Showing papers on "Harmonic wavelet transform published in 1998"
Book•
01 Jan 1998
TL;DR: An introduction to a Transient World and an Approximation Tour of Wavelet Packet and Local Cosine Bases.
Abstract: Introduction to a Transient World. Fourier Kingdom. Discrete Revolution. Time Meets Frequency. Frames. Wavelet Zoom. Wavelet Bases. Wavelet Packet and Local Cosine Bases. An Approximation Tour. Estimations are Approximations. Transform Coding. Appendix A: Mathematical Complements. Appendix B: Software Toolboxes.
17,693 citations
16 Sep 1998
TL;DR: A new implementation of the Discrete Wavelet Transform is presented, suitable for a range of signal and image processing applications, that employs a dual tree of wavelet lters to obtain the real and imaginary parts of complex wavelet coeecients.
Abstract: A new implementation of the Discrete Wavelet Transform is presented, suitable for a range of signal and image processing applications. It employs a dual tree of wavelet lters to obtain the real and imaginary parts of complex wavelet coeecients. This introduces limited redundancy (4:1 for 2-dimensional signals) and allows the transform to provide approximate shift in-variance and directionally selective lters (properties lacking in the traditional wavelet transform) while preserving the usual properties of perfect reconstruction and computational eeciency. An application to texture synthesis is presented.
605 citations
08 Sep 1998
TL;DR: It is shown how the dual-tree complex wavelet transform can provide a good basis for multi-resolution image denoising and de-blurring.
Abstract: A new implementation of the Discrete Wavelet Transform is presented for applications such as image restoration and enhancement. It employs a dual tree of wavelet filters to obtain the real and imaginary parts of the complex wavelet coefficients. This introduces limited redundancy (4 : 1 for 2-dimensional signals) and allows the transform to provide approximate shift invariance and directionally selective filters (properties lacking in the traditional wavelet transform) while preserving the usual properties of perfect reconstruction and computational efficiency. We show how the dual-tree complex wavelet transform can provide a good basis for multi-resolution image denoising and de-blurring.
309 citations
TL;DR: In this article, a method for global Hurst exponent determination based on wavelets was proposed, and the results were compared to those obtained with Fourier spectral analysis when many samples are available.
Abstract: We propose a method for (global) Hurst exponent determination based on wavelets. Using this method, we analyze synthetic data with predefined Hurst exponents, fracture surfaces, and data from economy. The results are compared to those obtained with Fourier spectral analysis. When many samples are available, the wavelet and Fourier methods are comparable in accuracy. However, when one or only a few samples are available, the wavelet method outperforms the Fourier method by a large margin.
252 citations
TL;DR: It is shown that this multiresolution watermarking method is more robust to proposed methods to some common image distortions, such as the wavelet transform based image compression, image rescaling/stretching and image halftoning.
Abstract: In this paper, we introduce a new multiresolution watermarking method for digital images. The method is based on the discrete wavelet transform (DWT). Pseudo-random codes are added to the large coefficients at the high and middle frequency bands of the DWT of an image. It is shown that this method is more robust to proposed methods to some common image distortions, such as the wavelet transform based image compression, image rescaling/stretching and image halftoning. Moreover, the method is hierarchical.
213 citations
TL;DR: In this paper, a ridge extraction procedure using the modulus of the wavelet transform is presented, which employs the slowly-varying, time-dependent amplitude and phase functions of the impulse response of the system.
197 citations
18 May 1998
TL;DR: In this article, the authors provide the theoretical basis for and demonstrate the practical application of power and rms measurements directly from the wavelet transform data associated with each voltage current element pair.
Abstract: This paper provides the theoretical basis for and demonstrates the practical application of power and rms measurements directly from the wavelet transform data associated with each voltage current element pair. The voltage and current wavelet transforms are derived from concurrent measurements using a common orthonormal wavelet basis. The advantage of using the wavelet transform data directly is that it provides the distribution of the power and energy with respect to the individual frequency bands associated with each level of the wavelet analysis. Frequency separation into the various wavelet levels is achieved using IIR filters because their magnitude characteristics are much better than typical FIR filters of equivalent complexity. The IIR polyphase network strategy yields a simpler wavelet filter bank design.
180 citations
12 May 1998
TL;DR: This paper develops two new adaptive wavelet transforms based on the lifting scheme, which exploits a spatial-domain, prediction-error interpretation of the wavelet transform and provides a powerful framework for designing customized transforms.
