Showing papers on "Harmonic wavelet transform published in 2002"

The curvelet transform for image denoising

Abstract: We describe approximate digital implementations of two new mathematical transforms, namely, the ridgelet transform and the curvelet transform. Our implementations offer exact reconstruction, stability against perturbations, ease of implementation, and low computational complexity. A central tool is Fourier-domain computation of an approximate digital Radon transform. We introduce a very simple interpolation in the Fourier space which takes Cartesian samples and yields samples on a rectopolar grid, which is a pseudo-polar sampling set based on a concentric squares geometry. Despite the crudeness of our interpolation, the visual performance is surprisingly good. Our ridgelet transform applies to the Radon transform a special overcomplete wavelet pyramid whose wavelets have compact support in the frequency domain. Our curvelet transform uses our ridgelet transform as a component step, and implements curvelet subbands using a filter bank of a/spl grave/ trous wavelet filters. Our philosophy throughout is that transforms should be overcomplete, rather than critically sampled. We apply these digital transforms to the denoising of some standard images embedded in white noise. In the tests reported here, simple thresholding of the curvelet coefficients is very competitive with "state of the art" techniques based on wavelets, including thresholding of decimated or undecimated wavelet transforms and also including tree-based Bayesian posterior mean methods. Moreover, the curvelet reconstructions exhibit higher perceptual quality than wavelet-based reconstructions, offering visually sharper images and, in particular, higher quality recovery of edges and of faint linear and curvilinear features. Existing theory for curvelet and ridgelet transforms suggests that these new approaches can outperform wavelet methods in certain image reconstruction problems. The empirical results reported here are in encouraging agreement.

The Illustrated Wavelet Transform Handbook

Abstract: (The correction deals with the fact that the complex Morlet wavelet has a non-zero See for example: The Illustrated Wavelet Transform Handbook: Introductory. The Illustrated Wavelet Transform Handbook: Introductory Theory and Applications in Science, Engineering, Medicine and Finance. CRC Press, Boca Raton. Tags: synchrosqueezing time-frequency analysis wavelet transform P.S. Addison, The Illustrated Wavelet Transform Handbook: Introductory Theory.

The Illustrated Wavelet Transform Handbook: Introductory Theory and Applications in Science, Engineering, Medicine and Finance

Abstract: PREFACE GETTING STARTED THE CONTINUOUS WAVELET TRANSFORM Introduction The Wavelet Requirements for the Wavelet The Energy Spectrum of the Wavelet The Wavelet Transform Identification of Coherent Structures Edge Detection The Inverse Wavelet Transform The Signal Energy: Wavelet-Based Energy and Power Spectra The Wavelet Transform in Terms of the Fourier Transform Complex Wavelets: The Morlet Wavelet The Wavelet Transform, Short Time Fourier Transform and Heisenberg Boxes Adaptive Transforms: Matching Pursuits Wavelets in Two or More Dimensions The CWT: Computation, Boundary Effects and Viewing Endnotes THE DISCRETE WAVELET TRANSFORM Introduction Frames and Orthogonal Wavelet Bases Discrete Input Signals of Finite Length Everything Discrete Daubechies Wavelets Translation Invariance Biorthogonal Wavelets Two-Dimensional Wavelet Transforms Adaptive Transforms: Wavelet Packets Endnotes FLUIDS Introduction Statistical Measures Engineering Flows Geophysical Flows Other Applications in Fluids and Further Resources ENGINEERING TESTING, MONITORING AND CHARACTERISATION Introduction Machining Processes: Control, Chatter, Wear and Breakage Rotating Machinery Dynamics Chaos Non-Destructive Testing Surface Characterisation Other Applications in Engineering and Further Resources MEDICINE Introduction The Electrocardiogram Neuroelectric Waveforms Pathological Sounds, Ultrasounds and Vibrations Blood Flow and Blood Pressure Medical Imaging Other Applications in Medicine FRACTALS, FINANCE, GEOPHYSICS AND OTHER AREAS Introduction Fractals Finance Geophysics Other Areas APPENDIX: USEFUL BOOKS, PAPERS AND WEBSITES Useful Books and Papers Useful Websites REFERENCES INDEX

Power quality analysis using S-transform

Abstract: This paper presents a new approach for power quality analysis using a modified wavelet transform known as the S-transform. The local spectral information of the wavelet transform can, with slight modification, be used to perform local cross spectral analysis with very good time resolution. The "phase correction" absolutely references the phase of the wavelet transform to the zero time point, thus assuring that the amplitude peaks are regions of stationary phase. The excellent time-frequency resolution characteristic of the S-transform makes it an attractive candidate for analysis of power system disturbance signals. Several power quality problems are analyzed using both the S-transform and discrete wavelet transform, showing clearly the advantage of the S-transform in detecting, localizing, and classifying the power quality problems.

