Showing papers on "Continuous wavelet transform published in 1997"

Wavelet transform methods for phase identification in three-component seismograms

Abstract: We apply the wavelet transform to seismic signals for the purpose of automatically identifying the P and S phase arrivals of seismic events. In this article, an algorithm is presented that locates these arrivals in single-station three-component short-period seismograms using polarization and amplitude information contained in the wavelet transform coefficients of the signals. The main idea is that strong features of the seismic signal appear in the wavelet coefficients across several scales. The first step in the algorithm is the wavelet decomposition of each component of a three-component short-period seismogram. The resulting multi-scalar representation is used to construct “locator” functions that identify the P and S arrivals. The P locator function is constructed by using polarization information across scales, and the S locator function is constructed using transverse over radial amplitude information across scales. These functions prove to be very effective at identifying the important P and S arrivals in the test data. The results are compared with arrival times picked by an analyst.

Measuring fiber orientation in nonwovens. part iii : fourier transform

Abstract: This paper addresses the development of an image analysis technique using the Fourier transform of the image to evaluate orientation in a fibrous assembly. The algorithms are evaluated using simulated images presented in Part I of the series. The results are compared with those for the tracking method presented in Part II.

Fractional wavelet transform.

Abstract: The wavelet transform, which has had a growing importance in signal and image processing, has been generalized by association with both the wavelet transform and the fractional Fourier transform. Possible implementations of the new transformation are in image compression, image transmission, transient signal processing, etc. Computer simulations demonstrate the abilities of the novel transform. Optical implementation of this transform is briefly discussed.

Speech enhancement with reduction of noise components in the wavelet domain

Abstract: This paper describes a general problem of removing additive background noise from the noisy speech in the wavelet domain. A semisoft thresholding is used to remove noise components from the wavelet coefficients of noisy speech. To prevent the quality degradation of the unvoiced sounds during the denoising process, the unvoiced region is classified first and then thresholding is applied in a different way. Experimental results demonstrate that the speech enhancement algorithm using the wavelet transform is very promising.

A security system based on human iris identification using wavelet transform

Abstract: A security system based on the recognition of the iris of human eyes using the wavelet transform is presented. The zero crossings of the wavelet transform are used to extract the unique features obtained from the grey level profiles of the iris. The recognition process is performed in two stages. The first stage consists of building a one dimensional representation of the grey level profiles of the iris followed by obtaining the wavelet transform zero crossings of the resulting representation. The second stage is the matching procedure for iris recognition. The proposed approach uses only a few selected intermediate resolution levels for matching, thus making it computationally efficient as well as less sensitive to noise and quantisation errors. A normalisation process is implemented to compensate for size variations due to the possible changes in the camera to face distance. The technique has been tested on real images in both noise free and noisy conditions. The technique is being investigated for real time implementation, as a standalone system, for access control to high security areas.

Solving the sideways heat equation by a wavelet - Galerkin method

Abstract: We consider a Cauchy problem for the heat equation in the quarter plane, where data are given at x = 1 and a solution is sought in the interval 0 < x < 1. This sideways heat equation is a model of a problem where one wants to determine the temperature on both sides of a thick wall, but where one side is inaccessible to measurements. The problem is ill-posed, in the sense that the solution (if it exists) does not depend continuously on the data. Meyer wavelets have the property that their Fourier transform has compact support. Therefore, by expanding the data and the solution in a basis of Meyer wavelets, high-frequency components can be filtered away. We show that using a wavelet - Galerkin approach, we restore continuous dependence on the data, and we give a recipe for choosing the coarse level resolution in the wavelet representation, depending on the noise level of the data. Furthermore, we solve the sideways problem numerically in the coarse level representation, as an ordinary differential equation in the space variable, where the time derivative is replaced by its wavelet representation. Numerical examples are given.

Time‐frequency decomposition of signals in a current disruption event

Abstract: Wavelet transform has recently been developed to the level of sophistication suitable for application to signal processing in magnetospheric research. We explore this new technique in decomposing signals in the time-frequency domain by first conducting continuous wavelet transform on a test signal to show its ability to resolve multiple-frequency components embedded within white noise of half the amplitude as the signal. We then use this tool to examine the large-amplitude magnetic fluctuations observed during a current disruption event. The results show the current disruption to be a multiscale phenomenon, encompassing low- as well as high-frequency components. The lowest-frequency component appears to behave quite independently from the higher-frequency components. The analysis shows for the first time that in current disruption the high-frequency components constitute a broadband excitation with a nonstationary nature, i.e., some oscillations appear to cascade from high to low frequency as time progresses.

