Wavelet Subspaces Research Articles

Self-similar, spatially localized structures in turbulent pipe flow from a data-driven wavelet decomposition

This study aims to extract and characterize structures in fully developed pipe flow at a friction Reynolds number of $\textit {Re}_\tau = 12\,400$ . To do so, we employ data-driven wavelet decomposition (DDWD) (Floryan & Graham, Proc. Natl Acad. Sci. USA, vol. 118, 2021, e2021299118), a method that combines features of proper orthogonal decomposition and wavelet analysis in order to extract energetic and spatially localized structures from data. We apply DDWD to streamwise velocity signals measured separately via a thermal anemometer at 40 wall-normal positions. The resulting localized velocity structures, which we interpret as being reflective of underlying eddies, are self-similar across streamwise extents of 40 wall units to one pipe radius, and across wall-normal positions from $y^+=350$ to $y/R=1$ . Notably, the structures are similar in shape to Meyer wavelets. Projections of the data onto the DDWD wavelet subspaces are found to be self-similar as well, but in Fourier space; the bounds of self-similarity are the same as before, except streamwise self-similarity starts at a larger length scale of $450$ wall units. The evidence of self-similarity provided in this study lends further support to Townsend's attached eddy hypothesis, although we note that the self-similar structures are detected beyond the log layer and extend to large length scales.

An attention-guided and wavelet-constrained generative adversarial network for infrared and visible image fusion

The GAN-based infrared and visible image fusion methods have gained ever-increasing attention due to its effectiveness and superiority. However, the existing methods adopt the global pixel distribution of source images as the basis for discrimination, which fails to focus on the key modality information. Moreover, the dual-discriminator based methods suffer from the confrontation between the discriminators. To this end, we propose an attention-guided and wavelet-constrained GAN for infrared and visible image fusion (AWFGAN). In this method, two unique discrimination strategies are designed to improve the fusion performance. Specifically, we introduce the spatial attention modules (SAM) into the generator to obtain the spatial attention maps, and then the attention maps are utilized to force the discrimination of infrared images to focus on the target regions. In addition, we extend the discrimination range of visible information to the wavelet subspace, which can force the generator to restore the high-frequency details of visible images. Ablation experiments demonstrate the effectiveness of our method in eliminating the confrontation between discriminators. And the comparison experiments on public datasets demonstrate the effectiveness and superiority of the proposed method.

Perturbation Theorems for Regular Sampling in Wavelet Subspaces

Perturbation Theorems for Regular Sampling in Wavelet Subspaces

Intelligent Extraction of Salient Feature From Electroencephalogram Using Redundant Discrete Wavelet Transform.

At present, electroencephalogram (EEG) signals play an irreplaceable role in the diagnosis and treatment of human diseases and medical research. EEG signals need to be processed in order to reduce the adverse effects of irrelevant physiological process interference and measurement noise. Wavelet transform (WT) can provide a time-frequency representation of a dynamic process, and it has been widely utilized in salient feature analysis of EEG. In this paper, we investigate the problem of translation variability (TV) in discrete wavelet transform (DWT), which causes degradation of time-frequency localization. It will be verified through numerical simulations that TV is caused by downsampling operations in decomposition process of DWT. The presence of TV may cause severe distortions of features in wavelet subspaces. However, this phenomenon has not attracted much attention in the scientific community. Redundant discrete wavelet transform (RDWT) is derived by eliminating the downsampling operation. RDWT enjoys the attractive merit of translation invariance. RDWT shares the same time-frequency pattern with that of DWT. The discrete delta impulse function is used to test the time-frequency response of DWT and RDWT in wavelet subspaces. The results show that DWT is very sensitive to the translation of delta impulse function, while RDWT keeps the decomposition results unchanged. This conclusion has also been verified again in decomposition of actual EEG signals. In conclusion, to avoid possible distortions of features caused by translation sensitivity in DWT, we recommend the use of RDWT with more stable performance in BCI research and clinical applications.

ESR Estimation for Aluminum Electrolytic Capacitor of Power Electronic Converter Based on Compressed Sensing and Wavelet Transform

The aluminum electrolytic capacitor (AEC) is one of the most important parts of a power electronic converter. Throughout its lifespan, the equivalent series resistance (ESR) of the AEC will increase, which will affect the performance of the power electronic converter. To guarantee the reliability of a converter, it is necessary to monitor the health state of the AEC, for which one common technique is to estimate the ESR of the AEC. Equipment with a high sampling rate is usually required because converter usually works at a high frequency. This requirement will increase the cost of ESR monitoring. To address this issue, this article proposes a novel method of estimating the ESR for an AEC. The proposed method uses an innovative compressed sensing approach to acquire the ripple voltage and current. Instead of complete reconstruction of the ripple voltage and current, only the high-frequency features in the wavelet subspace are reconstructed and used to calculate the ESR. The proposed method reduces the cost of data sampling, transmission, and storage. This method is not limited by the converter circuit structure and can be applied in various environments. Simulations and experiments were carried out to verify the effectiveness of the proposed method.

