Showing papers on "Harmonic wavelet transform published in 2016"
TL;DR: The new method is applied to continuous wave electron spin resonance spectra and it is found that it increases the signal-to-noise ratio (SNR) by more than 32 dB without distorting the signal, whereas standard denoising methods improve the SNR by less than 10 dB and with some distortion.
Abstract: A new method is presented to denoise 1-D experimental signals using wavelet transforms. Although the state-of-the-art wavelet denoising methods perform better than other denoising methods, they are not very effective for experimental signals. Unlike images and other signals, experimental signals in chemical and biophysical applications, for example, are less tolerant to signal distortion and under-denoising caused by the standard wavelet denoising methods. The new method: 1) provides a method to select the number of decomposition levels to denoise; 2) uses a new formula to calculate noise thresholds that does not require noise estimation; 3) uses separate noise thresholds for positive and negative wavelet coefficients; 4) applies denoising to the approximation component; and 5) allows the flexibility to adjust the noise thresholds. The new method is applied to continuous wave electron spin resonance spectra and it is found that it increases the signal-to-noise ratio (SNR) by more than 32 dB without distorting the signal, whereas standard denoising methods improve the SNR by less than 10 dB and with some distortion. In addition, its computation time is more than six times faster.
178 citations
TL;DR: The modified EWT (MEWT) method via data-driven adaptive Fourier spectrum segment is proposed for mechanical fault identification and the results show its outstanding performance.
128 citations
TL;DR: It is demonstrated that the WT can be an effective tool for unsupervised OA removal from single-channel EEG data for real-time applications.
Abstract: Electroencephalogram (EEG) is a technique for recording the asynchronous activation of neuronal firing inside the brain with non-invasive scalp electrodes. Artifacts, such as eye blink activities, can corrupt these neuronal signals. While ocular artifact (OA) removal is well investigated for multiple channel EEG systems, in alignment with the recent momentum toward minimalistic EEG systems for use in natural environments, we investigate unsupervised and effective removal of OA from single-channel streaming raw EEG data. In this paper, the unsupervised wavelet transform (WT) decomposition technique was systematically evaluated for the effectiveness of OA removal for a single-channel EEG system. A set of seven raw EEG data set was analyzed. Two commonly used WT methods, Discrete Wavelet Transform (DWT) and Stationary Wavelet Transform (SWT), were applied. Four WT basis functions, namely, haar, coif3, sym3, and bior4.4, were considered for OA removal with universal threshold and statistical threshold (ST). To quantify OA removal efficacy from single-channel EEG, five performance metrics were utilized: correlation coefficients, mutual information, signal-to-artifact ratio, normalized mean square error, and time-frequency analysis. The temporal and spectral analysis shows that the optimal combination could be DWT with ST with coif3 or bior4.4 to remove OA among 16 combinations. This paper demonstrates that the WT can be an effective tool for unsupervised OA removal from single-channel EEG data for real-time applications.
78 citations
TL;DR: In this paper, a nonlinear, invertible, low-level image processing transform based on combining the well-known Radon transform for image data, and the 1D cumulative distribution transform proposed earlier is described.
Abstract: Invertible image representation methods (transforms) are routinely employed as low-level image processing operations based on which feature extraction and recognition algorithms are developed. Most transforms in current use (e.g., Fourier, wavelet, and so on) are linear transforms and, by themselves, are unable to substantially simplify the representation of image classes for classification. Here, we describe a nonlinear, invertible, low-level image processing transform based on combining the well-known Radon transform for image data, and the 1D cumulative distribution transform proposed earlier. We describe a few of the properties of this new transform, and with both theoretical and experimental results show that it can often render certain problems linearly separable in a transform space.
64 citations
TL;DR: In this paper, the authors proposed a new transient feature extraction approach using the optimized Morlet wavelet transform, kurtosis index and soft-thresholding, which has lower computation complexity compared to the existing wavelet parameter optimization algorithm.
