Showing papers on "Multiresolution analysis published in 2008"

Content-Based Image Retrieval Using Multiresolution Color and Texture Features

Abstract: In this paper, we propose a content-based image retrieval method based on an efficient combination of multiresolution color and texture features. As its color features, color autocorrelo- grams of the hue and saturation component images in HSV color space are used. As its texture features, BDIP and BVLC moments of the value component image are adopted. The color and texture features are extracted in multiresolution wavelet domain and combined. The dimension of the combined feature vector is determined at a point where the retrieval accuracy becomes saturated. Experimental results show that the proposed method yields higher retrieval accuracy than some conventional methods even though its feature vector dimension is not higher than those of the latter for six test DBs. Especially, it demonstrates more excellent retrieval accuracy for queries and target images of various resolutions. In addition, the proposed method almost always shows performance gain in precision versus recall and in ANMRR over the other methods.

Wavelet Methods for Elliptic Partial Differential Equations

Abstract: 1. Introduction 2. Mulitscale Approximation and Multiresolution 3. Elliptic Boundary Value Problems 4. Multiresolution Galerkin Methods 5. Wavelets 6. Wavelet-Galerkin Methods 7. Adaptive Wavelet Methods 8. Wavelets on General Domains 9. Some Applications APPENDICES REFERENCES INDEX

Identifying Single-Phase-to-Ground Fault Feeder in Neutral Noneffectively Grounded Distribution System Using Wavelet Transform

Abstract: A scheme of single-phase-to-ground fault feeder identification in distribution networks with the application of a wavelet transform technique is presented in this paper. The scheme uses zero-sequence current traveling waves to identify the faulted feeder, and the busbar residual voltage to determine an event caused by fault or switch operation. The current traveling waves measured by zero-sequence current transducers are decomposed using wavelet multiresolution analysis. The local modulus maxima of the wavelet transform are extracted to determine the time of the initial traveling wave. The wavelet transforms on all feeders at the time are compared in magnitude and polarity with each other to identify the faulted feeder. The feeder identification is independent of the network neutral-point grounding mode. The proposed scheme was implemented and verified using Electromagnetic Transients Program (EMTP)-generated signals. The scheme proved to be robust against transients generated during normal events, such as feeder energizing and de-energizing as well as capacitor bank switching.

Automatic Classification and Characterization of Power Quality Events

Abstract: This paper presents a new technique for automatic monitoring of power quality events, which is based on the multiresolution S-transform and Parseval's theorem. In the proposed technique, the S-transform is used to produce instantaneous frequency vectors of the signals, and then the energies of these vectors, based on the Parseval's theorem, are utilized for automatically monitoring and classification of power quality events. The advantage of the proposed algorithm is its ability to distinguish different power quality classes easily. In addition, the magnitude, duration, and frequency content of the disturbances can be accurately identified in order to characterize the disturbances. The paper provides the theoretical background of the technique and presents a wide range of analyses to demonstrate its effectiveness.

High-impedance fault detection using multi-resolution signal decomposition and adaptive neural fuzzy inference system

Abstract: High-impedance faults (HIFs) on distribution systems create unique challenges to protection engineers. HIFs do not produce enough fault current to be detected by conventional overcurrent relays or fuses. A method for HIF detection based on the nonlinear behaviour of current waveforms is presented. Using this method, HIFs can be distinguished successfully from other similar waveforms such as nonlinear load currents, secondary current of saturated current transformers and inrush currents. A wavelet multi-resolution signal decomposition method is used for feature extraction. Extracted features are fed to an adaptive neural fuzzy inference system (ANFIS) for identification and classification. The effect of choice of mother wavelet is also analysed by investigating a large number of wavelet families. Various simulation results, which are obtained using an appropriate model, are summarised and efficiency of the proposed algorithm for dependable and secure HIF detection is determined.

