Showing papers on "Multiresolution analysis published in 2015"
01 Jan 2015
TL;DR: The continuous wavelet transform (CWT) of the current I(t) convolved by a given wavelet ψ is defined as P. S. Addison, The Illustrated Wavelet Transform Handbook: Introductory Theory and Applications in Science, Engineering, Medicine and Finance.
Abstract: temporal scale application dimension. In recent decades, SPI Use the cross wavelet transform to investigate the effect of large scale Addison, P.S., 2002. The Illustrated Wavelet Transform. Handbook: Introductory Theory and Applications. The Illustrated Wavelet Transform Handbook: Introductory Theory and Applications in Science, Engineering, Medicine and Finance. CRC Press, Boca Raton. The continuous wavelet transform (CWT) of the current I(t) convolved by a given wavelet ψ is defined as P. S. Addison, The Illustrated Wavelet Transform Handbook: Introductory Theory and Applications in Science, Engineering, Medicine.
93 citations
TL;DR: The features and capabilities of MADNESS are described and some current applications in chemistry and several areas of physics are discussed.
Abstract: MADNESS (multiresolution adaptive numerical environment for scientific simulation) is a high-level software environment for solving integral and differential equations in many dimensions that uses adaptive and fast harmonic analysis methods with guaranteed precision based on multiresolution analysis and separated representations. Underpinning the numerical capabilities is a powerful petascale parallel programming environment that aims to increase both programmer productivity and code scalability. This paper describes the features and capabilities of MADNESS and briefly discusses some current applications in chemistry and several areas of physics.
77 citations
TL;DR: In this article, a wavelet packet decomposition within the framework of multiresolution analysis theory is considered to analyze acoustic emission signals to investigate the failure of tribological systems, and a method for the extraction of single events in rail contact fatigue test is proposed.
75 citations
TL;DR: A hierarchical CRF (HIECRF) model for SAR image segmentation that effectively exploits the global and local image information, including the contextual structures, the image features, and the scattering statistics, to achieve the MPM segmentation.
Abstract: The conditional random field (CRF) model is suitable for the image segmentation because this model relaxes the assumption of conditional independence of the observed data and models the data-dependent label interaction in the image modeling. However, this model has a limited ability to capture the global and local image information from the perspective of multiresolution analysis. Moreover, for synthetic aperture radar (SAR) image segmentation, SAR scattering statistics that are essential to SAR image processing are not considered in the CRF model. In this paper, we propose a hierarchical CRF (HIECRF) model for SAR image segmentation. The HIECRF model belongs to the discriminative models according to the semantic structure. While inheriting the advantages of the CRF model, the HIECRF model achieves the integration of the image features and SAR scattering statistics and captures the contextual structure information in the spatial and scale spaces. Moreover, we derive a hierarchical inference algorithm for the HIECRF model in virtue of the mean-field approximation (MFA) to provide the maximization of the posterior marginal (MPM) estimate of the HIECRF model. Then, by the bottom-up and the top-down recursions in the hierarchical inference procedure, the HIECRF model effectively exploits the global and local image information, including the contextual structures, the image features, and the scattering statistics, to achieve the MPM segmentation. The effectiveness of the HIECRF model is demonstrated by the application to the semisupervised segmentation of the simulated images and the real SAR images.
59 citations
TL;DR: A wavelet fuzzy based protection scheme for a double line transmission system with unified power flow controller that makes use of current signals at both the ends of transmission line which are synchronized with the help of global position system clock is presented.
50 citations
TL;DR: This paper introduces and systematically study affine shear tight frames which include all known shearlet tight frames as special cases, and presents two different approaches, i.e., non-stationary and quasi- Stationary, for the construction of sequences of affineShear Tight frames with MRA structure such that all their generators are smooth (in the Schwarz class) and they have underlying filter banks.
38 citations
TL;DR: The number of samples that must be acquired to ensure a stable and accurate reconstruction scales linearly with the number of reconstructing wavelet functions.
Abstract: In this paper we analyze two-dimensional wavelet reconstructions from Fourier samples within the framework of generalized sampling. For this, we consider both separable compactly-supported wavelets and boundary wavelets. We prove that the number of samples that must be acquired to ensure a stable and accurate reconstruction scales linearly with the number of reconstructing wavelet functions. We also provide numerical experiments that corroborate our theoretical results.
