Multiresolution Wavelet Research Articles

An iris biometric protection scheme using 4D hyperchaotic system and modified equal modulus decomposition in hybrid multi resolution wavelet domain

In this paper, a hybrid iris biometric protection scheme using 4D hyperchaotic system by means of coherent superposition and modified equal modulus decomposition in hybrid multi-resolution wavelet domain is proposed. The 4D hyperchaotic framework is employed for producing the permutation keystream for pixel swap-over mechanism. The hybrid multi-resolution is produced by means of Kronecker product of Walsh transform and fractional Fourier transform of different orders. Fractional orders of the hybrid multiresolution wavelet along with the parameters and initial conditions of the 4D hyperchaotic framework, later fill in as additional keys, thus enhancing the key space of the proposed mechanism. The proposed scheme has nonlinear characteristics and has high robustness against brute-force attack attributable to its enormous key-space. Numerical simulations have been carried out on grayscale images to prove the authenticity and efficacy of the proposed cryptosystem. The functioning of the proposed cryptosystem is investigated against various attacks including special attack. Outcomes display that the proposed iris template protection scheme not only has higher robustness against noise attack but is also unassailable to the iterative transform-based attacks.

Design and Implementation of an Ultra-Low Resource Electrodermal Activity Sensor for Wearable Applications ‡

While modern low-power microcontrollers are a cornerstone of wearable physiological sensors, their limited on-chip storage typically makes peripheral storage devices a requirement for long-term physiological sensing—significantly increasing both size and power consumption. Here, a wearable biosensor system capable of long-term recording of physiological signals using a single, 64 kB microcontroller to minimize sensor size and improve energy performance is described. Electrodermal (EDA) signals were sampled and compressed using a multiresolution wavelet transformation to achieve long-term storage within the limited memory of a 16-bit microcontroller. The distortion of the compressed signal and errors in extracting common EDA features is evaluated across 253 independent EDA signals acquired from human volunteers. At a compression ratio (CR) of 23.3×, the root mean square error (RMSErr) is below 0.016 S and the percent root-mean-square difference (PRD) is below 1%. Tonic EDA features are preserved at a CR = 23.3× while phasic EDA features are more prone to reconstruction errors at CRs > 8.8×. This compression method is shown to be competitive with other compressive sensing-based approaches for EDA measurement while enabling on-board access to raw EDA data and efficient signal reconstructions. The system and compression method provided improves the functionality of low-resource microcontrollers by limiting the need for external memory devices and wireless connectivity to advance the miniaturization of wearable biosensors for mobile applications.

Volatility Spillover Effect of International Crude Oil Futures and China-Russia Stock Market: A Multivariate BEKK-GARCH Model Based on Wavelet Multiresolution Analysis

The increasingly prominent strategic position of crude oil determines its high impact on macro-economy. The value of crude oil is reflected in the price of crude oil futures. Stock market is the barometer of macro economy. To what extent does international crude oil futures price affect stock market? China and Russia are the biggest importer and exporter of crude oil, respectively. Crude oil is of strategic value to both countries. This study empirically investigates the volatility spillover effect of international crude oil futures and China-Russia stock market from April 24th, 2015 to April 20th, 2018, based on the data of international crude oil futures prices, China-Russia stock market composite index, and industry stock index. The empirical results show that there is a short-term relationship between China-Russia stock market composite index and international crude oil futures price. The international crude oil futures price has a greater explanatory power to Russian RTS index, but a smaller explanatory power to Shanghai composite index. All industry stock indices are cointegrated with international crude oil futures prices. Except for China industry and Russia energy, the adjustment coefficient of international crude oil futures price on stock index volatility of other industries is insignificant. This study mainly studies the relationship between international crude oil futures price and the comprehensive stock index and industry stock index of China and Russia, and compares the impact of international crude oil futures price on the stock market of the largest importer and the largest exporter of crude oil to explore the linkage between crude oil futures price and stock market, and puts forward policy implications based on the empirical results.

