Discrete Orthonormal S-transform Research Articles

Multiple discrete orthonormal S-transforms and its application in analyzing, modelling, and simulating random process and field

We examine the derivation and characteristics of the basis function employed in the discrete orthonormal S-transform (DOST). The examination is aimed at clarifying the interpretation of the power characteristics associated with the partitions and basis functions employed in DOST. Based on this examination, it is suggested that a one-half shift to the time index of the original DOST basis functions could be considered to facilitate the interpretation of the power distribution in the time–frequency domain. Although the non-redundant DOST is a highly efficient transform, its resolution in the time–frequency space is relatively coarse as compared to some of the continuous time–frequency decomposition techniques. To improve the resolution, and without significantly increasing the computational time, we propose the multiple DOSTs (MDOSTs) approach that uses M DOSTs, each associated with a different partition scheme in the time–frequency domain and a set of corresponding orthogonal basis functions. The redundancy factor of MDOSTs is simply equal to M. In addition, we show that the MDOSTs can be used to model and simulate nonstationary non-Gaussian processes and fields within the framework of the iterative power and amplitude correction algorithm. The use of MDOSTs for analyzing, modelling, and simulating seismic ground motion and corrosion surface is illustrated by numerical examples. The results show that using MDOSTs can effectively improve the time–frequency resolutions while maintaining high computational efficiency.

Genetic algorithm based image reconstruction applying the digital holography process with the Discrete Orthonormal Stockwell Transform technique for diagnosis of COVID-19

World Health Organization has described the real-time reverse transcription-polymerase chain reaction test method for the diagnosis of the novel coronavirus disease (COVID-19). However, the limited number of test kits, the long-term results of the tests, the high probability of the disease spreading during the test and imaging without focused images necessitate the use of alternative diagnostic methods such as chest X-ray (CXR) imaging. The storage of data obtained for the diagnosis of the disease also poses a major problem. This causes misdiagnosis and delays treatment. In this work, we propose a hybrid 3D reconstruction method of CXR images (CXRI) to detect coronavirus pneumonia and prevent misdiagnosis on CXRI. We used the digital holography technique (DHT) for obtaining a priori information of CXRI stored in created digital hologram (CDH). In this way, the elimination of the storage problem that requires high space was revealed. In addition, Discrete Orthonormal S-Transform (DOST) is applied to the reconstructed CDH image obtained by using DHT. This method is called CDH_DHT_DOST. A multiresolution spatial-frequency representation of the lung images that belong to healthy people and diseased people with the COVID-19 virus is obtained by using the CDH_DHT_DOST. Moreover, the genetic algorithm (GA) is adopted for the reconstruction process for optimization of the CDH image and then DOST is applied. This hybrid method is called CDH_GA_DOST. Finally, we compare the results obtained from CDH_DHT_DOST and CDH_GA_DOST. The results show the feasibility of reconstructing CXRI with CDH_GA_DOST. The proposed method holds promises to meet demands for the detection of the COVID-19 virus.

Data-driven simulation of multivariate nonstationary wind velocity with explicit introduction of the time-varying coherence functions

An S-transform (ST) based data-driven simulation methodology is proposed of multivariate nonstationary wind velocity with explicit introduction of the time-varying coherence functions. This framework differs from that based on the evolutionary spectral theory that uniform or non-uniform modulation functions needs to be assigned. In defining the time-frequency power spectral density (TFPSD) in accordance with the ST coefficients, the Parseval's theorem is considered to ensure energy preservation. The proposed method is firstly applied to simulated nonstationary wind velocity. For comparisons, the results of the discrete orthonormal S transform (DOST) are also included. The research demonstrates that the ST based results agree well with the original, but a bias exists between the results simulated by DOST and the original, indicating that the feasibility of the proposed method. Employing four measured downburst records to simulate multivariate nonstationary wind velocity by the proposed method further validates its feasibility. In order to enhance the simulation fidelity, the inverse S-transform (IST) based regulation and control method (IST-RCM) of high precision is developed, where the balancing parameter is defined and formulated to express quantitatively the relationship between accuracy and efficiency. It is found that the results with IST-RCM get more close to the actual wind velocity records.