Performance Evaluation of an Adaptive-Network-Based Fuzzy Inference System Approach for Location of Faults on Transmission Lines Using Monte Carlo Simulation

Abstract: This paper employs a wavelet multiresolution analysis (MRA) along with the adaptive-network-based fuzzy inference system to overcome the difficulties associated with conventional voltage- and current-based measurements for transmission-line fault location algorithms, due to the effect of factors such as fault inception angle, fault impedance, and fault distance. This proposed approach is different from conventional algorithms that are based on deterministic computations on a well-defined model to be protected, employing wavelet transform together with intelligent computational techniques, such as the fuzzy inference system (FIS), adaptive neurofuzzy inference system (ANFIS), and artificial neural network (ANN) in order to incorporate expert evaluation so as to extract important features from wavelet MRA coefficients for obtaining coherent conclusions regarding fault location. A comparative study establishes that the ANFIS approach has superiority over ANN- and FIS-based approaches for the location of line faults. In addition, the efficacy of the ANFIS is validated through the Monte Carlo simulation for incorporating the stochastic nature of fault occurrence in practical systems. Thus, this ANFIS-based digital relay can be used as an effective tool for real-time digital relaying purposes.

Integrated wavelet transform and its application to vibration mode shapes for the damage detection of beam-type structures

Abstract: Wavelet analysis has been extensively used in damage detection due to its inherent merits over traditional Fourier transforms, and it has been applied to identify abnormality from vibration mode shapes in structural damage identification. However, most related studies have only demonstrated its ability to identify the abnormality of retrieved mode shapes with a relatively higher signal-to-noise ratio, and its incapability of identifying slight abnormality usually corrupted by noise is still a challenge. In this paper, a new technique (so-called 'integrated wavelet transform (IWT)') of taking synergistic advantages of the stationary wavelet transform (SWT) and the continuous wavelet transform (CWT) is proposed to improve the robustness of abnormality analysis of mode shapes in damage detection. Two progressive wavelet analysis steps are considered, in which SWT-based multiresolution analysis (MRA) is first employed to refine the retrieved mode shapes, followed by CWT-based multiscale analysis (MSA) to magnify the effect of slight abnormality. The SWT-MRA is utilized to separate the multicomponent modal signal, eliminate random noise and regular interferences, and thus extract purer damage information, while the CWT-MSA is employed to smoothen, differentiate or suppress polynomials of mode shapes to magnify the effect of abnormality. The choice of the optimal mother wavelet in damage detection is also elaborately addressed. The proposed methodology of the IWT is evaluated using the mode shape data from the numerical finite element analysis and experimental testing of a cantilever beam with a through-width crack. The methodology presented provides a robust and viable technique to identify minor damage in a relatively lower signal-to-noise ratio environment.

Multiscale Penalized Weighted Least-Squares Sinogram Restoration for Low-Dose X-Ray Computed Tomography

Abstract: In this paper, we propose a novel multiscale penalized weighted least-squares (PWLS) method for restoration of low-dose computed tomography (CT) sinogram. The method utilizes wavelet transform for the multiscale or multiresolution analysis on the sinogram. Specifically, the Mallat-Zhong's wavelet transform is applied to decompose the sinogram to different resolution levels. At each decomposed resolution level, a PWLS criterion is applied to restore the noise-contaminated wavelet coefficients, where the penalty is adaptive to each resolution scale and the weight is updated by an exponential relationship between the data variance and mean at each scale and location. The proposed PWLS method is based on the observations that 1) noise in the CT sinogram after logarithm transform and calibration can be modeled as signal-dependent variables and the sample variance depends on the sample mean by an exponential relationship; and 2) noise reduction can be more effective when it is adaptive to different resolution levels. The effectiveness of the proposed multiscale PWLS method is validated by both computer simulations and experimental studies. The gain by multiscale approach over single scale means is quantified by noise-resolution tradeoff measures.

Biorthogonal multiple vector-valued multivariate wavelet packets associated with a dilation matrix☆

Abstract: In this paper, the notion of multiple vector-valued multiresolution analysis of space L 2 ( R s , C r × r ) is introduced A method for constructing biorthogonal multiple vector-valued wavelet packets in higher dimensions is presented and their properties is investigated by means of time–frequency analysis method, matrix theory and operator theory Three biorthogonality formulas concerning these wavelet packets are obtained Finally, new Riesz bases of space L2(Rs, Cr×r) is obtained by constructing a series of subspaces of biorthogonal multiple vector-valued wavelet packets

The Shiftable Complex Directional Pyramid—Part I: Theoretical Aspects

Abstract: This paper presents an over-complete multiscale decomposition by combining the Laplacian pyramid and the complex directional filter bank (DFB). The filter bank is constructed in such a way that each complex directional filter is analytical using the dual-tree structure of real fan filters. Necessary and sufficient conditions in order for the resulting multirate filter bank to be shift-invariant in energy sense (shiftability) are derived in terms of the magnitude and phase responses of these filters. Their connection to 2D Hilbert transform relationship is established. The proposed transform possesses several desirable properties including multiresolution, arbitrarily high directional resolution, low redundant ratio, and efficient implementation.

