Showing papers on "Harmonic wavelet transform published in 2005"
TL;DR: Several methods for filter design are described for dual-tree CWT that demonstrates with relatively short filters, an effective invertible approximately analytic wavelet transform can indeed be implemented using the dual- tree approach.
Abstract: The paper discusses the theory behind the dual-tree transform, shows how complex wavelets with good properties can be designed, and illustrates a range of applications in signal and image processing The authors use the complex number symbol C in CWT to avoid confusion with the often-used acronym CWT for the (different) continuous wavelet transform The four fundamentals, intertwined shortcomings of wavelet transform and some solutions are also discussed Several methods for filter design are described for dual-tree CWT that demonstrates with relatively short filters, an effective invertible approximately analytic wavelet transform can indeed be implemented using the dual-tree approach
2,407 citations
TL;DR: In this review, the emerging role of the wavelet transform in the interrogation of the ECG is discussed in detail, where both the continuous and the discrete transform are considered in turn.
Abstract: The wavelet transform has emerged over recent years as a powerful time-frequency analysis and signal coding tool favoured for the interrogation of complex nonstationary signals. Its application to biosignal processing has been at the forefront of these developments where it has been found particularly useful in the study of these, often problematic, signals: none more so than the ECG. In this review, the emerging role of the wavelet transform in the interrogation of the ECG is discussed in detail, where both the continuous and the discrete transform are considered in turn.
794 citations
TL;DR: In this letter, a precise relationship between RDWT-domain and original-signal-domain distortion for additive white noise in the RDWT domain is derived.
Abstract: The behavior under additive noise of the redundant discrete wavelet transform (RDWT), which is a frame expansion that is essentially an undecimated discrete wavelet transform, is studied. Known prior results in the form of inequalities bound distortion energy in the original signal domain from additive noise in frame-expansion coefficients. In this letter, a precise relationship between RDWT-domain and original-signal-domain distortion for additive white noise in the RDWT domain is derived.
331 citations
01 Jan 2005
TL;DR: In this article, the Plancherel Transform for Locally Compact Group (PCG) and Wavelet Transformer Transform for Group Representation (WPT) are presented.
Abstract: Introduction.- Wavelet Transforms and Group Representations.- The Plancherel Transform for Locally Compact Groups.- Plancherel Inversion and Wavelet Transforms.- Admissible Vectors for Group Extension.- Sampling Theorems for the Heisenberg Group.- References.- Index.
314 citations
TL;DR: Results prove that, with the proposed methodology, in conjunction with the algorithms proposed by the authors to select optimal mother wavelet and threshold values, significant improvement in denoising effect can be achieved.
Abstract: Recent research has shown that the wavelet transform (WT) can potentially be used to extract partial discharge (PD) pulses from severe noise. However, the method is more complex than the Fourier transform (FT), and requires expertise and experience to be applied to produce its best effect. The authors have previously published algorithms for selection of the most appropriate mother wavelet and for automatic determination of threshold values for applying the WT to PD measurement denoising. The present paper is to present an improved methodology to apply the discrete wavelet transform (DWT) with better denoising effect to PD measurement. Firstly the paper describes the structure of DWT's filter pairs. It then analyses the frequency bands of the wavelet coefficients in approximations and details, and energy distribution of a PD signal along each of the levels following the DWT. Finally a DWT-based denoising method is proposed and justified. Results prove that, with the proposed methodology, in conjunction with the algorithms proposed by the authors to select optimal mother wavelet and threshold values, significant improvement in denoising effect can be achieved.
185 citations
TL;DR: A new rotation-invariant texture-analysis technique using Radon and wavelet transforms and a k-nearest neighbors classifier is employed to classify texture patterns, it is shown that the extracted features generate an efficient orthogonal feature space.
Abstract: A new rotation-invariant texture-analysis technique using Radon and wavelet transforms is proposed. This technique utilizes the Radon transform to convert the rotation to translation and then applies a translation-invariant wavelet transform to the result to extract texture features. A k-nearest neighbors classifier is employed to classify texture patterns. A method to find the optimal number of projections for the Radon transform is proposed. It is shown that the extracted features generate an efficient orthogonal feature space. It is also shown that the proposed features extract both of the local and directional information of the texture patterns. The proposed method is robust to additive white noise as a result of summing pixel values to generate projections in the Radon transform step. To test and evaluate the method, we employed several sets of textures along with different wavelet bases. Experimental results show the superiority of the proposed method and its robustness to additive white noise in comparison with some recent texture-analysis methods.
