Showing papers on "Multiresolution analysis published in 2016"

Multiresolution Dynamic Mode Decomposition

Abstract: We demonstrate that the integration of the recently developed dynamic mode decomposition (DMD) with a multiresolution analysis allows for a decomposition method capable of robustly separating complex systems into a hierarchy of multiresolution time-scale components. A one-level separation allows for background (low-rank) and foreground (sparse) separation of dynamical data, or robust principal component analysis. The multiresolution DMD (mrDMD) is capable of characterizing nonlinear dynamical systems in an equation-free manner by recursively decomposing the state of the system into low-rank terms whose temporal coefficients in time are known. DMD modes with temporal frequencies near the origin (zero-modes) are interpreted as background (low-rank) portions of the given dynamics, and the terms with temporal frequencies bounded away from the origin are their sparse counterparts. The mrDMD method is demonstrated on several examples involving multiscale dynamical data, showing excellent decomposition results, ...

Spatial Methods for Multispectral Pansharpening: Multiresolution Analysis Demystified

Abstract: The majority of multispectral (MS) pansharpening methods may be labeled as spectral or spatial, depending on whether the geometric details that shall be injected into the interpolated MS bands are extracted from the panchromatic (P) image by means of a spectral transformation of MS pixels or a spatial transformation of the P image, achieved by means of linear shift-invariant digital filters. Spectral methods are known as component substitution; spatial methods are based on multiresolution analysis (MRA). In this paper, the authors show that, under the most general conditions, MRA-based pansharpening is characterized by a unique separable low-pass filter, which can be parametrically optimized based on the modulation transfer function (MTF) of the MS instrument, possibly followed by decimation and interpolation stages. This happens for the discrete wavelet transform (DWT) and its undecimated version (UDWT), for the “a-trous” wavelet (ATW) transform and its decimated version, i.e., the generalized Laplacian pyramid (GLP), and for nonseparable wavelet transforms, such as the nonsubsampled contourlet transform (NSCT). Hybrid methods, in which MRA fusion is performed on the intensity component derived from a spectral transformation, are equivalent to MRA fusion with a specific detail injection model. ATW and GLP are preferable to DWT, UDWT, and NSCT, because of computational benefits and of a looser choice of the low-pass filter, unconstrained from the requirement of generating a perfect reconstruction filter bank. Ultimately, GLP outperforms ATW, because its decimation and interpolation stages allow the aliasing impairments intrinsically present in the original MS bands to be removed from the pansharpened product.

Integrated Fault Location and Power-Quality Analysis in Electric Power Distribution Systems

Abstract: This paper presents a methodology for automated disturbance analysis and fault location on electric power distribution systems using a combination of modern techniques for network analysis, signal processing, and intelligent systems. New algorithms to detect, classify, and locate power-quality disturbances are developed. The continuous process of detecting these disturbances is accomplished through statistical analysis and multilevel signal analysis in the wavelet domain. The behavioral indices of the current and voltage signals are extracted by employing the discrete wavelet transform, multiresolution analysis, and the concept of signal energy. These indices are used by a number of independent Fuzzy-ARTMAP neural networks, which aim to classify the fault type and the power-quality events. The fault location is performed after the classification process. A real life three-phase distribution system with 134 nodes—13.8 kV and 7.065 MVA—was used to test the proposed algorithms, providing satisfactory results, attesting that the proposed algorithms are efficient, fast, and, above all, intelligent.

MADNESS: A Multiresolution, Adaptive Numerical Environment for Scientific Simulation

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 that are 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.

Discrete Wavelet Transform-Based Feature Extraction of Experimental Voltage Signal for Li-Ion Cell Consistency

Abstract: The difference in electrochemical characteristics among Li-ion cells in the battery pack inevitably result in voltage and state-of-charge (SOC) imbalances caused by cell-to-cell variation. Therefore, in this approach, with lower requirements of active and passive balancing circuits, a novel approach based on the discrete wavelet transform (DWT) that are well suitable for analyzing and evaluating an experimental charging/discharging voltage signal (ECDVS) is newly introduced to minimize the aforementioned problem. The ECDVS can be applied as source data in the DWT-based analysis because of its great ability to extract variable information of electrochemical characteristics from the nonstationary and transient phenomena simultaneously in both the time and frequency domains. By using the wavelet decomposition implementing the multiresolution analysis (MRA), it is possible to discriminate Li-ion cells that have similar electrochemical characteristics corresponding to information extracted from the ECDVS over wide frequency ranges. Consequently, experimental results showed the clearness of the proposed DWT-based approach for cell discrimination very well.

