Showing papers on "Multiresolution analysis published in 2019"

Novel Approaches for the Removal of Motion Artifact From EEG Recordings

Abstract: The electroencephalogram (EEG) signal is contaminated with various noises or artifacts during recording. For the automated detection of neurological disorders, it is a vital task to filter out these artifacts from the EEG signal. In this paper, we propose two novel approaches for the removal of motion artifact from the single channel EEG signal. These methods are based on the multiresolution total variation (MTV) and multiresolution weighted total variation (MWTV) filtering schemes. The multiresolution analysis using the discrete wavelet transform (DWT) helps to segregate the EEG signal into various subband signals. The total variation (TV) and weighted TV (WTV) are applied to the approximation subband signal. The filtered approximation subband signal is evaluated based on the difference between the noisy approximation subband signal and the output of the TV or WTV filter. The processed EEG signal is obtained using the multiresolution wavelet-based reconstruction. The difference in the signal to noise ratio ( $\Delta $ SNR) and the percentage of reduction in correlation coefficients ( $\eta $ ) is used for evaluating the diagnostic quality of the processed EEG signal. The experimental results demonstrate that the proposed MTV and MWTV approaches have better denoising performance with (average $\Delta $ SNR, and average $\eta $ ) values of (29.12 dB and 68.56%) and (29.29 dB and 67.51%), respectively, as compared to the existing techniques.

Hybrid SAR Speckle Reduction Using Complex Wavelet Shrinkage and Non-Local PCA-Based Filtering

Abstract: In this paper, a new hybrid despeckling method, based on Undecimated Dual-Tree Complex Wavelet Transform (UDT-CWT) using maximum a posteriori (MAP) estimator and non-local Principal Component Analysis (PCA)-based filtering with local pixel grouping (LPG-PCA), was proposed. To achieve a heterogeneous-adaptive speckle reduction, SAR image is classified into three classes of point targets, details, or homogeneous areas. The despeckling is done for each pixel based on its class of information. Logarithm transform was applied to the SAR image to convert the multiplicative speckle into additive noise. Our proposed method contains two principal steps. In the first step, denoising was done in the complex wavelet domain via MAP estimator. After performing UDT-CWT, the noise-free complex wavelet coefficients of the log-transformed SAR image were modeled as a two-state Gaussian mixture model. Furthermore, the additive noise in the complex wavelet domain was considered as a zero-mean Gaussian distribution. In the second step, after applying inverse UDT-CWT, an iterative LPG-PCA method was used to smooth the homogeneous areas and enhance the details. The proposed method was compared with some state-of-the-art despeckling methods. The experimental results showed that the proposed method leads to a better speckle reduction in homogeneous areas while preserving details.

Dynamic mode decomposition for multiscale nonlinear physics.

Abstract: We present a data-driven method for separating complex, multiscale systems into their constituent timescale components using a recursive implementation of dynamic mode decomposition (DMD). Local linear models are built from windowed subsets of the data, and dominant timescales are discovered using spectral clustering on their eigenvalues. This approach produces time series data for each identified component, which sum to a faithful reconstruction of the input signal. It differs from most other methods in the field of multiresolution analysis (MRA) in that it (1) accounts for spatial and temporal coherencies simultaneously, making it more robust to scale overlap between components, and (2) yields a closed-form expression for local dynamics at each scale, which can be used for short-term prediction of any or all components. Our technique is an extension of multi-resolution dynamic mode decomposition (mrDMD), generalized to treat a broader variety of multiscale systems and more faithfully reconstruct their isolated components. In this paper we present an overview of our algorithm and its results on two example physical systems, and briefly discuss some advantages and potential forecasting applications for the technique.