Modeling and simulating nonhomogeneous non-Gaussian corrosion fields on buried pipelines and its use in predicting burst capacities of corroded pipelines

The present study proposes an iterative algorithm to simulate nonhomogeneous non-Gaussian corrosion fields on buried oil and gas pipeline's external surfaces. The algorithm incorporates the concepts of the discrete orthonormal S-transform and the iterative amplitude adjusted Fourier transform algorithm. This results in the space-wavenumber power spectral density function and marginal distribution function of the simulated corrosion field matching, respectively, their corresponding targets that could be determined from the high-resolution corrosion measurement data obtained from naturally corroded pipe segments. The simulation results demonstrate that the use of the proposed algorithm is able to capture the statistical characteristics of naturally occurring corrosion fields on pipelines. Three-dimensional elasto-plastic finite element analyses are carried out to evaluate the burst capacities of pipe segments containing simulated corrosion fields. Combined with finite element analyses, this algorithm can be employed to conduct virtual full-scale burst tests of corroded pipe specimens, which is of great value to the pipeline corrosion management practice.

Modelling and simulating thunderstorm/downburst winds using S-transform and discrete orthonormal S-transform

Fluctuating winds from intense thunderstorm/downburst are often modelled as the amplitude modulated evolutionary stochastic processes and simulated based on the spectral representation method. Aspects of the modelling and simulation include assessing time and frequency dependent power spectrum, and the identification of the amplitude and frequency modulations are not straightforward. The present study uses the S-transform and discrete orthonormal S-transform to evaluate the time-frequency power spectral density (TFPSD) functions and coherence functions of nonstationary winds. The results for a thunderstorm/downburst event indicate that the coherence is time-dependent. The use of the TFPSD functions and a newly developed simulation method to generate winds acted on single and multiple points with a time-dependent coherence is shown. A comparison of the mean of the TFPSD of the simulated winds to its corresponding target is used to validate the adequacy of the simulation models. The use of the simulated records to assess the record-to-record variability on the maximum responses of a nonlinear inelastic single-degree-of-freedom system is given.

Despeckling of SAR Images Using Shrinkage of Two-Dimensional Discrete Orthonormal S-Transform

Speckles are inherent to SAR. They hide and undermine several relevant information contained in the SAR images. In this paper, a despeckling algorithm using the shrinkage of two-dimensional discrete orthonormal S-transform (2D-DOST) coefficients in the transform domain along with shock filter is proposed. Also, an attempt has been made as a post-processing step to preserve the edges and other details while removing the speckle. The proposed strategy involves decomposing the SAR image into low and high-frequency components and processing them separately. A shock filter is used to smooth out the small variations in low-frequency components, and the high-frequency components are treated with a shrinkage of 2D-DOST coefficients. The edges, for enhancement, are detected using a ratio-based edge detection algorithm. The proposed method is tested, verified, and compared with some well-known models on C-band and X-band SAR images. A detailed experimental analysis is illustrated.

A Time–Frequency Representation Model for Seismic Ground Motions

ABSTRACTA probabilistic model of the time–frequency power spectral density (TFPSD) is presented. The model is developed, based on the time–frequency representation of records from strike-slip earthquakes, in which the time–frequency representation is obtained by applying the S-transform (ST). The model for the TFPSD implicitly considers the amplitude modulation and frequency modulation for the nonstationary ground motions; this differs from the commonly used evolutionary PSD model. Predicting models for the model parameters, based on seismic source and site characteristics, are developed. The use of the model to simulate ground motions for scenario seismic events is illustrated, in which the simulation is carried out using a recently developed model that is based on the discrete orthonormal ST and ST. The illustrative example highlights the simplicity of using the proposed model and the physical meaning of some of the model parameters. A model validation analysis is carried out by comparing the statistics of the pseudospectral acceleration obtained from the simulated records to those obtained using a few ground-motion models available in the literature and considered actual records. The comparison indicates the adequacy of the proposed model.