167 citations
TL;DR: A new method is presented that is capable of extracting the full 2D phase distribution from a single fringe pattern and is compared with the Fourier transform and the integration methods, and an important conclusion that the phase of the optical fringe pattern is equal to thephase of its wavelet transform on the ridge of the wave let transform is theoretically clarified.
Abstract: A new method for phase retrieval of optical fringe patterns is presented This method is based on a wavelet transform and is capable of extracting the full 2D phase distribution from a single fringe pattern An important conclusion that the phase of the optical fringe pattern is equal to the phase of its wavelet transform on the ridge of the wavelet transform is theoretically clarified The method is compared with the Fourier transform and the integration methods A numerical simulation and an experimental example of phase retrieval are shown
153 citations
Journal Article•
TL;DR: In this article, the authors discuss discrete fractional Fourier transform (DFRFT), time-frequency distributions related to FRFT, optimal filter and beamformer in FRFT domain, filtering using window functions and other fractional transforms along with simulation results.
Abstract: The fractional Fourier transform (FRFT) is the generalization of the classical Fourier transform. It depends on a parameter ? (= a ?/2) and can be interpreted as a rotation by an angle ? in the time-frequency plane or decomposition of the signal in terms of chirps. This paper discusses discrete FRFT (DFRFT), time-frequency distributions related to FRFT, optimal filter and beamformer in FRFT domain, filtering using window functions and other fractional transforms along with simulation results.
103 citations
TL;DR: In this paper, a model-based approach to determine the propagation operator in the wavelet domain, which depends nonlinearly on a set of unknown parameters, explicitly defining the phase velocity, the group velocity and the attenuation.
Abstract: In this paper, we propose a method of surface waves characterization based on the deformation of the wavelet transform of the analysed signal. An estimate of the phase velocity (the group velocity) and the attenuation coefficient is carried out using a model-based approach to determine the propagation operator in the wavelet domain, which depends nonlinearly on a set of unknown parameters. These parameters explicitly define the phase velocity, the group velocity and the attenuation. Under the assumption that the difference between waveforms observed at a couple of stations is solely due to the dispersion characteristics and the intrinsic attenuation of the medium, we then seek to find the set of unknown parameters of this model. Finding the model parameters turns out to be that of an optimization problem, which is solved through the minimization of an appropriately defined cost function. We show that, unlike time-frequency methods that exploit only the square modulus of the transform, we can achieve a complete characterization of surface waves in a dispersive and attenuating medium. Using both synthetic examples and experimental data, we also show that it is in principle possible to separate different modes in both the time domain and the frequency domain
94 citations
16 May 2005
TL;DR: In this article, a wavelet-packet transform (WPT) was proposed to decompose the voltage/current waveforms into uniform frequency bands corresponding to the odd harmonic components of the signal, and the results obtained using DFT analysis and the harmonic group concept introduced by the International Electrotechnical Commission using different test waveforms proposed in standard IEC-61000-4-7.
Abstract: The paper proposes an algorithm based on the wavelet-packet transform for the analysis of harmonics in power systems. The algorithm proposed decomposes the voltage/current waveforms into uniform frequency bands corresponding to the odd harmonic components of the signal. First, the selection of the mother wavelet, the sampling frequency and the frequency characteristics of the selected wavelet filter bank are studied. Finally the performance of the method proposed is compared with the results obtained using DFT analysis and the harmonic group concept introduced by the International Electrotechnical Commission using different test waveforms proposed in standard IEC-61000-4-7
88 citations
TL;DR: Simulated data have been used to analyze the artefacts produced by the Lagrange interpolation and the proposed non-linear sampling scheme is simple and highly robust since no parameters need to be adjusted by the user.
Abstract: Rapid acquisition of high-resolution 2D and 3D NMR spectra is essential for studying biological macromolecules. In order to minimize the experimental time, a non-linear sampling scheme is proposed for the indirect dimensions of multidimensional experiments. These data can be processed using the algorithm proposed by Dutt and Rokhlin (Appl. Comp. Harm. Anal. 1995, 2, 85–100) for fast Fourier transforms of non equispaced data. Examples of 1H−15N HSQC spectra are shown, where crowded correlation peaks can be resolved using non-linear acquisition. Simulated data have been used to analyze the artefacts produced by the Lagrange interpolation. As compared to non-linear processing methods, this algorithm is simple and highly robust since no parameters need to be adjusted by the user.