Improvement in EEG Source Imaging Accuracy by Means of Wavelet Packet Transform and Subspace Component Selection

The electroencephalograph (EEG) source imaging (ESI) method is a non-invasive method that provides high temporal resolution imaging of brain electrical activity on the cortex. However, because the accuracy of EEG source imaging is often affected by unwanted signals such as noise or other source-irrelevant signals, the results of ESI are often incongruous with the real sources of brain activities. This study presents a novel ESI method (WPESI) that is based on wavelet packet transform (WPT) and subspace component selection to image the cerebral activities of EEG signals on the cortex. First, the original EEG signals are decomposed into several subspace components by WPT. Second, the subspaces associated with brain sources are selected and the relevant signals are reconstructed by WPT. Finally, the current density distribution in the cerebral cortex is obtained by establishing a boundary element model (BEM) from head MRI and applying the appropriate inverse calculation. In this study, the localization results obtained by this proposed approach were better than those of the original sLORETA approach (OESI) in the computer simulations and visual evoked potential (VEP) experiments. For epilepsy patients, the activity sources estimated by this proposed algorithm conformed to the seizure onset zones. The WPESI approach is easy to implement achieved favorable accuracy in terms of EEG source imaging. This demonstrates the potential for use of the WPESI algorithm to localize epileptogenic foci from scalp EEG signals.

Fractal geometry of wavelet decomposition in mechanical signature analysis

Multiple modes of vibration are usually incorporated in a single record of vibration measurement in condition monitoring of rotating machinery. Wavelet transform is an effective tool to detect and isolate transient fault features from other interfering modes. The conventional dyadic wavelet transform decomposes the signal into wavelet subspaces with distinct central frequencies and specific frequency bandwidths. In this paper, we propose a novel theory of centralized multiresolution analysis (CMR) and reveal the implicit fractal geometry properties in CMR. A concept of nested centralized wavelet packet space (NCWPS) is introduced to describe the self-similarity phenomenon in CMR. Within the theoretical framework, the classical dyadic wavelet packet is assimilated as a subordinated proper-subset of the augmented NCWPS. Moreover, the generalized CMR characterized by tunable and flexible frequency-scale topology configuration is established using harmonic wavelet transform. The CMR can be regarded as an improved transient signature dictionary. Therefore, the CMR is combined with an improved stationary signature dictionary to ensure enhanced performance in fault feature extraction in multiple modes coupled vibration measurements. The effectiveness of the proposed method is validated using numerical simulations, a rub-impact experiment, and a case study of vibration signal analysis in steel making industry.

Accurate classification of ECG arrhythmia using MOWPT enhanced fast compression deep learning networks

Accurate classification of electrocardiogram (ECG) signals is of significant importance for automatic diagnosis of heart diseases. In order to enable intelligent classification of arrhythmias with high accuracy, an accurate classification method based intelligent ECG classifier using the fast compression residual convolutional neural networks (FCResNet) is proposed. In the proposed method, the maximal overlap wavelet packet transform (MOWPT), which provides a comprehensive time-scale paving pattern and possesses the time-invariance property, was utilized for decomposing the original ECG signals into sub-signal samples of different scales. Subsequently, the samples of the five arrhythmia types were utilized as input to the FCResNet such that the ECG arrhythmia types were identified and classified. In the proposed FCResNet model, a fast down-sampling module and several residual block structural units were incorporated. The proposed deep learning classifier can substantially alleviate the problems of low computational efficiency, difficult convergence and model degradation. Parameter optimizations of the FCResNet were investigated via single-factor experiments. The datasets from MIT-BIH arrhythmia database were employed to test the performance of the proposed deep learning classifier. An averaged accuracy of 98.79% was achieved when the number of the wide-stride convolution in fast down-sampling module was set as 2, the batch size parameter was set as 20 and wavelet subspaces of low frequency bands in MOWPT were selected as input of the classifier. These analysis results were compared with those generated by some comparison methods to validate the superiorities and enhancements of the proposed method.

