Wavelet Convolution Research Articles

Enhancing the seismic response of faults by using a deep learning‐based method

AbstractThe accuracy of fault interpretation is generally influenced by the quality of seismic images. Because of the blurring effect of the migration process, faults with small throws may not be clearly imaged in seismic images, which will impose limitations on the fault detection. To address this issue, we propose a deep learning‐based method to enhance faults in poststack seismic images. We generate abundant training samples by convolving the three‐dimensional point‐spread functions with the noisy reflectivity models. The corresponding labels are synthesized using the one‐dimensional seismic wavelet convolution method, simulating conditions with perfect illumination. To train the network for optimal performance, we investigate the impact of different loss functions. Ultimately, we employ a mixed loss function combining structural similarity index measure and gradient difference loss, since the gradient difference loss focuses more on geological edge information, and the structural similarity index measure possesses excellent image perceptual capability and optimization property. Results from one synthetic seismic image and three real seismic data demonstrate that our proposed method can effectively restore the sharpness of fault surfaces, particularly for faults with small displacements. Compared to the structural smoothing method, the network we trained achieves optimal fault enhancement. Furthermore, coherence‐based fault images indicate that seismic images enhanced using our method can improve the accuracy of fault interpretation and yield more continuous fault maps.

A lightweight dynamic dual-damped wavelet-based convolutional neural network for interpretable bearing fault diagnosis

Wavelet-based convolutional neural networks (CNNS) have attracted widespread attention because they can improve the interpretability of intelligent fault diagnosis methods. However, the fault feature representation capability of typical wavelet-based convolution kernel frameworks must be strengthened to improve the diagnostic accuracy of complex faults. In the meantime, the large number of network parameters leads to high computational costs. To address these issues, a lightweight wavelet-based dynamic CNN, which comprises a dual-damping wavelet-based dynamic CNN (DWDC) block and a discrete wavelet transformation (DWT) enhancement (DWTE) block, is put forward. In the DWDC block, a wavelet convolution layer is initially designed, where a dual-damping wavelet is used as the kernel function to improve the match of the convolution kernel with fault impulses. Subsequently, a dynamic convolution layer with multiple parallel small-size convolutional kernels is designed to screen the fault features instead of a multilayer network structure, thereby greatly reducing the number of network parameters. Finally, the DWTE block is constructed by combining the DWT and residual dense block, and it can mine more fault information from the previously extracted features. The experiments on the variable speed bearing dataset, locomotive bearing dataset with constant speed and the Case Western Reserve University dataset prove that the proposed approach outperforms five classical CNN models and six advanced wavelet-based CNN models. In addition, it can effectively solve the issue of data imbalance because of its powerful feature extraction capability.

A novel subdomain adaptive intelligent fault diagnosis method based on multiscale adaptive residual networks

Traditional fault diagnosis methods may not capture key information during feature extraction due to the large distribution difference under different working conditions, which can result in poor accuracy of the diagnostic model. To address this issue, a subdomain adaptive bearing fault identification method guided by the local maximal mean difference (LMMD) under the multiscale adaptive residual network is proposed in this paper. The bearing vibration signals are preprocessed by wavelet convolution and wide convolution to generate initial features. Then, the multi-scale adaptive residual network is used to adjust the feature weights of different scales and extract richer feature information. To reduce the intra-class distribution difference, the LMMD is employed. Additionally, local interclass maximum mean difference (LIMMD) is used to increase the inter-class difference, preventing misclassification of samples from different classes due to their close proximity and achieving sub-domain distribution alignment. The fault diagnosis performance of the domain distance metric model guided by LMMD and LIMMD under the multiscale adaptive residual network is verified through two different bearing model validation experiments.