Deep Adaptive Wavelet Network

Abstract: Even though convolutional neural networks have become the method of choice in many fields of computer vision, they still lack interpretability and are usually designed manually in a cumbersome trial-and-error process. This paper aims at overcoming those limitations by proposing a deep neural network, which is designed in a systematic fashion and is interpretable, by integrating multiresolution analysis at the core of the deep neural network design. By using the lifting scheme, it is possible to generate a wavelet representation and design a network capable of learning wavelet coefficients in an end-to-end form. Compared to state-of-the-art architectures, the proposed model requires less hyper-parameter tuning and achieves competitive accuracy in image classification tasks

An implementation of Haar wavelet based method for numerical treatment of time-fractional Schrödinger and coupled Schrödinger systems

Abstract: The objective of this paper is to solve the time-fractional Schrodinger and coupled Schrodinger differential equations (TFSE) with appropriate initial conditions by using the Haar wavelet approximation. For the most part, this endeavor is made to enlarge the pertinence of the Haar wavelet method to solve a coupled system of time-fractional partial differential equations. As a general rule, piecewise constant approximation of a function at different resolutions is presentational characteristic of Haar wavelet method through which it converts the differential equation into the Sylvester equation that can be further simplified easily. Study of the TFSE is theoretical and experimental research and it also helps in the development of automation science, physics, and engineering as well. Illustratively, several test problems are discussed to draw an effective conclusion, supported by the graphical and tabulated results of included examples, to reveal the proficiency and adaptability of the method.

Biorthogonal-Wavelet-Based Method for Numerical Solution of Volterra Integral Equations

Abstract: Framelets theory has been well studied in many applications in image processing, data recovery and computational analysis due to the key properties of framelets such as sparse representation and accuracy in coefficients recovery in the area of numerical and computational theory. This work is devoted to shedding some light on the benefits of using such framelets in the area of numerical computations of integral equations. We introduce a new numerical method for solving Volterra integral equations. It is based on pseudo-spline quasi-affine tight framelet systems generated via the oblique extension principles. The resulting system is converted into matrix equations via these generators. We present examples of the generated pseudo-splines quasi-affine tight framelet systems. Some numerical results to validate the proposed method are presented to illustrate the efficiency and accuracy of the method.

Orthogonal wavelet multiresolution analysis of the turbulent boundary layer measured with two-dimensional time-resolved particle image velocimetry.

Abstract: The turbulent boundary layer flow measured by two-dimensional time-resolved particle image velocimetry is analyzed using the discrete orthogonal wavelet method. The Reynolds number of the turbulent boundary layer based on the friction velocity is ${\mathrm{Re}}_{\ensuremath{\tau}}=235$. The flow field is decomposed into a number of wavelet levels which have different characteristic scales. The velocity statistics and coherent structures at different wavelet levels are investigated. It is found that the fluctuation intensities and their peak locations differ for varying scales. The proper orthogonal decomposition (POD) of different wavelet components reveals a cascade of scales of coherent structures, especially the small-scale ones that are usually difficult to be identified in POD modes of the undecomposed flow field. The interactions among the scales are investigated in terms of large-scale amplitude modulations of the small-scale structures. In previous studies the velocity fluctuations are separated into two parts, the large scale and the small scale, divided usually by the boundary layer thickness. In the present study, however, the scales smaller than the boundary layer thickness are further separated. Therefore, the modulation analysis is a refined investigation that differentiates the modulation effects on separated small scales. The results reveal that the modulation effects vary among the small scales.

Recognition of electroencephalographic patterns related to human movements or mental intentions with multiresolution analysis

Abstract: We study the problem of recognizing specific oscillatory patterns in multichannel electroencephalograms (EEGs) of untrained volunteers arising during various types of movements and mental intentions that are associated with motor functions. To distinguish between the related patterns, we perform a multiresolution analysis based on discrete wavelet transform with the Daubechies basic functions. Using the standard deviation of the wavelet coefficients characterizing their variability in non-overlapping ranges of scales, we verify the ability to separate EEG segments during real and imaginary movements from the background EEG, which appeared in most recording channels. Recognizing the type of movement, such as, e.g., imaginary movement (i.e., the movement that a person performs mentally) by right arm or left leg, is a more complicated task that often can only be solved in few channels. Nevertheless, such recognition was demonstrated for real movements using about 6–8 channels out of 32, and for mental intentions using 1–2 channels. To improve the recognition of various imaginary movements, preliminary training seems mandatory.