Adaptive multiresolution discontinuous Galerkin schemes for conservation laws: multi-dimensional case

Abstract: The concept of multiresolution-based adaptive DG schemes for non-linear one-dimensional hyperbolic conservation laws has been developed and investigated analytically and numerically in (Math Comp, doi: 10.1090/S0025-5718-2013-02732-9 , 2013). The key idea is to perform a multiresolution analysis using multiwavelets on a hierarchy of nested grids for the data given on a uniformly refined mesh. This provides difference information between successive refinement levels that may become negligibly small in regions where the solution is locally smooth. Applying hard thresholding the data are highly compressed and local grid adaptation is triggered by the remaining significant coefficients. The focus of the present work lies on the extension of the originally one-dimensional concept to higher dimensions and the verification of the choice for the threshold value by means of parameter studies performed for linear and non-linear scalar conservation laws.

Applying a Locally Linear Embedding Algorithm for Feature Extraction and Visualization of MI-EEG

Abstract: Robotic-assisted rehabilitation system based on Brain-Computer Interface (BCI) is an applicable solution for stroke survivors with a poorly functioning hemiparetic arm. The key technique for rehabilitation system is the feature extraction of Motor Imagery Electroencephalography (MI-EEG), which is a nonlinear time-varying and nonstationary signal with remarkable time-frequency characteristic. Though a few people have made efforts to explore the nonlinear nature from the perspective of manifold learning, they hardly take into full account both time-frequency feature and nonlinear nature. In this paper, a novel feature extraction method is proposed based on the Locally Linear Embedding (LLE) algorithm and DWT. The multiscale multiresolution analysis is implemented for MI-EEG by DWT. LLE is applied to the approximation components to extract the nonlinear features, and the statistics of the detail components are calculated to obtain the time-frequency features. Then, the two features are combined serially. A backpropagation neural network is optimized by genetic algorithm and employed as a classifier to evaluate the effectiveness of the proposed method. The experiment results of 10-fold cross validation on a public BCI Competition dataset show that the nonlinear features visually display obvious clustering distribution and the fused features improve the classification accuracy and stability. This paper successfully achieves application of manifold learning in BCI.

Large Deformation Multiresolution Diffeomorphic Metric Mapping for Multiresolution Cortical Surfaces: A Coarse-to-Fine Approach

Abstract: Brain surface registration is an important tool for characterizing cortical anatomical variations and understanding their roles in normal cortical development and psychiatric diseases. However, surface registration remains challenging due to complicated cortical anatomy and its large differences across individuals. In this paper, we propose a fast coarse-to-fine algorithm for surface registration by adapting the large diffeomorphic deformation metric mapping (LDDMM) framework for surface mapping and show improvements in speed and accuracy via a multiresolution analysis of surface meshes and the construction of multiresolution diffeomorphic transformations. The proposed method constructs a family of multiresolution meshes that are used as natural sparse priors of the cortical morphology. At varying resolutions, these meshes act as anchor points where the parameterization of multiresolution deformation vector fields can be supported, allowing the construction of a bundle of multiresolution deformation fields, each originating from a different resolution. Using a coarse-to-fine approach, we show a potential reduction in computation cost along with improvements in sulcal alignment when compared with LDDMM surface mapping.

Interest rate next-day variation prediction based on hybrid feedforward neural network, particle swarm optimization, and multiresolution techniques

Abstract: Multiresolution analysis techniques including continuous wavelet transform, empirical mode decomposition, and variational mode decomposition are tested in the context of interest rate next-day variation prediction. In particular, multiresolution analysis techniques are used to decompose interest rate actual variation and feedforward neural network for training and prediction. Particle swarm optimization technique is adopted to optimize its initial weights. For comparison purpose, autoregressive moving average model, random walk process and the naive model are used as main reference models. In order to show the feasibility of the presented hybrid models that combine multiresolution analysis techniques and feedforward neural network optimized by particle swarm optimization, we used a set of six illustrative interest rates; including Moody’s seasoned Aaa corporate bond yield, Moody’s seasoned Baa corporate bond yield, 3-Month, 6-Month and 1-Year treasury bills, and effective federal fund rate. The forecasting results show that all multiresolution-based prediction systems outperform the conventional reference models on the criteria of mean absolute error, mean absolute deviation, and root mean-squared error. Therefore, it is advantageous to adopt hybrid multiresolution techniques and soft computing models to forecast interest rate daily variations as they provide good forecasting performance.