Electricity Price Forecasting in Ontario Electricity Market Using Wavelet Transform in Artificial Neural Network Based Model

Abstract: Electricity price forecasting has become an integral part of power system operation and control. In this paper, a wavelet transform (WT) based neural network (NN) model to forecast price profile in a deregulated electricity market has been presented. The historical price data has been decomposed into wavelet domain constitutive sub series using WT and then combined with the other time domain variables to form the set of input variables for the proposed forecasting model. The behavior of the wavelet domain constitutive series has been studied based on statistical analysis. It has been observed that forecasting accuracy can be improved by the use of WT in a forecasting model. Multi-scale analysis from one to seven levels of decomposition has been performed and the empirical evidence suggests that accuracy improvement is highest at third level of decomposition. Forecasting performance of the proposed model has been compared with (i) a heuristic technique, (ii) a simulation model used by Ontario's Independent Electricity System Operator (IESO), (iii) a Multiple Linear Regression (MLR) model, (iv) NN model, (v) Auto Regressive Integrated Moving Average (ARIMA) model, (vi) Dynamic Regression (DR) model, and (vii) Transfer Function (TF) model. Forecasting results show that the performance of the proposed WT based NN model is satisfactory and it can be used by the participants to respond properly as it predicts price before closing of window for submission of initial bids.

Face recognition using curvelet based PCA

Abstract: This paper identifies a novel feature space to address the problem of human face recognition from still images. This is based on the PCA space of the features extracted by a new multiresolution analysis tool called Fast Discrete Curvelet Transform. Curvelet Transform has better directional and edge representation abilities than widely used wavelet transform. Inspired by these attractive attributes of curvelets, we introduce the idea of decomposing images into its curvelet subbands and applying PCA (Principal Component Analysis) on the selected subbands in order to create a representative feature set. Experiments have been designed for both single and multiple training images per subject. A comparative study with wavelet-based and traditional PCA techniques is also presented. High accuracy rate achieved by the proposed method for two well-known databases indicates the potential of this curvelet based feature extraction method.

PET Image Denoising Using a Synergistic Multiresolution Analysis of Structural (MRI/CT) and Functional Datasets

Abstract: PET allows the imaging of functional properties of the living tissue, whereas other modalities (CT, MRI) provide structural information at significantly higher resolution and better image quality. Constraints for injected radioactivity, technologic limitations of current instrumentation, and inherent spatial uncertainties on the decaying process affect the quality of PET images. In this article we illustrate how structural information of matched anatomic images can be used in a multiresolution model to enhance the signal-to-noise ratio of PET images. The model states a flexible relation between function and structure in the brain and replaces high-resolution information of PET images with appropriately scaled MRI or CT local detail. The method can be naturally extended to other functional imaging modalities (SPECT, functional MRI). Methods: The methodology is based on the multiresolution property of the wavelet transform (WT). First, the coregistered structural image (MRI/CT) is downgraded to the resolution of the PET volume through appropriate filtering. Second, a redundant version of the WT is applied to both volumes. Third, a linear model is applied to the set of local coefficients of both image volumes and resulting parameters are recorded. The overall set of linear coefficients is then modeled as a mixture of multivariate gaussian distributions and fitted through a k-means algorithm. Finally, the local wavelet coefficients of the PET image are substituted by the corresponding values of the MRI/CT set calibrated according to the resulting clustering. The methodology was validated on digital simulated images and clinical data to evaluate its quantitative potential for individual as well as group analysis. Results: Application to real and simulated datasets shows very effective noise reduction (15% SD) while resolution is preserved. Conclusion: The methodology is robust to errors in the coregistration parameters, practical to implement, and computationally fast.

Wavelet Basis Function Neural Networks for Sequential Learning

Abstract: In this letter, we develop the wavelet basis function neural networks (WBFNNs). It is analogous to radial basis function neural networks (RBFNNs) and to wavelet neural networks (WNNs). In WBFNNs, both the scaling function and the wavelet function of a multiresolution approximation (MRA) are adopted as the basis for approximating functions. A sequential learning algorithm for WBFNNs is presented and compared to the sequential learning algorithm of RBFNNs. Experimental results show that WBFNNs have better generalization property and require shorter training time than RBFNNs.

