Multi-scale Wavelet Decomposition Research Articles

MultiWaveNet: A long time series forecasting framework based on multi-scale analysis and multi-channel feature fusion

Long time series forecasting is widely used in areas such as power dispatch, traffic control, and weather forecasting. The pattern of seasonality and trends in long time series are often complex, especially when they are presented at different time scales. Existing methods typically focus on only one scale or randomly select scales, which leads to a significant loss of valuable information. Additionally, current methods often transform multi-channel data into a single-channel format, ignoring interactions and complex relationships between channels. The paper proposes MultiWaveNet, a novel long time series forecasting framework that addresses seasonality as well as trends separately. For the seasonal component, the framework uses multi-scale wavelet decomposition to generate subseries at multiple scales. A learnable optimization factor is introduced simultaneously to separate high-frequency components mixed in low-frequency series after wavelet decomposition. In order to reduce information redundancy and model complexity, the paper develops a wavelet domain sampling encoder that consists of just one Transformer encoder, ensuring effective modeling of long-term dependencies while maintaining feature extraction effectiveness. As for the trend component, unlike previous research, the weights of channels are adjusted based on their importance, allowing the more crucial channels to have a greater impact and thereby addressing the limitations of individual processing methods. The paper performs extensive experiments on nine standard datasets, demonstrating that MultiWaveNet is the most competitive method.

Refinement of microplate boundaries assisted by integrated gravity analysis: Application to the Caribbean Sea

Under the long-term influence of subduction, collision and strike-slip faults, the Caribbean Sea and its surroundings have evolved complex topography and terranes, making it an excellent site to study the tectonic of microplates. However, some microplate boundaries of this area are still controversial or unclear. Here we employed the widely-used satellite-derived gravity dataset in combination with previous findings to conduct a detailed re-interpretation of tectonic boundaries. A newly proposed product of normalized multi-edge-attributes (PNMEA) with upward-continued free-air gravity anomalies (FGA) is used to constrain deep large-scale boundaries (i.e., oceanic trenches, deformed belts and fault systems). The residual crustal gravity anomalies (RCGA) obtained based on wavelet multi-scale decomposition further reveal density variations within the crust domain. The Tilt angle (TA) of FGA highlights fault strikes and patterns in the near-surface. Consequently, we refine the possible boundaries of microplates within the northern Caribbean boundary zone and the Nicaraguan Rise, and analyze the contact relationships among microplates. The results suggest a triple junction among the Gonave, Hispaniola and Septentrional microplates exists in the Windward Passage, and a zigzag low RCGA in the Mona Passage separates the Hispaniola and Puerto Rico microplates. In addition, the north and south Nicaraguan rises are inclined to be unaffiliated implied by the differences in multiple physical properties. We thus conclude that an integrated analytical approach involving potential-field edge detection and RCGA can provide additional constraints for identification of tectonic or microplate boundaries. Deep-shallow coupling and lithosphere-scale cooling differences may provide new perspectives to explain the complexity of temporal-spatial configuration due to multiple microplate interactions.

The effect of near-fault earthquakes and wavelet-generated artificial near-fault earthquakes on the seismic behavior of rockfill dams

Strong earth vibrations may destroy high asphalt concrete core rockfill dams (ACCRDs) and cause unanticipated economic and social losses. Due to favorable geographical, geological, and environmental characteristics, ACCRDs are always near ruptured fault zones. Compared to far-field and non-pulse earthquakes, near-fault (NF) earthquakes with pulse effect may put high dams under stress. However, seismic design and dynamic assessments of high ACCRDs under pulse-type earthquake stimulation are less popular than NF earthquake recordings. The fundamental explanation is that most earthquake data pertain to non-pulse-type seismic occurrences, whereas pulse-type earthquakes have more sophisticated seismology. This work uses the finite element approach to illustrate the seismic behavior of the ACCRD under pulse-type NF, non-pulse-type NF, and far-fault (FF) earthquake excitations. The pulse-type artificial NF earthquakes are generated using wavelet multi-scale decomposition incorporation (WMSDI), a simplified wavelet theory-based approach. Next, the WMSDI approach of artificial NF earthquake synthesis is tested and compared to earthquake data and structure responses. Forward-directivity pulse-type and fling-step pulse-type earthquakes may induce higher horizontal accelerations and stresses of the high ACCRD than FF earthquakes. FS and FD earthquake excitations with high PGV/PGA ratios cause severe residual deformation and relative settlement ratio to the high ACCRD. The dynamic response of the high ACCRD under pulse-type artificial NF earthquakes also depends on the pulse parameters of the artificial equivalent pulse mathematical models. Thus, pulse-type NF earthquake seismology should be included in rockfill dam seismic design assessments.

