Properties Of Multiresolution Analysis Research Articles

A Comparison of ECG Signal Pre-processing Using FrFT, FrWT and IPCA for Improved Analysis

ObjectiveElectrocardiogram (ECG) is a diagnostic tool for recording electrical activities of the human heart non-invasively. It is detected by electrodes placed on the surface of the skin in a conductive medium. In medical applications, ECG is used by cardiologists to observe heart anomalies (cardiovascular diseases) such as abnormal heart rhythms, heart attacks, effects of drug dosage on subject's heart and knowledge of previous heart attacks. Recorded ECG signal is generally corrupted by various types of noise/distortion such as cardiac (isoelectric interval, prolonged depolarization and atrial flutter) or extra cardiac (respiration, changes in electrode position, muscle contraction and power line noise). These factors hide the useful information and alter the signal characteristic due to low Signal-to-Noise Ratio (SNR). In such situations, any failure to judge the ECG signal correctly may result in a delay in the treatment and harm a subject (patient) health. Therefore, appropriate pre-processing technique is necessary to improve SNR to facilitate better treatment to the subject. Effects of different pre-processing techniques on ECG signal analysis (based on R-peaks detection) are compared using various Figures of Merit (FoM) such as sensitivity (Se), accuracy (Acc) and detection error rate (DER) along with SNR. MethodsIn this research article, a new fractional wavelet transform (FrWT) has been proposed as a pre-processing technique in order to overcome the disadvantages of other existing commonly used techniques viz. wavelet transform (WT) and the fractional Fourier transform (FrFT). The proposed FrWT technique possesses the properties of multiresolution analysis and represents signal in the fractional domain which consists of representation in terms of rotation of signals in the time–frequency plane. In the literature, ECG signal analysis has been improvised using statistical pre-processing techniques such as principal component analysis (PCA), and independent component analysis (ICA). However, both PCA and ICA are prone to suffer from slight alterations in either signal or noise, unless the basis functions are prepared with a worldwide set of ECG. Independent Principal Component Analysis (IPCA) has been used to overcome this shortcoming of PCA and ICA. Therefore, in this paper three techniques viz. FrFT, FrWT and IPCA are selected for comparison in pre-processing of ECG signals. ResultsThe selected methods have been evaluated on the basis of SNR, Se, Acc and DER of the detected ECG beats. FrWT yields the best results among all the methods considered in this paper; 34.37dB output SNR, 99.98% Se, 99.96% Acc, and 0.036% DER. These results indicate the quality of biology-related information retained from the pre-processed ECG signals for identifying different heart abnormalities. ConclusionCorrect analysis of the acquired ECG signal is the main challenge for cardiologist due to involvement of various types of noises (high and low frequency). Twenty two real time ECG records have been evaluated based on various FoM such as SNR, Se, Acc and DER for the proposed FrWT and existing FrFT and IPCA preprocessing techniques. Acquired real-time ECG database in normal and disease situations is used for the purpose. The values of FoMs indicate high SNR and better detection of R-peaks in a ECG signal which is important for the diagnosis of cardiovascular disease. The proposed FrWT outperforms all other techniques and holds both analytical attributes of the actual ECG signal and alterations in the amplitudes of various ECG waveforms adequately. It also provides signal portrayals in the time-fractional-frequency plane with low computational complexity enabling their use practically for versatile applications.

A supervised filter method for multi-objective feature selection in EEG classification based on multi-resolution analysis for BCI

This paper proposes a supervised filter method for evolutionary multi-objective feature selection for classification problems in high-dimensional feature space, which is evaluated by comparison with wrapper approaches for the same application. The filter method based on a set of label-aided utility functions is compared with wrapper approaches using the accuracy and generalization properties in the effective searching of the most adequate subset of features through an evolutionary multi-objective optimization scheme. The target application corresponds to a brain–computer interface (BCI) classification task based on linear discriminant analysis (LDA) classifiers, where the properties of multi-resolution analysis (MRA) for signal analysis in temporal and spectral domains have been used to extract features from electroencephalogram (EEG) signals. The results, corresponding to a dataset obtained from the databases of the BCI Laboratory of the University of Essex, UK, including ten subjects with three different imagery movements, have allowed us to evaluate the advantages and drawbacks of the different approaches with respect to time consumption, accuracy and generalization capabilities.

Customized lifting multiwavelet packet information entropy for equipment condition identification

Condition identification of mechanical equipment from vibration measurement data is significant to avoid economic loss caused by unscheduled breakdowns and catastrophic accidents. However, this task still faces challenges due to the complexity of equipment and the harsh environment. This paper provides a possibility for equipment condition identification by proposing a method called customized lifting multiwavelet packet information entropy. Benefiting from the properties of multi-resolution analysis and multiple wavelet basis functions, the multiwavelet method has advantages in characterizing non-stationary vibration signals. In order to realize the accurate detection and identification of the condition features, a customized lifting multiwavelet packet is constructed via a multiwavelet lifting scheme. Then the vibration signal from the mechanical equipment is processed by the customized lifting multiwavelet packet transform. The relative energy in each frequency band of the multiwavelet packet transform coefficients that equals a percentage of the whole signal energy is taken as the probability. The normalized information entropy is obtained based on the relative energy to describe the condition of a mechanical system. The proposed method is applied to the condition identification of a rolling mill and a demountable disk–drum aero-engine. The results support the feasibility of the proposed method in equipment condition identification.

