Showing papers on "S transform published in 2016"

Synchrosqueezing S-Transform and Its Application in Seismic Spectral Decomposition

Abstract: The synchrosqueezing transform (SST) is a novel approach for time-frequency (T-F) representation of non-stationary signals. By synchrosqueezing and reassigning the T-F spectrum of the wavelet transform (WT) or the short time Fourier transform (STFT) of a signal, the SST can obtain a high-resolution T-F spectrum. In the light of the superiority of S-transform (ST) over the WT and the STFT, especially, in representing a high-frequency weak-amplitude signal on its T-F spectrum, we propose a synchrosqueezing S-transform (SSST) which is realized by synchrosqueezing the spectrum of the ST. The formulas for the SSST and its inverse transform are derived. Synthetic examples show that the SSST has obviously higher resolution than the ST, and is superior to the SST like the ST to the WT. We then applied the SSST to perform the spectral decomposition of a marine seismic data for natural gas hydrate exploration. The results illustrate that the SSST can be used to well detect frequency spectral anomalies correlated with the gas hydrate and free-gas accumulations. We can also conclude that the SSST is a good potential technique to assist seismic interpretation.

Detection and Classification of Power Quality Disturbances Using Double Resolution S-Transform and DAG-SVMs

Abstract: The accurate detection and classification of power quality (PQ) disturbances in power systems is a key step to determine the causes of these events before any proper countermeasure could be taken. This paper presents a new algorithm for detection and classification of PQ disturbances based on the combination of double-resolution S-transform (DRST) and directed acyclic graph support vector machines (DAG-SVMs). The proposed method first employs DRST for an effective feature extraction from power signals. Then, the DAG-SVMs are used to predict the classes of PQ disturbances. The DRST not only has better time–frequency localization and stronger robustness but also reduces the computational complexity without losing the useful information of the original signal in comparison with the traditional S-transform. Through the combined use of DRST and DAG-SVMs, the algorithm can be easily implemented in embedded real-time applications. Finally, the implementation of the proposed algorithm in a digital signal processor + advanced reduced instruction set computing machine-based hardware test platform is introduced. The effectiveness of the proposed method is demonstrated by means of computer simulations and practical experiments with single and combined PQ disturbances.

Enhanced Multiple Transform for Video Coding

Abstract: The Discrete Cosine Transform (DCT), and in particular the DCT type II, has been widely used for image and video compression. Although DCT efficiently approximates the optimal Karhunen–Loeve transform under first-order Markov conditions with low complexity, the energy packing efficiency is still limited since a fixed transform cannot always capture the highly dynamic statistics of natural video content. In this paper, to further improve the transform efficiency, an Enhanced Multiple Transform (EMT) scheme is proposed. In the proposed EMT, a few sinusoidal transforms, other than DCT, have also been utilized for coding both Intra and Inter prediction residuals. The best transform, as selected from a pre-defined transform subset specified by prediction mode, is explicitly signaled in a joint coding block level manner. Moreover, to accelerate encoding process, fast methods have also been proposed by skipping unnecessary transform rate-distortion evaluations using previously encoding statistics. The proposed method has been implemented on top of High-Efficiency Video Coding (HEVC) reference software, and significant coding gain has been verified.

The Radon Cumulative Distribution Transform and Its Application to Image Classification

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.

The Use of Continuous Wavelet Transform Based on the Fast Fourier Transform in the Analysis of Multi-channel Electrogastrography Recordings

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.

Amplitude-preserving nonlinear adaptive multiple attenuation using the high-order sparse Radon transform

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.

A Simplified Proof of Uncertainty Principle for Quaternion Linear Canonical Transform

Abstract: We provide a short and simple proof of an uncertainty principle associated with the quaternion linear canonical transform (QLCT) by considering the fundamental relationship between the QLCT and the quaternion Fourier transform (QFT). We show how this relation allows us to derive the inverse transform and Parseval and Plancherel formulas associated with the QLCT. Some other properties of the QLCT are also studied.

A SAR Image Despeckling Method Based on Two-Dimensional S Transform Shrinkage

Abstract: Speckle is a granular disturbance that affects synthetic aperture radar (SAR) images. Over the last three decades, many methods have been proposed for speckle reduction, where a tradeoff between despeckling and detail preservation is required. As an attempt to balance the performance on both sides, in this paper, we propose a 2-D S transform shrinkage algorithm using adaptive soft threshold for SAR image despeckling. It follows the idea of the wavelet shrinkage algorithm, but extends its major steps to take into account the peculiarities of S transform, i.e., adding adaptivity in the estimation of speckle standard deviation and threshold function, in an optimized computation procedure. Homogeneous and heterogeneous SAR images are used for quantitative evaluations, and both vintage and prevailing algorithms are used for comparison, which demonstrates the validity of the proposed method. Additionally, some instructive pieces of advice are given on the selection of suitable parameters of the proposed method under different circumstances.

