Showing papers on "Harmonic wavelet transform published in 2014"
TL;DR: This work proposes a fast local search method for recovering a sparse signal from measurements of its Fourier transform (or other linear transform) magnitude which it refers to as GESPAR: GrEedy Sparse PhAse Retrieval, which does not require matrix lifting, unlike previous approaches, and therefore is potentially suitable for large scale problems such as images.
Abstract: We consider the problem of phase retrieval, namely, recovery of a signal from the magnitude of its Fourier transform, or of any other linear transform. Due to the loss of Fourier phase information, this problem is ill-posed. Therefore, prior information on the signal is needed in order to enable its recovery. In this work we consider the case in which the signal is known to be sparse, i.e., it consists of a small number of nonzero elements in an appropriate basis. We propose a fast local search method for recovering a sparse signal from measurements of its Fourier transform (or other linear transform) magnitude which we refer to as GESPAR: GrEedy Sparse PhAse Retrieval. Our algorithm does not require matrix lifting, unlike previous approaches, and therefore is potentially suitable for large scale problems such as images. Simulation results indicate that GESPAR is fast and more accurate than existing techniques in a variety of settings.
337 citations
04 May 2014
TL;DR: This paper adapts the formulation of the synchrosqueezing to the STFT and state a similar theoretical result to that obtained in the CWT framework, with the emphasis put on the differences with theCWT-based synchroquEEzing.
Abstract: The short-time Fourier transform (STFT) and the continuous wavelet transform (CWT) are extensively used to analyze and process multicomponent signals, i.e. superpositions of modulated waves. The synchrosqueezing is a post-processing method which circumvents the uncertainty relation inherent to these linear transforms, by reassigning the coefficients in scale or frequency. Originally introduced in the setting of the CWT, it provides a sharp, concentrated representation, while remaining invertible. This technique received a renewed interest with the recent publication of an approximation result related to the application of the synchrosqueezing to multi-component signals. In the current paper, we adapt the formulation of the synchrosqueezing to the STFT and state a similar theoretical result to that obtained in the CWT framework. The emphasis is put on the differences with the CWT-based synchrosqueezing with numerical experiments illustrating our statements.
203 citations
TL;DR: The theory of various established and novel techniques are reviewed, pointing out their assumptions, adaptability, and expected time-frequency localization, and their performances on a provided collection of benchmark signals are illustrated.
Abstract: Spectral estimation, and corresponding time-frequency representation for nonstationary signals, is a cornerstone in geophysical signal processing and interpretation. The last 10-15 years have seen the development of many new high-resolution decompositions that are often fundamentally different from Fourier and wavelet transforms. These conventional techniques, like the short-time Fourier transform and the continuous wavelet transform, show some limitations in terms of resolution (localization) due to the trade-off between time and frequency localizations and smearing due to the finite size of the time series of their template. Well-known techniques, like autoregressive methods and basis pursuit, and recently developed techniques, such as empirical mode decomposition and the synchrosqueezing transform, can achieve higher time-frequency localization due to reduced spectral smearing and leakage. We first review the theory of various established and novel techniques, pointing out their assumptions, adaptability, and expected time-frequency localization. We illustrate their performances on a provided collection of benchmark signals, including a laughing voice, a volcano tremor, a microseismic event, and a global earthquake, with the intention to provide a fair comparison of the pros and cons of each method. Finally, their outcomes are discussed and possible avenues for improvements are proposed.
171 citations
TL;DR: The Synchrosqueezing Transform (SST) as discussed by the authors is an extension of the wavelet transform incorporating elements of empirical mode decomposition and frequency reassignment techniques, which produces a well defined time-frequency representation allowing the identification of instantaneous frequencies in seismic signals.
Abstract: Time-frequency representation of seismic signals provides a source of information that is usually hidden in the Fourier spectrum. The short-time Fourier transform and the wavelet transform are the principal approaches to simultaneously decompose a signal into time and frequency components. Known limitations, such as trade-offs between time and frequency resolution, may be overcome by alternative techniques that extract instantaneous modal components. Empirical mode decomposition aims to decompose a signal into components that are well separated in the time-frequency plane allowing the reconstruction of these components. On the other hand, a recently proposed method called the “synchrosqueezing transform” (SST) is an extension of the wavelet transform incorporating elements of empirical mode decomposition and frequency reassignment techniques. This new tool produces a well-defined time-frequency representation allowing the identification of instantaneous frequencies in seismic signals to highlight ...