Fractionally delayed Legendre wavelet transform based detection and optimal features based classification of voltage sag causes

Abstract: Detection of underlying causes of voltage sag is more crucial than detection of voltage sag from the mitigation point of view. Therefore, this paper proposes the detection and classification of the eight causes of voltage sag. This approach augments the conventional technique of wavelet transform by designing the fractionally delayed Legendre wavelet as the signal processing tool. The unique event characteristics are sought from approximation, and detailed signal coefficients which are obtained by using 4-level multiresolution analysis. To achieve a higher classification rate, the best optimal features are rummaged around the extracted features by employing the ant lion optimization algorithm. This algorithm retains only the suitable features as per the fitness criterion based on the classification accuracy and number of features. The representative feature set is classified using the classifier ensemble employing plural majority voting. The classifier ensemble has three members which are support vector machine, probabilistic neural network, and multilayer neural network. Better performance of the classifier ensemble is observed as compared to individual members in classification of voltage sag causes. The efficacy of the proposed methodology has been validated in the presence of noise also. This approach has successfully classified the causes of voltage sag using optimal features with good accuracy in the case of both noiseless signals and noisy signals.

Geophysical Potential Field Anomaly Separation Method With Optimal Mother Wavelet and Spatial Locating Multiresolution Analysis (MRA)

Abstract: Gravity or magnetic field, say geophysical potential field, is the superposition of gravity or magnetic effects of all geological bodies of different depths, scales, and forms. The signal, say anomaly, caused by the target geological body must be separated from the measured potential field before used for inversion and interpretation. The classical separation methods based on multiresolution analysis (MRA) have two problems. One is how to choose the optimal mother wavelet to separate the anomalies. Another is how to separate the anomalies better when the spectrum of different geological bodies aliased each other in scale. For the first problem, we propose a quantitative evaluating indicator, sparse index (SI), to help us choose the optimal mother wavelet for the particular separation task. For the second problem, we separate the residual anomalies based on MRA with spatial locating, using the wavelet coefficients within particular spatial and scale arrange to reconstruct the regional and residual anomaly, respectively. The results of three experiments, including separating the magnetic anomalies of a 2D and a 3D geology model, show that our new approach combining optimal mother wavelet and spatial locating MRA separation is superior to the classical wavelet transform method and can improve the accuracy of separation result obviously.

Convolution Theorem with Its Derivatives and Multiresolution Analysis for Fractional S-Transform

Abstract: Fractional S-transform (FrST) is a time–frequency representation of signals with frequency-dependent resolution. FrST is also an advantageous technique for non-stationary signal processing applications. Till now, only linearity, scaling, time reversal, time marginal condition, and inverse FrST properties are documented. In this paper, some remaining properties of FrST are proposed to establish it as a complete transform technique. The proposed properties are convolution theorem, correlation theorem, and Parseval’s theorem. To expand the applicability of FrST as a mathematical transform tool, the multiresolution analysis concept is also documented. The multiresolution analysis has shown significant performance to develop the orthogonal kernel for FrST. Finally, the applications of proposed convolution theorem are demonstrated on multiplicative filtering for electrocardiogram signal and linear frequency-modulated signal under AWGN channel.

On Convergence Rate of Adaptive Multiscale Value Function Approximation for Reinforcement Learning

Abstract: In this paper, we propose a generic framework for devising an adaptive approximation scheme for value function approximation in reinforcement learning, which introduces multiscale approximation. The two basic ingredients are multiresolution analysis as well as tree approximation. Starting from simple refinable functions, multiresolution analysis enables us to construct a wavelet system from which the basis functions are selected adaptively, resulting in a tree structure. Furthermore, we present the convergence rate of our multiscale approximation which does not depend on the regularity of basis functions.

