Wavelet Library Research Articles

Using of Beylkin Wavelet for Speech Recognition

This paper describes the application of the Beylkin wavelet for speech segmentation. The problem of speech segmentation in the Yakut language is that there are segmentation difficulties due to the peculiarities of the language. The use of long vowels and double consonants in the Yakut language complicates the correct segmentation of oral speech. For the analysis, the window method of analyzing the energy of the wavelet signal is used. The experience of using different wavelet functions has shown that it is not always possible to accurately find the segment boundaries in some cases. The Scilab package has a large library of wavelets that allows extensive research into their applications in speech recognition. The results of the study show that there are difficulties due to various reasons, one of which is the presence of double sonorant consonants. The graphs of the analysis of doubled sonorant consonants are given.

Nonconvex optimization-based inverse spectral decomposition

Abstract As a time–frequency analysis tool, inverse spectral decomposition (ISD) could be utilized to obtain a high-resolution time–frequency map via the inversion strategy. In the established inversion function, an analytic signal is disintegrated as a coefficient matrix whose elements represent the weights of the wavelet components with the different dominant frequencies and the time location in the complex wavelet library. By using a sparse constraint, a high-quality inverse decomposition result could be generated. In this paper, a modified ISD technique based on a nonconvex optimization algorithm is proposed to pursue a sparser coefficient solution found in the inversion processing by decreasing the redundant information. This new approach applies the lp(0 < p < 1) penalty term to build an accurate mapping relationship between the original signal and its time–frequency spectrum. This adequate regularization in reconstructed function serves as a better alternative to the l1 norm one in conventional ISD. Lower signal-to-noise ratio (SNR) and much weaker incoherence of wavelet library cannot impact on the accuracy of output with the ISD based on the lp norm (0 < p < 1) constraint. Synthetic data tests with the Gabor transform, the conventional ISD method and the nonconvex optimization-based ISD are applied to demonstrate the performance gaps. In the real application area, a blended image with instantaneous spectral attribute volumes produced by the new approach assists the identification of the geological anomalous body, which is verified via a physical model data and field data tests.

Adaptive filtering algorithm based on a wavelet packet tree for heart sound signal analysis

In order to further highlight heart sound signals analysis, we developed an algorithm based on a wavelet packet tree; for possible discrimination depending on the severity of pathological cases for different heart sound signals. The algorithm functions select the most informative nodes combination of a wavelet packet tree as a basis for feature extraction. To generate this adaptive filter, we need to compute the best sub tree of an initial wavelet packet tree with respect for entropy type yardstick, the node combination with the lowest total cost is selected. The decomposition into wavelet packet offers a wavelet library organised according to their time-frequency analysis and location properties and therefore of pass-band filtering, according to a binary tree architecture. This architecture makes it possible to implement algorithms for searching for adapted bases to both the desired time-frequency properties and the analysed signal, which are conventionally called better bases.

Adaptive filtering algorithm based on a wavelet packet tree for heart sound signal analysis

In order to further highlight heart sound signals analysis, we developed an algorithm based on a wavelet packet tree; for possible discrimination depending on the severity of pathological cases for different heart sound signals. The algorithm functions select the most informative nodes combination of a wavelet packet tree as a basis for feature extraction. To generate this adaptive filter, we need to compute the best sub tree of an initial wavelet packet tree with respect for entropy type yardstick, the node combination with the lowest total cost is selected. The decomposition into wavelet packet offers a wavelet library organised according to their time-frequency analysis and location properties and therefore of pass-band filtering, according to a binary tree architecture. This architecture makes it possible to implement algorithms for searching for adapted bases to both the desired time-frequency properties and the analysed signal, which are conventionally called better bases.

A signal invariant wavelet function selection algorithm.

This paper addresses the problem of mother wavelet selection for wavelet signal processing in feature extraction and pattern recognition. The problem is formulated as an optimization criterion, where a wavelet library is defined using a set of parameters to find the best mother wavelet function. For estimating the fitness function, adopted to evaluate the performance of the wavelet function, analysis of variance is used. Genetic algorithm is exploited to optimize the determination of the best mother wavelet function. For experimental evaluation, solutions for best mother wavelet selection are evaluated on various biomedical signal classification problems, where the solutions of the proposed algorithm are assessed and compared with manual hit-and-trial methods. The results show that the solutions of automated mother wavelet selection algorithm are consistent with the manual selection of wavelet functions. The algorithm is found to be invariant to the type of signals used for classification.

An evolved wavelet library based on genetic algorithm.