148 citations
TL;DR: A novel parameter estimation method based on keystone transform and Radon-Fourier transform for space moving targets with high-speed maneuvering performance that can overcome the limitation of Doppler frequency ambiguity and correct range curvature for all targets in one processing step, which simplifies the operation procedure.
Abstract: This letter proposes a novel parameter estimation method based on keystone transform (KT) and Radon-Fourier transform (RFT) for space moving targets with high-speed maneuvering performance. In this method, second-order KT is used to correct the range curvature and part of the range walk for all targets simultaneously. Then, fractional Fourier transform is employed to estimate the targets' radial acceleration, followed by the quadric phase term compensation. Finally, RFT and Clean technique are carried out to correct the residual range walk, and the initial range and radial velocity of moving targets are further obtained. The advantage of the proposed method is that it can overcome the limitation of Doppler frequency ambiguity and correct range curvature for all targets in one processing step, which simplifies the operation procedure. Simulation results are presented to demonstrate the validity of the proposed method.
114 citations
TL;DR: In this article, two fast numerical methods for computing the nonlinear Fourier transform with respect to the Schrodinger equation (NSE) are presented, which achieves a runtime of O(D 2 ) floating point operations, where D is the number of sample points.
Abstract: The nonlinear Fourier transform, which is also known as the forward scattering transform, decomposes a periodic signal into nonlinearly interacting waves. In contrast to the common Fourier transform, these waves no longer have to be sinusoidal. Physically relevant waveforms are often available for the analysis instead. The details of the transform depend on the waveforms underlying the analysis, which in turn are specified through the implicit assumption that the signal is governed by a certain evolution equation. For example, water waves generated by the Korteweg-de Vries equation can be expressed in terms of cnoidal waves. Light waves in optical fiber governed by the nonlinear Schrodinger equation (NSE) are another example. Nonlinear analogs of classic problems such as spectral analysis and filtering arise in many applications, with information transmission in optical fiber, as proposed by Yousefi and Kschischang, being a very recent one. The nonlinear Fourier transform is eminently suited to address them -- at least from a theoretical point of view. Although numerical algorithms are available for computing the transform, a "fast" nonlinear Fourier transform that is similarly effective as the fast Fourier transform is for computing the common Fourier transform has not been available so far. The goal of this paper is to address this problem. Two fast numerical methods for computing the nonlinear Fourier transform with respect to the NSE are presented. The first method achieves a runtime of $O(D^2)$ floating point operations, where $D$ is the number of sample points. The second method applies only to the case where the NSE is defocusing, but it achieves an $O(D\log^2D)$ runtime. Extensions of the results to other evolution equations are discussed as well.
103 citations
TL;DR: The experiments results show that the proposed algorithm based on the fractional Fourier transform (FRFT) is very robust to JPEG compression noise attacks and image manipulation operations, but also can provide protection even under compound attacks.
89 citations
TL;DR: In this paper, a wavelet-based frequency response function (FRF) is proposed for vibration analysis of systems with time-varying parameters, which is extended to a representation in the combined time-frequency domain using wavelet analysis.
66 citations
TL;DR: The main objective of this paper is to study the fractional Fourier transform (FrFT) and the generalized continuous wavelet transform and some of their basic properties.
65 citations
TL;DR: Numerical simulation verifies the feasibility of the scheme and shows that the problem of insufficient capacity is better solved, and the flexibility of scheme increases.
Abstract: A multiple-image encryption scheme based on the optical wavelet transform (OWT) and the multichannel fractional Fourier transform (MFrFT) is proposed. The scheme can make full use of multi-resolution decomposition of wavelet transform (WT) and multichannel processing of MFrFT. The mentioned properties can achieve the encryption of multi-image and the encryption of single image. When encryption finished, each image gets its own fractional order and independent keys. Analysis of encrypted effects has been completed. Furthermore, the influence of WT type and order are analyzed, and the application and analysis of MFrFT are accomplished as well. Numerical simulation verifies the feasibility of the scheme and shows that the problem of insufficient capacity is better solved, and the flexibility of scheme increases. A simple opto-electronic mixed device to realize the scheme is proposed.
60 citations
TL;DR: In this article, the authors proposed a statistical approach to the identification of structural damages using guided waves, which not only provides a quantitative identification of the damages, but can also quantify the uncertainties associated with the damage identification results.
TL;DR: It is shown that the Transform K-SVD learns operators which are similar both in appearance and performance to the operators learned from the Analysis SVD, while its computational complexity stays much reduced compared to the Analysis K- SVD.