Abstract: This paper develops two new adaptive wavelet transforms based on the lifting scheme. The lifting construction exploits a spatial-domain, prediction-error interpretation of the wavelet transform and provides a powerful framework for designing customized transforms. We use the lifting construction to adaptively tune a wavelet transform to a desired signal by optimizing data-based prediction error criteria. The performances of the new transforms are compared to existing wavelet transforms, and applications to signal denoising are investigated.
152 citations
01 Mar 1998
TL;DR: In this paper, a novel approach using the short-time Fourier transform and wavelet transform (time-frequency analysis tools) for fault detection during impulse testing of power transformers is described.
Abstract: A novel approach using the short-time. Fourier transform and wavelet transform (time-frequency analysis tools) for fault detection during impulse testing of power transformers is described. The neutral and/or capacitively transferred currents which are recorded during an impulse test can be directly analysed with this approach. These currents are considered to be evolving in time, i.e. as nonstationary signals, especially when there is a fault. Results from simulation studies are presented wherein the fault condition is modelled as a fast decaying transient superposed on the neutral current. A comparison of the two transforms is made to assess their ability to detect as small a fault as possible and other implemenational issues. Advantages of these methods over the conventional transfer function method are demonstrated, and it appears that the wavelet transform is better suited for this task.
102 citations
01 Jan 1998
TL;DR: Comparison between the quincunx and the traditional wavelet decomposition suggests that the quINCunx transform is more appropriate for characterization of noisy data, and practical applications, requiring description with lower rotational sensitivity.
Abstract: This paper describes a new approach for texture characterization, based on nonseparable wavelet decomposition, and its application for the discrimination of visually similar diffuse diseases of liver. The proposed feature-extraction algo- rithm applies nonseparable quincunx wavelet transform and uses energies of the transformed regions to characterize textures. Classification experiments on a set of three different tissue types show that the scale/frequency approach, particularly one based on the nonseparable wavelet transform, could be a reliable method for a texture characterization and analysis of B-scan liver images. Comparison between the quincunx and the traditional wavelet decomposition suggests that the quincunx transform is more appropriate for characterization of noisy data, and practical applications, requiring description with lower rotational sensitivity.
98 citations
TL;DR: In this paper, a new approach for texture characterization, based on nonseparable wavelet decomposition, and its application for the discrimination of visually similar diffuse diseases of liver was described.
Abstract: This paper describes a new approach for texture characterization, based on nonseparable wavelet decomposition, and its application for the discrimination of visually similar diffuse diseases of liver. The proposed feature-extraction algorithm applies nonseparable quincunx wavelet transform and uses energies of the transformed regions to characterize textures. Classification experiments on a set of three different tissue types show that the scale/frequency approach, particularly one based on the nonseparable wavelet transform, could be a reliable method for a texture characterization and analysis of B-scan liver images. Comparison between the quincunx and the traditional wavelet decomposition suggests that the quincunx transform is more appropriate for characterization of noisy data, and practical applications, requiring description with lower rotational sensitivity.
TL;DR: In this paper, the authors introduced a wavelet transform technique based on the detection of the multi-scale view of the components of a signal, which can be used for space-frequency localization and analysis of roughness and waviness motifs.
Abstract: This work introduces a wavelet transform technique based on the detection of the multi-scale view of the components of a signal . The main advantages of wavelet transform over the existing signal processing techniques are its space-frequency localization and multi-scale analysis of roughness and waviness motifs. After an extensive review of the mathematical and signal processing fundamentals of the wavelet technique, numerical implementations are carried out to explore the potential applications of wavelet transform and its inverse transform multi-scale analysis of roughness and local morphological characterization by the detection of the roughness singularities and 21) motif size of an engineered surface.
TL;DR: This work allows the fractional Fourier transform orders to be specified independently for the two dimensions but also allow the input and output scale parameters and the residual spherical phase factors to be controlled.
Abstract: We provide a general treatment of optical two-dimensional fractional Fourier transforming systems. We not only allow the fractional Fourier transform orders to be specified independently for the two dimensions but also allow the input and output scale parameters and the residual spherical phase factors to be controlled. We further discuss systems that do not allow all these parameters to be controlled at the same time but are simpler and employ a fewer number of lenses. The variety of systems discussed and the design equations provided should be useful in practical applications for which an optical fractional Fourier transforming stage is to be employed.