Adjusting wavelet‐based multiresolution analysis boundary conditions for long‐term streamflow forecasting

Abstract: We propose a novel technique for improving a long-term multi-step-ahead streamflow forecast. A model based on wavelet decomposition and a multivariate Bayesian machine learning approach is developed for forecasting the streamflow 3, 6, 9, and 12 months ahead simultaneously. The inputs of the model utilize only the past monthly streamflow records. They are decomposed into components formulated in terms of wavelet multiresolution analysis. It is shown that the model accuracy can be increased by using the wavelet boundary rule introduced in this study. A simulation study is performed to evaluate the effects of different wavelet boundary rules using synthetic and real streamflow data from the Yellowstone River in the Uinta Basin in Utah. The model based on the combination of wavelet and Bayesian machine learning regression techniques is compared with that of the wavelet and artificial neural networks-based model. The robustness of the models is evaluated. Copyright © 2015 John Wiley & Sons, Ltd.

An Adaptive Filter for Aeromagnetic Compensation Based on Wavelet Multiresolution Analysis

Abstract: In aeromagnetic compensation, the multicolinearity of the Tolles–Lawson model is one of the main factors limiting the performance of the coefficient-estimating methods. Aside from the intrinsic characteristic of the Tolles–Lawson model, data filtering as a preprocessing step in estimating the coefficients has a significant impact on the multicolinearity. To solve this problem, an adaptive filter based on wavelet multiresolution analysis is proposed. By modifying the wavelet decomposition results of the Mallat algorithms and reconstructing the signal, the adaptive filter can be used to establish a system of linear equations not only by capturing the frequency characteristics of the aircraft maneuvers as is usual but also by having a weakened multicolinearity. Simulation results illustrate the effectiveness of the proposed adaptive filter.

A Comparative Evaluation of Denoising of Remotely Sensed Images Using Wavelet, Curvelet and Contourlet Transforms

Abstract: This paper presents an overview of remotely sensed image denoising based on multiresolution analysis. In this paper, the wavelet, curvelet and contourlet transforms are used for denoising of remotely sensed images with additive Gaussian noise. The curvelets and contourlets are two kinds of new multi-scale transforms which can capture the intrinsic geometrical structure of data. At first, we outline the implementation of these multiscale representation systems. The paper aims at the analysis of denoising of image using wavelets, curvelets and contourlets on high resolution multispectral images acquired by the QuickBird and medium resolution Landsat Thematic Mapper satellite systems. We apply these methods to the problem of restoring an image from noisy image and compare the effects of denoising. Two comparative measures are used for evaluation of the performance of the three methods for denoising. One of them is the peak signal to noise ratio and the second is the ability of the denoising scheme to preserve the sharpness of the boundaries. By both of these comparative measures, the curvelet has proved to be better than the other two.

Discrete wavelet transform based video watermarking technique

Abstract: In this paper, an effective algorithm for providing copyright protection is proposed by using a new embedding strategy for Discrete Wavelet Transform-based video watermarking. Discrete Wavelet Transform (DWT) is applied on the video, to convert the spatial data into frequency domain, having low pass and high pass components. The low frequency component is used for generating the key, by using the watermark image and the binarized Low frequency part (LL) of the video frame. Same procedure is applied on each frame to generate the key for corresponding frame. This generated key should be used at receiver for extracting the watermark which provides copyright protection. Blind watermarking technique is used in this paper which require only key to extract the embedded watermark. The original video is not required during extraction. To criticize the robustness of algorithm, the original watermark image is compared with extracted watermark image after several attacks and their Peak Signal to Noise Ratio (PSNR), Normalized Correlation Coefficient (NC) and Structural Similarity index (SSIM) are calculated. The experimental results demonstrate that the watermark is invisible and it is robust against the various attacks and addition of noise to the video.

Textural classification based on wavelet, curvelet and contourlet features

Abstract: Multi-resolution analysis (MRA) has been successfully used in image processing with the recent emergence of applications to texture classification. Several studies have investigated the discriminating power of wavelet-based features in various applications such as image compression, image denoising, and classification of natural textures. Recently, the curvelet and contourlet transforms have emerged as new multi-resolution analysis tools to deal with non-linear singularities present in the image. This article explores and proposes a texture based classification of remotely sensed multispectral images using features derived from the wavelet, curvelet and contourlet transforms. These features characterize the textural properties of the images and are used to train the classifier to recognize each texture class. Using these MRA based feature descriptors class separability is defined in feature space. The results are compared with Grey Level Co-occurrence Matrix (GLCM) based statistical features.