Wavelet analysis in SAR ocean image profiles for internal wave detection and wavelength estimation

Abstract: Oceanographers and remote sensing researchers have long recognized the potential of using satellite imagery for studying oceanic internal waves. Radars are able to image internal waves because they are particularly sensitive to changes in the small-scale surface roughness (i.e. the capillary and ultragravity waves) present on the ocean surface which are altered by the velocity field associated with the internal waves. If, as seems likely, the greytone patterns of these images can be confirmed to correspond to trough and crest patterns of internal waves, then a great deal can be learnt about internal waves from satellite data. In this paper, the utility of wavelet analysis as a tool for oceanic internal wave detection and wavelength estimation is examined using both continuous and discrete versions of the wavelet transform. The theoretical background of each procedure is briefly described and applied using a specific "wavelet" for each case. In this first approach, the authors only consider supervised detection for the internal wave train detection problem. Normally, an unsupervised method using the two-dimensional (2D) wavelet transform is required for internal wave detection and orientation, including land-sea separation to avoid false alarms. They first present the construction of an appropriate wavelet basis, based on an oceanographic soliton internal wave analytical model, to detect and localize nonlinear wave signatures from SAR ocean image profiles. The structure of arbitrary wavelet basis derived from the compactly supported orthonormal B-splines wavelets is studied so as to obtain more optimal discrete wavelet decompositions. Comparisons are made for wavelet decompositions based on several families of compactly supported wavelets. Finally, the continuous wavelet transform is applied to estimate energies and wavelengths within soliton peaks from the detected internal wave trains. The advantages and drawbacks of the continuous and discrete wavelet transforms for the internal wave detection problem from SAR ocean image profiles are also discussed. The results from this study show that wavelet analysis is an excellent tool to detect internal waves against background noise, and to estimate, with a good degree of precision, soliton wavelengths from SAR ocean image profiles.

Neural pattern identification of railroad wheel-bearing faults from audible acoustic signals: comparison of FFT, CWT, and DWT features

Abstract: Current railroad wayside Hot Bearing Detector systems were developed in the 1960s to identify failing friction bearings. While the electronics used in these systems have been upgraded to microprocessor technology, the basic detection principles have not changed over the last 30 years. In this paper, we present a novel method to detect, recognize, and classify a variety of railroad wheel-bearing defects using audible acoustic signals at several different train speeds. Our algorithm consists of a data preprocessor, a feature extractor, and a single multilayer neural network. The feature extractor can use any one of four different transforms to generate feature vectors from input acoustic data: the fast Fourier transform (FFT), the continuous wavelet transform, the discrete wavelet transform, and the wavelet packet. The classification performance using each feature vector type is presented. This algorithm can be applied to many kinds of bearings in rotational machinery to perform nondestructive fault detection and identification.© (1997) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

The Continuous Wavelet Transform and Variable Resolution Time-Frequency Analysis

Abstract: W avelet transforms have recently emerged as a mathematical tool for multiresolution decomposition of signals. They have potential applications in many areas of signal processing that require variable time‐frequency localization. The continuous wavelet transform is presented here, and its frequency resolution is derived analytically and shown to depend exclusively on one parameter that should be carefully selected in constructing a variable resolution time‐frequency distribution for a given signal. Several examples of application to synthetic and real data are shown.

Application of wavelets in Doppler ultrasound

Abstract: Provides an introduction into wavelets and illustrates their application with two examples. The wavelet transform provides the analyst with a scaleable time‐frequency representation of the signal, which may uncover details not evidenced by conventional signal processing techniques. The signals used in this paper are Doppler ultrasound recordings of blood flow velocity taken from the internal carotid artery and the femoral artery. Shows how wavelets can be used as an alternative signal processing tool to the short time Fourier transform for the extraction of the time‐frequency distribution of Doppler ultrasound signals. Implements wavelet‐based adaptive filtering for the extraction of maximum blood velocity envelopes in the post processing of Doppler signals.

