A study of wavelet transforms applied for fracture identification and fracture density evaluation

Combining wavelet transforms with conventional log differential curves is used to identify fractured sections is a new idea.In this paper,we first compute the mother wavelet transform of conventional logs and the wavelet decomposed signals are compared with fractures identified from image logs to determine the fracture-matched mother wavelet.Then the mother wavelet-based decomposed signal combined with the differential curves of conventional well logs create a fracture indicator curve,identifying the fractured zone.Finally the fracture density can be precisely evaluated by the linear relationship of the indicator curve and image log fracture density.This method has been successfully used to evaluate igneous reservoir fractures in the southern Songnan basin and the calculated density from the indicator curve and density from image logs are both basically consistent.

Inversion formula and Parseval theorem for complex continuous wavelet transforms studied by entangled state representation

In a preceding letter （2007 Opt. Lett. 32 554） we propose complex continuous wavelet transforms and found Laguerre-Gaussian mother wavelets family. In this work we present the inversion formula and Parseval theorem for complex continuous wavelet transform by virtue of the entangled state representation, which makes the complex continuous wavelet transform theory complete. A new orthogonal property of mother wavelet in parameter space is revealed.

Variable stiffness control algorithm for high-rising buildings of closely spaced frequencies based on wavelet transforms

To establish the algorithm of SAT-TMD system with the wavelet transform(WT),the modal mass participation ratio is proposed to distinguish if the high-rising structure has the characteristic of closely distributed frequencies.A time varying analytical model of high-rising structure such as TV-tower with the SAT-TMD is developed.The proposed new idea is to use WT to identify the dominant frequency of structural response in a segment time,and track its variation as a function of time to retune the SAT-TMD.The effectiveness of SAT-TMD is investigated and it is more robust to change in building stiffness and damping than that of the TMD with a fixed frequency corresponding to a fixed mode frequency of the building.It is proved that SAT-TMD is particularly effective in reducing the response even when the building stiffness is changed by ±15%;whereas the TMD loses its effectiveness under such building stiffness variations.

Audio Zero-Watermark Scheme Based on Discrete Cosine Transform-Discrete Wavelet TransformSingular Value Decomposition

Traditional watermark embedding schemes inevitably modify the data in a host audio signal and lead to the degradation of the host signal.In this paper,a novel audio zero-watermarking algorithm based on discrete wavelet transform(DWT),discrete cosine transform(DCT),and singular value decomposition(SVD) is presented.The watermark is registered by performing SVD on the coefficients generated through DWT and DCT to avoid data modification and host signal degradation.Simulation results show that the proposed zero-watermarking algorithm is strongly robust to common signal processing methods such as requantization,MP3 compression,resampling,addition of white Gaussian noise,and low-pass filtering.

Optical encryption with cascaded fractional wavelet transforms

On the basis of fractional wavelet transform, we propose a new method called cascaded fractional wavelet transform to encrypt images. It has the virtues of fractional Fourier transform and wavelet transform. Fractional orders, standard focal lengths and scaling factors are its keys. Multistage fractional Fourier transforms can add the keys easily and strengthen information se-curity. This method can also realize partial encryption just as wavelet transform and fractional wavelet transform. Optical reali-zation of encryption and decryption is proposed. Computer simulations confirmed its possibility.

Application of Bipartite Entangled States to Quantum Mechanical Version of Complex Wavelet Transforms

We introduce the bipartite entangled states to present a quantum mechanical version of complex wavelet transform. Using the technique of integral within an ordered product of operators we show that the complex wavelet transform can be studied in terms of various quantum state vectors in two-mode Fock space. In this way the creterion for mother wavelet can be examined quantum-mechanically and therefore more deeply.

Gauss linear frequency modulation wavelet transforms and its application to seismic phases identification

Based on the characteristics of gradual change style seismic signal onset which has more high frequency signal components but less magnitude, this paper selects Gauss linear frequency modulation wavelet as base function to study the change characteristics of Gauss linear frequency modulation wavelet transform with difference wavelet and signal parameters, analyzes the error origin of seismic phases identification on the basis of Gauss linear frequency modulation wavelet transform, puts forward a kind of new method identifying gradual change style seismic phases with background noise which is called fixed scale wavelet transform ratio, and presents application examples about simulation digital signal and actual seismic phases recording onsets identification.

Power System Transients Analysis by Wavelet Transforms

In contrast to Fourier transform, wavelet transform is especially suitable for transient analysis because of its time frequency characteristics with automatically adjusted window lengths. Research shows that wavelet transform is one of the most powerful tools for power system transient analysis. The basic ideas of wavelet transform are presented in the paper together with several power system applications. It is clear that wavelet transform has some clear advantages over other transforms in detecting, analyzing, and identifying various types of power system transients.