Mutual Information-Based 3D Object Tracking

Abstract: We propose a robust methodology for 3D model-based markerless tracking of textured objects in monocular image sequences. The technique is based on mutual information maximization, a widely known criterion for multi-modal image registration, and employs an efficient multiresolution strategy in order to achieve robustness while keeping fast computational time, thus achieving near real-time performance for visual tracking of complex textured surfaces.

Wavelet-based multiresolution analysis for data cleaning and its application to water quality management systems

Abstract: Data cleaning techniques are useful for extracting desirable knowledge or interesting patterns from existing databases in engineering applications. The major problems of conventional techniques (e.g., Fourier Transformation Technique) are that they are (1) more appropriate in linear systems than nonlinear systems, and (2) stringently depend on state space functions. In this study a wavelet-based multiresolution analysis technique (WMAT) is proposed for reducing noises induced by complex uncertainty. The approach is applied to a river water quality simulation system for showing its practicability in data cleaning and parameter estimation. Clean data are prepared through running a Thomas' river water quality model and polluted data are synthesized by mixing clean data with white Gaussian noises. The results show that WMAT will not distort the clean data, and can effectively reduce the noise in the polluted data. The data denoised by WMAT are furthermore used for estimating the modeling parameters. It is also indicated that the parameters estimated with the denoised data through WMAT are much closer to real values than those (1) with polluted data through WMAT and (2) with data through Fourier analysis technique. It is thus recommended that the prepared data be used for estimating the modeling parameters until being cleaned with WMAT.

A Fast Adaptive Wavelet Scheme in RBF Collocation for Nearly Singular Potential PDEs

Abstract: We present a wavelet based adaptive scheme and investigate the efficiency of this scheme for solving nearly singular potential PDEs. Multiresolution wavelet analysis (MRWA) provides a firm mathematical foundation by projecting the solution of PDE onto a nested sequence of approximation spaces. The wavelet coefficients then were used as an estimation of the sensible regions for node adaptation. The proposed adaptation scheme requires negligible calculation time due to the existence of the fast Discrete Wavelet Transform (DWT). Certain aspects of the proposed adaptive scheme are discussed through numerical examples. It has been shown that the proposed adaptive scheme can detect the singularities both in the domain and near the boundaries. Moreover, the proposed adaptive scheme can be utilized for capturing the regions with high gradient both in the solution and its spatial derivatives. Due to the simplicity of the proposed method, it can be efficiently applied to large scale nearly singular engineering problems.

Multiresolution Analysis and Wavelets on Vilenkin Groups

Abstract: This paper gives a review of multiresolution analysis and compactly sup- ported orthogonal wavelets on Vilenkin groups. The Strang-Fix condition, the partition of unity property, the linear independence, the stability, and the orthonormality of 'integer shifts' of the corresponding refinable functions are considered. Necessary and sufficient conditions are given for refinable functions to generate a multiresolution analysis in the L2-spaces on Vilenkin groups. Several examples are provided to illustrate these results. .

Optimized Wavelets for Blind Separation of Nonstationary Surface Myoelectric Signals

Abstract: Surface electromyography (EMG) signals detected over the skin surface may be mixtures of signals generated by many active muscles due to poor spatial selectivity of the recording. In this paper, we propose a new method for blind source separation (BSS) of nonstationary signals modeled as linear instantaneous mixtures. The method is based on whitening of the observations and rotation of the whitened observations. The rotation is performed by joint diagonalization of a set of spatial wavelet distributions (SWDs). The SWDs depend on the selection of the mother wavelet which can be defined by unconstrained parameters via the lattice parameterization within the multiresolution analysis framework. As the sources are classically supposed to be mutually uncorrelated, the design parameters of the mother wavelet can be blindly optimized by minimizing the average (over time lags) cross correlation between the estimated sources. The method was tested on simulated and experimental surface EMG signals and results were compared with those obtained with spatial time-frequency distributions and with second-order statistics (only spectral information). On a set of simulated signals, for 10-dB signal-to-noise ratio (SNR), the cross-correlation coefficient between original and estimated sources was 0.92plusmn0.07 with wavelet optimization, 0.74plusmn0.09 with the wavelet leading to the poorest performance, 0.85plusmn0.07 with Wigner-Ville distribution, 0.86plusmn0.07 with Choi-Williams distribution, and 0.73plusmn0.05 with second-order statistics. In experimental conditions, when the flexor carpi radialis and pronator teres were concomitantly active for 50% of the time, crosstalk was 55.2plusmn10.0% before BSS and was reduced to 15.2plusmn6.3% with wavelet optimization, 30.1plusmn15.0% with the worst wavelet, 28.3plusmn12.3% with Wigner-Ville distribution, 26.2plusmn12.0% with Choi-Williams distribution, and 35.1plusmn15.5% with second-order statistics. In conclusion, the proposed approach resulted in better performance than previous methods for the separation of nonstationary myoelectric signals.