Statistical analysis of fMRI using wavelets: Big Data, denoising, large‐p‐small‐n matrices

AbstractOver the past decade functional Magnetic Resonance Imaging (fMRI) has been intensively used to study the complex functional network organization of the human brain and how it changes in time. An fMRI machine produces 3D time‐course cerebral images that contain hundreds of thousands of voxels and each voxel is scanned for hundreds of times. This potentially allows the researchers to explore functional connectivity on a voxel‐to‐voxel level, and also yields a number of serious statistical complications. First of all, the high‐dimension property of fMRI data turns it into Big Data. Furthermore, the study of functional brain network for so many voxels involves the problem of estimation of and simultaneous inference for large‐p‐small‐n cross‐covariance matrices. Furthermore, all problems should be solved in the presence of notoriously large fMRI noise which often forces statisticians to average signals over large areas instead of considering a network between individual voxels. An attractive alternative to the averaging, discussed in the paper, is a multiresolution wavelet analysis complemented by special procedures of estimating noise and estimation and simultaneous inference for cross‐covariance and cross‐correlation matrices for hundreds of thousands pairs of voxels, and it is fair to say that if wavelets have not been already known, fMRI applications would necessitates their creation. Both task and resting‐state fMRI are considered, and lessons from the wavelet analysis of ultra‐fast and conventional neuroplasticity fMRI experiments are presented. The article is self‐contained and does not require familiarity with wavelets or fMRI.This article is categorized under: Algorithms and Computational Methods > Numerical Methods Applications of Computational Statistics > Signal and Image Processing and Coding

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

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 Re_{τ}=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.

The Volatility Spillover Effect Between the International Crude Oil Futures Price and China’s Stock Market - Multivariate BEKK-GARCH Model Based on Wavelet Multiresolution

This study aims to analyze the volatility spillover effect between the international crude oil futures market and China’s stock market. Using West Texas Intermediate (WTI) and the Shanghai Composite Index (SSEC) to represent the international crude oil futures market and China’s stock market respectively, this study selects data of WTI and the SSEC from August 10, 2007 to August 10, 2017. It processes these data via wavelet multiresolution to decompose them into different levels and then builds the data model based on the BEKK-GARCH model. By testing the parameters through the Wald test, it further explores whether the volatility spillover effect exists between WTI and the SSEC. Empirical evidence finds that the volatility spillover effect between WTI and the SSEC is significant in the short run, while, however, such a volatility spillover effect does not exist in the medium and long term.

HexaShrink, an exact scalable framework for hexahedral meshes with attributes and discontinuities: multiresolution rendering and storage of geoscience models

With huge data acquisition progresses realized in the past decades and acquisition systems now able to produce high resolution grids and point clouds, the digitization of physical terrains becomes increasingly more precise. Such extreme quantities of generated and modeled data greatly impact computational performances on many levels of high-performance computing (HPC): storage media, memory requirements, transfer capability, and finally simulation interactivity, necessary to exploit this instance of big data. Efficient representations and storage are thus becoming “enabling technologies” in HPC experimental and simulation science. We propose HexaShrink, an original decomposition scheme for structured hexahedral volume meshes. The latter are used for instance in biomedical engineering, materials science, or geosciences. HexaShrink provides a comprehensive framework allowing efficient mesh visualization and storage. Its exactly reversible multiresolution decomposition yields a hierarchy of meshes of increasing levels of details, in terms of either geometry, continuous or categorical properties of cells. Starting with an overview of volume meshes compression techniques, our contribution blends coherently different multiresolution wavelet schemes in different dimensions. It results in a global framework preserving discontinuities (faults) across scales, implemented as a fully reversible upscaling at different resolutions. Experimental results are provided on meshes of varying size and complexity. They emphasize the consistency of the proposed representation, in terms of visualization, attribute downsampling and distribution at different resolutions. Finally, HexaShrink yields gains in storage space when combined to lossless compression techniques.