MWDINet: A multilevel wavelet decomposition interaction network for stock price prediction

Stock price prediction is a classical interdisciplinary issue drawn from finance, computer science, econometrics, and mathematics. Most stock price data are nonlinear, nonstationary, and highly complex, making stock price prediction challenging. Recently, deep neural networks (DNNs) have demonstrated powerful learning capabilities and have yielded notable results in stock price prediction tasks. Most existing deep learning solutions, however, only consider time-domain information or lack effective modeling of frequency-domain information, thus failing to effectively utilize both time-domain and frequency-domain information of the data. Meanwhile, existing methods ignore autocorrelated errors in the stock price forecasting task due to missing valid information data, i.e., they do not consider the correlation between the error at the current time step and the error at the previous time step, which undermines the standard maximum likelihood estimation (MLE) assumption, thereby weakening the model’s performance. We propose a multilevel wavelet decomposition interaction network (MWDINet), an end-to-end framework for stock price prediction. MWDINet employs the multiscale wavelet decomposition interaction module (MWDI-Block) and the Hull Moving Average module (HMA-Block) to extract the data’s frequency-domain and time-domain information, respectively. In MWDI-Block, the traditional signal processing method of Maximum Overlapping Discrete Wavelet Transform (MODWT) is seamlessly embedded into a deep learning framework (named DMODWT). The DMODWT algorithm not only automatically extracts the frequency-domain information from the data, but also fine-tunes the wavelet filters. With HMA-Block, we improve the Hull Moving Average (HMA), commonly used in the industry, into a deep learning module, which learns how changes in different markets over time. Inspired by the research on correcting autocorrelated errors in linear models in econometrics, we further design a deep difference module (DIF-Block) to correct autocorrelated errors and thus improve the prediction performance of the model. Moreover, all components are integrated seamlessly in a unified end-to-end framework. Extensive experiments on real-world datasets demonstrate that MWDINet outperforms the state-of-the-art models and has remarkable potential in stock price prediction.

Distribution of Active Faults and Lithospheric Discontinuities in the Himalayan-Tibetan Orogenic Zone Identified by Multiscale Gravity Analysis

The lithospheric structure of the Tibetan Plateau and its adjacent area is a hot topic in geodynamic research. It is important to reveal the mechanism of crustal deformation and tectonic evolution of the study area. In this study, the techniques of wavelet multiscale decomposition and field edge detection were used to study the discontinuities of the lithosphere revealed by multilevel Bouguer gravity anomalies. Specifically, we evaluated the depth characteristics of the major active faults in the study area and identified 15 deep major faults that cut through the lithosphere. They are Chaman fault, Shyok suture zone, Altyn-Tagh fault, Karakash fault, Karakoram fault, Talas-Fergana fault, Kashgarr-Yeshgar transfer system, Rushan-Pshart suture zone, Sangri-Nacuo fault, Main Frontal thrust, Burmese fold belt, Yadong-Gulu fault, Gaoligong fault, Sagaing fault and Nujiang fault. We have also elucidated the tectonic mechanisms of two famous geodynamic phenomena in the Pamir Plateau. The first is the intense intermediate depth seismicity beneath Pamir-Hindukush. It cannot simply be described as the rupture of a subducted residual plate, which could be divided into two distinct tectonic units. One belongs to the Indian plate, the other to the Eurasian plate. Secondly, the mechanism of intense seismicity confined to the western upper crust of the Pamir Plateau could be explained as significant fragmentation of crustal material. Finally, and most importantly, we summarized the coupling mechanism between deep geodynamics and horizontal deformation as observed by modern geodetic techniques. In the upper mantle, the leading edge of the subducting Indian plate reached the SW boundary of Tarim basin and forms a closed structure in western Himalaya. Then, the Tibetan Plateau underwent a tectonic escape towards the east under the continuous compression between the Indian and Eurasian plates. During the process of tectonic escape, the role of the N–S direction normal faults in the Himalayan tectonic zone is limited.

