracy and strong robustness to marine environmental factors, which is of great significance to save fuel for ships, improve the energy utilization rate and assist the power dispatching and fuel dispatching of the marine power generation system.

A wavelet threshold denoising procedure for multimodel predictions: An application to economic time series

Noise‐affected economic time series, realizations of stochastic processes exhibiting complex and possibly nonlinear dynamics, are dealt with. This is often the case of time series found in economics, which notoriously suffer from problems such as low signal‐to‐noise ratios, asymmetric cycles and multiregimes patterns. In such a framework, even sophisticated statistical models might generate suboptimal predictions, whose quality can further deteriorate unless time consuming updating or deeper model revision procedures are carried out on a regular basis. However, when the models' outcomes are expected to be disseminated in timeliness manner (as in the case of Central Banks or national statistical offices), their modification might not be a viable solution, due to time constraints. On the other hand, if the application of simpler linear models usually entails relatively easier tuning‐up procedures, this would come at the expenses of the quality of the predictions yielded. A mixed, self‐tuning forecasting method is therefore proposed. This is an automatic, 2‐stage procedure, able to generate predictions by exploiting the denoising capabilities provided by the wavelet theory in conjunction with a compounded forecasting generator. Its out‐of‐sample performances are evaluated through an empirical study carried out on macroeconomic time series.

Frames arising from irreducible solvable actions I

In this work, we provide a unified method for the construction of reproducing systems arising from unitary irreducible representations of some solvable Lie groups. In contrast to other well-known techniques such as the coorbit theory, the generalized coorbit theory and other discretization schemes, we make no assumption on the integrability or square-integrability of the representations of interest. Moreover, our scheme produces explicit constructions of frames with precise frame bounds. As an illustration of the scope of our results, we highlight that a large class of representations which naturally occur in wavelet theory and time–frequency analysis is handled by our scheme. For example, the affine group, the generalized Heisenberg groups, the shearlet groups, solvable extensions of vector groups and various solvable extensions of non-commutative nilpotent Lie groups are a few examples of groups whose irreducible representations are handled by our method. The class of representations studied in this work is described as follows. Let G be a simply connected, connected, completely solvable Lie group with Lie algebra g=p+m. Next, let π be an infinite-dimensional unitary irreducible representation of G obtained by inducing a character from a closed normal subgroup P=exp⁡p of G. Additionally, we assume that G=P⋊M, M=exp⁡m is a closed subgroup of G, dμM is a fixed Haar measure on the solvable Lie group M and there exists a linear functional λ∈p⁎ such that the representation π=πλ=indPG(χλ) is realized as acting in L2(M,dμM). Making no assumption on the integrability of πλ, we describe explicitly a discrete subset Γ of G and a vector f∈L2(M,dμM) such that πλ(Γ)f is a tight frame for L2(M,dμM). We also construct compactly supported smooth functions s and discrete subsets Γ⊂G such that πλ(Γ)s is a frame for L2(M,dμM).

STUDY THE PERFORMANCE OF THE TWO WAVELET-BASED ADAPTATION SCHEMES FOR THE SHALLOW WATER FLOW MODELLING

This work proposed a new adaptive method which avails from the wavelets theory for transforming the local single resolution information into multiresolution information. This information became accessible and by deactivating or activating them, the spatial resolution adaptation was achieved. The adaptive technique was combined with two standard numerical modelling schemes (i.e. finite volume and discontinuous Galerkin schemes) to produce two new adaptive schemes for modelling one dimensional shallow water flows so-called the Haar wavelets finite volume (HWFV) and multiwavelet discontinuous Galerkin (MWDG) schemes. Both adaptive schemes were tested using hydraulic test cases. The results demonstrated that the proposed adaptive technique could serve as the foundation on which to construct complete adaptive schemes for simulating the real problems of shallow water flow.