LAMA-WAVELET: IMAGE IMPAINTING WITH HIGH QUALITY OF FINE DETAILS AND OBJECT EDGES

Context. The problem of the image impainting in computer graphic and computer vision systems is considered. The subject of the research is deep learning convolutional neural networks for image inpainting.
 Objective. The objective of the research is to improve the image inpainting performance in computer vision and computer graphics systems by applying wavelet transform in the LaMa-Fourier network architecture.
 Method. The basic LaMa-Fourier network decomposes the image into global and local texture. Then it is proposed to improve the network block, processing the global context of the image, namely, the spectral transform block. To improve the block of spectral transform, instead of Fourier Unit Structure the Simple Wavelet Convolution Block elaborated by the authors is used. In this block, 3D wavelet transform of the image on two levels was initially performed using the Daubechies wavelet db4. The obtained coefficients of 3D wavelet transform are splitted so that each subband represents a separate feature of the image. Convolutional layer, batch normalization and ReLU activation function are sequentially applied to the results of splitting of coefficients on each level of wavelet transform. The obtained subbands of wavelet coefficients are concatenated and the inverse wavelet transform is applied to them, the result of which is the output of the block. Note that the wavelet coefficients at different levels were processed separately. This reduces the computational complexity of calculating the network outputs while preserving the influence of the context of each level on image inpainting. The obtained neural network is named LaMa-Wavelet. The FID, PSNR, SSIM indexes and visual analysis were used to estimate the quality of images inpainted with LaMa-Wavelet network.
 Results. The proposed LaMa-Wavelet network has been implemented in software and researched for solving the problem of image inpainting. The PSNR of images inpainted using the LaMa-Wavelet exceeds the results obtained using the LaMa-Fourier network for narrow and medium masks in average by 4.5%, for large masks in average by 6%. The LaMa-Wavelet applying can enhance SSIM by 2–4% depending on a mask size. But it takes 3 times longer to inpaint one image with LaMa-Wavelet than with LaMa-Fourier network. Analysis of specific images demonstrates that both networks show similar results of inpainting of a homogeneous background. On complex backgrounds with repeating elements the LaMa-Wavelet is often more effective in restoring textures.
 Conclusions. The obtained LaMa-Wavelet network allows to improve the image inpainting with large masks due to applying wavelet transform in the LaMa network architecture. Namely, the quality of reconstruction of image edges and fine details is increased.

Wave packet transform and wavelet convolution product involving the index Whittaker transform

Wave packet transform and wavelet convolution product involving the index Whittaker transform

Micro-expression spotting with a novel wavelet convolution magnification network in long videos

Facial Micro-Expressions (MEs) are transient and spontaneous, reflecting a person's authentic internal emotions and have more significant value in many fields. Due to the presence of many background disturbances, including irrelevant motion (such as blinks and head movements) and noise in long videos, it is challenging to spot subtle MEs from these disturbances. To spot subtle MEs, a novel Wavelet Convolution Magnification Network (WCMN) with optical flow feature enhancement for spotting facial micro-expressions in long videos is proposed, which has a U-Net-like architecture and consists of discrete wavelet transform networks and an attention magnification mechanism. It can effectively suppress background disturbances and magnify the optical flow features of MEs, making them easy to detect. Experiments are conducted on two long video datasets (CAS(ME)2 and SAMM Long Videos). The results show that our WCMN outperforms the state-of-the-art ME spotting methods, achieving overall F1-scores of 0.3791 on CAS(ME)2, and 0.3272 on SAMM Long Videos, respectively. We also provide visualization and analysis to explain what the network enhances, and to demonstrate the effectiveness of our WCMN through ablation studies.

A Dynamic Weights-Based Wavelet Attention Neural Network for Defect Detection.

Automatic defect detection plays an important role in industrial production. Deep learning-based defect detection methods have achieved promising results. However, there are still two challenges in the current defect detection methods: 1) high-precision detection of weak defects is limited and 2) it is difficult for current defect detection methods to achieve satisfactory results dealing with strong background noise. This article proposes a dynamic weights-based wavelet attention neural network (DWWA-Net) to address these issues, which can enhance the feature representation of defects and simultaneously denoise the image, thereby improving the detection accuracy of weak defects and defects under strong background noise. First, wavelet neural networks and dynamic wavelet convolution networks (DWCNets) are presented, which can effectively filter background noise and improve model convergence. Second, a multiview attention module is designed, which can direct the network attention toward potential targets, thereby guaranteeing the accuracy for detecting weak defects. Finally, a feature feedback module is proposed, which can enhance the feature information of defects to further improve the weak defect detection accuracy. The DWWA-Net can be used for defect detection in multiple industrial fields. Experiment results illustrate that the proposed method outperforms the state-of-the-art methods (mean precision: GC10-DET: 6.0%; NEU: 4.3%). The code is made in https://github.com/781458112/DWWA.