Fine-Grained and Multiple Classification for Alzheimer's Disease With Wavelet Convolution Unit Network.

In this article, we propose a novel wavelet convolution unit for the image-oriented neural network to integrate wavelet analysis with a vanilla convolution operator to extract deep abstract features more efficiently. On one hand, in order to acquire non-local receptive fields and avoid information loss, we define a new convolution operation by composing a traditional convolution function and approximate and detailed representations after single-scale wavelet decomposition of source images. On the other hand, multi-scale wavelet decomposition is introduced to obtain more comprehensive multi-scale feature information. Then, we fuse all these cross-scale features to improve the problem of inaccurate localization of singular points. Given the novel wavelet convolution unit, we further design a network based on it for fine-grained Alzheimer's disease classifications (i.e., Alzheimer's disease, Normal controls, early mild cognitive impairment, late mild cognitive impairment). Up to now, only a few methods have studied one or several fine-grained classifications, and even fewer methods can achieve both fine-grained and multi-class classifications. We adopt the novel network and diffuse tensor images to achieve fine-grained classifications, which achieved state-of-the-art accuracy for all eight kinds of fine-grained classifications, up to 97.30%, 95.78%, 95.00%, 94.00%, 97.89%, 95.71%, 95.07%, 93.79%. In order to build a reference standard for Alzheimer's disease classifications, we actually implemented all twelve coarse-grained and fine-grained classifications. The results show that the proposed method achieves solidly high accuracy for them. Its classification ability greatly exceeds any kind of existing Alzheimer's disease classification method.

Crustal Structure and Geothermal Mechanism of the Gonghe-Guide Basin Based on EIGEN-6C4 Satellite Gravity and Aeromagnetic Data

The Gonghe-Guide Basin is situated in the northeastern edge of the Tibetan Plateau, one of China’s main targets for geothermal research and exploitation. We present a new crustal structure of the entire basin by using EIGEN-6C4 satellite gravity and aeromagnetic data aimed to further recognize the geothermal mechanisms. The data are processed using the wavelet multi-scale decomposition method and the iterative compact depth from extreme points imaging method. The gravity inversion results reveal distinct low-density regions in the middle-upper crust at 15–35 km depth, which is most likely caused by partial melting. The magnetic inversion results show negative or no magnetism within a similar depth range. But at shallow depths of the same horizontal positions, there is high positive magnetism, which can be interpreted as granite. The results correspond well with the magnetotelluric and seismic results and can be an effective supplement. To confirm and validate this conclusion, a 2D geological model of a profile from a typical area is created to show the detailed tectonic. Based on the new crustal structure results, the suggested geothermal target is the low/negative density corresponding to low/negative magnetism located at deep depths and high/positive magnetism located at shallow depths. Then we established a geological conceptual model to illustrate this process. This indicates that tectonic movement is taking place in the deep part of the earth in the Gonghe-Guide Basin. The research on the geological structure and geothermal heat source mechanism in the Gonghe-Guide Basin can provide a primary reference for research on geothermal resources in other areas with similar geological structures.

Three-dimensional density distribution and earthquake activity of the northern Lancangjiang fault in eastern Tibet

Due to the collision and lateral compression of the Indian-Asian plate, the Lancangjiang fault has become one of the most active strike-slip faults in the Qiangtang plate. The Qamdo 2013 Ms6.1 earthquake was induced from the northern section of the fault (the northern Lancangjiang fault). The destruction of the earthquake seriously endangers human activities and the construction of the Sichuan-Tibet Railway. However, there are few high-resolution geophysical data in this area, which limits the understanding of the deep structure, motion mode and seismic activity of the northern Lancangjiang active fault. In this paper, new gravity data were observed at a scale of 1: 200,000, covering an area of 1500km2. Based on wavelet multiscale decomposition, scratch analysis and 3-D inversion of gravity data methods, we obtained gravity anomalies of different scales, faults distribution and density structure. The results show that the overall crustal density change in Qamdo area is obvious and closely related to the distribution of faults. The Qamdo earthquake occurred at the layered interface with steep density change and the result from scratch analysis shows that the stress is concentrated at this position. We believe that the existence of stratigraphic density difference leads to different ability of strata to withstand regional tectonic stress, which is an important cause of the Qamdo earthquake. We analyzed the differences magnitude of earthquake activity between the northern Lancangjiang fault and Kamaduo-Gangtuo fault and believe that the northern Lancangjiang fault is more conducive to the preparation of large earthquakes. Otherwise, this paper provides geophysical evidence for the hypothesis that the northern Lancangjiang fault thrusts to the Qamdo Basin at a high angle.