TL;DR: In this article, an asymptotic expression of the full propagator in wavelet space that comprises the phase velocity as well is given, which establishes a relationship between the observed signals at two different stations during wave propagation in a dispersive and attenuating medium.
Abstract: In the estimate of dispersion with the help of wavelet analysis considerable emphasis has been put on the extraction of the group velocity using the modulus of the wavelet transform. In this paper we give an asymptotic expression of the full propagator in wavelet space that comprises the phase velocity as well. This operator establishes a relationship between the observed signals at two different stations during wave propagation in a dispersive and attenuating medium. Numerical and experimental examples are presented to show that the method accurately models seismic wave dispersion and attenuation.
TL;DR: In this paper, the authors discuss the principle and procedures of the second-generation wavelet transform and its application to the denoising of seismic data, which is a flexible wavelet construction method using linear and nonlinear spatial prediction.
Abstract: This paper discusses the principle and procedures of the second-generation wavelet transform and its application to the denoising of seismic data. Based on lifting steps, it is a flexible wavelet construction method using linear and nonlinear spatial prediction and operators to implement the wavelet transform and to make it reversible. The lifting scheme transform -includes three steps: split, predict, and update. Deslauriers-Dubuc (4, 2) wavelet transforms are used to process both synthetic and real data in our second-generation wavelet transform. The processing results show that random noise is effectively suppressed and the signal to noise ratio improves remarkably. The lifting wavelet transform is an efficient algorithm.
TL;DR: Kingsbury's dual-tree complex wavelet transform in the frequency domain is examined, where it can be formulated for standard wavelet filters without special filter design and applied to the classification of signals.
Abstract: We examine Kingsbury's dual-tree complex wavelet transform in the frequency domain, where it can be formulated for standard wavelet filters without special filter design and apply the method to the classification of signals. The obtained transforms achieve low shift sensitivity and better directionality compared to the real discrete wavelet transform while retaining the perfect reconstruction property.
01 Oct 2005
TL;DR: This work combines wavelet filters adaptive to edge orientations with quincunx subsampling to form a 2-D nonseparable transform through lifting that exploits local image properties for image compression.
Abstract: We propose a novel adaptive wavelet transform that exploits local image properties for image compression. It combines wavelet filters adaptive to edge orientations with quincunx subsampling to form a 2-D nonseparable transform through lifting. Filter selections are efficiently represented. Significant improvement on both subjective and objective quality over the conventional separable transform is observed. In addition, unlike previous adaptive transforms, the symmetry in quincunx subsampling enables even quality for image features along different directions and the compression performance is insensitive to image orientation
TL;DR: The contribution of this work is to generalize the real and complex wavelet transforms and to derive for the first time a quaternionic wavelet pyramid for multi-resolution analysis using the quaternion phase concept.
Abstract: This paper presents the theory and practicalities of the quaternion wavelet transform. The contribution of this work is to generalize the real and complex wavelet transforms and to derive for the first time a quaternionic wavelet pyramid for multi-resolution analysis using the quaternion phase concept. The three quaternion phase components of the detail wavelet filters together with a confidence mask are used for the computation of a denser image velocity field which is updated through various levels of a multi-resolution pyramid. Our local model computes the motion by the linear evaluation of the disparity equations involving the three phases of the quaternion detail high-pass filters. A confidence measure singles out those regions where horizontal and vertical displacement can reliably be estimated simultaneously. The paper is useful for researchers and practitioners interested in the theory and applications of the quaternion wavelet transform.
TL;DR: In this paper, a multidimensional, mapping-based, complex wavelet transform is proposed to overcome the drawbacks of the discrete wavelet transformation (DWT) such as shift sensitivity, poor directionality, and lack of phase information.
