Multiresolution Analysis Method Research Articles

A New Multi-resolution Analysis Method for Electrooculography Signals.

Electrooculography (EOG) signals indicate the degree and direction of eye movements. Hence, EOG signals have been useful in eye movement controlled rehabilitation systems. Denoising and accurate identification of the type of eye movement in EOG signals are the major challenges in their analysis. The state-of-the-art techniques for EOG signal analysis concerning denoising and eye movement extraction are based on multi-resolution analysis using wavelet bases, such as Haar or Daubechies. However, these wavelets are designed for general purpose signal processing applications and hence are not optimized for the EOG signal structures. In this paper, we propose a new multi-resolution basis specific to the analysis of EOG signals. The scaling and wavelet functions for the basis are derived from the signatures of blinks and saccades respectively, and hence we name them as blinklets and saclets accordingly, thereby forming a new multi-resolution basis. These descriptors are found to be more effective than standard wavelets for EOG signals, signal denoising, and for identifying the different eye movement signatures such as saccades, blinks, smooth pursuits, and fixations, as tested on the Physiosig and Centre for Biomedical Cybernetics Eye Movement (CBC-EM) EOG Databases.

IMAGE FUSION AND DEEP LEARNING BASED EAR RECOGNITION USING THERMAL AND VISIBLE IMAGES

Advances in imaging and deep learning have fueled interest in ear biometrics, as the structure of the ear offers unique identification features. Thermal and visible ear images capture different aspects of these features. Thermal images are light-independent, and visible images excel at capturing texture details. Combining these images creates more feature-rich composite images. This study examines the fusion of thermal and visible ear images taken under varying lighting conditions to enhance automatic ear recognition. The image fusion process involved three distinct multiresolution analysis methods: discrete wavelet transform, ridgelet transform, and curvelet transform. Subsequently, a specially designed deep learning model was used for ear recognition. The results of this study reveal that employing the complex-valued curvelet transform and thermal images achieved an impressive recognition rate of 96.82%, surpassing all other methods. Conversely, visible images exhibited the lowest recognition rate of 75.00%, especially in low-light conditions. In conclusion, the fusion of multiple data sources significantly enhances ear recognition effectiveness, and the proposed model consistently achieves remarkable recognition rates even when working with a limited number of fused ear images.

A Triple-Double Convolutional Neural Network for Panchromatic Sharpening.

Pansharpening refers to the fusion of a panchromatic (PAN) image with a high spatial resolution and a multispectral (MS) image with a low spatial resolution, aiming to obtain a high spatial resolution MS (HRMS) image. In this article, we propose a novel deep neural network architecture with level-domain-based loss function for pansharpening by taking into account the following double-type structures, i.e., double-level, double-branch, and double-direction, called as triple-double network (TDNet). By using the structure of TDNet, the spatial details of the PAN image can be fully exploited and utilized to progressively inject into the low spatial resolution MS (LRMS) image, thus yielding the high spatial resolution output. The specific network design is motivated by the physical formula of the traditional multi-resolution analysis (MRA) methods. Hence, an effective MRA fusion module is also integrated into the TDNet. Besides, we adopt a few ResNet blocks and some multi-scale convolution kernels to deepen and widen the network to effectively enhance the feature extraction and the robustness of the proposed TDNet. Extensive experiments on reduced- and full-resolution datasets acquired by WorldView-3, QuickBird, and GaoFen-2 sensors demonstrate the superiority of the proposed TDNet compared with some recent state-of-the-art pansharpening approaches. An ablation study has also corroborated the effectiveness of the proposed approach. The code is available at https://github.com/liangjiandeng/TDNet.

Wavelet transform for rotary machine fault diagnosis:10 years revisited

As a multi-resolution analysis method rooted rigorously in mathematics, wavelet transform (WT) has shown its great potential in rotary machine fault diagnosis, characterized by continued development and innovative new applications. In traditional fault diagnosis, WT has been widely used for fault feature extraction and extensively studied for performance improvement. With the emergence of data-driven intelligent fault diagnosis, especially deep learning techniques, WT has attracted renewed attention for its ability of adding interpretability into the intelligent diagnosis models. This paper aims to highlight the advancement of WT-based fault diagnosis research over the last decade. Toward this end, a comprehensive overview of WT method is given, followed by a summary of WT for fault diagnosis from two perspectives: traditional fault diagnosis and intelligent fault diagnosis. Finally, future research trends are discussed, including benchmarking, wavelet base design, integration with other methods, and enhancement through deep learning.