38 citations
TL;DR: The multiresolution approach effectively prevents the appearance of non-physical geometry oscillations in the optimised shapes due to the absence of a volume mesh and there is no need for mesh regeneration or smoothing during the optimisation.
38 citations
TL;DR: It is shown that MEMD overcomes problems by being fully data adaptive and by aligning common frequency scales from multiple channels, thus enabling their comparison at a pixel level and subsequent fusion at multiple data scales.
Abstract: A novel scheme to perform the fusion of multiple images using the multivariate empirical mode decomposition (MEMD) algorithm is proposed. Standard multi-scale fusion techniques make a priori assumptions regarding input data, whereas standard univariate empirical mode decomposition (EMD)-based fusion techniques suffer from inherent mode mixing and mode misalignment issues, characterized respectively by either a single intrinsic mode function (IMF) containing multiple scales or the same indexed IMFs corresponding to multiple input images carrying different frequency information. We show that MEMD overcomes these problems by being fully data adaptive and by aligning common frequency scales from multiple channels, thus enabling their comparison at a pixel level and subsequent fusion at multiple data scales. We then demonstrate the potential of the proposed scheme on a large dataset of real-world multi-exposure and multi-focus images and compare the results against those obtained from standard fusion algorithms, including the principal component analysis (PCA), discrete wavelet transform (DWT) and non-subsampled contourlet transform (NCT). A variety of image fusion quality measures are employed for the objective evaluation of the proposed method. We also report the results of a hypothesis testing approach on our large image dataset to identify statistically-significant performance differences.
35 citations
TL;DR: In this paper, a novel multiscale decomposition based on a normalized nonlocal means (NNLM) filter is developed to extract the spatial detail in the pansharpening product by exploiting the normalized intensity value and the mean value jointly.
Abstract: Pansharpening aims to synthesize a high-spatial-resolution multispectral (MS) image by fusing a panchromatic (PAN) image and a low-resolution MS image. The multiresolution analysis (MRA)-based methods are a popular group of pansharpening methods. However, in the MRA-based methods, spatial distortions may occur in the pansharpened product due to the misalignment of PAN and MS data. To address the spatial distortion issue in MRA-based methods, this paper proposes a two-step approach, which consists of the coarse step and the refined step. The coarse step produces a preliminary result using the traditional details injection model. Then, the preliminary product is refined with a second details injection operation in the refined step. Moreover, in our proposed two-step approach, a novel multiscale decomposition based on a normalized nonlocal means (NNLM) filter is developed to extract the spatial detail. Compared with the original nonlocal means filter, the designed NNLM makes the similarity measure more robust and accurate by exploiting the normalized intensity value and the mean value jointly. The experimental results on various satellite data demonstrate the superiority of the proposed pansharpening scheme by comparing with ten well-known methods.
34 citations
TL;DR: This study applies the discrete wavelet transform theory and multiresolution analysis (MRA) to vibration signals to find characteristic patterns of shafts with a transversal crack to constitute an automatic monitoring system with a fast diagnosis online capability.
Abstract: In the maintenance of motor driven systems, detection of cracks in shafts play a critical role. Condition monitoring and fault diagnostics detect and distinguish different kinds of machinery faults...
TL;DR: In this article, a combination of wavelet Galerkin method and X-FEM with a high-order interpolant is used to solve 2D linear fracture mechanics problems.
Abstract: Two-dimensional (2D) crack problems are solved employing a novel technique based on a combination of wavelet Galerkin method and X-FEM with a high-order interpolant. Multiresolution analysis of the wavelet basis functions (scaling/wavelet functions) plays an important role in the numerical simulation. High-order B-spline scaling/wavelet functions are chosen as the basis functions. Severe stress concentration near a crack tip is represented by superposing the multiresolution wavelet functions. In addition, the crack modeling is easy to treat by introducing enrichment functions of the X-FEM. In the proposed approach, the governing equation is discretized based on fixed grid, and fracture mechanics problems with complicated shaped geometries can be analyzed effectively, reducing the model generation tasks. 2D linear fracture mechanics problems are solved, and the accuracy is studied for numerical examples.