Interpretable real-time monitoring of pipeline weld crack leakage based on wavelet multi-kernel network

The deep learning technology used for pipeline weld crack leakage monitoring lacks physical interpretability, which makes it difficult to provide theoretical support to decision-makers, reducing the practicality and applicability of the technology. To solve this problem, a deep learning framework that combines interpretability and feature fusion is proposed to solve the real-time monitoring problem of pipeline leaks. First, three different wavelet basis functions are used to analyze the leakage acoustic emission signal, and the resulting time-frequency features exhibit correlation and complementarity. Based on this, an interpretable neural network with different wavelet convolution kernels is designed to extract abstract feature details of wideband acoustic emission signals through multi-level dynamic receptive fields. Then, a feature fusion module based on channel importance weighting was designed to optimize the learning process of the network by highlighting the contribution of different channels. Finally, the effectiveness and superiority of the proposed method were verified through pipeline leakage acoustic emission monitoring experiments. The results show that the proposed method can effectively extract distinguishing features of leak acoustic emission signals, and the recognition accuracy of different leakage states can reach 98.32%, which is significantly higher than that of typical deep learning methods. In addition, feature map visualization proves that the proposed method has physical interpretability in abstract feature extraction, which will provide a reference basis for correct decision-making by industrial technicians.

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.

Efficient key frame extraction and hybrid wavelet convolutional manta ray foraging for sports video classification

ABSTRACT Sports video classification (SVC) is now considered a challenging topic, therefore, developing an automatic sports scene classification technique has received tremendous interest. This research develops an efficient key frame extraction method and hybrid Wavelet Convolution Neural Network (WCNN) framework with optimization scheme to classify sports videos. Initially, input videos are converted into number of frames, and keyframes are extracted using Enhanced threshold with Discrete Wavelet Transform (ETDWT) method. Then, Cross Guided Bilateral Filter (CGBF) method eliminates the noise from the keyframe. After that, segmentation process is performed by the Fuzzy Equilibrium Optimizer (FEO) algorithm, and then motions are detected using the Farneback optical flow (OF) method. Finally, classification process is performed using Hybrid Wavelet Convolutional Manta Ray Foraging Optimization (HWCMRFO) algorithm to categorize different sports videos. The overall work is implemented using Python language. Simulation results proved that the proposed work achieved the highest accuracy (93.17%) compared to existing approaches.

Aging attenuated theta response during multistable perception.

Multistable stimuli are physically unchanging, but elicit spontaneous perceptual reversals between multiple internally generated perceptual alternatives. Perceptual reversal rates seem to decrease in older adults; however, there is no literature on the electrophysiological correlates of this performance decrease. Here, we aimed to identify age-related changes in theta activity that relate to decreased reversal rates of older adults. Electroencephalography (EEG) of young (n=15) and older adults (n=15) was recorded during presentation of stroboscopic alternative motion (SAM) and a control stimulus. Time-frequency amplitudes were extracted in 4-8Hz via Morlet wavelet convolution. Older adults had lower SAM reversals as well as decreased accuracy, increased reaction time (RT) and increased RT variability in the control task. In older adults, reversal-related frontal theta response was diminished, yet parietal theta was intact. In the parietal area, the relationship between theta response and reversal rates was robust, but in the frontal area, was dependent on age-related variance. Result indicated that, in older adults, top-down facilitation of perceptual reversals was impaired. This appears to result in a predominantly bottom-up resolution of perceptual multistability. Age-related degradation of sensory areas in this bottom-up-driven resolution process might have slowed reversals. This study presents the first electrophysiological correlates of age-related impairment in multistable perceptual integration.

Denoising Fault-Aware Wavelet Network: A Signal Processing Informed Neural Network for Fault Diagnosis

Deep learning (DL) is progressively popular as a viable alternative to traditional signal processing (SP) based methods for fault diagnosis. However, the lack of explainability makes DL-based fault diagnosis methods difficult to be trusted and understood by industrial users. In addition, the extraction of weak fault features from signals with heavy noise is imperative in industrial applications. To address these limitations, inspired by the Filterbank-Feature-Decision methodology, we propose a new Signal Processing Informed Neural Network (SPINN) framework by embedding SP knowledge into the DL model. As one of the practical implementations for SPINN, a denoising fault-aware wavelet network (DFAWNet) is developed, which consists of fused wavelet convolution (FWConv), dynamic hard thresholding (DHT), index-based soft filtering (ISF), and a classifier. Taking advantage of wavelet transform, FWConv extracts multiscale features while learning wavelet scales and selecting important wavelet bases automatically; DHT dynamically eliminates noise-related components via point-wise hard thresholding; inspired by index-based filtering, ISF optimizes and selects optimal filters for diagnostic feature extraction. It's worth noting that SPINN may be readily applied to different deep learning networks by simply adding filterbank and feature modules in front. Experiments results demonstrate a significant diagnostic performance improvement over other explainable or denoising deep learning networks. The corresponding code is available at https://github.com/albertszg/DFAWnet.