Topology optimization via implicit neural representations

Along with the rapid development of artificial intelligence (AI) technology, scientific research enters a new era of AI. Topology optimization (TO) and AI technology are recently showing a growing trend of cross development, which has received continuous attentions from relative researchers. In this paper, we introduce a concept of Implicit Neural Representations from AI into TO field and establish a novel TO framework which is named as TOINR. In TOINR, the Topology Description Function is the inherent combination factor, which is constructed by a Neural Network (NN) and determines the topology statuses of structural materials in the design domain. We adopt sine as a periodic activation function combined with MLP as the architecture of the NN. The inputs of NN are a predefined set of spatial points’ coordinates, while the outputs are the implicit representations of corresponding topological boundaries. Along with updating NN’s parameters (i.e., design variables), the structural topologies iteratively evolve according to the responses analysis results and optimization functions. A boundary-adaptive multi-resolution finite element analysis method is developed to improve the physical response accuracy. At each step of TOINR, we ensure the computational differentiability. Thus, the automatic differentiation is used in sensitivity analysis. The multi-penalty function approach is applied to handle objects with constraints. Besides, we design an adaptive adjustment scheme for learning rates to enhance the stability of the optimization process. Numerical examples illustrate that TOINR can stably obtain optimized structures for different problems with high performance and robustness.

Application of Wavelet Transform in The Construction of Short-term Memory EEG Information Transmission Model

Wavelet transform is an analysis method that combines time, frequency (or scale) domains. It has: (1) Multi-resolution; (2) The relative bandwidth is constant; (3) Proper selection of basic wavelet can make wavelet have the ability to represent the local characteristics of signals in both time and frequency domains, and it is known as "the microscope for analyzing signals". An analysis method of EEG signal based on autoregressive model (ARM) and wavelet transform is proposed, and it is used to eliminate noise interference in EEG signal. Wavelet transform is a multi-resolution time scale analysis method, which can divide the signal into sub-band signals of different frequency bands. According to this characteristic of wavelet transform, the EEG signals obtained by sampling are decomposed and denoised at various scales, and the results of decomposition and denoising at various scales are given. Wavelet transform can effectively remove noise interference from EEG signals. Wavelet transform is a multi resolution time scale analysis method that can divide signals into subband signals of different frequency bands. According to this characteristic of wavelet transform, the sampled EEG signal is decomposed and denoised at various scales, and the decomposition and denoising results at each scale are given. Wavelet transform can effectively remove noise interference from EEG signals.

Multiresolution Analysis Pansharpening Based on Variation Factor for Multispectral and Panchromatic Images From Different Times

Most pansharpening methods refer to the fusion of the original low-resolution multispectral (MS) and high-resolution panchromatic images (PAN) acquired simultaneously over the same area. Due to its good robustness, multiresolution analysis (MRA) has become one of the important categories of pansharpening methods. However, when only MS and PAN images acquired at different times can be provided, the fusion results from current MRA methods are often not ideal due to the failure to effectively analyze multitemporal misalignments between MS and PAN images from different times. To solve this issue, MRA pansharpening based on variation factor for MS and PAN images from different times is proposed. The multi-resolution analysis pansharpening based on dual-scale regression model is first established, and the variation factor is then introduced to effectively analyze the multitemporal misalignments by using alternating direction method of multipliers (ADMM), yielding the final fusion results. Experiments with synthetic and real datasets show that the proposed method exhibits significant performance improvement compared to the traditional pansharpening methods, as well as the state-of-the-art MRA methods. Visual comparisons demonstrate that the variation factor introduces encouraging improvements in the compensation of multi-temporal misalignments in ground objects and advances pansharpening applications for MS and PAN images acquired at different times.

Pansharpening scheme using spatial detail injection–based convolutional neural networks

Pansharpening produces a high spatial-spectral resolution pansharpened image by combining multispectral (MS) and panchromatic (PAN) images. In the traditional multi-resolution analysis (MRA) method, detailed PAN images are extracted by transformation methods that are injected into MS images. This gives spatial and spectral distortions in the pansharpened image. These distortions can be reduced in the pansharpened image by the correct matching of the PAN detail image component. This correct matching is possible by the convolutional neural network (CNN)–based models. This paper obtains the detailed image component using the CNN models. This CNN model extracts the PAN detail image that is suitable for the MRA-based pansharpening scheme which significantly reduces the spatial and spectral distortions. It is demonstrated by qualitative and quantitative analysis applied on GeoEye-1 and IKONOS satellite images and shows the effectiveness of the proposed scheme.