Wavelet power spectrum and cross-coherency of Spanish economic variables

We analyze six relevant economic and financial variables for the period 2000M1–2015M3 in the context of the Spanish economy: a financial index (IBEX35), a commodity (crude oil price in euros), a foreign exchange index (EUR/USD), a bond (Spanish 10-year bond), the Spanish national debt and the consumer price index. The goal of this paper is to analyze the main relationships between them by computing, using a special toolbox in MATLAB, the wavelet power spectrum and the cross-wavelet coherency associated with Morlet wavelets, focusing our interest on the period variable. We decompose the time–frequency effects and improve the interpretation of the results by non-expert users in the theory of wavelets. This yields empirical evidence on instability periods and reveals various changes and breaks in the causality relationships for the data available from recent years. Moreover, we introduce a comparison with Gaussian wavelets and use the MATLAB software suite for computing, taking the scale instead of the period as the reference variable. These same variables were analyzed individually in a previous paper that specifically considered the decomposition of non-stationary monthly rate series in the period 2000M1–2014M12 using Daubechies wavelets db8 to visualize high frequency variance, seasonality and trend.

Theory of wavelet-based coarse-graining hierarchies for molecular dynamics.

We present a multiresolution approach to compressing the degrees of freedom and potentials associated with molecular dynamics, such as the bond potentials. The approach suggests a systematic way to accelerate large-scale molecular simulations with more than two levels of coarse graining, particularly applications of polymeric materials. In particular, we derive explicit models for (arbitrarily large) linear (homo)polymers and iterative methods to compute large-scale wavelet decompositions from fragment solutions. This approach does not require explicit preparation of atomistic-to-coarse-grained mappings, but instead uses the theory of diffusion wavelets for graph Laplacians to develop system-specific mappings. Our methodology leads to a hierarchy of system-specific coarse-grained degrees of freedom that provides a conceptually clear and mathematically rigorous framework for modeling chemical systems at relevant model scales. The approach is capable of automatically generating as many coarse-grained model scales as necessary, that is, to go beyond the two scales in conventional coarse-grained strategies; furthermore, the wavelet-based coarse-grained models explicitly link time and length scales. Furthermore, a straightforward method for the reintroduction of omitted degrees of freedom is presented, which plays a major role in maintaining model fidelity in long-time simulations and in capturing emergent behaviors.

A novel method of medical image enhancement based on wavelet decomposition

The efficiency of image enhancement algorithms depends on the quality and processing speed of image enhancement. There are many algorithms to implement image enhancement using wavelet theory. These algorithms have one thing in common: they all capture image details by decomposing low frequency sub-images. In fact, a lot of details in high-frequency sub-images are also found. Enlightened by the above-mentioned facts, a novel medical image enhancement method based on wavelet decomposition is proposed by adding details from the high-frequency sub-images and decomposing the image specially with ant-symmetric biorthogonal wavelet instead of some traditional wavelets. It not only improves the image enhancement, but also overcomes the shortcomings of large computation with faster computational speed and satisfies the real-time requirement in edge detection. Simulation experiments of mammographic images are implemented by Matlab with several different methods, the results show that the proposed method is superior to some popular methods, such as histogram equalization and wavelet nonlinear enhancement.

Quaternionic continuous wavelet transform on a quaternionic Hilbert space

In this paper we consider the new concept of the quaternionic unitary representation of a locally compact group to the unitary group of a quaternionic Hilbert space, and study its properties. Also, we establish a continuous wavelet transform by means of a special case of such representations to extend the continuous wavelet transform related to semidirect product groups. The results may be useful in development of wavelet theory.

Identification and Localization of non-zero Resistance Short circuit Faults in Distribution Feeders Based on the Theory of Wavelets and Artificial Intelligence

This paper introduces a radial distribution feederprotection scheme based on certain features extraction fromcurrent signals measurement at the substation. The featuresare captured using the discrete wavelet transform (DWT). Twodigital signals processing methods are used to introduce thosefeatures to the 1) fault detection 2) identification and 3)localization schemes; the first one is the energy method and thesecond one is the root mean square method. For the purpose offault type identification, two systems are tested and compared,a Fuzzy Inference System (FIS) and Artificial Neural Network(ANN). Fault location scheme is then built based on ANNs. Aneffort is made to reduce the computational burden and thespeed of detection provided by the fault detection andidentification schemes. Since the short circuit faults are themost likely types of faults that can occur in power systems, theten types of these faults taking into account different faultresistances are simulated in MATLAB environment and theprotection scheme is built based on the idea of overcurrent.The power quality disturbances such as switching transientsevents on the feeder are also taken into account in order to builda reliable and secure protection scheme.