On the use of multiresolution analysis for subsurface object detection using deep ground penetrating radar

Abstract: New ground penetrating radars for the vehicle mounted system can penetrate further into the ground, providing the opportunity of detecting objects that are deeply buried. A deep target has less obvious edge behaviors, especially if it has low-metal or non-metal content, making the edge based algorithm less effective for the detection. We shall explore the use of multiresolution time-frequency analysis technique by the log-Gabor filters to improve the detection of deep targets. They act on the 2-D image at an alarm location, generate multiresolution outputs and produce classification features for detection. The multiresolution analysis is able to preserve the edge behavior while at the same time forms the extra dimension of resolution (frequency) to better characterize a target signature for distinction with false alarms. Results on the detection performance at two government test sites validate the encouraging performance of the proposed detector.

An Open and Parallel Multiresolution Framework Using Block-Based Adaptive Grids

Abstract: A numerical approach for solving evolutionary partial differential equations in two and three space dimensions on block-based adaptive grids is presented. The numerical discretization is based on high-order, central finite-differences and explicit time integration. Grid refinement and coarsening are triggered by multiresolution analysis, i.e. thresholding of wavelet coefficients, which allow controlling the precision of the adaptive approximation of the solution with respect to uniform grid computations. The implementation of the scheme is fully parallel using MPI with a hybrid data structure. Load balancing relies on space filling curves techniques. Validation tests for 2D advection equations allow to assess the precision and performance of the developed code. Computations of the compressible Navier-Stokes equations for a temporally developing 2D mixing layer illustrate the properties of the code for nonlinear multi-scale problems. The code is open source.

A Learning Approach for Wavelet Design

Abstract: Wavelet analysis and perfect reconstruction filterbanks (PRFBs) are closely related. Desired properties on the wavelet could be translated to equivalent properties on a PRFB. We propose a new learning-based approach towards designing compactly supported orthonormal wavelets with a specified number of vanishing moments. We view PRFBs as a special class of convolutional autoencoders, which places the problem of wavelet/PRFB design within a learning framework. One could then deploy several state-of-the-art deep learning tools to solve the design problem. The PRFBs are learned by minimizing a squared-error loss function using gradient-descent optimization. The model is trained using a dataset containing random samples drawn from the standard normal distribution. We demonstrate that imposing orthonormality and vanishing moment constraints in the learning framework gives rise to filters that generate an orthonormal wavelet basis. We present results for learning PRFBs with filter lengths 2 and 8. As an illustration, we show that the proposed framework is able to learn the Daubechies wavelet with four vanishing moments, as well as wavelets with an arbitrary number of vanishing moments. For all our results, the signal-to-reconstruction error ratio is greater than 200 dB, implying that perfect reconstruction is indeed achieved accurately up to machine precision.

A note on Legendre, Hermite, Chebyshev, Laguerre and Gegenbauer wavelets with an application on sbvps arising in real life

Abstract: Getting solution near singular point of any non-linear BVP is always tough because solution blows up near singularity. In this article our goal is to construct a general method based on orthogonal polynomial and then use different orthogonal polynomials as particular wavelets. To show importance and accuracy of our method we have solved non-linear singular BVPs with help of constructed methods and compare with exact solution. Our result shows that these method converge very fast. Convergence of constructed method is also proved in this paper. We can notice algorithm based on these methods is very fast and easy to handle. In this work we discuss multiresolution analysis for wavelets generated by orthogonal polynomials, e.g., Legendre, Chebyshev, Lagurre, Gegenbauer. Then we use these wavelets for solving nonlinear SBVPs. Wavelets are able to deal with singularity easily and efficiently.

Multiresolution wavelet analysis applied to GRACE range-rate residuals

Abstract: . For further improvements of gravity field models based on Gravity Recovery and Climate Experiment (GRACE) observations, it is necessary to identify the error sources within the recovery process. Observation residuals obtained during the gravity field recovery contain most of the measurement and modeling errors and thus can be considered a realization of actual errors. In this work, we investigate the ability of wavelets to help in identifying specific error sources in GRACE range-rate residuals. The multiresolution analysis (MRA) using discrete wavelet transform (DWT) is applied to decompose the residual signal into different scales with corresponding frequency bands. Temporal, spatial, and orbit-related features of each scale are then extracted for further investigations. The wavelet analysis has proven to be a practical tool to find the main error contributors. Besides the previously known sources such as K-band ranging (KBR) system noise and systematic attitude variations, this method clearly shows effects which the classic spectral analysis is hardly able or unable to represent. These effects include long-term signatures due to satellite eclipse crossings and dominant ocean tide errors.