Abstract: Aimed at solving the key problem in weak transient detection, the present study proposes a new transient feature extraction approach using the optimized Morlet wavelet transform, kurtosis index and soft-thresholding. Firstly, a fast optimization algorithm based on the Shannon entropy is developed to obtain the optimized Morlet wavelet parameter. Compared to the existing Morlet wavelet parameter optimization algorithm, this algorithm has lower computation complexity. After performing the optimized Morlet wavelet transform on the analyzed signal, the kurtosis index is used to select the characteristic scales and obtain the corresponding wavelet coefficients. From the time-frequency distribution of the periodic impulsive signal, it is found that the transient signal can be reconstructed by the wavelet coefficients at several characteristic scales, rather than the wavelet coefficients at just one characteristic scale, so as to improve the accuracy of transient detection. Due to the noise influence on the characteristic wavelet coefficients, the adaptive soft-thresholding method is applied to denoise these coefficients. With the denoised wavelet coefficients, the transient signal can be reconstructed. The proposed method was applied to the analysis of two simulated signals, and the diagnosis of a rolling bearing fault and a gearbox fault. The superiority of the method over the fast kurtogram method was verified by the results of simulation analysis and real experiments. It is concluded that the proposed method is extremely suitable for extracting the periodic impulsive feature from strong background noise.
55 citations
TL;DR: This paper presents the analysis of multi-channel electrogastrographic (EGG) signals using the continuous wavelet transform based on the fast Fourier transform (CWTFT) which is the completely new solution.
Abstract: This paper presents the analysis of multi-channel electrogastrographic (EGG) signals using the continuous wavelet transform based on the fast Fourier transform (CWTFT). The EGG analysis was based on the determination of the several signal parameters such as dominant frequency (DF), dominant power (DP) and index of normogastria (NI). The use of continuous wavelet transform (CWT) allows for better visible localization of the frequency components in the analyzed signals, than commonly used short-time Fourier transform (STFT). Such an analysis is possible by means of a variable width window, which corresponds to the scale time of observation (analysis). Wavelet analysis allows using long time windows when we need more precise low-frequency information, and shorter when we need high frequency information. Since the classic CWT transform requires considerable computing power and time, especially while applying it to the analysis of long signals, the authors used the CWT analysis based on the fast Fourier transform (FFT). The CWT was obtained using properties of the circular convolution to improve the speed of calculation. This method allows to obtain results for relatively long records of EGG in a fairly short time, much faster than using the classical methods based on running spectrum analysis (RSA). In this study authors indicate the possibility of a parametric analysis of EGG signals using continuous wavelet transform which is the completely new solution. The results obtained with the described method are shown in the example of an analysis of four-channel EGG recordings, performed for a non-caloric meal.
53 citations
TL;DR: In this paper, the high-order sparse Radon transform (HOSRT) method is introduced to protect the amplitude variation with offset information during the multiple subtraction procedures, and a fast nonlinear filter is adopted in the adaptive subtraction step to avoid the orthogonality assumption.
Abstract: The Radon transform is widely used for multiple elimination. Since the Radon transform is not an orthogonal transform, it cannot preserve the amplitude of primary reflections well. The prediction and adaptive subtraction method is another widely used approach for multiple attenuation, which demands that the primaries are orthogonal with the multiples. However, the orthogonality assumption is not true for non-stationary field seismic data. In this paper, the high-order sparse Radon transform (HOSRT) method is introduced to protect the amplitude variation with offset information during the multiple subtraction procedures. The HOSRT incorporates the high-resolution Radon transform with the orthogonal polynomial transform. Because the Radon transform contains the trajectory information of seismic events and the orthogonal polynomial transform contains the amplitude variation information of seismic events, their combination constructs an overcomplete transform and obtains the benefits of both the high-resolution property of the Radon transform and the amplitude preservation of the orthogonal polynomial transform. A fast nonlinear filter is adopted in the adaptive subtraction step in order to avoid the orthogonality assumption that is used in traditional adaptive subtraction methods. The application of the proposed approach to synthetic and field data examples shows that the proposed method can improve the separation performance by preserving more useful energy.
53 citations
TL;DR: A new active control algorithm based on discrete wavelet transform (DWT) for both stationary and non-stationary noise control that has greatly reduced complexity and a better convergence performance compared to a time domain filtered-x least mean square (TD-FXLMS) algorithm.