The design of approximate Hilbert transform pairs of wavelet bases

Abstract: Several authors have demonstrated that significant improvements can be obtained in wavelet-based signal processing by utilizing a pair of wavelet transforms where the wavelets form a Hilbert transform pair. This paper describes design procedures, based on spectral factorization, for the design of pairs of dyadic wavelet bases where the two wavelets form an approximate Hilbert transform pair. Both orthogonal and biorthogonal FIR solutions are presented, as well as IIR solutions. In each case, the solution depends on an allpass filter having a flat delay response. The design procedure allows for an arbitrary number of vanishing wavelet moments to be specified. A Matlab program for the procedure is given, and examples are also given to illustrate the results.

Structural Damage Assessment Based on Wavelet Packet Transform

Abstract: Wavelet transform (WT) is a mathematical tool that can decompose a temporal signal into a summation of time-domain basis functions of various frequency resolutions. This simultaneous time-frequency decomposition gives the WT a special advantage over the traditional Fourier transform in analyzing nonstationary signals. One drawback of the WT is that its resolution is rather poor in the high-frequency region. Since structural damage is typically a local phenomenon captured most likely by high frequency modes, this potential drawback can affect the application of the wavelet-based damage assessment techniques. The wavelet packet transform (WPT) adopts redundant basis functions and hence can provide an arbitrary time-frequency resolution. In this study, a WPT-based method is proposed for the damage assessment of structures. Dynamic signals measured from a structure are first decomposed into wavelet packet components. Component energies are then calculated and used as inputs into neural network models for dama...

Studying Contact Stress Fields Caused by Surface Tractions With a Discrete Convolution and Fast Fourier Transform Algorithm

Abstract: The knowledge of contact stresses is critical to the design of a tribological element. It is necessary to keep improving contact models and develop efficient numerical methods for contact studies, particularly for the analysis involving coated bodies with rough surfaces. The fast Fourier Transform technique is likely to play an important role in contact analyses. It has been shown that the accuracy in an algorithm with the fast Fourier Transform is closely related to the convolution theorem employed. The algorithm of the discrete convolution and fast Fourier Transform, named the DC-FFT algorithm includes two routes of problem solving: DC-FFT/Influence coefficients/Green's, function for the cases with known Green's functions and DC-FFT/Influence coefficient/conversion, if frequency response functions are known. This paper explores the method for the accurate conversion for influence coefficients from frequency response functions, further improves the DC- FFT algorithm, and applies this algorithm to analyze the contact stresses in an elastic body under pressure and shear tractions for high efficiency and accuracy. A set of general formulas of the frequency response function for the elastic field is derived and verified. Application examples are presented and discussed.

Interpretation of wavelet analysis and its application in partial discharge detection

Abstract: The objective of the paper is to discuss a tool which is proving extremely efficient in partial discharge measurement studies. Though the technique itself is not new, its application to partial discharge studies is. It will be demonstrated in this paper that it has tremendous power and this accounts for its rapid growth as an application in this field. The paper begins with the description of the fundamentals of wavelet analysis, wavelet categories and the properties of the associated wavelet transforms. PD pulses as acquired from detectors composed of different detection circuits are investigated and numerically simulated, and a method on how to select optimally the wavelet corresponding to the representative forms of PD pulse is then presented. Finally, applications of wavelet analysis to partial discharge studies are explored. The paper demonstrates that the wavelet based denoising method proposed in the paper can be employed in separating PD pulses from electrical noise successfully and can be used in pulse propagation studies of partial discharge in distributed impedance plant to provide enhanced information and further infer the original site of the PD pulse.

Comparison of Wavelet Transform and FFT Methods in the Analysis of EEG Signals

Abstract: In this study, whether the wavelet transform method is better for spectral analysis of the brain signals is investigated For this purpose, as a spectral analysis tool, wavelet transform is compared with fast Fourier transform (FFT) applied to the electroencephalograms (EEG), which have been used in the previous studies In addition, the time-domain characteristics of the wavelet transform are also detected The comparison results show that the wavelet transform method is better in detecting brain diseases

Integer fast Fourier transform

Abstract: A concept of integer fast Fourier transform (IntFFT) for approximating the discrete Fourier transform is introduced. Unlike the fixed-point fast Fourier transform (FxpFFT), the new transform has the properties that it is an integer-to-integer mapping, is power adaptable and is reversible. The lifting scheme is used to approximate complex multiplications appearing in the FFT lattice structures where the dynamic range of the lifting coefficients can be controlled by proper choices of lifting factorizations. Split-radix FFT is used to illustrate the approach for the case of 2/sup N/-point FFT, in which case, an upper bound of the minimal dynamic range of the internal nodes, which is required by the reversibility of the transform, is presented and confirmed by a simulation. The transform can be implemented by using only bit shifts and additions but no multiplication. A method for minimizing the number of additions required is presented. While preserving the reversibility, the IntFFT is shown experimentally to yield the same accuracy as the FxpFFT when their coefficients are quantized to a certain number of bits. Complexity of the IntFFT is shown to be much lower than that of the FxpFFT in terms of the numbers of additions and shifts. Finally, they are applied to noise reduction applications, where the IntFFT provides significantly improvement over the FxpFFT at low power and maintains similar results at high power.