A new binary hybrid particle swarm optimization with wavelet mutation

Particle swarm optimization (PSO) is a population-based stochastic optimization algorithm, where individual elements, termed as particles, move around a multi-dimensional problem space at different directions (i.e., trajectories) and speeds (i.e., velocities) to find the best solution for non-deterministic polynomial time. The movement for a particle is determined by its previous best result and the previous best result of the entire population. In one of the current PSO variants called Hybrid Particle Swarm Optimisation (HPSOWM), where a mutation process based on wavelet theory was added to the original PSO to prevent premature conclusion of the best solution. This hybridisation with PSO has improved both solution stability and quality over the original algorithm as well as many other hybrid PSO algorithms. However, this solution is not practicable and very limited to work on a continuous problem space. As such, in this research, we propose a discrete binary HPSOWM which operates on binary-based problem space, and termed as “Binary Hybrid Particle Swarm Optimization with Wavelet Mutation” (BHPSOWM). In this work, the movement mechanism of particles as well as the mutation process are modified and transformed to work with binary elements. We conduct a series of experiments to compare the performance of the binary versions of three algorithms: Genetic Algorithm (GA), Particle Swarm Optimization (BPSO) against our proposed algorithm - BHPSOWM. The experiment results show that our proposed model delivers better performance in terms of the mean cost value, standard deviation and the convergence rate under the same settings.

Land Surface Temperature and Emissivity Retrieval from Field-Measured Hyperspectral Thermal Infrared Data Using Wavelet Transform

Currently, the main difficulty in separating the land surface temperature (LST) and land surface emissivity (LSE) from field-measured hyperspectral Thermal Infrared (TIR) data lies in solving the radiative transfer equation (RTE). Based on the theory of wavelet transform (WT), this paper proposes a method for accurately and effectively separating LSTs and LSEs from field-measured hyperspectral TIR data. We show that the number of unknowns in the RTE can be reduced by decomposing and reconstructing the LSE spectrum, thus making the RTE solvable. The final results show that the errors introduced by WT are negligible. In addition, the proposed method usually achieves a greater accuracy in a wet-warm atmosphere than that in a dry-cold atmosphere. For the results under instrument noise conditions (NE∆T = 0.2 K), the overall accuracy of the LST is approximately 0.1–0.3 K, while the Root Mean Square Error (RMSE) of the LSEs is less than 0.01. In contrast to the effects of instrument noise, our method is quite insensitive to noises from atmospheric downwelling radiance, and all the RMSEs of our method are approximately zero for both the LSTs and the LSEs. When we used field-measured data to better evaluate our method’s performance, the results showed that the RMSEs of the LSTs and LSEs were approximately 1.1 K and 0.01, respectively. The results from both simulated data and field-measured data demonstrate that our method is promising for decreasing the number of unknowns in the RTE. Furthermore, the proposed method overcomes some known limitations of current algorithms, such as singular values and the loss of continuity in the spectrum of the retrieved LSEs.

Topological features in signal processing using frame theory and persistent homology

We present some interactions between frame theory and persistent homology as a new way to construct classification mechanisms in signal processing. On the one hand, frame theory generalizes basic ideas from time-frequency analysis including aspects of short term Fourier transformations and wavelet theory. On the other hand, persistent homology provides new algorithms applying concepts from algebraic topology to data analysis. The question of finding adequate sparse representations of data can be seen from several points of view, including dimensionality reduction and modern developments in neural networks. Persistent homology, as a topic in topological data analysis, presents alternative mechanisms for finding adequate sparse representations of data. We explain some interactions between these tools with applications to the analysis of acoustic signals.

Discrete frequency slice wavelet transform

This paper introduces a new kind of Time-Frequency Representation (TFR) method called Discrete Frequency Slice Wavelet Transform (DFSWT). It is an improved version of Frequency Slice Wavelet Transform (FSWT). The previous researches on FSWT show that it is a new efficientTFR in an easy way without strict limitation as traditional wavelet theory. DFSWT as well as FSWT are defined directly in frequency domain, and still keep its properties in time-frequency domain as FSWT decomposition, reconstruction and filter design, etc. However, the original signal is decomposed and reconstructed on a Chosen Frequency Domains (CFD) as need of application. CFD means that the decomposition and reconstruction are not completed on all frequency components. At first, it is important to discuss the necessary condition of CFD to reconstruct the original signal. And then based on norm l2, an optimization algorithm is introduced to reconstruct the original signal even accurately. Finally, for a test example, the TFR analysis of a real life signal is shown. Some conclusions are drawn that the concept of CFD is very useful to application, and the DFSWT can become a simple and easy tool of TFR method, and also provide a new idea of low speed sampling of high frequency signal in applications.