Abstract: Although the discrete wavelet transform (DWT) is a powerful tool for signal and image processing, it has three serious disadvantages: shift sensitivity, poor directionality, and lack of phase information. To overcome these disadvantages, we introduce multidimensional, mapping-based, complex wavelet transforms that consist of a mapping onto a complex function space followed by a DWT of the complex mapping. Unlike other popular transforms that also mitigate DWT shortcomings, the decoupled implementation of our transforms has two important advantages. First, the controllable redundancy of the mapping stage offers a balance between degree of shift sensitivity and transform redundancy. This allows us to create a directional, nonredundant, complex wavelet transform with potential benefits for image coding systems. To the best of our knowledge, no other complex wavelet transform is simultaneously directional and nonredundant. The second advantage of our approach is the flexibility to use any DWT in the transform implementation. As an example, we exploit this flexibility to create the complex double-density DWT: a shift-insensitive, directional, complex wavelet transform with a low redundancy of (3/sup M/-1)/(2/sup M/-1) in M dimensions. No other transform achieves all these properties at a lower redundancy, to the best of our knowledge. By exploiting the advantages of our multidimensional, mapping-based complex wavelet transforms in seismic signal-processing applications, we have demonstrated state-of-the-art results.
14 Nov 2005
TL;DR: The proposed hybrid wavelets and DFB (HWD) transform family provides visual and PSNR improvements over the wavelet and contourlet transforms.
Abstract: We propose a new family of perfect reconstruction, non-redundant, and multiresolution geometrical image transforms using the wavelet transform in conjunction with modified versions of directional filter banks (DFB). In the proposed versions of DFB, we use either horizontal or vertical directional decomposition. Taking advantage of the wavelet transform that has efficient nonlinear approximation property, we add the important feature of directionality by applying the modified and regular DFB to the subbands of a few finest wavelet levels. This way we can eliminate a major portion of the artifacts usually introduced when DFB are used. The proposed hybrid wavelets and DFB (HWD) transform family provides visual and PSNR improvements over the wavelet and contourlet transforms.
01 Jan 2005
TL;DR: Two performance criteria are proposed to measure the quality of a wavelet, based on the principle of maximization of variance, which is illustrated and evaluated by means of a worked example from biomedicine in the area of cardiac signal processing.
Abstract: The question of designing the best wavelet for a given signal is discussed from the perspective of orthogonal filter banks. Two performance criteria are proposed to measure the quality of a wavelet, based on the principle of maximization of variance. The method is illustrated and evaluated by means of a worked example from biomedicine in the area of cardiac signal processing. The experimental results show the potential of the approach
01 Jan 2005
TL;DR: This paper suggests the absolute sum of the second-level detailed image of DWT as focus measure and shows that setting a threshold on the wavelet coefficients can dramatically increase the discriminative power of the focus measure in noisy condition.
Abstract: In this paper we propose a robust technique for image focus measure based on discrete wavelet transform (DWT) We suggest the absolute sum of the second-level detailed image of DWT as focus measure In the experiment the absolute-sum based measure shows equally well performance as the energy-based measure while enhancing computation efficiency Comparison to other benchmarking measures is also discussed Our measure exhibits more robustness to Gaussian noise Moreover, we show that setting a threshold on the wavelet coefficients can dramatically increase the discriminative power of the focus measure in noisy condition
TL;DR: This work introduces a method of wavefield separation from multicomponent data sets based on the use of the continuous wavelet transform, and shows how to construct filters tailored to separate different wave types by designing the filter in the time–frequency domain.
Abstract: We introduce a method of wavefield separation from multicomponent data sets based on the use of the continuous wavelet transform. Our method is a further generalization of the approach proposed by Morozov and Smithson, in that by using the continuous wavelet transform, we can achieve a better separation of wave types by designing the filter in the time–frequency domain. Furthermore, using the instantaneous polarization attributes defined in the wavelet domain, we show how to construct filters tailored to separate different wave types (elliptically or linearly polarized), followed by an inverse wavelet transform to obtain the desired wave type in the time domain. Using synthetic and experimental data, we show how the present method can be used for wavefield separation.
01 Jan 2005
TL;DR: This paper has shown that the new method of image restoration, using complex wavelet transform, has been devised and applied to deblur in the presence of high speckle noise and outperforms the Weiner filtering and Fourier-wavelet regularized deconvolution methods for both ultrasonic and CT images.
Abstract: Deblurring in the presence of non-Gaussian noise is a hard problem, specially in ultrasonic and CT images. In this paper, a new method of image restoration, using complex wavelet transform, has been devised and applied to deblur in the presence of high speckle noise. It has been shown that the new method outperforms the Weiner filtering and Fourier-wavelet regularized deconvolution (ForWaRD) methods for both ultrasonic and CT images. Unlike Fourier and real wavelet transforms, complex wavelet transform is nearly shift-invariant. This gives complex wavelet transform an edge over other traditional methods when applied simultaneously for deblurring as well as denoising. The proposed method is independent of any assumption about the degradation process. It is adaptive, as it uses shrinkage function based on median and mean of absolute wavelet coefficient as well as standard deviation of wavelet coefficients. Its application on real spiral CT images of inner ear has shown a clear improvement over other methods
TL;DR: An analytic wavelet transform, based on Hilbert wavelet pairs, is applied to bivariate time-varying spectral estimation for neurophysiological time series under the assumption of an underlying block stationary process.