An Evaluation of Pan-Sharpening Methods forSuperView-1Satellite Imagery

At present, little research focuses on the application of pan-sharpening methods to SuperView-1 satellite imagery. There is a lack of suitability assessment for existing pan-sharpening methods applied to SuperView-1 images. This study proposes an evaluation method that integrates visual evaluation, spectral analysis of typical objects, and quantitative indicators to evaluate the advantages of different pan-sharpening methods in different scenes of SuperView-1 imagery. Four scenes (urban areas, farmland, sparse vegetation, mixed surfaces) are selected to evaluate eight typical pan-sharpening methods (Brovey, principal component analysis (PCA), Gram-Schmidt (GS), band-dependent spatial-detail (BDSD), high-pass filtering (HPF), smoothing filter-based intensity modulation (SFIM), modulation transfer function-generalized Laplacian pyramid (MTF-GLP), MTF-GLP-high pass modulation (MTF-GLP-HPM). The results show that the suitability of each pan-sharpening method is different in various scenes. PCA, Brovey, and GS distort the spectral information greatly, and the stability of the pan-sharpening results in different scenes which are poor. BDSD has strong stability and can better balance the relationship between spectral distortion and spatial distortion in different scenes. The multi-resolution analysis method has better applicability and stability for SuperView-1 imagery, among which MTF-GLP and MTF-GLP-HPM perform better in the pan-sharpening results. This study provides a reference for the selection of pan-sharpening methods for SuperView-1 imagery in different application fields.

The Evolution of Preseismic Patterns Related to the Central Crete (Mw6.0) Strong Earthquake on 27 September 2021 Revealed by Multiresolution Wavelets and Natural Time Analysis

On 27 September 2021, a shallow earthquake with focal depth of 10 km and moment magnitude Mw6.0 occurred onshore in central Crete (Greece). The evolution of possible preseismic patterns in the area of central Crete before the Mw6.0 event was investigated by applying the method of multiresolution wavelet analysis (MRWA), along with that of natural time (NT). The monitoring of preseismic patterns by critical parameters defined by NT analysis, integrated with the results of MRWA as the initiation point for the NT analysis, forms a promising framework that may lead to new universal principles that describe the evolution patterns before strong earthquakes. Initially, we apply MRWA to the interevent time series of the successive regional earthquakes in order to investigate the approach of the regional seismicity towards critical stages and to define the starting point of the natural time domain. Then, using the results of MRWA, we apply the NT analysis, showing that the regional seismicity approached criticality for a prolonged period of ~40 days before the occurrence of the Mw6.0 earthquake, when the κ1 natural time parameter reached the critical value of κ1 = 0.070, as suggested by the NT method.

Detail-Injection-Based Multiscale Asymmetric Residual Network for Pansharpening

Although the multiresolution analysis (MRA)-based pansharpening methods are able to generate high-resolution multispectral (HRMS) images with good spectral retention, they are prone to spatial distortion. To address this problem, this letter combines deep learning (DL) with the MRA methods and proposes a novel detail-injected-based multiscale asymmetric residual network. The difference strategy is combined with MRA methods and the corresponding injection coefficients are obtained using the multiscale residual block (MSRB) to effectively map spatial information to each waveband of the multispectral (MS) images. In addition, asymmetric convolution block (ACB) is embedded in the residual network to obtain more robust features, and an inception feature pyramid network (FPN) is designed to enrich the spatial information of the fusion results while fusing features at different levels. Experimental results show that the method proposed in this letter outperforms the state-of-the-art pansharpening methods.

Multiresolution Analysis Based on Dual-Scale Regression for Pansharpening

Pansharpening technique is used to merge the original multispectral image (MS) with a high spatial resolution panchromatic image (PAN). Due to its robustness, the multiresolution analysis (MRA) is an important part of pansharpening. The scale regression model is effective for improving MRA. However, the existing MRA based on scale regression results into single-scale regression information, thus affecting the final pansharpening result. To address this problem, in this work, we propose a dual-scale regression-based MRA for pansharpening. First, we establish a scale regression-based model. Then, this model is improved using a high-pass modulation (HPM) injection scheme. Finally, the dual-scale information is added to the scale regression to construct the dual-scale regression for obtaining the final pansharpening result. We perform experiments using five datasets. The results show that the proposed method obtains a better pansharpening result as compared to various state-of-the-art MRA methods. In addition, the quantitative and qualitative analysis of the results shows that the proposed method achieves appropriate spatial and spectral resolution fusion. Therefore, it has a great potential in pansharpening technique.