47 citations
TL;DR: This paper will explore the relationship and implications of the wavelet method developed as an extension of the Fourier transform and the Hilbert-Huang transform for the analysis of electrochemical noise.
46 citations
TL;DR: This work proposes a novel image watermarking method using LCWT and QR decomposition that is not only feasible, but also robust to some geometry attacks and image processing attacks.
Abstract: Inspired by the fact that wavelet transform can be written as a classical convolution form, a new linear canonical wavelet transform (LCWT) based on generalised convolution theorem associated with linear canonical transform (LCT) is proposed recently. The LCWT not only inherits the advantages of multi-resolution analysis of wavelet transform (WT), but also has the capability of image representations in the LCT domain. Based on these good properties, the authors propose a novel image watermarking method using LCWT and QR decomposition. Compared with the existing image watermarking methods based on discrete WT or QR, this novel image watermarking method provides more flexibility in the image watermarking. Peak signal-to-noise ratio, normalised cross and structural similarity index measure are used to verify the advantages of the proposed method in simulation experiments. The experiment results show that the proposed method is not only feasible, but also robust to some geometry attacks and image processing attacks.
44 citations
TL;DR: A new generalized fractional Fourier transform is presented, which can overcome the problem of multi-decryption-key hinders the application of this algorithm and enlarge the key space.
TL;DR: The design and implementation of a polyphase-decomposition-based new architecture of wavelet filter for power system harmonics estimation using discrete wavelet packet transform (DWPT) is presented.
Abstract: Computational time and hardware resource are key issues in hardware implementation of any signal-processing algorithm. This paper presents the design and implementation of a polyphase-decomposition-based new architecture of wavelet filter for power system harmonics estimation using discrete wavelet packet transform (DWPT). Usually, DWPT provides coefficients as the output; however, the proposed architecture also includes provision for providing root mean square values directly. The proposed method reduces computational requirements and save memory resources. Xilinx system generator, a higher abstraction level tool, has been used to simulate and implement the proposed scheme on the Xilinx Artix-7 field-programming gate array AC701 board. Performance of the proposed architecture has been validated and compared through hardware cosimulation with variety of synthetic and experimental signals.
TL;DR: This work gives the first proof of near-optimal recovery from discrete Fourier samples taken according to an appropriate variable density sampling scheme, taking into account such structured sparsity as sparsity in levels-as opposed to just sparsity.
Abstract: We consider signal recovery from Fourier measurements using compressed sensing (CS) with wavelets. For discrete signals with structured sparse Haar wavelet coefficients, we give the first proof of near-optimal recovery from discrete Fourier samples taken according to an appropriate variable density sampling scheme. Crucially, in taking into account such structured sparsity—known as sparsity in levels—as opposed to just sparsity, this result yields recovery guarantees that agree with the empirically observed recovery properties of CS in this setting. This result complements a recent theorem in Adcock et al. [Breaking the coherence barrier: A new theory for compressed sensing, arXiv preprint arXiv: 1302.0561, 2014.], which addressed the case of continuous time signals. Moreover, we provide a significantly shorter and more expositional argument, which clearly illustrates the key factors governing recovery in this setting: namely the division of frequency space into dyadic bands corresponding to wavelet scales, the near-block diagonality of the Fourier/wavelet cross-Gramian matrix, and the structured sparsity of wavelet coefficients.
TL;DR: The dual-tree complex wavelet transform (DTCWT) is introduced into the MSTSR method, which makes it possible to further improve the system output signal-to-noise ratio and the accuracy of fault diagnosis by the merits of DTCWT.