A Temporal Neural Trace of Wavelet Coefficients in Human Object Vision: An MEG Study.

Wavelet transform has been widely used in image and signal processing applications such as denoising and compression. In this study, we explore the relation of the wavelet representation of stimuli with MEG signals acquired from a human object recognition experiment. To investigate the signature of wavelet descriptors in the visual system, we apply five levels of multi-resolution wavelet decomposition to the stimuli presented to participants during MEG recording and extract the approximation and detail sub-bands (horizontal, vertical, diagonal) coefficients in each level of decomposition. Apart from, employing multivariate pattern analysis (MVPA), a linear support vector classifier (SVM) is trained and tested over the time on MEG pattern vectors to decode neural information. Then, we calculate the representational dissimilarity matrix (RDM) on each time point of the MEG data and also on wavelet descriptors using classifier accuracy and one minus Pearson correlation coefficient, respectively. Given the time-courses calculated from performing the Pearson correlation between the wavelet descriptors RDMs and MEG decoding accuracy in each time point, our result shows that the peak latency of the wavelet approximation time courses occurs later for higher level coefficients. Furthermore, studying the neural trace of detail sub-bands indicates that the overall number of statistically significant time points for the horizontal and vertical detail coefficients is noticeably higher than diagonal detail coefficients, confirming the evidence of the oblique effect that the horizontal and vertical lines are more decodable in the human brain.

An asymmetric hybrid cryptosystem using hyperchaotic system and random decomposition in hybrid multi resolution wavelet domain

In this paper, an asymmetric hybrid cryptosystem utilizing four-dimensional (4D) hyperchaotic framework by means of coherent superposition and random decomposition in hybrid multi-resolution wavelet domain is put forward. The 4D hyperchaotic framework is utilized for creating permutation keystream for a pixel swapping procedure. The hybrid multi-resolution wavelet is formed by combining Walsh transform and fractional Fourier transform of various orders. The 4D hyperchaotic framework’s parameters and preliminary conditions alongside the fractional orders extend the key-space and consequently give additional strength to the proposed cryptosystem. The proposed cryptosystem has an extended key-space to avoid any brute-force attack and is nonlinear in nature. The scheme is validated on greyscale images. Computer-based simulations have been executed to validate the robustness of the proposed scheme against different types of attacks. Results demonstrate that the proposed cryptosystem along with offering higher protection against noise and occlusion attacks is also unassailable to special attack.

Design of dynamic ECG diagnosis system based on multiresolution

This article proposes a multi-resolution wavelet peak detection method for R wave localization to realize dynamic ECG diagnosis including RR interval, heart rate counting, bradycardia and bradycardia. Detection of R wave involves lots of cardiovascular diseases diagnosis, and plays an important role in ECG signal detection. Wavelet transform can describe the time-frequency characteristics of signals, allowing different resolutions to represent the time characteristics of signals; therefore, it is an appropriate tool for analyzing ECG signals. This method has been verified by MIT-BIH database’s R-wave records. The sensitivity of R wave method is 99.92%, and the positive predictive rate is 99.93%, and the dynamic ECG diagnostic system performs well.

A wavelet multiresolution interpolation Galerkin method for targeted local solution enrichment

A novel wavelet multiresolution interpolation formula is developed for approximating continuous functions defined on an arbitrary two-dimensional domain represented by a set of scattered nodes. The present wavelet interpolant is created explicitly without the need for matrix inversion. It possesses the Kronecker delta function property and does not contain any ad-hoc parameters, leading to an excellent stability and usefulness for function approximation. Using the wavelet multiresolution interpolant to construct trial and weight functions, a wavelet multiresolution interpolation Galerkin method (WMIGM) is proposed for solving elasticity problems. In this WMIGM, the essential boundary conditions can be imposed with ease as in the conventional finite element method. The stiffness matrix can be efficiently obtained through semi-analytical integration using an underlying general database, instead of the numerical integration usually requiring a mesh. The accuracy of the WMIGM is examined through theoretical analysis and benchmark problems. Results demonstrate that the proposed WMIGM has an excellent accuracy, optimal rate of convergence and competitive efficiency, as well as an excellent stability against irregular nodal distribution. Most importantly, by adding more nodes into local region only, a high resolution of localized steep gradients can be achieved as desired without changing the existing nodes.