Fast wave-front reconstruction in large adaptive optics systems with use of the Fourier transform.

Abstract: Wave-front reconstruction with the use of the fast Fourier transform (FFT) and spatial filtering is shown to be computationally tractable and sufficiently accurate for use in large Shack–Hartmann-based adaptive optics systems (up to at least 10,000 actuators). This method is significantly faster than, and can have noise propagation comparable with that of, traditional vector–matrix-multiply reconstructors. The boundary problem that prevented the accurate reconstruction of phase in circular apertures by means of square-grid Fourier transforms (FTs) is identified and solved. The methods are adapted for use on the Fried geometry. Detailed performance analysis of mean squared error and noise propagation for FT methods is presented with the use of both theory and simulation.

Power quality disturbance data compression, detection, and classification using integrated spline wavelet and S-transform

Abstract: In this paper, power quality transient data are compressed and stored for analysis and classification purposes. From the compressed data set, original data are reconstructed and then analyzed using a modified wavelet transform known as S-transform. Compression techniques using splines are performed through signal decomposition, thresholding of wavelet transform coefficients, and signal reconstruction. Finally, the authors present compression results using splines and examine the application of splines compression in power quality monitoring to mitigate against data-communication and data-storage problems. Since S-transform has better time frequency and localization property, power quality disturbances are detected and then classified in a superior way than the recently used wavelet transform.

A simple adjustable window algorithm to improve FFT measurements

Abstract: The Fourier spectrum of a periodic signal may be obtained by fast Fourier transform algorithms, but, as is well known, special care must be taken to avoid severe distortions introduced by the sampling process. The main problem is the leakage generated by the truncation required to obtain a finite length sampled data. The usual procedure to reduce leakage is to multiply the sampled signal by a weighting window. Several kinds of windows have been proposed in the literature, and today they are also included in many commercial instruments. A simple alternative procedure is proposed in this paper. It is implemented with a PC compatible data acquisition board (DAQ) and consists of an algorithm that uses decimation and interpolation techniques. This algorithm is equivalent to the use of an adjustable sampling frequency and correspondingly an adjustable window size. Results obtained by this method on both harmonic and polyharmonic signals are empirically analyzed and compared with those given by an instrument with built-in FFT capabilities.

Wavelet transform applications in analytical chemistry

Abstract: The wavelet transform has been established with the Fourier transform as a data-processing method in analytical chemistry. The main fields of application in analytical chemistry are related to denoising, compression, variable reduction, and signal suppression. Analytical applications were selected showing prospects and limitations of the wavelet transform. An important aspect consists in showing the advantage of wavelet transform over Fourier transform with respect to dual localization of a signal in both the original and the transformed domain enabling principal new application fields in comparison with Fourier transform.

Wavelet transform-based fast feature extraction from temperature modulated semiconductor gas sensors

Abstract: We demonstrate that a single, thermally modulated tungsten oxide-based resistive sensor can discriminate between different vapours. The method uses a novel feature extraction and pattern classification method, which is based on the discrete wavelet transform (DWT). It was found that DWT outperformed fast Fourier transform (FFT) in the extraction of important features from the sensor response and, allowed for straightforward gas recognition in feature space.

Overcomplete image coding using iterative projection-based noise shaping

Abstract: Overcomplete transforms, like the dual-tree complex wavelet transform, offer more flexible signal representations than critically-sampled transforms. Large numbers of transform coefficients can be discarded without much reconstruction quality loss by forcing compensatory changes in the remaining coefficients. We develop and demonstrate a new and unique system for achieving these transform coding aims of coefficient elimination and compensation. The system is based on iterative projection of signals between the image domain and transform domain.

Undecimated Wavelet Transforms for Image De-noising

Abstract: A few different approaches exist for computing undecimated wavelet transform. In this work we construct three undecimated schemes and evaluate their performance for image noise reduction. We use standard wavelet based de-noising techniques and compare the performance of our algorithms with the original undecimated wavelet transform, as well as with the decimated wavelet transform. The experiments we have made show that our algorithms have better noise removal/blurring ratio.

Fast Fourier Transform for Discrete Asian Options

Abstract: This paper presents an e±cient methodology for the discrete Asian options consistent with di®erent types of underlying densities, especially non-normal returns as suggested by the empirical literature (Mandelbrot (1963) and Fama (1965)). Based on Fast Fourier Transform, the method is an enhanced version of the algorithm of Caverhill and Clewlow (1992). The contribution of this paper is to improve their algorithm and to adapt it to non-lognormal densities. This enables us to examine the impact of fat-tailed distribution on price