Enhancing the Odd Peaks Detection in OFDM Systems Using Wavelet Transforms

This work aims to study the effect of unwanted peaks and enhance the performance of wireless systems on the basis of tackling such peaks. A new proposition has been made based on wavelet transform method and its entropy. Signals with large peak-to-average power ratio (PAPR) will be examined such as the ones that are considered as the major Orthogonal Frequency Division Multiplexing (OFDM) systems drawbacks. Furthermore, aspatial diversity Multiple-Input Multiple- Out-put (MIMO) technology is used to overcome the complexity addition that could arise in our proposition. To draw the best performance of this work, a MATLAB simulation has been used;it is divided into three main stages, namely, MIMO-OFDM symbols’ reconstruction based on wavelet transform, a predetermined thresholding formula, and finally, moving filter. This algorithm is called Peaks’ detection based Entropy Wavelet Transform;PD-EWT. Based on the simulation, and under some constrains such as the bandwidth occupancy and the complexity structure of the transceivers, a peak detection ratio has been achieved and reaches around 0.85. Comparing with our previously published works, the PD-EWT enhances detection ratio for 0.25 more peaks.

Three-dimensional quantum wavelet transforms

Wavelet transform is being widely used in the field of information processing.One-dimension and two-dimension quantum wavelet transforms have been investigated as important tool algorithms.However,three-dimensional quantum wavelet transforms have not been reported.This paper proposes a multi-level three-dimensional quantum wavelet transform theory to implement the wavelet transform for quantum videos.Then,we construct the iterative formulas for the multi-level three-dimensional Haar and Daubechies D4 quantum wavelet transforms,respectively.Next,we design quantum circuits of the two wavelet transforms using iterative methods.Complexity analysis shows that the proposed wavelet transforms offer exponential speed-up over their classical counterparts.Finally,the proposed quantum wavelet transforms are selected to realize quantum video compression as a primary application.Simulation results reveal that the proposed wavelet transforms have better compression performance for quantum videos than two-dimension quantum wavelet transforms.

A lightweight symmetric image encryption cryptosystem in wavelet domain based on an improved sine map

In the era of big data,the number of images transmitted over the public channel increases exponentially.As a result,it is crucial to devise the efficient and highly secure encryption method to safeguard the sensitive image.In this paper,an improved sine map(ISM)possessing a larger chaotic region,more complex chaotic behavior and greater unpredictability is proposed and extensively tested.Drawing upon the strengths of ISM,we introduce a lightweight symmetric image encryption cryptosystem in wavelet domain(WDLIC).The WDLIC employs selective encryption to strike a satisfactory balance between security and speed.Initially,only the low-frequency-low-frequency component is chosen to encrypt utilizing classic permutation and diffusion.Then leveraging the statistical properties in wavelet domain,Gaussianization operation which opens the minds of encrypting image information in wavelet domain is first proposed and employed to all sub-bands.Simulations and theoretical analysis demonstrate the high speed and the remarkable effectiveness of WDLIC.

Image Hiding with High Robustness Based on Dynamic Region Attention in the Wavelet Domain

Hidden capacity,concealment,security,and robustness are essential indicators of hiding algorithms.Currently,hiding algorithms tend to focus on algorithmic capacity,concealment,and security but often overlook the robustness of the algorithms.In practical applications,the container can suffer from damage caused by noise,cropping,and other attacks during transmission,resulting in challenging or even impossible complete recovery of the secret image.An image hiding algorithm based on dynamic region attention in the multi-scale wavelet domain is proposed to address this issue and enhance the robustness of hiding algorithms.In this proposed algorithm,a secret image of size 256×256 is first decomposed using an eight-level Haar wavelet transform.The wavelet transform generates one coefficient in the approximation component and twenty-four detail bands,which are then embedded into the carrier image via a hiding network.During the recovery process,the container image is divided into four non-overlapping parts,each employed to reconstruct a low-resolution secret image.These lowresolution secret images are combined using densemodules to obtain a high-quality secret image.The experimental results showed that even under destructive attacks on the container image,the proposed algorithm is successful in recovering a high-quality secret image,indicating that the algorithm exhibits a high degree of robustness against various attacks.The proposed algorithm effectively addresses the robustness issue by incorporating both spatial and channel attention mechanisms in the multi-scale wavelet domain,making it suitable for practical applications.In conclusion,the image hiding algorithm introduced in this study offers significant improvements in robustness compared to existing algorithms.Its ability to recover high-quality secret images even in the presence of destructive attacksmakes it an attractive option for various applications.Further research and experimentation can explore the algorithm’s performance under different scenarios and expand its potential applications.