A sampling theorem with error estimation for S-transform

Abstract: S-transform (ST) is an extension of wavelet transform (WT) and short-time Fourier transform (STFT). The ST is depended on a scalable and moving Gaussian window. It overcomes the low-resolution factor of STFT and tackles with a lack of phase in WT. The ST is a useful tool for signal processing and analysis. In this paper, the multiresolution analysis (MRA) related with ST is introduced and after that a sampling theorem associated with ST is proposed which is based on multiresolution subspace. Additionally, truncation and aliasing error generated due to the sampling process, are also derived. The theoretical determinations are exhibited and validated using simulation results.

Combining ensemble Kalman filter and multiresolution analysis for efficient assimilation into adaptive mesh models

Abstract: A new approach is developed for data assimilation into adaptive mesh models with the ensemble Kalman filter (EnKF). The EnKF is combined with a wavelet-based multiresolution analysis (MRA) scheme to enable robust and efficient assimilation in the context of reduced-complexity adaptive spatial discretization. The wavelet representation of the solution enables the use of different meshes that are individually adapted to the corresponding members of the EnKF ensemble. The analysis step of the EnKF is then performed by involving coarsening, refinement, and projection operations on its ensemble members. Depending on the choice of these operations, five variants of the MRA-EnKF are introduced, and tested on the one-dimensional Burgers equation with periodic boundary condition. The numerical results suggest that, given an appropriate tolerance value for the coarsening operation, four out of the five proposed schemes significantly reduce the computational complexity of the assimilation system, with marginal accuracy loss compared to the reference, full resolution, and EnKF solution. Overall, the proposed framework offers the possibility of capitalizing on the advantages of adaptive mesh techniques, and the flexibility of choosing suitable context-oriented criteria for efficient data assimilation.

A Novel MFDFA Algorithm and Its Application to Analysis of Harmonic Multifractal Features

Abstract: A power grid harmonic signal is characterized as having both nonlinear and nonstationary features. A novel multifractal detrended fluctuation analysis (MFDFA) algorithm combined with the empirical mode decomposition (EMD) theory and template movement is proposed to overcome some shortcomings in the traditional MFDFA algorithm. The novel algorithm is used to study the multifractal feature of harmonic signals at different frequencies. Firstly, the signal is decomposed and the characteristics of wavelet transform multiresolution analysis are employed to obtain the components at different frequency bands. After this, the local fractal characteristic of the components is studied by utilizing the novel MFDFA algorithm. The experimental results show that the harmonic signals exhibit obvious multifractal characteristics and that the multifractal intensity is related to the signal frequency. Compared with the traditional MFDFA algorithm, the proposed method is more stable in curve fitting and can extract the multifractal features more accurately.

Wavelet Packets Transform processing and Genetic Neuro-Fuzzy classification to detect faulty bearings:

Abstract: A great investment is made in maintenance of machinery in any industry. A big percentage of this is spent both in workers and in materials in order to prevent potential issues with said devices. In...

Remote sensing image fusion algorithm based on mutual-structure for joint filtering using saliency detection

Abstract: Multimodality image fusion provides more comprehensive information and has an increasingly wide range of uses. For the remote sensing image fusion, traditional multiresolution analysis (MRA)-based methods always have insufficiencies in contrast with spatial details. At the same time, traditional sum of modified Laplace may do blocking artifacts. In order to overcome these deficiencies, we propose a remote sensing image fusion method based on the mutual-structure for joint filtering and saliency detection. Our method uses joint filtering to facilitate the correct extraction of the high and low frequency from source images. The saliency detection method also improves the effect of low-frequency fusion, and the high-frequency sub-bands calculate the extended sum of modified Laplace for better fusion. The method is compared with other five classical fusion methods. The experimental results show that the algorithm effectively preserves the structural information and textural information of the image and improves the sharpness of the fused image. It turns out to have many advantages in subjective and objective evaluation.