As the size of the images being captured increases, there is a need for a robust algorithm for image compression which satiates the bandwidth limitation of the transmitted channels and preserves the image resolution without considerable loss in the image quality. Many conventional image compression algorithms use wavelet transform which can significantly reduce the number of bits needed to represent a pixel and the process of quantization and thresholding further increases the compression. In this paper the authors evolve two sets of wavelet filter coefficients using genetic algorithm (GA), one for the whole image portion except the edge areas and the other for the portions near the edges in the image (i.e., global and local filters). Images are initially separated into several groups based on their frequency content, edges, and textures and the wavelet filter coefficients are evolved separately for each group. As there is a possibility of the GA settling in local maximum, we introduce a new shuffling operator to prevent the GA from this effect. The GA used to evolve filter coefficients primarily focuses on maximizing the peak signal to noise ratio (PSNR). The evolved filter coefficients by the proposed method outperform the existing methods by a 0.31 dB improvement in the average PSNR and a 0.39 dB improvement in the maximum PSNR.

Modeling Fuzziness Measures for Best Wavelet Selection

Uncertainty measures model different types of uncertainty that are inherent in complex information systems. Measures that model either fuzzy or probabilistic uncertainty types have been explored in the literature. This paper shows that a combination of fuzzy and probabilistic uncertainty types, combined with the generalized maximum uncertainty principle, can be applied to time-series sequence classification and analysis. We present a novel algorithm that selects a wavelet from a wavelet library such that it best represents a time-series sequence, in a maximum uncertainty sense. Transformation coefficients are combined together in feature vectors that capture sequence temporal trends. A neural network is trained and tested using extracted gait sequence temporal features. Results have shown that models that combine together fuzzy and probabilistic uncertainty types better classify time-series gait sequences.

Geophysical wavelet library: Applications of the continuous wavelet transform to the polarization and dispersion analysis of signals

In the present paper, we consider and summarize applications of the continuous wavelet transform to 2C and 3C polarization analysis and filtering, modeling the dispersed and attenuated wave propagation in the time–frequency domain, and estimation of the phase and group velocity and the attenuation from a seismogram. Along with a mathematical overview of each of the presented methods, we show that all these algorithms are logically combined into one software package “Geophysical Wavelet Library” developed by the authors. The novelty of this package is that we incorporate the continuous wavelet transform into the library, where the kernel is the time–frequency polarization and dispersion analysis. This library has a wide range of potential applications in the field of signal analysis and may be particularly suitable in geophysical problems that we illustrate by analyzing synthetic, geomagnetic and real seismic data.

Wavelet classification of high frequency pupillary responses

This paper addresses the problem of classifying users with different visual abilities on the basis of their pupillary response while performing computer-based tasks. Multiscale Schur monotone (MSM) summaries of high frequency pupil diameter measurements are utilized as feature (or input) vectors in this classification. Various MSM measures, such as Shannon, Picard, and Emlen entropies, the Gini coefficient and the Fishlow measure, are investigated to assess their discriminatory characteristics. A combination of classifiers, motivated by a Bayesian paradigm, is proposed to minimize and stabilize the misclassification rate in training and test sets with the goal of improving classification accuracy. In addition, the issue of wavelet basis selection for optimal classification performance is discussed. The members of the Pollen wavelet library are included as competitors. The proposed methodology is validated with extensive simulation and applied to high-frequency pupil diameter measurements collected from 36 individuals with varying ocular abilities and pathologies. The expected misclassification rate of our procedure can be as low as 21% by appropriately choosing the Schur monotone summary and using a properly selected wavelet basis.

Shannon Wavelet Approach to Sub-Band Coding

It is well known that the Shannon Sampling Theorem allows us to fully recover a continuous-time bandlimited signal from its digital samples, as long as the sampling rate to be chosen is not smaller than the Nyquist frequency. This theory applies to all bandlimited signals, which may or may not occupy the entire frequency band. Hence, it is intuitively convincing that for continuous-time signals, such as those in speech, that do not fully utilize the entire frequency intervals, less digital samples are required for their full recovery. Current techniques in sub-band coding are used for achieving this goal. The objective of this paper is to present a wavelet theory for establishing the mathematical foundation of this sub-band coding approach. A wavelet packet decomposition of the signal provides the optimal sub-band coding bit-rate by using the Shannon wavelet library introduced in this paper.

WAVELET ANALYSIS IN SPACES OF SLOWLY GROWING SPLINES VIA INTEGRAL REPRESENTATION

In this paper we consider polynomial splines with equidistant nodes which may grow as Ojxj s . We present an integral representation of such splines with a distribution kernel where exponential splines are used as basic functions. By this means we characterize splines possessing the property that translations of any such spline form a basis of corresponding spline space. It is shown that any such spline is associated with a dual spline whose translations form the biorthogonal basis. We suggest a scheme of wavelet analysis in the spaces of growing splines based on integral representation of the splines. The key point of that scheme is the renement equation for the exponential splines which contains only two terms. We construct the so called exponential wavelets. We establish conditions for a spline to be a basic wavelet which enable us to form a library of such wavelets. We give formulas for the decomposition of a spline into a weak orthogonal sum of the sparse-grid spline and an element of the corresponding wavelet space. Reconstruction formulas are presented which permit the use of arbitrary bases of spline and wavelet spaces.