Multivariate bounded support Laplace mixture model

In this paper, bounded Laplace mixture model (BLMM) is proposed. The parameters of proposed model are estimated by maximum likelihood approach via expectation maximization and Newton–Raphson algorithm. The model is proposed for data modeling to perform clustering using synthetic data for univariate and multivariate examples and real datasets of different medical experiments. BLMM is validated through correctness of estimated parameters for synthetic data and clustering accuracy of medical datasets. A new modeling scheme is also introduced for wavelet coefficients which is based on BLMM. It is applied to image clustering and content-based image retrieval (CBIR) for feature extraction in wavelet domain. For feature extraction in this application, each image is decomposed into a set of wavelet subspaces and BLMM with two components is adopted to model the statistical characteristics of the wavelet coefficients for each wavelet subspace. The model parameters adapted from BLMM represent the image features in wavelet domain for each subspace and selected to formulate the feature space which is further used in clustering and CBIR. In the framework for clustering and image retrieval, features extracted in wavelet domain are further modeled through BLMM to categorize images into different groups and trained model is adopted for CBIR. In order to perform image retrieval with trained model via BLMM, city block distance, posterior probability and Kullback–Leibler divergence are introduced. We also propose a novel solution to compute Kullback–Leibler divergence which is very effective for image retrieval due to its low computational complexity and high retrieval rate. The effectiveness and viability of BLMM in texture image clustering and CBIR are demonstrated through UIUC, KTH-TIPS, DTD, STex and Kylberg databases. Different experiments are performed in the chosen applications, and from the results, BLMM has demonstrated its effectiveness in modeling synthetic data, real datasets from medical experiments, feature extraction in wavelet domain, image clustering and CBIR.

Sparse grid approximation spaces for space–time boundary integral formulations of the heat equation

The aim of this paper is to develop and analyse stable and accurate numerical approximation schemes for boundary integral formulations of the heat equation with Dirichlet boundary conditions. The accuracy of Galerkin discretisations for the resulting boundary integral formulations strongly depends on the choice of discretisation space. We develop a-priori error analysis utilising a proof technique that involves norm bounds in hierarchical wavelet subspace decompositions. We apply this to full tensor product discretisations and anisotropic sparse grid discretisations and demonstrate improvements over existing results in both cases. Finally, a simple adaptive scheme is proposed to suggest an optimal shape for the sparse grid index sets.

Enhancement of Fault Feature Extraction from Displacement Signals by Suppressing Severe End Distortions via Sinusoidal Wave Reduction

Displacement signals, acquired by eddy current sensors, are extensively used in condition monitoring and health prognosis of electromechanical equipment. Owing to its sensitivity to low frequency components, the displacement signal often contains sinusoidal waves of high amplitudes. If the digitization of the sinusoidal wave does not satisfy the condition of full period sampling, an effect of severe end distortion (SED), in the form of impulsive features, is likely to occur because of boundary extensions in discrete wavelet decompositions. The SED effect will complicate the extraction of weak fault features if it is left untreated. In this paper, we investigate the mechanism of the SED effect using theories based on Fourier analysis and wavelet analysis. To enhance feature extraction performance from displacement signals in the presence of strong sinusoidal waves, a novel method, based on the Fourier basis and a compound wavelet dictionary, is proposed. In the procedure, ratio-based spectrum correction methods, using the rectangle window as well as the Hanning window, are employed to obtain an optimized reduction of strong sinusoidal waves. The residual signal is further decomposed by the compound wavelet dictionary which consists of dyadic wavelet packets and implicit wavelet packets. It was verified through numerical simulations that the reconstructed signal in each wavelet subspace can avoid severe end distortions. The proposed method was applied to case studies of an experimental test with rub impact fault and an engineering test with blade crack fault. The analysis results demonstrate the proposed method can effectively suppress the SED effect in displacement signal analysis, and therefore enhance the performance of wavelet analysis in extracting weak fault features.

Generalized average sampling and reconstruction for wavelet subspaces

As an extension of the average sampling, we analyse generalized average sampling and reconstruction problem over some wavelet subspaces of \(L^{2}({{\mathbb {R}}})\). For closed subspaces \(V_{0}\) of \(L^{2}({{\mathbb {R}}})\), we present a necessary and sufficient condition under which there is the generalized average sampling expansion for every \(f \in V_{0}\).