Triebel–Lizorkin spaces and shearlets on the cone in [formula omitted

The shearlets are a special case of the wavelets with composite dilation that, among other things, have a basis-like structure and multi-resolution analysis properties. These relatively new representation systems have encountered wide range of applications, generally surpassing the performance of their ancestors due to their directional sensitivity. Both theories of coorbit spaces and decomposition spaces provide a way of associating some kind of smoothness spaces to shearlets. However, these smoothness spaces are closer to classical Besov type spaces. Here, instead, we define a kind of highly anisotropic inhomogeneous Triebel–Lizorkin spaces and prove that it can be characterized with the so-called “shearlets on the cone” coefficients. We first prove the boundedness of the analysis and synthesis operators with the “traditional” shearlets coefficients. Then, with the development of the smooth Parseval frames of shearlets of Guo and Labate we are able to prove a reproducing identity, which was previously possible only for the L2 case. We also find some embeddings of the (classical) dyadic spaces into these highly anisotropic spaces, and vice versa, for certain ranges of parameters. In order to keep a concise document we develop our results in the “weightless” case (w=1) and give hints on how to develop the weighted case.

Voice activity detection based on using wavelet packet

This paper, presents a robust voice activity detection (VAD) technique based on wavelet packet. In this technique sub-bands and their amplitudes are represented as the vectors for each sample time in order to find a new feature from the frequency and amplitude changes. On the other hand, the multi-resolution analysis property of the wavelet packet transform (WPT), the voiced, unvoiced, and transient components of speech can be distinctly discriminated. Then, a new feature extraction method is implemented based on observations of the angles between vectors. This feature extraction method retains most unvoiced sounds in a voice active frame. Experimental results show that the proposed WT feature parameter can extract the speech activity under poor SNR conditions and that it is also insensitive to variable-level of noise.

Multiresolution analysis, self-similar tilings and Haar wavelets on the Heisenberg group

In this article, the properties of multiresolution analysis and self-similar tilings on the Heisenberg group are studied. Moreover, we establish a theory to construct an orthonormal Haar wavelet base in L 2(ℍ d ) by using self-similar tilings for the acceptable dilations on the Heisenberg group.

MULTIRESOLUTION ANALYSIS AND HAAR WAVELETS ON THE PRODUCT OF HEISENBERG GROUP

In this paper, the properties of multiresolution analysis on the product of Heisenberg group are investigated. Moreover, orthonormal Haar wavelet bases for L2(ℋn) are constructed.

A Construction of Multiresolution Analysis on Interval

We present a concrete method of constructing multiresolution analysis on interval. The method generalizes the corresponding results of Cohen, Daubechies and Vial [Appl. Comput. Harmonic Anal., 1(1993), 54–81]. By the use of the subdivision operator, the expressions of the constructed functions are more compact. Furthermore, the method reveals more clearly some properties of multiresolution analysis with certain approximation order.

An efficient wavelet finite element method in fault prognosis of incipient crack

The method of constructing any scale wavelet finite element (WFE) based on the one-dimensional or two-dimensional Daubechies scaling functions was presented, and the corresponding WFE adaptive lifting algorithm was given. In order to obtain the nested increasing approximate subspaces of multiscale finite element, the Daubechies scaling functions with the properties of multi-resolution analysis were employed as the finite ele-ment interpolating functions. Thus, the WFE could adaptively mesh the singularity domain caused by local cracks, which resulted in better approximate solutions than the traditional finite element methods. The calculations of natural frequencies of cracked beam were used to check the accuracy of given methods. In addition, the results of cracked cantilever beam and engineering application were satisfied. So, the current methods can provide effective tools in the numerical modeling of the fault prognosis of incipient crack.

A novel document retrieval method using the discrete wavelet transform

Current information retrieval methods either ignore the term positions or deal with exact term positions; the former can be seen as coarse document resolution, the latter as fine document resolution. We propose a new spectral-based information retrieval method that is able to utilize many different levels of document resolution by examining the term patterns that occur in the documents. To do this, we take advantage of the multiresolution analysis properties of the wavelet transform. We show that we are able to achieve higher precision when compared to vector space and proximity retrieval methods, while producing fast query times and using a compact index.

Adaptive multiscale solution of dynamical systems in chemical processes using wavelets

Most chemical processes occur at different spatial and temporal scales such as turbulence or chromatographic separations. Irregular features, singularities and steep changes emerge, which require solution procedures that can resolve these varying scales in the most efficient manner. Wavelets with their multiresolution analysis properties have the potential to express the solution from the coarsest to the finest scale with minimal effort. In this paper, a dynamically adaptive algorithm for solving PDEs in simple geometry using Wavelet–Galerkin (WG) discretization is presented. The algorithm is applied to a convection-diffusion problem and a reverse flow reactor. Using the residual and/or the absolute value of the wavelet coefficients as a measure of error, the algorithm could track the moving fronts and irregularities and sequentially refine the solution in the partial domain of interest. Also, it enables solving a coupled set of PDEs at different resolutions, exploiting the differences in differential operator stiffness. Issues regarding stability of multiresolution analysis for high Peclet number and the treatment of non-linearities are discussed.

On multiresolution analysis of multiplicityd

In this paper we study some basic properties of multiresolution analysis of multiplicityd in several variables and discuss some examples related to the spaces of cardinal splines with respect to the unidiagonal or the crisscross partition of the plane. Furthermore, in analogy with [8], we show that if the scaling functions are compactly supported, then it is possible to find compactly supported mother waveletsψl,l=1,...,2nd−d, in such a way that the family {2jn/2ψl(2jx−v)} is a semiorthogonal basis ofL2 (ℝn).