TL;DR: In this article, a characterization of wavelets on local fields of positive characteristic based on results on affine and quasi-affine frames is provided, and all wavelets associated with a multiresolution analysis on such a local field are also characterized.
Abstract: We provide a characterization of wavelets on local fields of positive characteristic based on results on affine and quasi-affine frames. This result generalizes the characterization of wavelets on Euclidean spaces by means of two basic equations. We also give another characterization of wavelets. Further, all wavelets which are associated with a multiresolution analysis on such a local field are also characterized.
18 Sep 2015
TL;DR: Two-channel (low-pass and high-pass) wavelet filterbanks for graph signals are introduced and a wavelet-regularized semi-supervised learning algorithm is proposed that is competitive for certain synthetic and real-world data.
Abstract: Multiresolution analysis is important for understanding graph signals , which represent graph-structured data. Wavelet filterbanks permit multiscale analysis and processing of graph signals—particularly, useful for harvesting large-scale data. Inspired by first-order spline wavelets in classical signal processing, we introduce two-channel (low-pass and high-pass) wavelet filterbanks for graph signals. This class of filterbanks boasts several useful properties, such as critical sampling, perfect reconstruction, and graph invariance. We consider an application in graph semisupervised learning and propose a wavelet-regularized semisupervised learning algorithm that is competitive for certain synthetic and real-world data.
TL;DR: A new fast one-pass algorithm for recognition (segmentation and fitting) of planar segments from a point cloud is proposed that exploits the orthonormality of certain wavelets to polynomial function, as well as their sensitivity to abrupt changes.
Abstract: Within industrial automation systems, three-dimensional (3-D) vision provides very useful feedback information in autonomous operation of various manufacturing equipment (e.g., industrial robots, material handling devices, assembly systems, and machine tools). The hardware performance in contemporary 3-D scanning devices is suitable for online utilization. However, the bottleneck is the lack of real-time algorithms for recognition of geometric primitives (e.g., planes and natural quadrics) from a scanned point cloud. One of the most important and the most frequent geometric primitive in various engineering tasks is plane. In this paper, we propose a new fast one-pass algorithm for recognition (segmentation and fitting) of planar segments from a point cloud. To effectively segment planar regions, we exploit the orthonormality of certain wavelets to polynomial function, as well as their sensitivity to abrupt changes. After segmentation of planar regions, we estimate the parameters of corresponding planes using standard fitting procedures. For point cloud structuring, a z-buffer algorithm with mesh triangles representation in barycentric coordinates is employed. The proposed recognition method is tested and experimentally validated in several real-world case studies.
TL;DR: By means of well-known 1D and 2D benchmark problems, it is verified that multiwavelet-based grid adaptation can significantly reduce the computational cost by sparsening the computational grids, while retaining accuracy and keeping well-balancing and positivity.
TL;DR: A new image denoising method with using bivariate shrinkage threshold on the coefficients of DCT, which achieves better performance than those outstanding Denoising algorithms in terms of peak signal-to-noise ratio (PSNR), as well as visual quality.
TL;DR: In this paper, the wavelet Galerkin method was used to solve 2D dynamic stress concentration problems and evaluate the dynamic stress intensity factor (DSIF) of 2D cracked solids.
Abstract: Two-dimensional (2D) dynamic stress concentration problems are analyzed using the wavelet Galerkin method (WGM). Linear B-spline scaling/wavelet functions are employed. We introduce enrichment functions for the X-FEM to represent a crack geometry. In the WGM, low-resolution scaling functions are periodically located across the entire analysis domain to approximate deformations of a body. High-resolution wavelet functions and enrichment functions including crack tip singular fields are superposed on the scaling functions to represent the severe stress concentration around holes or crack tips. Heaviside functions are also enriched to treat the displacement discontinuity of the crack face. Multiresolution analysis of the wavelet basis functions plays an important role in the WGM. To simulate the transients, the wavelet Galerkin formulation is discretized using a Newmark-β time integration scheme. A path independent J-integral is adopted to evaluate the dynamic stress intensity factor (DSIF). We solve dynamic stress concentration problems and evaluate DSIF of 2D cracked solids. The accuracy and effectiveness of the proposed method are discussed through the numerical examples.