Research on the denoising method of infrared thermogram during rock fracture

In order to overcome the defects of low contrast and low signal-to-noise ratio of the infrared thermal image of rock (ITIR), a joint denoising method of additive and multiplicative noise is proposed for infrared radiation thermal image of rock bearing fracture process. ITIR is de-noised using background phase subtraction, adaptive median filtering, and wavelet multi-scale decomposition threshold denoising Firstly, the noise types in ITIR are analyzed, the basic principles and implementation steps of the denoising method are described, and the denoising effects of different combinations of wavelet basis functions with different decomposition scales in the wavelet threshold denoising process are simulated. Finally, the denoising effect was evaluated in terms of peak signal-to-noise ratio (PSNR), root mean square error (RMSE), and blind/referenceless image spatial quality evaluator (BRISQE). The results show that the PSNR of ITIR is increased by 15.01 % based on removing additive noise. The image quality scores increased by 49.54 % before and after overall denoising. The studies have significance for IR signal extraction and denoising in rocks and solid materials.

Arrhythmia Disease Diagnosis Based on ECG Time-Frequency Domain Fusion and Convolutional Neural Network.

Electrocardiogram (ECG) signals are often used to diagnose cardiac status. However, most of the existing ECG diagnostic methods only use the time-domain information, resulting in some obviously lesion information in frequency-domain of ECG signals are not being fully utilized. Therefore, we propose a method to fuse the time and frequency domain information in ECG signals by convolutional neural network (CNN). First, we adapt multi-scale wavelet decomposition to filter the ECG signal; Then, R-wave localization is used to segment each individual heartbeat cycle; And then, the frequency domain information of this heartbeat cycle is extracted via fast Fourier transform. Finally, the temporal information is spliced with the frequency domain information and input to the neural network for classification. The experimental results show that the proposed method has the highest recognition accuracy (99.43%) of ECG singles compared with state-of-the-art methods. Clinical and Translational Impact Statement- The proposed ECG classification method provides an effective solution for ECG interrogation to quickly diagnose the presence of arrhythmia in a patient from the ECG signal. It can increase the efficiency of the interrogating physician by aiding diagnosis.

A New X-ray Medical-Image-Enhancement Method Based on Multiscale Shannon-Cosine Wavelet.

Because of noise interference, improper exposure, and the over thickness of human tissues, the detailed information of DR (digital radiography) images can be masked, including unclear edges and reduced contrast. An image-enhancement algorithm based on wavelet multiscale decomposition is proposed to address the shortcomings of existing single-scale image-enhancement algorithms. The proposed algorithm is based on Shannon-Cosine wavelets by taking advantage of the interpolation, smoothness, tight support, and normalization properties. Next a multiscale interpolation wavelet operator is constructed to divide the image into several sub-images from high frequency to low frequency, and to perform different multi-scale wavelet transforms on the detailed image of each channel. So that the most subtle and diagnostically useful information in the image can be effectively enhanced. Moreover, the image will not be over-enhanced and combined with the high contrast sensitivity of the human eye's visual system in smooth regions, different attenuation coefficients are used for different regions to achieve the purpose of suppressing noise while enhancing details. The results obtained by some simulations show that this method can effectively eliminate the noise in the DR image, and the enhanced DR image detail information is clearer than before while having high effectiveness and robustness.

Analysing Time-frequency Relationship between Oil price and Sectoral Indices in India using Wavelet Techniques

Oil is considered an essential factor of any economy. This paper examines the time-varying correlation between oil price return, BSE SENSEX, and 14 sectoral indexes in India using multiscale wavelet decomposition and wavelet coherence analysis. The maximal wavelet discrete wavelet transform analysis shows a feedback relationship between 13 sectors at higher time horizons (dC4, dC5, and dC6). Based on the wavelet coherence plot, the oil price and sectoral index return show a high co-movement at 32 to 128 weeks. The wavelet coherence plot shows that the oil price and sectoral index return show a high co-movement during the period of Mar-May 2020 (especially during the period of financial crisis widely spread due to the COVID19 pandemic and nationwide lockdown notification announced by the Government of India). We discuss the implications of these studies in detail.