Abstract: Recently there has been increasing attention directed towards the analysis sparsity models. Consequently, there is a quest for learning the operators which would enable analysis sparse representations for signals in hand. Analysis operator learning algorithms such as the Analysis K-SVD have been proposed. Sparsifying transform learning is a paradigm which is similar to the analysis operator learning, but they differ in some subtle points. In this paper, we propose a novel transform operator learning algorithm called as the Transform K-SVD, which brings the transform learning and the K-SVD based analysis dictionary learning approaches together. The proposed Transform K-SVD has the important advantage that the sparse coding step of the Analysis K-SVD gets replaced with the simple thresholding step of the transform learning framework. We show that the Transform K-SVD learns operators which are similar both in appearance and performance to the operators learned from the Analysis K-SVD, while its computational complexity stays much reduced compared to the Analysis K-SVD.
01 Jan 2014
TL;DR: In this article, the authors proposed an efficient wavelet-based approach to determine the modal parameters of a structure from its ambient vibration responses, which integrates the time series autoregressive (AR) model with the stationary wavelet packet transform.
Abstract: Ambient vibration tests are conducted widely to estimate the modal parameters of a structure. The work proposes an efficient wavelet-based approach to determine the modal parameters of a structure from its ambient vibration responses. The proposed approach integrates the time series autoregressive (AR) model with the stationary wavelet packet transform. In addi- tion to providing a richer decomposition and allow- ing for an improved time-frequency localization of signals over that of the discrete wavelet transform, the stationary wavelet packet transform also has significantly higher computational efficiency than the wavelet packet transform in terms of decomposing time-shifted signals because the former has a time-invariance property. The correlation matrices needed in determining the coefficient matrices in an AR model are established in subspaces expanded by stationary wavelet packets. The formula- tion for estimating the correlation matrices is shown for the first time. Because different subspaces contain sig- nals with different frequency subbands, the fine filtering property enhances the ability of the proposed approach to identify not only the modes with strong modal in- terference, but also many modes from the responses of *To whom correspondence should be addressed. E-mail: cshuang@
TL;DR: The work proposes an efficient wavelet-based approach to determine the modal parameters of a structure from its ambient vibration responses that integrates the time series autoregressive (AR) model with the stationary wavelet packet transform.
Abstract: Ambient vibration tests are conducted widely to estimate the modal parameters of a structure. The work proposes an efficient wavelet-based approach to determine the modal parameters of a structure from its ambient vibration responses. The proposed approach integrates the time series autoregressive (AR) model with the stationary wavelet packet transform. In addition to providing a richer decomposition and allowing for an improved time–frequency localization of signals over that of the discrete wavelet transform, the stationary wavelet packet transform also has significantly higher computational efficiency than the wavelet packet transform in terms of decomposing time-shifted signals because the former has a time-invariance property. The correlation matrices needed in determining the coefficient matrices in an AR model are established in subspaces expanded by stationary wavelet packets. The formulation for estimating the correlation matrices is shown for the first time. Because different subspaces contain signals with different frequency subbands, the fine filtering property enhances the ability of the proposed approach to identify not only the modes with strong modal interference, but also many modes from the responses of very few measured degrees of freedom. The proposed approach is validated by processing the numerically simulated responses of a seven-floor shear building, which has closely spaced modes, with considering the effects of noise and incomplete measurements. Furthermore, the present approach is employed to process the velocity responses of an eight-storey steel frame subjected to white noise input in a shaking table test and ambient vibration responses of a cable-stayed bridge.
TL;DR: The generalized wavelet transform (GWT) as discussed by the authors is a time-frequency transformation tool based on the idea of the linear canonical transform (LCT) and is capable of representing signals in the time-fractional frequency plane.
TL;DR: Simulation results proved that the proposed inverse synthetic aperture radar imaging algorithm is much more effective and computationally efficient than the previously reported range-instantaneous Doppler algorithms such as the Radon-Wigner transform algorithm.
Abstract: A novel inverse synthetic aperture radar imaging algorithm is proposed for application when the maneuverability of an uncooperative target is not too severe, and the Doppler variation of the subechoes from the scatterers can be considered a first-order polynomial. Based on a modified keystone transform, the proposed algorithm can simultaneously transform all multicomponent linear frequency modulation subechoes into multicomponent single-frequency signals. Hence, the fast Fourier transform can be used for cross-range imaging. Simulation results also proved that the proposed algorithm is much more effective and computationally efficient than the previously reported range-instantaneous Doppler algorithms such as the Radon-Wigner transform algorithm.