Curvature variation factor and its application

Evaluation on curvature variation is a significant problem in the field of curve fairing, and traditional evaluation is generally performed by observing curvature plots qualitatively. By using the theory of B-spline wavelet, the concept of curvature variation factor (CVF) is put forth in this paper to describe curvature variation quantitatively. It is verified that the quantitative evaluation results by the CVF method agree well with the traditional qualitative judgments. Based on CVF, a new curve-fairing algorithm is further put forward, whose validness is verified by an example. The advantage of the CVF-based algorithm is that it can realize different fairing effect to meet different requirements under diverse circumstances only by adjusting the shape error.

Creation of codes based on wavelet transformation and its application in ADV612 chips

Theory of wavelet transform is a powerful tool for image and video processing. Mathematical concepts of wavelet transform and filter bank have been studied carefully in many works. This work presents application of new construction of linear and robust codes based on wavelet decomposition and its application in ADV612 chips. We present the model of the error-coding scheme that allows to detect errors in the ADV612 chips with high probability. In our work, we will show that developed and presented scheme of protection drastically improves the resistance of ADV612 chips to malfunctions and errors.

APPLICATION OF MORLET WAVELET IN THE DIAGNOSIS OF NOISE SIGNAL CHARACTERISTICS OF A WIND TURBINE BLADE IN ABNORMAL OPERATION

This study developed an estimation model for noise signal characteristic diagnosis based on the time-frequency analysis technique. The time-frequency analysis theory uses the relatively mature and extensively used wavelet method as the basis of signal analysis, but wavelet analysis generates wavelet theories different from other mother wavelet methods. This study used the Morlet Transform, which is a type of wavelet transform using a mother wavelet for wavelet analysis of signals. The time axis was integrated according to the result of time-frequency analysis in order to obtain the marginal spectrum value of the frequency domain. Finally, statistical regression analysis was used as the estimation method of feature extraction. This study determined and validated the behavior estimation functional equation of a wind turbine blade in normal operation versus the signal of a wind turbine blade in abnormal operation. The proposed model can be used as a diagnostic method of early warning and health management of a wind turbine.

A new approach to flow simulation using hybrid models

The necessity of flow prediction in rivers, for proper management of water resource, and the need for determining the inflow to the dam reservoir, designing efficient flood warning systems and so forth, have always led water researchers to think about models with high-speed response and low error. In the recent years, the development of Artificial Neural Networks and Wavelet theory and using the combination of models help researchers to estimate the river flow better and better. In this study, daily and monthly scales were used for simulating the flow of Gamasiyab River, Nahavand, Iran. The first simulation was done using two types of ANN and ANFIS models. Then, using wavelet theory and decomposing input signals of the used parameters, sub-signals were obtained and were fed into the ANN and ANFIS to obtain hybrid models of WANN and WANFIS. In this study, in addition to the parameters of precipitation and flow, parameters of temperature and evaporation were used to analyze their effects on the simulation. The results showed that using wavelet transform improved the performance of the models in both monthly and daily scale. However, it had a better effect on the monthly scale and the WANFIS was the best model.

Method for diagnosis of on‐load tap changer based on wavelet theory and support vector machine

Method for diagnosis of on‐load tap changer based on wavelet theory and support vector machine

A Proposed Approach for Image Compression based on Wavelet Transform and Neural Network

Over the last years, wavelet theory has been used with great success in a wide range of applications as signal de-noising and image compression. An ideal image compression system must yield high-quality compressed image with high compression ratio. This paper attempts to find the most useful wavelet function to compress an image among the existing members of wavelet families. Our idea is that a backpropagation neural network is trained to select the suitable wavelet function between the two families: orthogonal (Haar) and biorthogonal (bior4.4), to be used to compress an image efficiently and accurately with an ideal and optimum compression ratio. The simulation results indicated that the proposed technique can achieve good compressed images in terms of peak signal to noise ratio (PSNR) and compression ratio (t) in comparison with random selection of the mother wavelet.