TL;DR: In this article, the phase-corrected maximal overlap discrete wavelet packet transform (MODWPT) is applied to a non-stationary time series of hourly averaged Southern Hemisphere solar magnetic field magnitude data acquired by the Ulysses spacecraft.
Abstract: This paper is concerned with the development and application of the phase–corrected maximal overlap discrete wavelet packet transform (MODWPT). The discrete cyclic filtering steps of the MODWPT are fully explained. Energy preservation is proven. With filter coefficients chosen from Daubechie's least asymmetric class, the optimum time shifts to apply to ensure approximate zero phase filtering at every level of the MODWPT are studied, and applied to the wavelet packet coefficients to give phase corrections which ensure alignment with the original time series. Also, the time series values at each time are decomposed into details associated with each frequency band, and these line up perfectly with features in the original time series since the details are shown to arise through exact zero phase filtering.
The phase–corrected MODWPT is applied to a non–stationary time series of hourly averaged Southern Hemisphere solar magnetic field magnitude data acquired by the Ulysses spacecraft. The occurrence times of the shock waves previously determined via manual pattern matching on the raw data match those times in the time–frequency plot where a broadband spectrum is obtained; in other words, the phase–corrected MODWPT provides an approach to picking the location of complicated events. We demonstrate the superiority of the MODWPT in interpreting timing information over two competing methods, namely the cosine packet transform (or ‘local cosine transform’), and the short–time Fourier transform.
TL;DR: Although there exists an infinite variety of wavelet transformations, 22 orthonormal wavelet transforms that are typically used, which include Haar, 9 daublets, 5 coiflets, and 7 symmlets, were evaluated and four threshold selection methods have been studied.
Abstract: Discrete wavelet transform (DWT) denoising contains three steps: forward transformation of the signal to the wavelet domain, reduction of the wavelet coefficients, and inverse transformation to the native domain. Three aspects that should be considered for DWT denoising include selecting the wavelet type, selecting the threshold, and applying the threshold to the wavelet coefficients. Although there exists an infinite variety of wavelet transformations, 22 orthonormal wavelet transforms that are typically used, which include Haar, 9 daublets, 5 coiflets, and 7 symmlets, were evaluated. Four threshold selection methods have been studied: universal, minimax, Stein's unbiased estimate of risk (SURE), and minimum description length (MDL) criteria. The application of the threshold to the wavelet coefficients includes global (hard, soft, garrote, and firm), level-dependent, data-dependent, translation invariant (TI), and wavelet package transform (WPT) thresholding methods. The different DWT-based denoising m...
Book•
30 Nov 1998TL;DR: In this article, the NDFT was used to construct a 1-D and 2-D antenna pattern synthesis with Prescribed Nulls, and the Dual-Tone Multi-Frequency Signal Decoding (DTMSD) was proposed.
Abstract: 1. Introduction. 2. The Nonuniform Discrete Fourier Transform. 3. 1-D Fir Filter Design Using the NDFT. 4. 2-D Fir Filter Design Using the NDFT. 5. Antenna Pattern Synthesis with Prescribed Nulls. 6. Dual-Tone Multi-Frequency Signal Decoding. 7. Conclusions. References. Index.
TL;DR: By using the Fourier representation and the fast Fourier transform, one generation of the infinite population simple genetic algorithm can be computed in time O(cl log2 3), where c is arity of the alphabet and l is the string length.
Abstract: This paper is the first part of a two-part series. It proves a number of direct relationships between the Fourier transform and the simple genetic algorithm. (For a binary representation, the Walsh transform is the Fourier transform.) The results are of a theoretical nature and are based on the analysis of mutation and crossover. The Fourier transform of the mixing matrix is shown to be sparse. An explicit formula is given for the spectrum of the differential of the mixing transformation. By using the Fourier representation and the fast Fourier transform, one generation of the infinite population simple genetic algorithm can be computed in time O(cl log2 3), where c is arity of the alphabet and l is the string length. This is in contrast to the time of O(c3l) for the algorithm as represented in the standard basis. There are two orthogonal decompositions of population space that are invariant under mixing. The sequel to this paper will apply the basic theoretical results obtained here to inverse problems and asymptotic behavior.
Book•
01 Jan 1998
TL;DR: In this article, the Generalized Gabor Scheme and its application in Signal and Image Representation are discussed, as well as its applications in signal processing and image analysis. But the authors do not discuss the application of the generalized Gabor scheme in signal and image representation.