Asymmetric hybrid encryption scheme based on modified equal modulus decomposition in hybrid multi-resolution wavelet domain

ABSTRACTIn this paper, an asymmetric hybrid encryption scheme, using coherent superposition and modified equal modulus decomposition in a hybrid multi-resolution wavelet, is proposed. The hybrid multi-resolution wavelet is generated using fractional Fourier transform of multiple orders and Walsh transform. The fractional orders of the fractional Fourier transform increase the key space and hence provide additional strength to the cryptosystem. The designed scheme has a large key space to avoid brute-force attack and is non-linear in nature. The scheme is validated on grey-scale images. Computer-based simulations have been performed to verify the validity and performance of the proposed scheme against various attacks. Scheme's robustness to the special attack is also checked. Results show that single equal modulus decomposition with fractional Fourier transform and hybrid transform are vulnerable to the special attack, whereas the proposed scheme endures the special attack.

Myographic Interference Filtering from ECG Signals Using Multiresolution Wavelet Transform

Myographic Interference Filtering from ECG Signals Using Multiresolution Wavelet Transform

A novel dyadic multiresolution wavelet image steganography using N-ary

Steganography plays an important role in information sharing. In this paper a wavelet based image steganography using Haar wavelet and an N-ary notation is proposed. The high and middle frequency coefficients are selected based on the Shannon entropy value to identify the best sub band for data hiding. Peak signal to noise ratio and Structure similarity index metric values are computed from the stego image. The empirical results show the proposed method provides good, better imperceptibility and data capacity with average peak signal to noise ratio 53.60 dB for 359,112 bits in terms of effectiveness. To prove this accomplishment of the method, several experiments were conducted and compared the results with existing works.

A novel dyadic multiresolution wavelet image steganography using N-ary

Steganography plays an important role in information sharing. In this paper a wavelet based image steganography using Haar wavelet and an N-ary notation is proposed. The high and middle frequency coefficients are selected based on the Shannon entropy value to identify the best sub band for data hiding. Peak signal to noise ratio and Structure similarity index metric values are computed from the stego image. The empirical results show the proposed method provides good, better imperceptibility and data capacity with average peak signal to noise ratio 53.60 dB for 359,112 bits in terms of effectiveness. To prove this accomplishment of the method, several experiments were conducted and compared the results with existing works.

Multiresolution wavelet bases with augmentation method for solving singularly perturbed reaction–diffusion Neumann problem

This paper developed the anti-derivative wavelet bases to handle the more general types of boundary conditions: Dirichlet, mixed and Neumann boundary conditions. The boundary value problem can be formulated by the variational approach, resulting in a system involving unknown wavelet coefficients. The wavelet bases are constructed to solve the unknown solutions corresponding to the types of solution spaces. The augmentation method is presented to reduce the dimension of the original system, while the convergence rate is in the same order as the multiresolution method. Some numerical examples have been shown to confirm the rate of convergence. The examples of the singularly perturbed problem with Neumann boundary conditions are also demonstrated, including highly oscillating cases.

Fractal approximation of chaos game representations using recurrent iterated function systems

We demonstrate that chaos game representations of Cannabis sativa may be approximated by the chaos game approximation of a recurrent iterated function system attractor. Via numerical experiments, we then study the fractal scaling properties of both objects and apply a wavelet decomposition in order to investigate scale-invariant patterns. We show that the attractor of a recurrent iterated function system scales similarly to the chaos game representation and has a similar wavelet multiresolution analysis profile.