17 Mar 2015
TL;DR: Some fundamental mathematical properties of wavelet families are discussed and how these properties influence the appearance of the characteristic pattern caused by failure, since they provide the most satisfactory results regarding the pattern detection.
Abstract: In previous research works dealing with induction motor rotor assessment it has been shown that, when broken rotor bars exist, the analysis of the stator start-up current using the Discrete Wavelet Transform (DWT) leads to clearly recognizable patterns associated with the failure. This is valid for different operating conditions (loaded and unloaded machine, periodical fluctuation in the supply voltage, pulsating load torques…) and for distinct start-up modalities (direct start-up, stardelta start-up, soft-starter-operated motors). However, this fault-related pattern can significantly vary or even may not appear depending on the wavelet family used for the analysis. This paper discusses about some fundamental mathematical properties of wavelet families and how these properties influence the appearance of the characteristic pattern caused by failure. For this purpose, Daubechies, Meyer and Symlet families are considered in the work, since they have provided the most satisfactory results regarding the pattern detection.
17 Jul 2015
TL;DR: An efficient object recognition system is presented based on Empirical Wavelet Transform (EWT), a multiresolution analysis where the energy features obtained form the EWT decomposed image is used as features for the given object.
Abstract: Object recognition is the method of finding an object in an image. We recognize objects without any effort easily. It is a challenging task for computer vision systems due to the size, shape, and structure of objects in an image. In this paper, an efficient object recognition system is presented based on Empirical Wavelet Transform (EWT). The energy features obtained form the EWT decomposed image is used as features for the given object. As EWT, a multiresolution analysis, the given image is decomposed at various level of decomposition and the obtained features are analyzed at each level of decomposition. The evaluation of the system is carried on Columbia Object Image Library Dataset (COIL) which consists of 100 objects captured at different orientations. The classification is done with K- nearest neighbor (KNN) which gives 98.42% accuracy.
TL;DR: It is shown in this paper that the original IMF can be perfectly reconstructed and computer numerical simulation results show that the proposed method can reach a component with less number of levels of decomposition compared to that of the conventional linear and nonadaptive wavelets and filter bank approaches.
20 Jul 2015
TL;DR: The proposed scheme depicts a shallow architecture of Convolutional Neural Network (CNN) providing deep learning: for each image, the connection weights between the input layer and the hidden layer based on MultiResolution Analysis at different levels of abstraction are calculated.
Abstract: This paper presents a new scheme for image classification The proposed scheme depicts a shallow architecture of Convolutional Neural Network (CNN) providing deep learning: For each image, we calculated the connection weights between the input layer and the hidden layer based on MultiResolution Analysis (MRA) at different levels of abstraction Then, we selected the best features, representing well each class of images, with their corresponding weights using Adaboost algorithm These weights are used as the connection weights between the hidden layer and the output layer, and will be used in the test phase to classify a given query image The proposed approach was tested on different datasets and the obtained results prove the efficiency and the speed of the proposed approach
01 Oct 2015
TL;DR: A novel approach of automatic detection and classification of single and hybrid PQ disturbances using Discrete Wavelet Transform (DWT) and Modular Probabilistic Neural Network (MPNN) to show that the classifier has an excellent performance in terms of accuracy and reliability even in the case of PQ signals under noisy condition.
Abstract: Power Quality (PQ) monitoring in a systematic and automated way is the important issue to prevent detrimental effects on power system. The development of new methods for the automatic classification of PQ disturbances is at present a major concern. This paper presents a novel approach of automatic detection and classification of single and hybrid PQ disturbances using Discrete Wavelet Transform (DWT) and Modular Probabilistic Neural Network (MPNN). The automatic classification of the PQ disturbances consists of three stages i) data generation, ii) feature extraction and iii) disturbance classification. The data is generated by synthetic models of single and hybrid PQ disturbance signals based on IEEE 1159 standard. DWT with multiresolution analysis was applied for feature extraction from the PQ waveforms. The entropy and energy features extracted from the detail and approximation coefficients were applied as the training and testing data to MPNN in order to accomplish the automatic classification process. The effectiveness of the proposed algorithm has been validated by using a typical real-time underground distribution network in Malaysia which was simulated in PSCAD/EMTDC power system software to generate PQ disturbances. The simulation results show that the classifier has an excellent performance in terms of accuracy and reliability even in the case of PQ signals under noisy condition.