Abstract: Variations of Windowed Fourier Transform and Applications: M. An, A. Brozdzik, I. Gertner, and R. Tolimieri, Weyl-Heisenberg Systems and the Finite Zak Transform. M.J. Bastiaans, Gabors Expansion and the Zak Transform for Continuous-Time and Discrete-Time Signals. W. Schempp, Non-Commutative Affine Geometry and Symbol Calculus: Fourier Transform Magnetic Resonance Imaging and Wavelets. M. Zibulski and Y.Y. Zeevi, The Generalized Gabor Scheme and Its Application In Signal and Image Representation. Construction for Special Waveforms for Specific Tasks: J.S. Byrnes, A Low Complexity Energy Spreading Transform Coder. A. Cohen and N. Dyn, Nonstationary Subdivision Schemes, Multiresolution Analysis, and Wavelet Packets. J. Prestin and K. Selig, Interpolatory and Orthonormal Trigonometric Waves. Redundant Waveform Representations for Signal Processing and Image Analysis: J.J. Benedetto, Noise Reduction in Termsof the Theory of Frames. F. Bergeaud and S. Mallat, Matching Pursuit of Images. Z. Cvetkovi( and M. Vetterli, Overcomplete Expansions and Robustness. Numerical Compression and Applications: A. Averbuch, G. Beylkin, R. Coifman, and M.Israeli, Multiscale Inversion of Elliptic Operators. A. Harten, Multiresolution Representation of Cell-Averaged Data: A Promotional Review. Analysis of Waveform Representations: C.K. Chui and C. Li, Characterizations of Smoothness viaFunctional Wavelet Transforms. M.A. Kon and L.A. Raphael, Characterizing Convergence Rates for Multiresolution. B. Rubin, On Calderon's Reproducing Formula. B. Rubin, Continuous Wavelet Transforms on a Sphere. V.A. Zheludev, Periodic Splines, Harmonic Analysis, and Wavelets. Filter Banks and Image Coding: A.J.E.M. Janssen, A Density Theorem for Time-Continuous Filter Banks. V.E. Katsnelson, Sampling and Interpolation for Functions with Multi-Band Spectrum: The Mean Periodic Continuation Method. R. Lenz and J. Svanberg, Group Theoretical Transforms, Statistical Properties of Image Spaces and Image Coding. Subject Index.
TL;DR: The continuous wavelet transform can be used to produce spectrograms which show the frequency content of sounds (or other signals) as a function of time in a manner analogous to sheet music as discussed by the authors.
Abstract: The continuous wavelet transform can be used to produce spectrograms which show the frequency content of sounds (or other signals) as a function of time in a manner analogous to sheet music. While this technique is commonly used in the engineering community for signal analysis, the physics community has, in our opinion, remained relatively unaware of this development. Indeed, some find the very notion of frequency as a function of time troublesome. Here spectrograms will be displayed for familiar sounds whose pitches change with time, demonstrating the usefulness of the continuous wavelet transform.
14 Oct 1998
TL;DR: The Fourier transform is a very useful tool for signal studies as mentioned in this paper. Nevertheless there are many problems in using it; but these problems are very well known and correctly explained in literature.
Abstract: The Fourier transform is a very useful tool for signal studies. Nevertheless there are many problems in using it; but these problems are very well known and correctly explained in literature. Wavelets are not usual in power network analysis. However, they are easy to use and give good results; the edge effects are transient and the computation time may be reasonable. Prony analysis is only found in a few papers about power networks. There are few high-performance decomposition programs. The best ones remain sensitive to noise. They require a long observation time with many samples. But, when the analysis succeed, this method is the most powerful to explain what happens in a power network transient. This paper explains as simply as possible the wavelet and the Prony analyses and shows, qualitatively, their performances and their limits.
TL;DR: In this paper, a novel method based on wavelet transform is proposed for approximate derivative calculation. And the optimal results for both synthetic and experimental data were obtained with the use of the Daubechies wavelet functions D8 and D18.
Abstract: A novel method based on wavelet transform is proposed in this work for approximate derivative calculation. An approximate first derivative of an analytical signal can be expressed as the difference between the two scale coefficients C1, which were generated from any two Daubechies wavelet functions. The optimal results for both synthetic and experimental data were obtained with the use of the Daubechies wavelet functions D8 and D18. Our work demonstrated that the new method can enhance the signal-to-noise ratio at higher order derivative calculation and retain all major properties of the conventional methods.