TL;DR: A new FrFT-based chirp scaling algorithm (CSA) is developed and its performance with the classical CSA based on the fast Fourier transform (FFT).
Abstract: The fractional Fourier transform (FrFT), which is a generalized form of the well-known Fourier transform, has only recently started to appear in the field of signal processing. This has opened up the possibility of a new range of potentially promising and useful applications. In this letter, we develop a new FrFT-based chirp scaling algorithm (CSA) and compare its performance with the classical CSA based on the fast Fourier transform (FFT). Simulation results show that the FrFT-based CSA can offer significantly enhanced features compared to the classical FFT-based approach.
Patent•
01 Mar 2005
TL;DR: In this paper, a curved wavelet transform and a related image/video compression system are disclosed, which is carried out by applying one-dimensional (1-D) wavelet filters along curves, rather than along only horizontal and vertical directions.
Abstract: A curved wavelet transform and a related image/video compression system are disclosed. The curved wavelet transform (CWT) is carried out by applying one-dimensional (1-D) wavelet filters along curves, rather than along only horizontal and vertical directions. The image/video compression system includes a curve determination unit, a curved wavelet transform unit, a wavelet coefficient quantization unit, a wavelet coefficient coding unit, and a curve coding unit. The quantization and coding of the wavelet coefficients are related to the curves. In one embodiment, recursive wavelet filters are used for inverse wavelet decomposition. The system provides higher compression capability than conventional wavelet-based image compression systems.
12 Dec 2005
TL;DR: A genetic algorithm systemically evolves a new set of coefficients that significantly reduces mean squared error for various classes of one-dimensional signal reconstruction under lossy conditions due to quantization.
Abstract: This paper describes a genetic algorithm that evolves optimized sets of coefficients for one-dimensional signal reconstruction under lossy conditions due to quantization. Beginning with a population of mutated copies of the set of coefficients describing a standard wavelet-based inverse transform, the genetic algorithm systemically evolves a new set of coefficients that significantly reduces mean squared error (relative to the performance of the selected wavelet) for various classes of one-dimensional signals. The evolved transforms also outperform wavelets when subsequently tested against random signals from the same class
Patent•
26 Jul 2005TL;DR: In this paper, the wavelet transform coefficients are multiplied by weighting coefficients from one sub-band to another, determined using the analysis information of a specified block area in a picture, such as motion information and texture fineness information.
Abstract: In wavelet transform encoding, high-quality encoding is to be realized by enabling picture quality control from one fractional area to another. An input picture 100 is read out in an amount corresponding to a number of lines required for wavelet transform and buffered in a memory unit 6. The input picture then is wavelet transformed in a wavelet transform unit 2 and quantized in a coefficient quantizing unit 3. In quantizing wavelet transform coefficients, the wavelet transform coefficients are multiplied by weighting coefficients from one sub-band to another. The weighting coefficients are determined using the analysis information of a specified block area in a picture, such as motion information and texture fineness information. This enables fine quantization control in terms of a picture block as a unit.
TL;DR: In this paper, a special class of non-linear damping models is studied in which the damping force is proportional to the product of positive powers of the absolute values of displacement and velocity.
TL;DR: Both computer simulation and experimental results of practical surface 2D/3D filtering prove that the DT-CWT filter is very suitable for the separation and extraction of frequency components such as surface roughness, waviness and form.
Abstract: The metrological characteristics of a newly developed dual-tree complex wavelet transform (DT-CWT) for surface analysis are investigated, especially on the aspect of transmission characteristics analysis. The property of zero/linear phase by the DT-CWT ensures filtering results with no distortion and good ability for feature localization. Due to the 'steep transmission curve' property of the amplitude transmission characteristic, the DT-CWT can separate different frequency components efficiently. Both computer simulation and experimental results of practical surface 2D/3D filtering prove that the DT-CWT filter is very suitable for the separation and extraction of frequency components such as surface roughness, waviness and form.