Automated detection system for texture feature based classification on different image datasets using S-transform

The objective of this study is to present a computer-aided diagnosis (CAD) system for automatic detection of brain tumors in brain magnetic resonance (MR) image data sets as we consider the brain image dataset from the different datasets. The proposed system initially pre-processes the input images using Fuzzy C-means (FCM) for image segmentation. Subsequently, it utilizes variant of S-transform namely discrete orthonormal S-transform (DOST) to extract the texture features and its dimensionality is reduced using Principal component analysis (PCA) and linear discriminant analysis (LDA). The reduced features are then supplied to the proposed Adaboost algorithm with Random Forest (ADBRF) classifier where the random forest is used as the base classifier for classifying the abnormal brain tumors in MRI image datasets. The simulation results based on the five runs of k-fold stratified cross-validation indicate that the proposed method yields superior accuracy (98.26%) as compared to existing schemes.

Time–Frequency Spectral Representation Models to Simulate Nonstationary Processes and Their Use to Generate Ground Motions

In the present study, two new models are proposed to model nonstationary stochastic processes with time-frequency-dependent spectra and coherence. The models are developed based on the discrete orthonormal S-transform and are enhanced by using the time-frequency representation from the S-transform. One of the models is shown to be usable in carrying out the conditional simulation. A parallel is drawn between the proposed models and those based on the spectral representation method using the ordinary Fourier analysis to facilitate an understanding of the proposed models. Unlike the use of the evolutionary spectral theory, no amplitude modulation or frequency modulation functions need to be assigned and identified for the proposed models because they are included explicitly in the time-frequency spectra. Moreover, the use of the S-transform and discrete orthonormal S-transform provides a familiar time-frequency spectral representation rather than the timescale representation obtained from the wavelet transform. The exposition and use of the models are focused on the simulation of ground motions at single and multiple support, although the models can be equally applicable to nonstationary processes, such as the winds and waves. The adequacy of the simulated ground motion records is assessed in terms of the time-frequency spectral representation and response spectrum. Numerical examples, including conditionally simulate ground motions, are also given.

Resilience-oriented protection scheme for TCSC-compensated line

This paper presents a resilience-oriented protection scheme for TCSC-compensated Line. A cross-differential protection scheme is proposed to enhance the resilience of a parallel transmission line (PTL) in the presence of a thyristor controlled series capacitor (TCSC). The faulty phase(s) is (are) identified by estimating the spectral energy of the three-phase currents and computed by applying an efficient powerful signal processing tool known as fast discrete orthonormal S-transform (FDOST). The proposed scheme is widely evaluated against various faults and dynamic power system conditions. The obtained results indicate the proposed resilience-oriented protection scheme is adaptable to different power system scenarios. The scheme precisely classifies the fault with effective discrimination between internal and external faults on a transmission line and a response time of a maximum one cycle from the fault inception.

Use of Discrete Orthonormal S-Transform to Simulate Earthquake Ground Motions

ABSTRACTThe S-transform and discrete orthonormal S-transform (DOST) produce time–frequency representations, which is in contrast to the wavelet transformations. Similar in the Fourier transform, the use of the S-transform and DOST provides frequency-dependent resolution with absolutely referenced phase information. Although the decomposed signal using DOST is expressed as a sum of orthonormal basis function, this is not the case if the S-transform is used. In the present study, a procedure to simulate nonstationary ground motions based on DOST is proposed based on a seed record or given a target amplitude of DOST coefficients. It is shown that the model has zero mean, and its variance equals the assigned target. Using five real records, each from a larger earthquake, the application of the DOST and S-transform to the records is carried out. Although the time–frequency resolution obtained from DOST is coarse as compared to that obtained using the S-transform, its use identifies clearly time–frequency characteristics. Samples of ground motions are simulated using the proposed method based on the amplitude of the DOST coefficients of a seed record or on the average amplitude of the DOST coefficients of a set of actual records. The comparison of the time–frequency resolution, Fourier spectrum, time-varying power distribution, and response spectrum of the simulated and seed records indicates that the proposed simulation model is a useful and practical tool to simulate nonstationary ground motions.