Wavelet subspace decomposition of thermal infrared images for defect detection in artworks

Health of ancient artworks must be routinely monitored for their adequate preservation. Faults in these artworks may develop over time and must be identified as precisely as possible. The classical acoustic testing techniques, being invasive, risk causing permanent damage during periodic inspections. Infrared thermometry offers a promising solution to map faults in artworks. It involves heating the artwork and recording its thermal response using infrared camera. A novel strategy based on pseudo-random binary excitation principle is used in this work to suppress the risks associated with prolonged heating. The objective of this work is to develop an automatic scheme for detecting faults in the captured images. An efficient scheme based on wavelet based subspace decomposition is developed which favors identification of, the otherwise invisible, weaker faults. Two major problems addressed in this work are the selection of the optimal wavelet basis and the subspace level selection. A novel criterion based on regional mutual information is proposed for the latter. The approach is successfully tested on a laboratory based sample as well as real artworks. A new contrast enhancement metric is developed to demonstrate the quantitative efficiency of the algorithm. The algorithm is successfully deployed for both laboratory based and real artworks.

An analogue of the Littlewood–Paley theorem for orthoprojectors onto wavelet subspaces

We prove an analogue of the Littlewood–Paley theorem for orthoprojectors onto wavelet subspaces corresponding to a non-isotropic multiresolution analysis generated by the tensor product of smooth scaling functions of one variable with sufficiently rapid decay at infinity.

An analogue of the Littlewood-Paley theorem for orthoprojectors onto wavelet subspaces

Доказано утверждение, представляющее собой аналог теоремы Литтлвуда-Пэли для ортопроекторов на подпространства всплесков, соответствующие неизотропному кратномасштабному анализу, порожденному тензорным произведением гладких достаточно быстро стремящихся к нулю на бесконечности масштабирующих функций одной переменной. Библиография: 20 наименований.

Robust Environmental Sound Recognition With Fast Noise Suppression for Home Automation

This paper proposes a robust environmental sound recognition system using a fast noise suppression approach for home automation applications. The system comprises a fast subspace-based noise suppression module and a sound classification module. For the noise suppression module, we propose a noise suppression method that applies fast subspace approximations in the wavelet domain. We show that this method offers a lower computational cost than conventional methods. In the sound classification module, we use a feature extraction method that is also based on the wavelet subspace, derived from seventeen critical bands in a signal's wavelet packet transform. Furthermore, we create a multiclass support vector machine by employing probability product kernels. The experimental results for ten classes of various environmental sounds show that the proposed system offers robust performance in environmental sound recognition tasks.

Two-channel sampling in wavelet subspaces

Abstract We develop two-channel sampling theory in the wavelet subspace V 1 from the multi resolution analysis {Vj } j ∈𝕫. Extending earlier results by G. G. Walter [11], W. Chen and S. Itoh [2] and Y. M. Hong et al [5] on the sampling theory in the wavelet or shift invariant spaces, we find a necessary and sufficient condition for two-channel sampling expansion formula to hold in V 1.

Mutual Information-Assisted Wavelet Function Selection for Enhanced Rolling Bearing Fault Diagnosis

This paper presents an enhanced rolling bearing fault diagnosis approach, based on optimized wavelet packet transform (WPT) assisted with quantitative wavelet function selection. Mutual information is utilized as a quantitative measure to select the most suitable wavelet function for the WPT-based vibration analysis. Energy features from coefficients of an optimal set of orthogonal wavelet subspaces which resulted from the WPT-based vibration analysis are input to different classifiers. The fault states of the rolling bearings can then be identified. Experiment studies conducted on a rolling bearing test system have verified the effectiveness of the proposed approach for rolling bearing fault diagnosis.

Wavelet Subspace Based Integrated Face Recognition Scheme

In this paper, based on the study of the Two-Dimensional Principal Component Analysis (2DPCA), Two-Dimensional Principal Component Analysis (2DPCA) and fuzzy set theory, we propose a integrated face recognition algorithm based on wavelet subspace. This method can make good use of the advantages of each single method, and also can make up for the defect of each other. The comparison of the results of the different methods identification effect on the ORL、YALE and FERET face database show, the integrated method proposed in this paper improves the recognition rate, and it also reduces the training and classification time as well.

The Detection Data of Mammary Carcinoma Processing Method Based on the Improved HHT

This paper presents a new algorithm for the analysis of spectral properties of signal of BRATUMASS (Breast tumor microwave sensor system) using the wavelet packet transform (WPT) and the Hilbert-Huang transform (HHT). A wavelet subspace algorithm combined with the empirical mode decomposition (EMD) is introduced to create subdivided intrinsic mode functions (IMFs) and a cross-correlation analysis is applied to remove pseudo-spectral components. The algorithm proposed by this paper is able to correctly identify spectral patterns of our signal.