TL;DR: An adaptive multiresolution method for the numerical simulation of ideal magnetohydrodynamics in two space dimensions with good results for solving the MHD equations using divergence cleaning yield excellent results.
16 Feb 2015
TL;DR: The multiresolution analysis of Alpert is considered in this article, where explicit formulas for the entries in the matrix coefficients of the refinement equation are given in terms of hypergeometric functions.
Abstract: The multiresolution analysis of Alpert is considered. Explicit formulas for the entries in the matrix coefficients of the refinement equation are given in terms of hypergeometric functions. These entries are shown to solve generalized eigenvalue equations as well as partial difference equations. The matrix coefficients in the wavelet equation are also considered and conditions are given to obtain a unique solution.
TL;DR: A framework for representing functions dened on high-dimensional data is introduced, which includes both the Haar basis as well as the eigenvectors of the graph Laplacian, as its two extremes.
16 Feb 2015
TL;DR: In this article, a notion of frame multiresolution analysis on local fields of positive characteristic based on the theory of shift-invariant spaces is presented, where the associated subspace has a frame, a collection of translates of the scaling function of the form, where is the set of nonnegative integers.
Abstract: We present a notion of frame multiresolution analysis on local fields of positive characteristic based on the theory of shift-invariant spaces. In contrast to the standard setting, the associated subspace of has a frame, a collection of translates of the scaling function of the form , where is the set of nonnegative integers. We investigate certain properties of multiresolution subspaces which provides the quantitative criteria for the construction of frame multiresolution analysis (FMRA) on local fields of positive characteristic. Finally, we provide a characterization of wavelet frames associated with FMRA on local field of positive characteristic using the shift-invariant space theory.
01 Dec 2015
TL;DR: The results of the experiments indicate that the proposed scheme outperforms other competent schemes in terms of classification accuracy with relatively small number of features.
Abstract: Developing automatic and accurate computer-aided diagnosis (CAD) systems for detecting brain disease in magnetic resonance imaging (MRI) are of great importance in recent years. These systems help the radiologists in accurate interpretation of brain MR images and also substantially reduce the time needed for it. In this paper, a new system for abnormal brain detection is presented. The proposed method employs a multiresolution approach (discrete wavelet transform) to extract features from the MR images. Kernel principal component analysis (KPCA) is harnessed to reduce the dimension of the features, with the goal of obtaining the discriminant features. Subsequently, a new version of support vector machine (SVM) with low computational cost, called least squares SVM (LS-SVM) is utilized to classify brain MR images as normal or abnormal. The proposed scheme is validated on a dataset of 90 images (18 normal and 72 abnormal). A 6-fold stratified cross-validation procedure is implemented and the results of the experiments indicate that the proposed scheme outperforms other competent schemes in terms of classification accuracy with relatively small number of features.
01 Feb 2015
TL;DR: The algorithm presents the comparative analysis for the selection of optimal wavelet and it is shown that the soft thresholding is best suited to remove the noise, but weak in preserving the edges and the hard thresholding has been shown to be best suited for preserves the edges, but strong in denoising the signal.
Abstract: Partial Discharge (PD) signal denoising is very significant in analyzing its characteristics and its effect on high voltage insulation equipments. Mainly, the PD information is lost in the presence of various noises. The wavelet transform provides a better platform for PD signal pre and post processing. The wavelet adaptive thresholding denoising techniques provides a better method to reduce noise. This paper adopts the various adaptive thresholding techniques such as VisuShrink, SureShrink, combination of the two called Heursure and the minimax thresholding which are broadly classified as Global and Local thresholding methods. The algorithm presents the comparative analysis for the selection of optimal wavelet. Once the optimal mother wavelet is chosen, selection of best thresholding rule is identified by comparing the values of signal to noise ratio (SNR), mean square error (MSE) and root mean square error (RMSE) of all the techniques. The algorithm also presents the comparison between Hard and Soft thresholding. It is shown that the soft thresholding is best suited to remove the noise, but weak in preserving the edges and the hard thresholding is best suited for preserving the edges, but weak in denoising the signal. The simulated damped exponential pulse (DEP) and damped oscillatory pulse (DOP) has been used to check the performance of the algorithm.