Power Quality Disturbances Feature Selection and Recognition Using Optimal Multi-Resolution Fast S-Transform and CART Algorithm

Abstract: In order to improve the recognition accuracy and efficiency of power quality disturbances (PQD) in microgrids, a novel PQD feature selection and recognition method based on optimal multi-resolution fast S-transform (OMFST) and classification and regression tree (CART) algorithm is proposed. Firstly, OMFST is carried out according to the frequency domain characteristic of disturbance signal, and 67 features are extracted by time-frequency analysis to construct the original feature set. Subsequently, the optimal feature subset is determined by Gini importance and sorted according to an embedded feature selection method based on the Gini index. Finally, one standard error rule subtree evaluation methods were applied for cost complexity pruning. After pruning, the optimal decision tree (ODT) is obtained for PQD classification. The experiments show that the new method can effectively improve the classification efficiency and accuracy with feature selection step. Simultaneously, the ODT can be constructed automatically according to the ability of feature classification. In different noise environments, the classification accuracy of the new method is higher than the method based on probabilistic neural network, extreme learning machine, and support vector machine.

Gabor Wavelets in Image Processing

Abstract: This work shows the use of a two-dimensional Gabor wavelets in image processing. Convolution with such a two-dimensional wavelet can be separated into two series of one-dimensional ones. The key idea of this work is to utilize a Gabor wavelet as a multiscale partial differential operator of a given order. Gabor wavelets are used here to detect edges, corners and blobs. A performance of such an interest point detector is compared to detectors utilizing a Haar wavelet and a derivative of a Gaussian function. The proposed approach may be useful when a fast implementation of the Gabor transform is available or when the transform is already precomputed.

Analysis of time-frequency scattering transforms

Abstract: In this paper we address the problem of constructing a feature extractor which combines Mallat's scattering transform framework with time-frequency (Gabor) representations. To do this, we introduce a class of frames, called uniform covering frames, which includes a variety of semi-discrete Gabor systems. Incorporating a uniform covering frame with a neural network structure yields the Fourier scattering transform $\mathcal{S}_\mathcal{F}$ and the truncated Fourier scattering transform. We prove that $\mathcal{S}_\mathcal{F}$ propagates energy along frequency decreasing paths and its energy decays exponentially as a function of the depth. These quantitative estimates are fundamental in showing that $\mathcal{S}_\mathcal{F}$ satisfies the typical scattering transform properties, and in controlling the information loss due to width and depth truncation. We introduce the fast Fourier scattering transform algorithm, and illustrate the algorithm's performance. The time-frequency covering techniques developed in this paper are flexible and give insight into the analysis of scattering transforms.

The Ray Space Transform: A New Framework for Wave Field Processing

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.

A Universal High Impedance Fault Detection Technique for Distribution System Using S-Transform and Pattern Recognition

Abstract: This paper describes a new method for high impedance fault (HIF) detection based on s-transform (ST) and pattern recognition technique. Conventional distance, over current and ground fault relays are difficult to apply for High Impedance Fault (HIF) detection in distribution line because of sensitivity, diversity, selectivity issues in case of low value of fault current. Recently, s-transform has been successfully applied for different power system protection problem. It is a very useful tool to analyze transient fault signal to provide both time and frequency information unlike Fourier transform and the same has been considered for high impedance fault detection in this work. The features extracted using s-transform to train and test the two different intelligent classifier like artificial neural network (ANN) and support vector machine (SVM) separately, to discriminate the HIF with other transient phenomenon (Load switching, capacitor Switching) and also normal fault condition. A comparative study of these two classifiers has been reported based on their detection accuracy. It has been found that the proposed techniques are highly effective for high impedance fault detection under a wide range of operating conditions and noisy environment in a high voltage distribution network. The proposed scheme is fully simulated and analyzed by MATLAB/SIMULINK environment.

Logarithmic uncertainty principle for quaternion linear canonical transform

Abstract: The quaternion linear canonical transform (QLCT) can be thought as a generalization of the linear canonical transform (LCT) to quaternion algebra. The relationship between the QLCT and the quaternion Fourier transform (QFT) is derived. Based on this fact and properties of the QLCT, a logarithmic uncertainty principle associated with the quaternion linear canonical transform is established.