Intelligent Turning Tool Monitoring with Neural Network Adaptive Learning

Tool state monitoring is a key technology in intelligent manufacturing. But it is still in a research stage and lacks general adaptability for different machining conditions. To overcome this limitation, this work systematically investigates an intelligent, real‐time, and visible tool state monitoring through adopting integrated theories and technologies, i.e., (a) through distinctively designed experimental technique with comprehensive consideration of cutting parameters and tool wear values as variables, (b) through bisensor fusion for simultaneous measurements of low and high frequency signals, (c) through multitheory fusion of wavelet decomposition and the Relief‐F algorithm for performing dual feature extraction and feature dimension reduction to achieve more accurate state identification using neural network, and (d) through an innovative programming technique of MATLAB‐nested labVIEW. This tool monitoring system has neural network adaptive learning ability with the change of the experimental sample signals which are collected simultaneously by selected vibration and acoustic emission (AE) sensors in all factors turning experiments. Based on LabVIEW and MATLAB hybrid programming, the waveforms of signals are observed and the significant characteristics of signals are extracted through the time‐frequency domain analysis and then the calculation of the energy proportion of each frequency band obtained using 4 levels of wavelet packet decompositions of the vibration signal as well as 8 levels of wavelet multiresolution decompositions of the AE signal; the ensuing Relief‐F algorithm is used to further reextract the features that are most relevant to the tool state as input of neural network pattern recognition. Through the BP neural network adaptive learning, tool state recognition model is finally established. The results show that the correct recognition rate of BP network model after samples training is 92.59%, which can more accurately and intelligently monitor the tool wear state.

Eccentricity Failure Detection of Brushless DC Motors From Sound Signals Based on Density of Maxima

Brushless Direct Current (BLDC) motors have been used in a wide range of fields. In some critical applications, failures in these machines can cause operational disasters and cost lives if they are not detected in advance. The classical methods for detecting incipient faults in BLDC motors perform processing of the current signal to obtain the required information. In this work, the SAC-DM (Signal Analysis based on Chaos using Density of Maxima) technique is applied for the first time in the diagnosis of failures of electromechanical systems from sound signals. Wavelet Multiresolution Analysis (WMA) is used to separate a chaotic signal component from the sound emitted by the motor. This work demonstrates that it is feasible to perform dynamic eccentricity diagnosis in BLDC motors by identifying variations of the SAC-DM of the sound signal. The technique exposed in this work requires low computational cost and achieves high success rate. To validate the method, tests were carried out on a small BLDC motor normally used in Unmanned Aerial Vehicle (UAV), demonstrating the ability of the method to detect the speed of the motor in 95.89% of the cases and to detect eccentricity problems at a fixed speed in 88.34% of the cases.

Wavelet-Multi Resolution Analysis Based ANN Architecture for Fault Detection and Localization in DC Microgrids

DC microgrids present an effective power system solution for increased integration of renewable sources while providing clear benefits, such as high efficiency and simpler control. However, the protection of DC networks still remains a challenge due to strict time limits for fault interruption imposed by fast rising fault currents in DC systems, and absence of frequency and phasor information. This paper introduces a technique for fast detection and isolation of the faults in the DC microgrids without de-energizing the whole network. In the proposed algorithm, branch current measurements are sampled and Wavelet transform is applied to capture the characteristic changes in the current signals caused by network faults. The temporal variations in the relative wavelet energy within the frequency bands are acquired to construct the feature vector for classification. Artificial neural networks are used as the classifier as it provides a soft criterion for fault detection, featuring smart fault detection capability. The relatively fast calculation time of artificial neural networks makes it a good candidate for this application, due to the strict time restrictions inherited in DC fault isolation. To evaluate the performance, a comprehensive study on the proposed scheme is presented. The results demonstrate the effectiveness of the proposed scheme in terms of fast and reliable fault detection and inbuilt accurate fault localization capability.