MULTIRESOLUTION ON n-DIMENSIONAL SPHERES

Abstract: In the present paper, multiscale systems of polynomial wavelets on an n-dimensional sphere are constructed. Scaling functions and wavelets are investigated,and their reproducing and localization properties and positive definiteness are examined. Decomposition and reconstruction algorithms for the wavelet transform are presented. Formulae for variances in space and momentum domain, as well as for the uncertainty product, of zonal functions over n-dimensional spheres are derived and applied to the scaling functions.

Weekly Load Prediction Using Wavelet Neural Network Approach

Abstract: Electric load prediction has drawn attention of many researchers due to its prerequisite concern for accurate scheduling, planning and operations of electric power system. There are many factors which affect electrical load forecasting. Therefore, a hybrid model is required to improve the forecast and make it more accurate. This paper presents a new hybrid load estimation method using two approaches: Wavelet transform (WT) and Artificial neural network (ANN). In order to take into account the large asymmetric time-varying electric raw data set, wavelet technique is used to decompose the data in terms of both time and frequency. Several wavelet functions are available, but selecting a proper wavelet function plays a crucial role in designing the model. In present work, the following types of wavelet functions, namely Haar, Deubechies, Symlet, Coiflet have been used to disintegrate the electrical load data into distinct segments. Later, ANN has been employed to forecast the non-linear data of the load. The proposed model is validated through AEMO data for 24 hours of a day over a one-week period.

Discrete Wavelet Transforms in the Large Time-Frequency Analysis Toolbox for MATLAB/GNU Octave

Abstract: The discrete wavelet transform module is a recent addition to the Large Time-Frequency Analysis Toolbox (LTFAT). It provides implementations of various generalizations of Mallat's well-known algorithm (iterated filterbank) such that completely general filterbank trees, dual-tree complex wavelet transforms, and wavelet packets can be computed. The resulting transforms can be equivalently represented as filterbanks and analyzed as filterbank frames using fast algorithms.

High-order adaptive finite-volume schemes in the context of multiresolution analysis for dyadic grids

Abstract: This paper considers the design of adaptive finite-volume discretizations for conservation laws. The methodology comes from the context of multiresolution representation of functions, which is based on cell averages on a hierarchy of nested grids. The refinement process is performed by the partition of each cell at a certain level into two equal child cells at the next refined level by a hyperplane perpendicular to one of the coordinate axes, which varies cyclically from level to level. The resulting dyadic grids allow the organization of the multiscale information by the same binary-tree data structure for domains in any dimension. Cell averages of neighbouring stencil cells, chosen on the subdivision direction axis, are used to approximate the cell average of the child cells in terms of a classical A. Harten prediction formula for 1D discretizations. The difference between successive refinement levels is encoded as the prediction errors (wavelet coefficients) in one of the child cells. Adaptivity is obtained by interrupting the refinement at the cells where the wavelet coefficients are sufficiently small. The efficiency of the adaptive method is analysed in applications to typical test problems in one and two space dimensions for second- and third-order schemes for the space discretization (WENO) and time integration (explicit Runge–Kutta). The results show that the adaptive solutions fit the reference finite-volume solution on the finest regular grid, and memory and CPU requirements can be considerably reduced, thanks to the efficient self-adaptive grid refinement.

Impulsive noise rejection for ZigBee communication systems using Error-Balanced Wavelet filtering

Abstract: The physical (PHY) layer of ZigBee communication systems was defined by IEEE 802.15.4 and has good external white noise resistance due to its spread spectrum characteristic and error correction of the baseband coding process. However, previous research has shown the performance of ZigBee to degrade in the presence of impulsive noise. In this regard, an improvement of the ZigBee receiver is warranted in order to improve the decoding process. A novel Error-Balanced Wavelet filtering approach utilizing the multiresolution property is proposed to suppress the impact of impulsive noise prior to symbol detection and thus improve the bit error rate (BER) performance of the ZigBee demodulation process. This assessment is based on computer simulations and verifies that the overall transmission performance is improved by our proposed approach. The results obtained are also compared with existing impulsive noise suppression approaches and it is shown that our wavelet-based method outperforms other methods in improving the system BER.