TL;DR: A filtering design technique that obtains the coefficients of the filters at each harmonic by imposing the maximally flat conditions to the polynomials defining their frequency responses, which can be used to solve the LS problem at each particular harmonic frequency, without the need of obtaining the whole set.
Abstract: Recently, the Taylor-Fourier transform (TFT) was proposed to analyze the spectrum of signals with oscillating harmonics. The coefficients of this linear transformation were obtained through the calculation of the pseudoinverse matrix, which provides the classical solution to the normal equations of the least-squares (LS) approximation. This paper presents a filtering design technique that obtains the coefficients of the filters at each harmonic by imposing the maximally flat conditions to the polynomials defining their frequency responses. This condition can be used to solve the LS problem at each particular harmonic frequency, without the need of obtaining the whole set, as in the classical pseudoinverse solution. In addition, the filter passband central frequency can follow the fluctuations of the fundamental frequency. Besides, the method offers a reduction of the computational burden of the pseudoinverse solution. An implementation of the proposed estimator as an adaptive algorithm using its own instantaneous frequency estimate to relocate its bands is shown, and several tests are used to compare its performance with that of the ordinary TFT.
TL;DR: An image denoising procedure based on a 2D scale-mixing complex-valued wavelet transform that exhibits excellent quantitative and visual performance is introduced and demonstrated by simulation on standard test images.
Abstract: This paper introduces an image denoising procedure based on a 2D scale-mixing complex-valued wavelet transform. Both the minimal (unitary) and redundant (maximum overlap) versions of the transform are used. The covariance structure of white noise in wavelet domain is established. Estimation is performed via empirical Bayesian techniques, including versions that preserve the phase of the complex-valued wavelet coefficients and those that do not. The new procedure exhibits excellent quantitative and visual performance, which is demonstrated by simulation on standard test images.
TL;DR: Comparison of the input image is enhanced using proposed singular value decomposition and high frequency subbands are obtained using dual-tree complex wavelet transform and contrast enhanced low resolution image and highfrequency sub bands are interpolated using Lanczos interpolator.
TL;DR: This paper utilizes wavelet coefficients deduced from the Shannon mother wavelet function with varying dilation and translation parameters to create 2-D gray-level images and extracts features by generating global neighborhood structure maps, which are used to extract global image features.
Abstract: This paper proposes an approach for a 2-D representation of Shannon wavelets for highly reliable fault diagnosis of multiple induction motor defects. Since the wavelet transform is efficient for analyzing non-stationary and non-deterministic vibration signals, this paper utilizes wavelet coefficients deduced from the Shannon mother wavelet function with varying dilation and translation parameters to create 2-D gray-level images. Using the resulting images and their associated texture characteristics, this paper extracts features by generating global neighborhood structure maps, which are used to extract global image features. The texture features are then used as inputs in one-against-all multi-class support vector machines to identify faults in the induction machine. To evaluate the performance of the proposed approach, it is compared with five conventional state-of-the-art algorithms in terms of classification accuracy. In addition, this paper explores the robustness of the proposed approach in noisy environments by adding white Gaussian noise to the acquired vibration signals. The experimental results indicate that the proposed approach outperforms conventional algorithms in terms of the classification accuracy. Moreover, the proposed approach achieves higher classification accuracy, even in noisy environments.
01 Jan 2014
TL;DR: A novel quantum encryption scheme for quantum images based on quantum wavelet transform (QWT) and double diffusions is proposed and the corresponding quantum circuits are designed to demonstrates that the reasonable of the proposed scheme.
Abstract: In this paper, a novel quantum encryption scheme for quantum images based on quantum wavelet transform (QWT) and double diffusions is proposed. Firstly, diffusion operation applied on the input quantum image, and then QWT worked on the new quantum image to transform this image to the frequency domain. and following the diffusion operation is implemented on the QWT transformed quantum image. finally ,inverse QWT are used.The encryption keys are generated by a sensitive chaotic logistic map, which guarantee the security of the scheme. at the same time,we designed the corresponding quantum circuits to demonstrates that the reasonable of the proposed scheme.
TL;DR: A new denoising algorithm based on the dual-tree complex wavelet transform (DTCWT) can remove noise more thoroughly and better retain the boundary and texture of the signal.