Abstract: It is very difficult to detect weak fault signatures due to the large amount of noise in a wind turbine system. Multiscale noise tuning stochastic resonance (MSTSR) has proved to be an effective way to extract weak signals buried in strong noise. However, the MSTSR method originally based on discrete wavelet transform (DWT) has disadvantages such as shift variance and the aliasing effects in engineering application. In this paper, the dual-tree complex wavelet transform (DTCWT) is introduced into the MSTSR method, which makes it possible to further improve the system output signal-to-noise ratio and the accuracy of fault diagnosis by the merits of DTCWT (nearly shift invariant and reduced aliasing effects). Moreover, this method utilizes the relationship between the two dual-tree wavelet basis functions, instead of matching the single wavelet basis function to the signal being analyzed, which may speed up the signal processing and be employed in on-line engineering monitoring. The proposed method is applied to the analysis of bearing outer ring and shaft coupling vibration signals carrying fault information. The results confirm that the method performs better in extracting the fault features than the original DWT-based MSTSR, the wavelet transform with post spectral analysis, and EMD-based spectral analysis methods.
TL;DR: This new approach is based on reusing the calculations of the STFT at consecutive time instants, which leads to significant savings in hardware components with respect to fast Fourier transform based STFTs.
Abstract: This brief presents the feedforward short-time Fourier transform (STFT). This new approach is based on reusing the calculations of the STFT at consecutive time instants. This leads to significant savings in hardware components with respect to fast Fourier transform based STFTs. Furthermore, the feedforward STFT does not have the accumulative error of iterative STFT approaches. As a result, the proposed feedforward STFT presents an excellent tradeoff between hardware utilization and performance.
TL;DR: In this article, a signal processing synthesizing Wavelet transform and Hilbert transform is employed to measurement of uniform or non-uniform vibrations in self-mixing interferometer on semiconductor laser diode with quantum well.
TL;DR: The ray space transform for acoustic field representation is introduced, based on a short space-time Fourier transform of the signals captured by a microphone array, using discrete Gabor frames, and enables the definition of analysis and synthesis operators, which exhibit perfect reconstruction capabilities.
Abstract: Soundfield imaging is a special analysis methodology aimed at capturing the directional components of the acoustic field and mapping them onto a domain called “ray space”, where relevant acoustic objects become linear patterns, i.e., sets of collinear points. This allows us to overcome resolution issues while easing far-field assumptions. In this paper, we generalize this concept by introducing the ray space transform for acoustic field representation. The transform is based on a short space-time Fourier transform of the signals captured by a microphone array, using discrete Gabor frames. The resulting transform coefficients are parameterized in the same ray space used for soundfield imaging. The resulting transform enables the definition of analysis and synthesis operators, which exhibit perfect reconstruction capabilities. We show examples of applications of the ray space transform to source localization and spot spatial filtering.
TL;DR: In this article, the quaternion Fourier transform (QFT) and its properties are reviewed under the polar coordinate form for quaternions and the conditions that give rise to the equal relations of two uncertainty principles are given to verify the results.
Abstract: The quaternion Fourier transform (QFT) and its properties are reviewed in this paper. Under the polar coordinate form for quaternion-valued signals, we strengthen the stronger uncertainty principles in terms of covariance for quaternion-valued signals based on the right-sided quaternion Fourier transform in both the directional and the spatial cases. We also obtain the conditions that give rise to the equal relations of two uncertainty principles. Examples are given to verify the results.
TL;DR: The dual-tree complex wavelet transform (DTCWT) solves the problems of shift variance and low directional selectivity in two and higher dimensions found with the commonly used discrete wavelettransform (DWT).
Abstract: The dual-tree complex wavelet transform (DTCWT) solves the problems of shift variance and low directional selectivity in two and higher dimensions found with the commonly used discrete wavelet transform (DWT). It has been proposed for applications such as texture classification and content-based image retrieval. In this paper, the performance of the dual-tree complex wavelet transform for fabric defect detection is evaluated. As experimental samples, the fabric images from TILDA, a textile texture database from the Workgroup on Texture Analysis of the German Research Council (DFG), are used. The mean energies of real and imaginary parts of complex wavelet coefficients taken separately are identified as effective features for the purpose of fabric defect detection. Then it is shown that the use of the dual-tree complex wavelet transform yields greater performance as compared to the undecimated wavelet transform (UDWT) with a detection rate of 4.5% to 15.8% higher depending on the fabric type.