Discrete Fourier And Wavelet Transforms: An Introduction Through Linear Algebra With Applications To Signal Processing

Abstract: This textbook for undergraduate mathematics, science, and engineering students introduces the theory and applications of discrete Fourier and wavelet transforms using elementary linear algebra, without assuming prior knowledge of signal processing or advanced analysis. It explains how to use the Fourier matrix to extract frequency information from a digital signal and how to use circulant matrices to emphasize selected frequency ranges. It introduces discrete wavelet transforms for digital signals through the lifting method and illustrates through examples and computer explorations how these transforms are used in signal and image processing. Then the general theory of discrete wavelet transforms is developed via the matrix algebra of two-channel filter banks. Finally, wavelet transforms for analog signals are constructed based on filter bank results already presented, and the mathematical framework of multiresolution analysis is examined.

Adaptive Gradient-Augmented Level Set Method with Multiresolution Error Estimation

Abstract: A space---time adaptive scheme is presented for solving advection equations in two space dimensions. The gradient-augmented level set method using a semi-Lagrangian formulation with backward time integration is coupled with a point value multiresolution analysis using Hermite interpolation. Thus locally refined dyadic spatial grids are introduced which are efficiently implemented with dynamic quadtree data structures. For adaptive time integration, an embedded Runge---Kutta method is employed. The precision of the new fully adaptive method is analysed and speed up of CPU time and memory compression with respect to the uniform grid discretization are reported.

Multiresolution analysis (discrete wavelet transform) through Daubechies family for emotion recognition in speech

Abstract: We propose a study of the mathematical properties of voice as an audio signal -- This work includes signals in which the channel conditions are not ideal for emotion recognition -- Multiresolution analysis- discrete wavelet transform – was performed through the use of Daubechies Wavelet Family (Db1-Haar, Db6, Db8, Db10) allowing the decomposition of the initial audio signal into sets of coefficients on which a set of features was extracted and analyzed statistically in order to differentiate emotional states -- ANNs proved to be a system that allows an appropriate classification of such states -- This study shows that the extracted features using wavelet decomposition are enough to analyze and extract emotional content in audio signals presenting a high accuracy rate in classification of emotional states without the need to use other kinds of classical frequency-time features -- Accordingly, this paper seeks to characterize mathematically the six basic emotions in humans: boredom, disgust, happiness, anxiety, anger and sadness, also included the neutrality, for a total of seven states to identify

Experimenting multiresolution analysis for identifying regions of different classification complexity

Abstract: Systems for assessing the classification complexity of a dataset have received increasing attention in research activities on pattern recognition. These systems typically aim at quantifying the overall complexity of a domain, with the goal of comparing different datasets. In this work, we propose a method for partitioning a dataset into regions of different classification complexity, so to highlight sources of complexity inside the dataset. Experiments have been carried out on relevant datasets, proving the effectiveness of the proposed method.

Icosahedral maps for a multiresolution representation of earth data

Abstract: The icosahedral non-hydrostatic (ICON) model is a digital Earth model based on an icosahedral representation and used for numerical weather prediction. In this paper, we introduce icosahedral maps that are designed to fit the geometry of different cell configurations in the ICON model. These maps represent the connectivity information in ICON in a highly structured two-dimensional hexagonal representation that can be adapted to fit different cell configurations. Our maps facilitate the execution of a multiresolution analysis on the ICON model. We demonstrate this by applying a hexagonal version of the discrete wavelet transform in conjunction with our icosahedral maps to decompose ICON data to different levels of detail and to compress it via a thresholding of the wavelet coefficients.

Econometric-wavelet prediction in spatial aspect

Abstract: The aim of this article is the prediction of GDP Polish and other selected European countries. For this purpose integrated into one algorithm econometric methods and wavelet analysis. Econometric methods and wavelet transform are combined goal of constructing a copyright model for predicting macroeconomic indicators. In the article, for estimating the macroeconomic indicators on the example of GDP proposed authorial algorithm that combines the following methods: a method trend creep method of alignment exponential and analysis multiresolution. Used econometric methods, this is a trend crawling and alignment exponential have been modified in several major stages. The aim of the merger of these methods is the construction of algorithm to predict short-term time series. In the copyright algorithm was applied wavelet continuous compactly supported. wavelet used Daubechies. The Daubechies wavelets, are a family of orthogonal wavelets and characterized by a maximal number of vanishing moments for some given support. With each wavelet type of this class, there is a scaling function which generates an orthogonal multiresolution analysis.