Book•
31 Aug 1998
TL;DR: Signals and Systems.
Abstract: Signals and Systems. Fourier Analysis. Sampling. The Z-Transform. Transform Analysis of Systems. The DFT. The Fast Fourier Transform. Implementation of Discrete-Time Systems. Filter Design.
TL;DR: In this article, a fast pseudospectral method on the sphere developed by Merilees in 1973, recently revived by Fornberg, was examined and compared to the traditional spectral transform method.
TL;DR: The fundamentals of Fourier analysis are reviewed with emphasis on the analysis of transient signals, and the human saccade is considered to illustrate the pitfalls and advantages of various Fourier analyses.
TL;DR: In this paper, a numerical algorithm based on a single fast Fourier transform is proposed, which shows better precision and calculation efficiency than those of previously published algorithms, and if specific conditions are met, the numerical calculations of two successive fractional Fourier transforms produce results that are similar to the analytical solution.
Abstract: A numerical algorithm based on a single fast Fourier transform is proposed. Its precision and calculation efficiency show better performance than those of previously published algorithms. It is also shown that if specific conditions are met, the numerical calculations of two successive fractional Fourier transforms produce results that are similar to the analytical solution.
13 Sep 1998
TL;DR: A combination of the discrete wavelet transform and the Wiener filter is applied to the noise-reduction of high-resolution ECG signals and was compared to a popular de-noising algorithm by Donoho (1993) on artificially generated signals and on a high- resolution ECG signal corrupted by noise.
Abstract: In this study the authors applied a combination of the discrete wavelet transform and the Wiener filter to the noise-reduction of high-resolution ECG signals. The procedure is optimal in the least squares sense in that it separates a signal from additive noise. It was compared to a popular de-noising algorithm by Donoho (1993) on artificially generated signals and on a high-resolution ECG signal corrupted by noise.
TL;DR: The coefficient position retaining (CPR) method is proposed to handle data with length of odd number and it is indicated that the proposed WT methods works better than FFT in compression of IR spectra and spectral library searching.
TL;DR: Frick et al. as discussed by the authors proposed a modified continuous wavelet transform for spectral analysis of data with gaps, which is based on a family of functions called "gapped wavelets" which fulfill the admissibility condition on the gapped support.
Abstract: A recently introduced algorithm [Frick et al., Astrophys. J. 483, 426 (1997)] of spectral analysis of data with gaps via a modified continuous wavelet transform is developed and studied. This algorithm is based on a family of functions called "gapped wavelets" which fulfill the admissibility condition on the gapped support. The wavelet family is characterized by an additional parameter which should be calculated for every scale and position. Three theorems concerning the properties of gapped wavelet transform are formulated and proved. They affirm the global stability of the algorithm as well as its stability in both limits of large and small scales. These results are illustrated by some numerical examples, which show that the algorithm really attenuates the artifacts coming from gaps (and/or boundaries), and is particularly efficient at small and large scales.
Patent•
16 Sep 1998
TL;DR: In this article, a modified transform method is used to transform the transformed domain image back to the original spatial domain image, which yields spatial domain images that are re-sized versions of the original space domain image.
Abstract: Digital images are represented in the spatial domain by numbers that correspond to pixels and may be transformed to a transform domain image by means of a Transform Method. Other Transform Methods are used to transform the transform domain image back to the original spatial domain image. In this invention, these other Transform Methods are modified in such a way that the Modified Transform Method yields spatial domain images that are re-sized versions of the original spatial domain image. Methods are disclosed for employing the Modified Transform Method to implement zoomed and panned versions of the re-sized images. The re-sized images do not require pixel-level smoothing filters and other methods for removing image distortions due to re-sizing.
TL;DR: A recursive algorithm to implement phase retrieval from two intensities in the fractional Fourier transform domain is proposed that can significantly simplify computational manipulations and does not need an initial phase estimate compared with conventional iterative algorithms.
Abstract: We first discuss the discrete fractional Fourier transform and present some essential properties. We then propose a recursive algorithm to implement phase retrieval from two intensities in the fractional Fourier transform domain. This approach can significantly simplify computational manipulations and does not need an initial phase estimate compared with conventional iterative algorithms. Simulation results show that this approach can successfully recover the phase from two intensities.