Improved transient signal detection using a wavepacket-based detector with an extended translation-invariant wavelet transform

Abstract: This paper presents the theory of M-band, extended translation-invariant (ETI) wavelet transforms. The ETI generalizes the translation-invariant wavelet transform of Weiss (1933). It is shown that iteration of the ETI, in a tree structure, provides a signal decomposition into an orthonormal wavepacket basis. Other properties such as translation invariance and invertibility of the transform are proven. The theory is then applied to transient signal detection through development of a family of translation-invariant wavepacket-based detectors. This family of detectors provides improved the performance over previously defined wavepacket-based detectors. A performance analysis is conducted. ROC curves generated by Monte-Carlo simulation are presented, indicating the detector performance. The detector performance is demonstrated to be independent of the signal translation.

Optical implementation of the fractional Hilbert transform for two-dimensional objects.

Abstract: The classical Hilbert transform can be implemented optically as a spatial-filtering process, whereby half the Fourier spectrum is π-phase shifted. Recently the Hilbert transform was generalized. The generalized version, called the fractional Hilbert transform, is quite easy to implement optically if the input is one dimensional. Here we show how to implement the fractional Hilbert transform for two-dimensional inputs. Hence the new transform is now suitable for image processing.

Method and apparatus for processing data from a tomographic imaging system

Abstract: An algorithm is created and applied to reconstruct the wavelet coefficients of an image from the Radon transform data for use in computed tomography, with a disclosed method that uses the properties of wavelets to localize the Radon transform such that a local region of the cross section of a body can be reconstructed using almost completely local data to significantly reduce the amount of exposure and computations in X-ray tomography. The described algorithm is based on the observation that for some wavelet bases with sufficiently many vanishing moments, the ramp-filtered version of the scaling function as well as the wavelet function has extremely rapid decay, with the variance of the elements of the nullspace is being negligible in the locally reconstructed image.

Wavelet for speech denoising

Abstract: This paper presents the use of the wavelet transform for noise reduction in noisy speech signals. The use of different wavelets and different orders have been evaluated for their suitability as a transform for speech noise removal. The wavelets evaluated are the biorthogonal wavelets, Daubechies wavelets, coiflets as well as symlets. Also two different means of filtering the noise in the transformed coefficients are presented. The first method is based on magnitude subtraction while the second method is based on the Wiener filter with a priori signal to noise ratio estimation.

The red-black wavelet transform

Abstract: We present a new kind of second generation wavelets on a rectangular grid. These wavelets are constructed using a 2D lifting scheme which is based on a red-black blocking scheme. Compared to classical tensor product wavelets on the same grid, these new wavelets show less anisotropy. The performance of the new wavelets is compared to tensor product wavelets in an image denoising application.

Wavelet Analysis of Wall-Pressure Fluctuations in a Supersonic Blunt-Fin Flow

Abstract: Measurements of wall-pressureuctuations in a Mach 3 ¯ ow over a blunt ® n wereanalyzed with the continuous wavelet transform. This technique offers a fresh approach to the problem of inferringow structure from the wall-pressure signal. The time scales associated with large-scale structures in theow turbulence and with shock crossing events are identi® ed as distinct local maxima in the distribution of energy over the wavelet scales. By using the extrema in the wavelet spectrum as a reference, the signal can be ® ltered in the space of wavelet scales to separate the contribution to the pressureuctuations ofow turbulence and separation shock motion.

Object wavelet transform for coding of arbitrarily shaped image segments

Abstract: Object-based coding is one of the most challenging key features which the ISO/IEC MPEG-4 is trying to standardize. One approach to transform an arbitrary shaped image region is addressed. The proposed approach called object-based wavelet transform (OWT), is simple to implement and is a smooth extension of regular wavelet transform (WT). The OWT consist of two phase processes: one is an extrapolation phase for regular WT and the other is a coefficients handling phase for eliminating redundancy caused by the extrapolation. Due to some experimental results, it is confirmed that the method performs the same as other shape-adaptive approaches with low complexity.