Fault Type Classification of 150 kV Transmission Line using Wavelet Multi-Resolution Analysis Method

To identify the fault, wavelet method is used in solving complex protection problems. This study uses a new approach, namely the wavelet multi resolution analysis method with its application where multi resolution analysis works to analyze signals at different frequencies with the same resolution. In this study, the classification of fault types that occur in the 150 kV transmission line quickly and accurately is carried out using the wavelet multi resolution analysis method. This research is included in applied research and was designed using computer simulation software, namely ATP and MATLAB. The data transmission system used is the Maninjau Hydroelectric Power Plant transmission line to Pauh Limo Substation. The modeled transmission system is given 1-phase to ground, 2-phase to ground, 2- phase, 3-phase and lightning faults. To determine the accuracy of this classification, the fault is varied according to the distance and impedance of the disturbance. From the analysis of the simulation results and calculations, based on the wavelet multi resolution analysis method used in fault classifying, the average value of the approximation coefficient used to classify the type of fault is obtained. Based on the results of the study, it can be said that all types of fault analyzed in this study have met the classification requirements using the wavelet multi resolution analysis method

Fault Type Classification of 150 kV Transmission Line using Wavelet Multi-Resolution Analysis Method

To identify the fault, wavelet method is used in solving complex protection problems. This study uses a new approach, namely the wavelet multi resolution analysis method with its application where multi resolution analysis works to analyze signals at different frequencies with the same resolution. In this study, the classification of fault types that occur in the 150 kV transmission line quickly and accurately is carried out using the wavelet multi resolution analysis method. This research is included in applied research and was designed using computer simulation software, namely ATP and MATLAB. The data transmission system used is the Maninjau Hydroelectric Power Plant transmission line to Pauh Limo Substation. The modeled transmission system is given 1-phase to ground, 2-phase to ground, 2- phase, 3-phase and lightning faults. To determine the accuracy of this classification, the fault is varied according to the distance and impedance of the disturbance. From the analysis of the simulation results and calculations, based on the wavelet multi resolution analysis method used in fault classifying, the average value of the approximation coefficient used to classify the type of fault is obtained. Based on the results of the study, it can be said that all types of fault analyzed in this study have met the classification requirements using the wavelet multi resolution analysis method

Fusion of CT and MR Liver Images Using Multiresolution Analysis Methods

There are various medical imaging techniques such as Computed Tomography (CT) and Magnetic Resonance (MR) techniques. Both techniques give complex features of the region to be imaged. This study proposes an approach that uses Multiresolution Analysis (MRA) methods to fuse CT and MR liver images to obtain as detailed images as possible for medical diagnostic purposes. The transform coefficients are obtained by applying MRA methods to the images. Images are combined by applying 3 different fusion rules to these transform coefficients. Peak Signal to Noise Rate (PSNR), Structural Similarity Index Measure (SSIM) and Mean Square Error (MSE) values are calculated to evaluate the fused images. When comparing the methods, the best result was obtained using complex-valued curvelet transform.

Identifying and understanding alternative states of dryland landscape: A hierarchical analysis of time series of fractional vegetation-soil nexuses in China’s Hexi Corridor