FDOST-Based Fault Classification Scheme for Fixed Series Compensated Transmission System

This paper proposes a new method for diagnosis of fault type and faulty phase of a series compensated transmission line. The standard deviation (SD) principle together with the fast discrete orthonormal s-transform (FDOST) and the decision tree (DT) is applied for the purpose of fault classification. The FDOST, as an efficient signal processing tool, is used for extracting the features from a half cycle window of voltage and current signals sampled from one end of the power system network. Finally, the SD of a half cycle post-fault samples of the FDOST coefficients is calculated to form the input feature vector for the DT-based classifier. The features are processed by the DT to classify faults. The practicability of the proposed method is validated by modified Western System Coordinating Council 3-machine 9-bus system simulated in the PSCAD/EMTDC software and field fault data captured from a real transmission network of Chhattisgarh state, India. The results confirm that the proposed method reliably classifies all types of faults with high efficacy.

Investigation of power quality disturbances by using 2D discrete orthonormal S-transform, machine learning and multi-objective evolutionary algorithms

Abstract The aim of this paper is to investigate the power quality analysis by using 2D discrete orthonormal S-transform, machine learning and multi-objective evolutionary algorithms. The fact that PQ signals are one-dimensional (1D) signals due to their nature leads to the search for feature extraction approaches based on 1D signal processing methods. Due to the electric network is getting more and more complicated day by day, it is necessary to determine effectively the disturbances events. In the proposed method, extraction of a new feature based on two-dimensional (2D) signal processing by 2D Fast Discrete Orthonormal Stockwell Transform (2D-FDOST) method and determination of the most suitable feature group by Non-dominated Sorting Genetic Algorithm II (NSGA-II) method are performed. Eleven different PQ events are synthetically produced based on mathematical modelling. 1D signals are transformed into 2D signals with equal row and column numbers. Statistical and image-based features are created on the amplitude and phase matrices obtained by 2D-FDOST method from 2D signals. The NSGA-II method, which is one of the multi-objective evolutionary optimization methods, is used to convert a large number of feature vectors into a small number of useful feature groups. NSGA-II produces the optimal solution for two different fitness functions that calculate the number of features and classifier performance. By using different machine learning classifiers for selected features, a model classifying PQ disturbances with high performance and robust structure against noisy situations is created.

Texture feature based classification on microscopic blood smear for acute lymphoblastic leukemia detection

Abstract This paper presents an effective scheme for classification of the normal white blood cells from the affected cells in a microscopic image. The proposed method initially pre-processes the input images using Y component of the CMYK image and a triangle method of thresholding. Subsequently, it utilizes discrete orthonormal S-transform (DOST) to extract the texture features, and its dimensionality is reduced using linear discriminant analysis. The reduced features are then supplied to the proposed Adaboost algorithm with RF (ADBRF) classifier where the random forest is used as the base classifier. A publicly available dataset, ALL-IDB1 is used to validate the proposed scheme. The simulation results based on the five runs of k-fold stratified cross-validation indicate that the proposed method yields superior accuracy (99.66%) as compared to existing schemes.

A Novel Fault Classification Scheme for Series Capacitor Compensated Transmission Line Based on Bagged Tree Ensemble Classifier

This paper presents a novel intelligent fault classification scheme for fixed series capacitor compensated transmission line. The singular value decomposition principle is applied along with the fast discrete orthonormal S-transform (FDOST) and bagged tree ensemble classifier for classification of faults under different scenarios. Classification input features are extracted from 1/2 cycle post-fault current data through the FDOST. The feasibility of the proposed relaying scheme is tested on a modified WSCC 3-machine 9-bus system under different fault conditions using PSCAD/EMTDC, and the results indicate the proposed scheme to be fast and accurate. The robustness of the proposed scheme to noise and current transformer saturation is also established. The obtained results under different fault scenarios confirm the efficacy of the proposed scheme.