TL;DR: In this article, the use of Fourier and Wavelet transform in denoising the log data for obtaining formation interfaces is demonstrated in the Upper Assam Basin, which are self-potential, gamma ray, and resistivity log responses.
TL;DR: A method for compression of various medical images using Fast Discrete Curvelet Transform based on wrapping technique, which demonstrates significant improvement in performance parameters like Peak Signal to Noise Ratio (PSNR) and Compression Ratio (CR).
Abstract: Due to the development of CT (Computed Tomography), MRI (Magnetic Resonance Imaging), PET (Positron Emission Tomography), EBCT (Electron Beam Computed Tomography), SMRI (Stereotactic Magnetic Resonance Imaging), etc. has enhanced the distinguishing rate and scanning rate of the imaging equipments. The diagnosis and the process of getting useful information from the image are got by processing the medical images using the wavelet technique. Wavelet transform has increased the compression rate. Increasing the compression performance by minimizing the amount of image data in the medical images is a critical task. Crucial medical information like diagnosing diseases and their treatments is obtained by modern radiology techniques. Medical Imaging (MI) process is used to acquire that information. For lossy and lossless image compression, several techniques were developed. Image edges have limitations in capturing them if we make use of the extension of 1-D wavelet transform. This is because wavelet transform cannot effectively transform straight line discontinuities, as well geographic lines in natural images cannot be reconstructed in a proper manner if 1-D transform is used. Differently oriented image textures are coded well using Curvelet Transform. The Curvelet Transform is suitable for compressing medical images, which has more curvy portions. This paper describes a method for compression of various medical images using Fast Discrete Curvelet Transform based on wrapping technique. After transformation, the coefficients are quantized using vector quantization and coded using arithmetic encoding technique. The proposed method is tested on various medical images and the result demonstrates significant improvement in performance parameters like Peak Signal to Noise Ratio (PSNR) and Compression Ratio (CR).
TL;DR: In this paper, a piecewise Hilbert transform was proposed to suppress the background intensity of the deformed fringe pattern using only one fringe pattern in Fourier transform profilometry according to the approximation that the background of the fringe is a slowly varying function and its distribution in each half period of a fringe can be regarded as a constant.
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TL;DR: In this article, it was shown that the energy contained in high order scattering coefficients is upper bounded by the energy in the high frequencies of the signal, and that the decay of the scattering coefficients of a signal can be linked with the decay in its Fourier transform.
Abstract: We study an aspect of the following general question: which properties of a signal can be characterized by its scattering transform? We show that the energy contained in high order scattering coefficients is upper bounded by the energy contained in the high frequencies of the signal This result links the decay of the scattering coefficients of a signal with the decay of its Fourier transform Additionally, it allows to generalize some results of Mallat (2012), by relaxing the admissibility condition on the wavelet family
TL;DR: In this paper, a new method based on the shearlet transform is presented for phase extraction in fringe projection profilometry (FPP) from a single fringe pattern, which is more effective and accurate than the Fourier transform method and wavelet transform method.
01 Jan 2016
TL;DR: The the fourier transform and its application is universally compatible with any devices to read and is available in the book collection an online access to it is set as public so you can download it instantly.
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TL;DR: In this paper, a real inversion formula in the differential operator form for the Mexican hat wavelet transform is established and its properties are studied, which is supported by a nice example.
Abstract: Theory of Weierstrass transform is exploited to derive many interesting new properties of the Mexican hat wavelet transform. A real inversion formula in the differential operator form for the Mexican hat wavelet transform is established. Mexican hat wavelet transform of distributions is defined and its properties are studied. An approximation property of the distributional wavelet transform is investigated which is supported by a nice example.
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TL;DR: An additional fuzzy thresholding approach for automatic determination of the rate threshold level around the traditional wavelet noise thresholding is applied, and used for the soft or hard-threshold performed on all the high frequency subimages.