Understanding and early identification of state transitions in dryland systems’ landscape pattern are challenging but critical for conservation planning and sustainable management strategies. Currently the alternative states of drylands have been identified based on dynamics of single vegetation index (i.e., normalized difference vegetation index), with the interactions between vegetation and soil components often being neglected. Here, we proposed a framework for identifying the alternative states in relation to land degradation based on the interactive pathways of fractional vegetation and soil-related endmember nexuses. In this framework, we initially generated 16-day fractional green vegetation endmember (green vegetation [GV]) and soil-related endmembers (sand [SL], saline [SA], dark surface [DA]) time series using a standardized linear spectral mixture analysis model in the Hexi Corridor during 2001–2017. A discrete wavelet transform based trends and turning points detection (DWT-TTD) algorithm was proposed to detect trends, turning point types, and timing of these time series records. These metrics were subsequently used to identify eight state transition pathways for each endmember and synthetic degradation processes at the appropriate 5–10 year scale. We found that the unmixed fractional endmembers exhibited a consistent agreement with both field abundance values and estimated fractions from high-spatial-resolution Google Earth images. Based on the DWT-TTD algorithm derived alternative pathways, we found that four positive pathways of GV and DA fractions can be observed in the vegetated areas were integrated with corresponding negative pathways of SA and SL fractions. These pathways resulted in remarkably increasing GV (+4551.81 km2) and DA (+9749.26 km2) and significantly declining SA (−1452.70 km2) and SL (−9555.57 km2) from 2001 to 2017. These processes were linked to increased precipitation and temperature and reduced drought degree. Also, the timing of the turning points (around 2007 and 2013) was largely coincidental with the timing of ecological management, suggesting that ecological governance played a crucial role in the state shifts. However, because of drought trends in the barren regions, land desertification exhibited an increasing occurrence in extent (+2.5% of total pixels) during the study period, which may increase in the future, as indicated by the large pixel proportion of initially positive reversal pathway for SL (9.31%). Compared to state-of-the-art approaches, the DWT-TTD algorithm, as a multi-resolution analysis method, has the potential to detect hierarchical temporal changes and disentangle the cross-scale inherent shifts of vegetation-soil systems. The framework can help devise sustainable management practices that maintain land degradation neutrality, especially when integrated with land use cover change analysis.

Spatial Multiresolution Analysis Approach to Identify Crash Hotspots and Estimate Crash Risk

AbstractIn this paper, we evaluate the performance of a spatial multiresolution analysis (SMA) method, that behaves like a variable bandwidth kernel density estimation (KDE) method, for hazardous r...

Construction of MRA and non-MRA wavelet sets on Cantor dyadic group

W. C. Lang determined wavelets on Cantor dyadic group by using Multiresolution analysis method. In this paper we have given characterization of wavelet sets on Cantor dyadic group which provides another method for the construction of wavelets. All the wavelets originating from wavelet sets are not necessarily associated with a multiresolution analysis. We have also established relation between multiresolution analysis and wavelets determined from wavelet sets.

Research on volatility spillover effect between foreign exchange and stock market based on computer simulation multi resolution analysis

In order to analyze the volatility spillover effect between foreign exchange and stock market, this paper adopts the wavelet multi-resolution analysis method of computer simulation. Firstly, aiming at the problem of high and low frequency oscillation and exchange rate de-noising, we adopts the generalized autoregressive conditional heteroskedasticity (GARCH) model to carry out the oscillation correction and exponential modification of the exchange rate denoising signal based on wavelet multi-resolution, and carries out the corresponding decomposition and fitting combined with the wavelet multi-resolution of the state transition GARCH. Then, through the computer simulation of the modified wavelet multi-resolution analysis, this paper studies the volatility spillover effect between the foreign exchange market and the stock market from different scales, so as to explore the simultaneous research from the time domain and frequency domain. The empirical results show that the low-frequency signals of RMB exchange rate volatility (RMB-ERV) and stock price volatility (SPV) have co-integration relationship. It is unique in that the volatility spillover effect in different trading cycles is inconsistent: in the short term, it is mainly manifested in the volatility spillover from the stock market (VS-SM) to the foreign exchange market (VS-FEM); and with the extension of the trading cycle, it shows both sides of effects on the VS.

Contour Feature Extraction of Medical Image Based on Multi-Threshold Optimization

During the process of fine segmentation of medical images, although a single threshold can improve the efficiency of processing, there will be the problem of fuzzy features and non-convergence of threshold in denoising of details such as contour extraction. To extract contour information of medical images, a method based on multi-threshold optimization is proposed. This paper analyzes the influence of contour wave transformation on gray correlation degree and noise intensity of different medical images and improves the Bayesian threshold. The middle threshold function was improved by correlation characteristics of contour wave coefficients, and contour features of medical images were constrained by multiple thresholds. Based on the above, the dimension of the medical image was reduced by the wavelet multi-resolution analysis method, and the corresponding threshold search space was obtained. A genetic algorithm was used to find the best quasi threshold in the search space. Through this value, the attribute histogram of the medical image was established, the best feature extraction threshold of the medical image was obtained by the golden section method, and contour feature information of the medical image was extracted. The experimental results show that the proposed method can achieve the fast extraction of the contour feature information of running image, get an ideal feature extraction effect, and has high efficiency of feature extraction.