Detection of linear features using a localized Radon transform with a wavelet filter

Abstract: One problem of interest to the oceanic engineering community is the detection and enhancement of internal wakes in open water synthetic aperture radar (SAR) images. Internal wakes, which occur when a ship travels in a stratified medium, have a "V" shape extending from the ship, and a chirp-like feature across each arm. The Radon transform has been applied to the detection and the enhancement problems in internal wake images to account for the linear features while the wavelet transform has been applied to the enhancement problem in internal wake images to account for the chirp-like features. In this paper, a new transform, a localized Radon transform with a wavelet filter (LRTWF), is developed which accounts for both the linear and the chirp-like features of the internal wake. This transform is then incorporated into optimal and sub-optimal detection schemes for images (with these features) which are contaminated by additive Gaussian noise.

Spatio-temporal wavelet transforms for motion tracking

Abstract: This paper addresses the problem of detecting and tracking moving objects in digital image sequences. The main goal is to detect and select mobile objects in a scene, construct the trajectories, and eventually reconstruct the target objects or their signatures. It is assumed that the image sequences are acquired from imaging sensors. The method is based on spatio-temporal continuous wavelet transforms, discretized for digital signal analysis. It turns out that the wavelet transform can be used efficiently in a Kalman filtering framework to perform detection and tracking. Several families of wavelets are considered for motion analysis according to the specific spatio-temporal transformation. Their construction is based on mechanical parameters describing uniform motion, translation, rotation, acceleration, and deformation. The main idea is that each kind of motion generates a specific signal transformation, which is analyzed by a suitable family of continuous wavelets. The analysis is therefore associated with a set of operators that describe the signal transformations at hand. These operators are then associated with a set of selectivity criteria. This leads to a set of filters that are tuned to the moving objects of interest.

Wavelet modelling of transients in power systems

Abstract: This paper presents a new scheme to model transients in power systems. Since transients are nonstationary both in time and space, their analysis and characterization are difficult, and the traditional method of Fourier transform and short-time Fourier transform have their limitations in transient analysis. Here, the authors propose the use of a new time-frequency multiresolution wavelet analysis of transients in power systems. The final objective is to build an intelligent transient recorder, which is capable of detecting and classifying power system transients by type from the transient waveform signature based on an effective and efficient wavelet modelling and characterization.

Crackle detection and classification based on matched wavelet analysis

Abstract: Crackles have an explosive pattern in the time domain, with a rapid onset and a short duration. The timing, repeatability and shape of crackles are important parameters for diagnosis. Therefore, automatic detection of crackles and their classification have important clinical value. Since crackles have a general characteristic shape, it is obvious that wavelet analysis can be exploited to detect crackles and to classify them. In this paper, we present a new method for crackle detection which is based on a 'matched' wavelet transform. We first model crackles as a mathematical function. Then we design a matched wavelet based on this model. Applying a soft threshold to the results of the continuous wavelet transform to suppress noise further, the optimal scale can be obtained. Crackles can be detected based on the envelope of the signal at an optimal scale, and can be classified based on the energy distribution with scale. Theory, methods and experimental results are given in detail in this paper.

A comparative study of two biorthogonal wavelet transforms in time series prediction

Abstract: We present comparative results of time-series prediction preprocessed with two different wavelet transforms: (1) the compactly supported biorthogonal wavelet transform developed by Cohen, Daubechies, and Feauveau (1992), and (2) the semi-orthogonal wavelet transform, a class of biorthogonal wavelet transform, constructed by Cai and Wang (1996). Both theoretical and computational results of the two wavelet transforms are discussed. The major difference between the two wavelet transforms is the computational procedure. So far, only the semi-orthogonal wavelet transform of Cai and Wang can compute wavelet coefficients from a coarse scale level to a fine scale level, which makes the computation more flexible and cost effective. However, the compactly supported biorthogonal wavelet transform of Cohen et al. Has better decorrelation property. Thus, we found that the semi-orthogonal wavelet transform of Cai and Wang provides a faster computation process while the compactly supported biorthogonal wavelet transform provides better predicted wavelet coefficients in our experimental results. Based on the wavelet coefficients computed from signals, nonlinear prediction models utilizing recurrent neural networks are applied to predict wavelet coefficients at each scale level, Thus, the predicted signal is obtained from the reconstruction of predicted wavelet coefficients, In our experiments, the multi-step prediction using wavelet transforms gives much superior results than those obtained without using wavelet transforms. We applied our method to predict specific time series, intracranial pressure, acquired from head-trauma patients in the neuro intensive care unit at the University of Pittsburgh Medical Center.