Origin of microplates under oblique subduction system in New Guinea: Inferences from gravity and magnetic data

The New Guinea Island is formed under the oblique subduction of the Pacific Plate. The formation and evolution of the microplates around the New Guinea Island are complex and still poorly understood. Here we use the published gravity, magnetic datasets and the CRUST1.0 model, combined with the wavelet multi-scale decomposition and residual crustal gravity anomaly separation, to analyze the crustal structure and boundary characteristics of different microplates. The results show that the gravity and magnetic anomalies have good responses to microplate boundaries, such as deep-seated large-scale faults and subduction zones. Seven microplates (including the Caroline, the North Bismarck, the Manus, the South Bismarck, the Solomon Sea, the Woodlark and the Ontong Java Plateau microplates) have been identified based on their different geophysical properties. Combined with other geological records and plate reconstruction, we analyze the regional tectonic activity, dynamics and microplate evolution in this region. The New Guinea Island was formed and shaped by the oblique subduction of the South Pacific since the Late Cretaceous. Several key events are recorded at 45 Ma, 25 Ma and 5 Ma, which are highly related to the formation of the microplates in the convergent margin. The key events mainly involve the formation and termination of the Melanesian Arc, the collision between the Ontong Java Plateau and the Solomon Islands, and the arc-continent collision at the New Britain Island Arc. These events contributed to a series of island arcs and back-arc basins that further evolved into relatively independent microplates. By analyzing the formation patterns and boundaries of microplates, we classify these microplates into the accretion-derived, collision-derived and back-arc rifting-derived types. The evolution history of each type of microplate is reconstructed in details, which provides additional constraints on the Cenozoic tectonic reconstruction of the Southwest Pacific region.

Active Depths of Main Faults in the Ying-Qiong Basin Investigated by Multi-Scale Wavelet Decomposition of Bouguer Gravity Anomalies and Power Spectral Methods

Active Depths of Main Faults in the Ying-Qiong Basin Investigated by Multi-Scale Wavelet Decomposition of Bouguer Gravity Anomalies and Power Spectral Methods

Daily streamflow forecasting using hybrid long short-term memory model

Characterized by heterogeneity, complexity and non-stationary, streamflow forecasting has always been a challenge in hydrological sciences. In this study, a multiscale wavelet decomposition method with long short-term memory model (WLSTM) is developed to handle the daily streamflow forecasting. Discrete wavelet transform (DWT) is employed to extract multiscale features, which are then simulated by long short-term memory models (LSTMs), respectively. The outputs of the different scales LSTMs are finally reconstructed toward the forecasting results. Seven years daily streamflow sequences of three tributaries and one mainstream in the upper reaches of the Yangtze River are investigated by the WLSTM models. For comparison, standard LSTM, and traditional ANN are chosen for the same streamflow forecasting task. Experimental results show that the proposed hybrid model is better than other comparison models in terms of evaluation indicators. Considering that large floods often occur in the Yangtze River Basin, the performance of flood forecasting is also analyzed and the result shows that forecasting errors of WLSTM are more concentrated, which means WLSTM outperforms traditional ANN and LSTM for the extreme flood forecasting.

Tennis Serve Trajectory Capture Algorithm Based on Wavelet Multiscale Decomposition

Human motion analysis is one of the important research directions in computer vision technology. Aiming at the problems of poor effect, accuracy, and efficiency in the current tennis serve trajectory capture process, a tennis serve trajectory capture algorithm based on wavelet multiscale decomposition is proposed. This article analyzes the related concepts and principles of wavelet transform and multiresolution analysis, uses the computer three-dimensional vision acquisition method to collect the tennis serve trajectory image, and uses the mean filter to smooth and denoise the collected tennis serve trajectory image. The wavelet multiscale decomposition algorithm is used to process the tennis serve trajectory image after smooth denoising, find the local maximum point through the modulus value and phase angle value, and obtain the initial tennis serve trajectory image. Using the local layer threshold method, the adaptive threshold is set, and the trajectory line under each scale is obtained to capture the trajectory line of tennis serve. It can be observed from the experimental and simulation results that the trajectory capture effect of the proposed algorithm is good, and it can effectively improve the accuracy and efficiency of trajectory capture.