Research on the longitudinal protection of a through-type cophase traction direct power supply system based on the empirical wavelet transform

This paper proposes a longitudinal protection scheme utilizing empirical wavelet transform(EWT)for a through-type cophase traction direct power supply system,where both sides of a traction network line exhibit a distinctive boundary structure.This approach capitalizes on the boundary’s capacity to attenuate the high-frequency component of fault signals,resulting in a variation in the high-frequency transient energy ratio when faults occur inside or outside the line.During internal line faults,the high-frequency transient energy at the checkpoints located at both ends surpasses that of its neighboring lines.Conversely,for faults external to the line,the energy is lower compared to adjacent lines.EWT is employed to decompose the collected fault current signals,allowing access to the high-frequency transient energy.The longitudinal protection for the traction network line is established based on disparities between both ends of the traction network line and the high-frequency transient energy on either side of the boundary.Moreover,simulation verification through experimental results demonstrates the effectiveness of the proposed protection scheme across various initial fault angles,distances to faults,and fault transition resistances.

Olive Leaf Disease Detection via Wavelet Transform and Feature Fusion of Pre-Trained Deep Learning Models

Olive trees are susceptible to a variety of diseases that can cause significant crop damage and economic losses.Early detection of these diseases is essential for effective management.We propose a novel transformed wavelet,feature-fused,pre-trained deep learning model for detecting olive leaf diseases.The proposed model combines wavelet transforms with pre-trained deep-learning models to extract discriminative features from olive leaf images.The model has four main phases:preprocessing using data augmentation,three-level wavelet transformation,learning using pre-trained deep learning models,and a fused deep learning model.In the preprocessing phase,the image dataset is augmented using techniques such as resizing,rescaling,flipping,rotation,zooming,and contrasting.In wavelet transformation,the augmented images are decomposed into three frequency levels.Three pre-trained deep learning models,EfficientNet-B7,DenseNet-201,and ResNet-152-V2,are used in the learning phase.The models were trained using the approximate images of the third-level sub-band of the wavelet transform.In the fused phase,the fused model consists of a merge layer,three dense layers,and two dropout layers.The proposed model was evaluated using a dataset of images of healthy and infected olive leaves.It achieved an accuracy of 99.72%in the diagnosis of olive leaf diseases,which exceeds the accuracy of other methods reported in the literature.This finding suggests that our proposed method is a promising tool for the early detection of olive leaf diseases.

Weak Fault Feature Extraction of the Rotating Machinery Using Flexible Analytic Wavelet Transform and Nonlinear Quantum Permutation Entropy

Addressing the challenges posed by the nonlinear and non-stationary vibrations in rotating machinery,where weak fault characteristic signals hinder accurate fault state representation,we propose a novel feature extraction method that combines the Flexible Analytic Wavelet Transform(FAWT)with Nonlinear Quantum Permutation Entropy.FAWT,leveraging fractional orders and arbitrary scaling and translation factors,exhibits superior translational invariance and adjustable fundamental oscillatory characteristics.This flexibility enables FAWT to provide well-suited wavelet shapes,effectively matching subtle fault components and avoiding performance degradation associated with fixed frequency partitioning and low-oscillation bases in detecting weak faults.In our approach,gearbox vibration signals undergo FAWT to obtain sub-bands.Quantum theory is then introduced into permutation entropy to propose Nonlinear Quantum Permutation Entropy,a feature that more accurately characterizes the operational state of vibration simulation signals.The nonlinear quantum permutation entropy extracted from sub-bands is utilized to characterize the operating state of rotating machinery.A comprehensive analysis of vibration signals from rolling bearings and gearboxes validates the feasibility of the proposed method.Comparative assessments with parameters derived from traditional permutation entropy,sample entropy,wavelet transform(WT),and empirical mode decomposition(EMD)underscore the superior effectiveness of this approach in fault detection and classification for rotating machinery.

Efficient simulation of spatially correlated non-stationary ground motions by wavelet-packet algorithm and spectral representation method

Although the classical spectral representation method(SRM)has been widely used in the generation of spatially varying ground motions,there are still challenges in efficient simulation of the non-stationary stochastic vector process in practice.The first problem is the inherent limitation and inflexibility of the deterministic time/frequency modulation function.Another difficulty is the estimation of evolutionary power spectral density(EPSD)with quite a few samples.To tackle these problems,the wavelet packet transform(WPT)algorithm is utilized to build a time-varying spectrum of seed recording which describes the energy distribution in the time-frequency domain.The time-varying spectrum is proven to preserve the time and frequency marginal property as theoretical EPSD will do for the stationary process.For the simulation of spatially varying ground motions,the auto-EPSD for all locations is directly estimated using the time-varying spectrum of seed recording rather than matching predefined EPSD models.Then the constructed spectral matrix is incorporated in SRM to simulate spatially varying non-stationary ground motions using efficient Cholesky decomposition techniques.In addition to a good match with the target coherency model,two numerical examples indicate that the generated time histories retain the physical properties of the prescribed seed recording,including waveform,temporal/spectral non-stationarity,normalized energy buildup,and significant duration.