ECG signal analysis using wavelet coherence and s-transform for classification of cardiovascular diseases

Abstract: The spontaneous classification of cardiovascular diseases is a challenging task and can be made more feasible with proper ECG fluctuation analysis. In this contribution we perform a qualitative analysis of the ECG data using complex Gaussian wavelets to investigate the multi-scale, self similar behaviour and deviation via phase plots of the wavelet cross spectrum of the ECG signals. We further analyze ECG signals using S transform to overcome the limitations of continuous wavelet transform and make the results more consistent and reliable. The results obtained are promising and the inferences drawn to aid in disease classification using the ECG signals are also discussed.

On-line recursive method of phasor and frequency estimation for power system monitoring and relaying

Abstract: A real-time method of phasor and frequency estimation is proposed in this study. The method is based on the recently developed signal processing tool, S-transform. It is implemented recursively by taking advantage of recursive complex band pass infinite impulse response filters with a low computational burden, using only 10 samples of the previous output and nine samples of the input signal. The method is implemented in the Matlab software and its performance is appraised considering the decaying DC component, noise and severe harmonic and inter-harmonic distortions and dynamic conditions. Moreover, a wavelet based method, a discrete Fourier and a recursive discrete Fourier based method for phasor estimation have been implemented and the performances of the methods have been compared in various operating conditions. To assess methods performances for real signals, the recorded signals of a differential relay have been fed to all of the methods and their performances compared. In addition, a power system has been simulated in the EMTP software, and performances of the methods have been assessed using the recorded fault signals of the EMTP software. Both the real data and simulation results indicate that the proposed S-transform based method is superior to other methods considering dynamic and static conditions.

Zak transform and uncertainty principles associated with the linear canonical transform

Abstract: Several new results about Zak transform and uncertainty principles in the linear canonical transform (LCT) domains are presented. The results obtained rely mainly on relationship between the LCT and the classical Fourier transform. The findings will likely have potential applications in optics and signal processing.

Multiplicative filtering in the linear canonical transform domain

Abstract: As a generalisation of fractional Fourier transform, Fresnel transform and Fourier transform, the linear canonical transform (LCT) is a four parameter class of integral transform and has been used in many fields of optics and signal processing. In this study, the authors present a model of multiplicative filtering for the band-limited signals in the LCT domain by using the convolution theorem given in the literature. Finally, practical applications of filtering in LCT domain are discussed based on the presented model of multiplicative filtering and results are compared with that of frequency domain filtering and fractional domain filtering. It is found from the simulation results that mean square error is minimum for different values of signal-to-noise ratio in case of LCT domain filtering.

An Amplitude Preserving S-Transform for Seismic Data Attenuation Compensation

Abstract: The S-transform (ST), as a time–frequency analysis tool, has been widely used, but the amplitude preserving property is a little poor near the boundary of the selected discrete signal. The reason lies that the summation of the product between the analytical window and the comprehensive window over the sliding step deviates from unity near the boundary in the discrete cases. In order to hold the amplitude preserving property for the discrete signal recovery analysis, an amplitude preserving S-transform (APST) is proposed based on a novel analytical window selection. First, lots of numerical tests are used to analyze the shortcomings of the ST near the boundary for the selected discrete signal and demonstrate the effectiveness and the validity of the proposed APST using the novel analytical window. After that, the proposed APST is used for seismic data attenuation compensation, during which the attenuation function is estimated based on the minimum phase assumption using a statistical variable-step hyperbolic smoothing method. Numerical examples on synthetic and field data demonstrate the validity of the proposed method using the seismogram and time–frequency spectrum comparisons. Besides, the proposed APST can be easily extended into a generalized ST which is more flexible compared with the ST, and it can also be used in seismology, remote sensing, and other related discrete signal analysis fields.

Optical spectrum encryption in associated fractional Fourier transform and gyrator transform domain

Abstract: An optical spectrum encryption algorithm for hyperspectral image is proposed in this paper, in which the spatial and spectrum information can be encrypted simultaneously. The Baker mapping is utilized to scramble each band of the hyperspectral cube before the optical transform. Subsequently, 100 bands are divided into real part and imaginary part of the complex function expressing light field. Then, the scrambled data is imported into fractional Fourier transform and gyrator transform system. A random binary vector is designed and employed in the optical transform for enhancing the security of the encryption system. The amplitude and phase information in the output plane can be regarded as the encrypted information. Some numerical simulations are made to demonstrate the performance of the proposed encryption system.

Quaternionic Stockwell transform

Abstract: In this article, we extend the Stockwell transform to the space of all square integrable quaternion-valued functions on the real line, using the convolution of quaternion-valued functions. We prove that the extended Stockwel transform satisfies the Parseval's formula, inversion formula, and uncertainty principle. We also characterize the range of the Stockwell transform on L2(R,H) and prove a convolution theorem for the extended Stockwell transform. Applying the convolution theorem, we extend the transform to a suitable Boehmian space of quaternion-valued functions.