A multi-scale approach to hyperbolic evolution equations with limited smoothness

Abstract: We discuss how techniques from multiresolution analysis and phase space transforms can be exploited in solving a general class of evolution equations with limited smoothness. We have wave propagati...

Fusion of IKONOS Satellite Imagery Using IHS Transform and Local Variation

Abstract: The intensity-hue-saturation (IHS) technique is a well-known merging approach for its computational efficiency and spatial definition holding. However, it results in color distortion particularly for the remote sensing images of IKONOS and QuickBird as some other fusion methods, such as principal component analysis, and Brovey transform. Although wavelet-based image fusion approaches can provide a better tradeoff between spatial and spectral quality, the fused images with these methods often have a spatial resolution that is less than that of the IHS-based algorithm. A remote sensing image fusion algorithm based on IHS transform and local variation and its modified approach with low computational complexity are proposed. Visual effect and quantity evaluation results show that the proposed simple algorithm outperforms the conventional image fusion methods in the spectral domain with the spatial quality similar to that of the undecimated wavelet transform-based scheme. The proposed modified method can obtain the similar spatial resolution of the merged image with the IHS-based fusion algorithm and the better spectral quality in the green vegetation areas.

Tracking the Best Quantizer

Abstract: An algorithm is presented for online prediction that allows to track the best expert efficiently even when the number of experts is exponentially large, provided that the set of experts has a certain additive structure. As an example, we work out the case where each expert is represented by a path in a directed graph and the loss of each expert is the sum of the weights over the edges in the path. These results are then used to construct universal limited-delay schemes for lossy coding of individual sequences. In particular, we consider the problem of tracking the best scalar quantizer that is adaptively matched to the source sequence with piecewise different behavior. A randomized algorithm is presented which can perform, on any source sequence, asymptotically as well as the best scalar quantization algorithm that is matched to the sequence and is allowed to change the employed quantizer for a given number of times. The complexity of the algorithm is quadratic in the sequence length, but at the price of some deterioration in performance, the complexity can be made linear. Analogous results are obtained for sequential multiresolution and multiple description scalar quantization of individual sequences.

Selection of a suitable mother wavelet for analyzing power system fault transients

Abstract: In the literature, wavelet techniques are proposed for the analysis of power system transients. Many mother wavelets have been used for this analysis such as Haar, Daubechies (db), Symlets, and Coiflets. This paper describes a strategy to choose a suitable mother wavelet for this analysis. It also shows the deviation between Matlab and theoretical (mathematically calculated) db-wavelets when they are used for the analysis of power system transient. The simulation study is carried out using PSCAD simulation program and Matlab wavelet toolbox. The simulation results show that the theoretical db wavelet is more suitable for analyzing power system fault transients than the Matlab db wavelet.

Wavelets Applied to CMB Maps: a Multiresolution Analysis for Denoising

Abstract: Analysis and denoising of Cosmic Microwave Background (CMB) maps are performed using wavelet multiresolution techniques. The method is tested on 12 ◦ .8×12 ◦ .8 maps with resolution resembling the experimental one expected for future high resolution space observations. Semianalytic formulae of the variance of wavelet coefficients are given for the Haar and Mexican Hat wavelet bases. Results are presented for the standard Cold Dark Matter (CDM) model. Denoising of simulated maps is carried out by removal of wavelet coefficients dominated by instrumentalnoise. CMB maps with a signal-to-noise, S/N � 1, are denoised with an error improvement factor between 3 and 5. Moreover we have also tested how well the CMB temperature power spectrum is recovered after denoising. We are able to reconstruct the Cl’s up to l � 1500 with errors always below 20% in cases with S/N > 1.