Deep neural network based on multi-level wavelet and attention for structured illumination microscopy

Structured illumination microscopy(SIM)is a popular and powerful super-resolution(SR)technique in biomedical research.However,the conventional reconstruction algorithm for SIM heavily relies on the accurate prior knowledge of illumination patterns and signal-to-noise ratio(SNR)of raw images.To obtain high-quality SR images,several raw images need to be captured under high fluorescence level,which further restricts SIM’s temporal resolution and its applications.Deep learning(DL)is a data-driven technology that has been used to expand the limits of optical microscopy.In this study,we propose a deep neural network based on multi-level wavelet and attention mechanism(MWAM)for SIM.Our results show that the MWAM network can extract high-frequency information contained in SIM raw images and accurately integrate it into the output image,resulting in superior SR images compared to those generated using wide-field images as input data.We also demonstrate that the number of SIM raw images can be reduced to three,with one image in each illumination orientation,to achieve the optimal tradeoff between temporal and spatial resolution.Furthermore,our MWAM network exhibits superior reconstruction ability on low-SNR images compared to conventional SIM algorithms.We have also analyzed the adaptability of this network on other biological samples and successfully applied the pretrained model to other SIM systems.

Performance of Continuous Wavelet Transform over Fourier Transform in Features Resolutions

This study presents a comparative analysis of two image enhancement techniques, Continuous Wavelet Transform (CWT) and Fast Fourier Transform (FFT), in the context of improving the clarity of high-quality 3D seismic data obtained from the Tano Basin in West Africa, Ghana. The research focuses on a comparative analysis of image clarity in seismic attribute analysis to facilitate the identification of reservoir features within the subsurface structures. The findings of the study indicate that CWT has a significant advantage over FFT in terms of image quality and identifying subsurface structures. The results demonstrate the superior performance of CWT in providing a better representation, making it more effective for seismic attribute analysis. The study highlights the importance of choosing the appropriate image enhancement technique based on the specific application needs and the broader context of the study. While CWT provides high-quality images and superior performance in identifying subsurface structures, the selection between these methods should be made judiciously, taking into account the objectives of the study and the characteristics of the signals being analyzed. The research provides valuable insights into the decision-making process for selecting image enhancement techniques in seismic data analysis, helping researchers and practitioners make informed choices that cater to the unique requirements of their studies. Ultimately, this study contributes to the advancement of the field of subsurface imaging and geological feature identification.

Variational Mode Decomposition-Informed Empirical Wavelet Transform for Electric Vibrator Noise Analysis

Electric vibrators find wide applications in reliability testing, waveform generation, and vibration simulation, making their noise characteristics a topic of significant interest. While Variational Mode Decomposition (VMD) and Empirical Wavelet Transform (EWT) offer valuable support for studying signal components, they also present certain limitations. This article integrates the strengths of both methods and proposes an enhanced approach that integrates VMD into the frequency band division principle of EWT. Initially, the method decomposes the signal using VMD, determining the mode count based on residuals, and subsequently employs EWT decomposition based on this information. This addresses mode aliasing issues in the original method while capitalizing on VMD’s adaptability. Feasibility was confirmed through simulation signals and ultimately applied to noise signals from vibrators. Experimental results demonstrate that the improved method not only resolves EWT frequency band division challenges but also effectively decomposes signal components compared to the VMD method.

Wavelet Multiview-Based Hybrid Deep Learning Model for Forecasting El Niño-Southern Oscillation Cycles

The El Niño-Southern Oscillation (ENSO) is a significant climate phenomenon with far-reaching impacts on global weather patterns, ecosystems, and economies. This study aims to enhance ENSO forecasting with the Extended Reconstruction Sea Surface Temperature v5 (ERSSTv5) climate model. The M-band discrete wavelet transforms (DWT) are utilized to capture multi-scale temporal and spatial features effectively. Long-short term memory (LSTM) autoencoders are also used to capture significant spatial and temporal patterns in sea surface temperature (SST) anomaly data. Deep learning techniques such as the convolutional neural networks (CNN) are used with non-image and image time series data. We also employ parallel computing in a various support vector regression (SVR) approximators to enhance accuracy. Preliminary results indicate that this hybrid model effectively identifies key precursors and patterns associated with El Niño events, surpassing traditional forecasting methods. Results of the hybrid model produce a correlation of 0.93 in 4-month lagged forecasting of the Oceanic Niño Index (ONI)—indicative of high success rate of the model. Future work will focus on evaluating the model’s performance using additional reanalysis datasets and other methods of deep learning to further refine its robustness and applicability. We propose wavelet-based deep learning models which have potential to shine a light on achieving United Nations’ 2030 Agenda for Sustainable Development’s goal 13: “Climate Action”, as an innovation with potential in improving time series image forecasting in all fields.