WIANet: A Wavelet-Inspired Attention-Based Convolution Neural Network for Land Cover Classification

General convolutional neural networks (CNNs) process the data in the spatial domain and lack efficacy in modeling the spectral context in multispectral image processing task. To address this limitation, in this letter, we propose a wavelet-inspired attention-based convolution neural network (WIANet) architecture that combines the modeling of the spatio-spectral resolution of multispectral remote sensing (RS) images with a wavelet convolution and attention unit into a single deep learning architecture for land cover classification. Our aim is to add the characteristics of both wavelet transform (WT) and attention mechanism into an UNet-based architecture to better exploit the spectral and texture information for distinguishing classes with high similarity in the spectral signatures. We evaluate the performance of the proposed approach on a multilabel multispectral Sentinel-2 dataset. The experiment shows that the proposed approach performs better than the reference methods in different conditions on the number of training samples.

Multiscale Wavelet Prototypical Network for Cross-Component Few-Shot Intelligent Fault Diagnosis

The techniques of machine learning, as well as deep learning (DL) methods, have seen a wide application in the intelligent fault diagnosis field these years. However, contemporary methods are still restricted under some drawbacks: 1) conventional DL-based models always rely on the quality and amount of the data. However, there are usually insufficient samples in practical scenarios because of suddenly happened failures and 2) the existing DL models cannot be well implemented in different rotating components, which have different distributions and label space, such as from bearings to gears. To address these problems, a novel multiscale wavelet prototypical network (MWPN) is proposed in this study. It is designed to solve the few-shot fault diagnosis of the cross-component problem in rotating machines: the model is trained by one component with sufficient data and tested in another component with little data. First, a multiscale wavelet convolution module is designed to extract abundant features. Second, a metric meta-learner module is applied to measure the distance distribution between the labeled and unlabeled data. With the episode training strategy, the model is optimized and can adapt to similar tasks in a new machine and classify the unknown fault categories with few labeled samples. Experiments on three datasets are carried out to demonstrate the effectiveness of MWPN. Extensive experimental results show that MWPN outperforms many baseline methods on few-shot learning tasks in different working conditions and components.

WATSON WAVELET TRANSFORM: CONVOLUTION PRODUCT AND TWO-WAVELET MULTIPLIERS

In this paper, utilizing the theory of Watson transform and Watson convolution, we explore the Watson wavelet convolution product and its related properties. The relation between the Watson Wavelet convolution product and Watson convolution is also computed. Watson wavelet transform and its inversion formula are analyzed heuristically. Watson two-wavelet multipliers and its trace class are derived from Watson wavelet convolution product

Modelling traffic as multi-graph signals: Using domain knowledge to enhance the network-level passenger flow prediction in metro systems

Network-level metro passenger flow prediction has always been one of the most important but most challenging scientific problems in intelligent transportation systems (ITS). However, conventional methods ignore the multi-dimensional topological relationships in the subway system or directly learn from the physical topological structure and fail to explore the spatial-temporal evolution of passenger flow fully. Moreover, due to the highly punctual operation feature, the metro system has high-degree controllability and regularity, which is usually not considered in the traditional model. To address this problem, we model a metro system based on various topological structures and propose a novel spatial-temporal multi-graph convolutional wavelet network (ST-MGCWN) with unique metro system state characteristics. The core of this approach is to combine the domain knowledge of transportation and deep learning models. To be precise, there are three main modules in the proposed framework: (i). The graph wavelet convolution captures the dynamic spatial dependence between nodes on the established multiple graphs and synthesizes topological features through the graph fusion module. (ii). The various approaches based on the gated recurrent model are designed to capture the long-term periodicity and short-term trends. (iii). The transformation of the metro state characteristics reflects the change of the train density on the operation diagram, which is approximated by the distribution of the local peaks of passenger flow. Experimental results show that our proposed model achieves up to about 5% improvement over the state-of-the-art approach for the network-level passenger flow prediction task. In addition, we conduct a detailed analysis of the contribution of each component to enhance interpretability and reliability.

Decreased delta-band event-related power in dementia with Lewy bodies with a mutation in the glucocerebrosidase gene