Abstract: In biomedical signal processing, Gibbs oscillation and severe frequency aliasing may occur when using the traditional discrete wavelet transform (DWT). Herein, a new denoising algorithm based on the dual-tree complex wavelet transform (DTCWT) is presented. Electrocardiogram (ECG) signals and heart sound signals are denoised based on the DTCWT. The results prove that the DTCWT is efficient. The signal-to-noise ratio (SNR) and the mean square error (MSE) are used to compare the denoising effect. Results of the paired samples t-test show that the new method can remove noise more thoroughly and better retain the boundary and texture of the signal.
TL;DR: A two-dimensional continuous wavelet transform algorithm that has a remarkable ability to accurately and automatically extract full-field phase distribution from two phase-shifted interferograms where they may contain arbitrary and unknown phase shift.
TL;DR: Applications of wavelet transform and wavelet-packet transform in spectral analysis from 2002 to 2013 are reviewed, clearly stating that wavelet methods significantly outperform other traditional methods of signal processing.
Abstract: Wavelets are a topic of pure mathematics. But over the past decade, they have shown great promise and are now being adapted for a vast number of signal-processing applications. One of the main advantages of wavelet analysis is the amount of information that can be extracted from a signal. It has demonstrated unprecedented success in terms of asymptotic optimality, spatial adaptivity and computational efficiency. Applications of wavelet transform and wavelet-packet transform in spectral analysis from 2002 to 2013 are reviewed in this article, clearly stating that wavelet methods significantly outperform other traditional methods of signal processing.
TL;DR: In this paper, a discrete wavelet transform (DWT) is applied to analyze electrochemical characteristics and state-of-health (SOH) diagnosis of a Li-ion cell.
TL;DR: This paper shows that the image representation obtained with this redundant transform is a frame expansion, and derive the analysis and synthesis operators associated with it, and explores the use of this frame operators to image denoising and deblurring, and demonstrates in both cases state-of-the-art results.
Abstract: In our previous work [1] we have introduced a redundant tree-based wavelet transform (RTBWT), originally designed to represent functions defined on high dimensional data clouds and graphs. We have further shown that RTBWT can be used as a highly effective image-adaptive redundant transform that operates on an image using orderings of its overlapped patches. The resulting transform is robust to corruptions in the image, and thus able to efficiently represent the unknown target image even when it is calculated from its corrupted version. In this paper, we utilize this redundant transform as a powerful sparsity-promoting regularizer in inverse problems in image processing. We show that the image representation obtained with this transform is a frame expansion, and derive the analysis and synthesis operators associated with it. We explore the use of this frame operators to image denoising and deblurring, and demonstrate in both these cases state-of-the-art results.
18 Dec 2014
TL;DR: The optimized code is evaluated for performance and compared to the reference implementation as well as the FFTW library, and the main result is that, depending on the input parameters, the optimized Sparse Fast Fourier Transform library is two to five times faster than theReference implementation.
Abstract: The Sparse Fast Fourier Transform is a recent algorithm developed by Hassanieh et al. at MIT for Discrete Fourier Transforms on signals with a sparse frequency domain. A reference implementation of the algorithm exists and proves that the Sparse Fast Fourier Transform can be faster than modern FFT libraries. However, the reference implementation does not take advantage of modern hardware features like vector instruction sets or multithreading. In this Master Thesis the reference implementation’s performance will be analyzed and evaluated. Several optimizations are proposed and implemented in a high-performance Sparse Fast Fourier Transform library. The optimized code is evaluated for performance and compared to the reference implementation as well as the FFTW library. The main result is that, depending on the input parameters, the optimized Sparse Fast Fourier Transform library is two to five times faster than the reference implementation.
08 May 2014
TL;DR: A technique to extract energy features obtained using 2-D discrete wavelet transform can be used to distinguish between normal and glaucomatous images with very high accuracy.
Abstract: Wavelet Transforms is a part of large community of mathematical function approximation method, they are being increasing and being deployed in image processing for segmentation, filtering, classification etc. This work is based on image classification with the use of single level Discrete Wavelet Transform (DWT). Wavelets have been employed in many applications of signal processing. The texture features within images are extracted for accurate and efficient Glaucoma Classification. Energy is distributed over the wavelet sub-bands to find these important texture features. The discriminatory potential of wavelet features obtained from the daubechies (db3), symlets (sym3), and reverse biorthogonal (rbio3.3, rbio3.5, and rbio3.7) wavelet filters. We propose a technique to extract energy features obtained using 2-D discrete wavelet transform. The energy features obtained from the detailed coefficients can be used to distinguish between normal and glaucomatous images with very high accuracy. The effectiveness is evaluated using K-NN classifier by taking 30 normal and glaucoma images, 15 images are used for training and 15 images for testing.