Visual Saliency via Multiscale Analysis in Frequency Domain and Its Applications to Ship Detection in Optical Satellite Images.

This article proposes a bottom-up visual saliency model that uses the wavelet transform to conduct multiscale analysis and computation in the frequency domain. First, we compute the multiscale magnitude spectra by performing a wavelet transform to decompose the magnitude spectrum of the discrete cosine coefficients of an input image. Next, we obtain multiple saliency maps of different spatial scales through an inverse transformation from the frequency domain to the spatial domain, which utilizes the discrete cosine magnitude spectra after multiscale wavelet decomposition. Then, we employ an evaluation function to automatically select the two best multiscale saliency maps. A final saliency map is generated via an adaptive integration of the two selected multiscale saliency maps. The proposed model is fast, efficient, and can simultaneously detect salient regions or objects of different sizes. It outperforms state-of-the-art bottom-up saliency approaches in the experiments of psychophysical consistency, eye fixation prediction, and saliency detection for natural images. In addition, the proposed model is applied to automatic ship detection in optical satellite images. Ship detection tests on satellite data of visual optical spectrum not only demonstrate our saliency model's effectiveness in detecting small and large salient targets but also verify its robustness against various sea background disturbances.

Inversion of Soil Iron Oxide Based on Multi-Scale Continuous Wavelet Decomposition

Inversion of Soil Iron Oxide Based on Multi-Scale Continuous Wavelet Decomposition

Toward Smart Condition Monitoring of Rotatory Machines: An Optimized Probabilistic Signal Reconstruction Methodology for Fault Prediction With Multisource Uncertainties

Faults in the critical components of a large rotatory machine often result in unplanned breakdowns, leading to a significant loss of property and life. Condition monitoring, as a key component in the smart maintenance of industrial equipment, has become a promising tool for providing automatic early alerting of potential damage to critical components, thus reducing potential outages and improving system safety and reliability while lowering maintenance costs. This is still a very challenging topic in various industrial fields because of data imperfection and multivariate correlation, as well as the variation in faults and components in different machines. This paper presents an optimized probabilistic signal reconstruction methodology to address these challenges in the fault prediction of rotatory machines using multivariate vibration signals. Three signal reconstruction methods, that is, Bayesian wavelet multiscale decomposition, probabilistic principal component analysis, and auto-associative kernel regression, were seamlessly integrated to address the noise, high dimensionality, and correlation in the sensed multivariate vibration data for accurate fault prediction. The bandwidth parameter in the auto-associative kernel regression approach was optimized to represent the health status of the rotatory machine. The obtained model was further utilized to predict the responses under unknown conditions. The alerting threshold, based on the squared mean errors of the predicted and measured time series, was automatically adjusted using a rolling window strategy and then employed to predict the possible fault. Finally, the validity, feasibility and generalization of the proposed methodology are illustrated by applying two cases of different rotating machines: centrifugal compressor and gas turbine.

Trajectory Tracking Method of Volleyball Player’s Arm Hitting Image Based on D-P Algorithm

Aiming at the problems of poor image tracking effect, low precision, and long time in the process of image tracking of volleyball player’s arm hitting, a volleyball player's arm hitting image tracking method based on D-P algorithm is proposed. This paper analyzes the basic concept, basic principle, and basic equation of D-P algorithm and collects the arm stroke trajectory image of volleyball players under the three-dimensional visual model. Using wavelet multiscale decomposition method, the arm stroke trajectory of volleyball players is filtered, and the edge contour feature points of the arm stroke image of volleyball players are extracted. Using the gray histogram feature extraction method, the gray information of volleyball player's arm hitting trajectory image is enhanced. Combined with pixel adaptive enhancement technology, the key action feature points of volleyball player's arm hitting image trajectory are located. Based on D-P algorithm, the volleyball player's arm hitting image trajectory is adjusted and modified to realize the correct tracking of volleyball player's arm hitting image trajectory. The experimental results show that the trajectory tracking effect of volleyball player's arm hitting image is better, which can effectively improve the tracking accuracy and shorten the tracking time.