ObjectiveTo compare event-related oscillations in patients with dementia with Lewy bodies (DLB) who are carriers and non-carriers of glucocerebrosidase (GBA) mutations. MethodsEEG was recorded during a visual oddball task in eight Ashkenazi Jewish DLB patients with the N370S mutation in theGBAgene (GBA-DLB) and eleven DLB non-carriers. The time–frequency power and inter-trial phase clustering were calculated from the Morlet wavelet convolution for the midline electrodes. ResultsTask performance and cognitive assessments were comparable between groups. While the within-non-GBA-DLB group analysis revealed delta-band power synchronization relative to the baseline (p = 0.01, Cohen's d = 1.0), the within-GBA-DLB-group analysis detected no event-related changes in power. Both groups showed an increase relative to the baseline in the delta and theta bands inter-trial phase clustering (all p < 0.03, d > 1.3). The between-group analysis revealed that event-related power – but not clustering – was lower in GBA-DLB compared to non-carriers in the delta band at Fz and Cz (p = 0.04, d = -0.9). ConclusionsGBA-DLB patients showed decreased delta-band power compared to non-carriers despite the similar cognitive performance, whereas inter-trial phase clustering was comparable in both groups. SignificancePreserved inter-trial phase clustering possibly compensates for the impaired power by eliciting the appropriate functional configuration needed for stimulus processing and task performance.

Ball Screw Fault Diagnosis Based on Wavelet Convolution Transfer Learning.

The ball screw is the core component of the CNC machine tool feed system, and its health plays an important role in the feed system and even in the entire CNC machine tool. This paper studies the fault diagnosis and health assessment of ball screws. Aiming at the problem that the ball screw signal is weak and susceptible to interference, using a wavelet convolution structure to improve the network can improve the mining ability of signal time domain and frequency domain features; aiming at the challenge of ball screw sensor installation position limitation, a transfer learning method is proposed, which adopts the domain adaptation method as jointly distributed adaptation (JDA), and realizes the transfer diagnosis across measurement positions by extracting the diagnosis knowledge of different positions of the ball screw. In this paper, the adaptive batch normalization algorithm (AdaBN) is introduced to enhance the proposed model so as to improve the accuracy of migration diagnosis. Experiments were carried out using a self-made lead screw fatigue test bench. Through experimental verification, the method proposed in this paper can extract effective fault diagnosis knowledge. By collecting data under different working conditions at the bearing seat of the ball screw, the fault diagnosis knowledge is extracted and used to identify and diagnose the position fault of the nut seat. In this paper, some background noise is added to the collected data to test the robustness of the proposed network model.

An Improved MobileNet Network with Wavelet Energy and Global Average Pooling for Rotating Machinery Fault Diagnosis.

In recent years, neural networks have shown good performance in terms of accuracy and efficiency. However, along with the continuous improvement in diagnostic accuracy, the number of parameters in the network is increasing and the models can often only be run in servers with high computing power. Embedded devices are widely used in on-site monitoring and fault diagnosis. However, due to the limitation of hardware resources, it is difficult to effectively deploy complex models trained by deep learning, which limits the application of deep learning methods in engineering practice. To address this problem, this article carries out research on network lightweight and performance optimization based on the MobileNet network. The network structure is modified to make it directly suitable for one-dimensional signal processing. The wavelet convolution is introduced into the convolution structure to enhance the feature extraction ability and robustness of the model. The excessive number of network parameters is a challenge for the deployment of networks and also for the running performance problems. This article analyzes the influence of the full connection layer size on the total network. A network parameter reduction method is proposed based on GAP to reduce the network parameters. Experiments on gears and bearings show that the proposed method can achieve more than 97% classification accuracy under the strong noise interference of −6 dB, showing good anti-noise performance. In terms of performance, the network proposed in this article has only one-tenth of the number of parameters and one-third of the running time of standard networks. The method proposed in this article provides a good reference for the deployment of deep learning intelligent diagnosis methods in embedded node systems.

A sparse graph wavelet convolution neural network for video-based person re-identification

Video-based person re-identification (Re-ID) aims to match identical person sequences captured across non-overlapping surveillance areas. It is an essential yet challenging task to effectively embed spatial and temporal information into the video feature representation. For one thing, we observe that different frames in the video can provide complementary information for each other. Also, local features which is lost due to target occlusion or visual ambiguity in one frame can be supplemented by the same pedestrian part in other frames. For another thing, graph neural network enables the contextual interactions between relevant regional features. Therefore, we propose a novel sparse graph wavelet convolution neural network (SGWCNN) for video-based person Re-ID. Distinct from previous graph-based Re-ID methods, we exploit the weighted sparse graph to model the semantic relation among the local patches of pedestrians in the video. Each local patch in one frame can extract supplementary information from highly related patches in other frames. Moreover, to effectively solve the problems of short time occlusion and pedestrian misalignment, the graph wavelet convolution neural network is adopted for feature propagation to refine regional features iteratively. Experiments and evaluation on three challenging benchmarks, that is, MARS, DukeMTMC-VideoReID, and iLIDS-VID, show that the proposed SGWCNN effectively improves the performance of video-based person re-identification.