Abstract: The application of wavelet transforms to Synthetic Aperture Radar (SAR) imagery has improved despeckling performance. To deduce the problem of filtering the multiplicative noise to the case of an additive noise, the wavelet decomposition is performed on the logarithm of the image gray levels. The detail coefficients produced by the bidimensional discrete wavelet transform (DWT-2D) needs to be thresholded to extract out the speckle in highest subbands. An initial threshold value is estimated according to the noise variance. In this paper, an additional fuzzy thresholding approach for automatic determination of the rate threshold level around the traditional wavelet noise thresholding (initial threshold) is applied, and used for the soft or hard-threshold performed on all the high frequency subimages. The filtered logarithmic image is then obtained by reconstruction from the thresholded coefficients. This process is applied a single time, and exclusively to the first level of decomposition. The exponential function of this reconstructed image gives the final filtered image. Experimental results on test images have demonstrated the effectiveness of this method compared to the most of methods in use at the moment.
TL;DR: In this paper, a denoising method based on wavelet analysis is presented for the removal of noise (background noise and random spike) from time domain electromagnetic (TEM) data.
Abstract: A denoising method based on wavelet analysis is presented for the removal of noise (background noise and random spike) from time domain electromagnetic (TEM) data. This method includes two signal processing technologies: wavelet threshold method and stationary wavelet transform. First, wavelet threshold method is used for the removal of background noise from TEM data. Then, the data are divided into a series of details and approximations by using stationary wavelet transform. The random spike in details is identified by zero reference data and adaptive energy detector. Next, the corresponding details are processed to suppress the random spike. The denoised TEM data are reconstructed via inverse stationary wavelet transform using the processed details at each level and the approximations at the highest level. The proposed method has been verified using a synthetic TEM data, the signal-to-noise ratio of synthetic TEM data is increased from 10.97 dB to 24.37 dB at last. This method is also applied to the noise suppression of the field data which were collected at Hengsha island, China. The section image results shown that the noise is suppressed effectively and the resolution of the deep anomaly is obviously improved.
17 Mar 2016
TL;DR: The results of MATLAB simulations show that the algorithm based on double-density dual-tree discrete wavelet transform is more effective and gives better performance in terms of both SNR and RMSE.
Abstract: Denoising is considered as one of the important tasks in signal processing. ECG signal analysis is very important for detecting heart diseases. The amplitude and frequency of ECG signals may vary due to corruption of noises and that may further cause problems to detect the actual abnormality. In this paper performance comparison of denoising of ECG signals based on different wavelet transform techniques is implemented. Discrete wavelet transform (DWT) and its expansive forms such as double-density discrete wavelet transform (DDDWT), dual-tree discrete wavelet transform (DTDWT) and double-density dual-tree discrete wavelet transform (DDDTDWT) techniques employing thresholding algorithm are presented for signal denoising. The ECG signals taken from MIT-BIH arrhythmia database are corrupted with different types of noise and used for the analysis. The results of MATLAB simulations show that the algorithm based on double-density dual-tree discrete wavelet transform is more effective and gives better performance in terms of both SNR and RMSE.
TL;DR: In this paper, a comparison of three feature extraction methods to denoise partial discharge (PD) signals is presented, which employ the Stationary Wavelet Transform (SWT) associated to a spatially-adaptive selection procedure based on the coefficients propagation along decomposition levels.
Abstract: This paper presents a comparison of three feature extraction methods to denoise partial discharge (PD) signals. The denoising technique employs the Stationary Wavelet Transform (SWT) associated to a spatially-adaptive selection procedure based on the coefficients propagation along decomposition levels (scales). The PD and noise related coefficients are identified and separated by an automatic data classifier using Support Vector Machines (SVM). The first and second feature extraction methods act directly on the SWT coefficients and differ only on the procedures to characterize the propagation. The third method relies on Cycle Spinning (CS) on the several translated Discrete Wavelet Transform (DWT) obtained from SWT. We conducted an empirical study using Analysis of Variance (ANOVA) to evaluate the influence of the methods on denoising performance and to guarantee the statistical significance of the tests. Afterwards, performance was evaluated considering real PD signals measured in air and in solid dielectrics, corrupted by several types of interferences, both stationary and time-varying. The results show that the three approaches allow robust signal recovering and significant noise rejection, but differ substantially on the quality of the reconstructed signals.