EEG artifact removal and noise suppression by Discrete Orthonormal S-Transform denoising

Electroencephalographic data is often contaminated by artifacts produced from non-cerebral sources such as muscle activity, eye movements and other electrical disturbances. Artifact removal and noise suppression is essential prior to information extraction from Electroencephalogram signals. In this paper, a novel automated methodology of artifact removal and noise suppression of Electroencephalogram data is proposed. The proposed methodology relies on two distinct techniques such as Independent Component Analysis and Discrete Orthonormal S-Transform. The method is carried out in four methodological steps viz. Blind Source Separation of artifact contaminated Electroencephalographic data in independent components, automated identification of artifactual independent components, Discrete Orthonormal S-Transform denoising of artifactual independent components and reconstruction of clean Electroencephalogram data. The efficacy of the methodology is evaluated on simulated as well as experimental artifactual Electroencephalogram data. The proposed methodology effectively removed large proportion of artifacts and noise while preserved useful cerebral activity.

New Speech Enhancement based on Discrete Orthonormal Stockwell Transform

S-transform is an effective time-frequency representation which gives simultaneous frequency and time distribution information alike the wavelet transforms (WT). However, the ST redundantly doubles the dimension of the original data set and the Discrete Orthonormal S-Transform (DOST) can decrease the redundancy of S-transform farther. So, this paper aims to propose a new method to remove additive background noise from noisy speech signal using DOST which supplies a multi-resolution analysis (MRA) spatial-frequency representation of image processing and signal analysis. Hence, the performances of the applied speech enhancement technique have been evaluated objectively and subjectively in comparison with respect to many other methods in four background noises at different SNR levels.

New Pattern-Recognition Method for Fault Analysis in Transmission Line With UPFC

In this paper, a new set of time-frequency features for fault-type identification, fault-loop status supervision, and fault-zone detection modules in a compensated transmission line with a unified power-flow controller is proposed. Some features are extracted from a one-cycle data window of one side of the compensated line, including 3/16 cycle of postfault data by the fast discrete orthonormal S-Transform (FDOST). The computation burden of the FDOST as a time-frequency decomposition is the same as the fast Fourier transform. The support vector machine is employed for classification of the ranked features by the Gram-Schmidt method. The graphical representations of extracted features and the obtained numerical results under different conditions confirm the efficacy of the proposed scheme.

Classification of mammogram using two-dimensional discrete orthonormal S-transform for breast cancer detection.

An efficient approach for classification of mammograms for detection of breast cancer is presented. The approach utilises the two-dimensional discrete orthonormal S-transform (DOST) to extract the coefficients from the digital mammograms. A feature selection algorithm based the on null-hypothesis test with statistical 'two-sample t-test' method has been suggested to select most significant coefficients from a large number of DOST coefficients. The selected coefficients are used as features in the classification of mammographic images as benign or malignant. This scheme utilises an AdaBoost algorithm with random forest as its base classifier. Two standard databases Mammographic Image Analysis Society (MIAS) and Digital Database for Screening Mammography (DDSM) are used for the validation of the proposed scheme. Simulation results show an optimal classification performance with respect to accuracies of 98.3 and 98.8% and AUC (receiver operating characteristic) values of 0.9985 and 0.9992 for MIAS and DDSM, respectively. Comparative analysis shows that the proposed scheme outperforms its competent schemes.

Classification of handwritten Odia basic character using Stockwell transform

In this paper, we have proposed a scheme for the recognition of handwritten basic isolated Odia characters. Our method utilises chain code histogram (CCH) to split the overall dataset into two different groups. Preprocessing is carried out for noise removal and enhancement of the character images in each group. Discrete orthonormal S-transform (DOST) features are extracted followed by a PCA-based feature reduction scheme to derive discriminant features to be used by the ANN for classification. Comparative analysis has been performed on a reasonably large dataset with the competent schemes. From experimental results, we conclude that our proposed scheme outperforms other schemes on the dataset that we have designed and provides an overall accuracy of 98.55%.