Directional Wavelet Research Articles

Damage identification in composite structures using high-speed 3D digital image correlation and wavelet analysis of mode shapes

ABSTRACT In this study, the damage identification procedure combining the advantages of high-speed 3D digital image correlation (DIC) that is used for modal analysis and wavelet-based processing algorithm is presented. The proposed procedure has been successfully validated on sandwich composite structures with internal damage of a core and impact damage, and its performance was demonstrated by detection, localisation, and identification of shapes of damage in tested structures, comparable to the results from scanning laser Doppler vibrometry (SLDV). The effectiveness in damage identification was achieved by the development of processing algorithm of acquired mode shapes, which uses a 2D double-density directional wavelet transform with increased sensitivity with entropic weights allowing to automatically select those wavelet coefficients and mode shapes, which are most sensitive to damage. The procedure presented in this paper demonstrates the performance of 3D DIC for damage identification as a cost-effective alternative to the procedures based on SLDV measurements.

Recession fears and stock markets: An application of directional wavelet coherence and a machine learning-based economic agent-determined Google fear index

Recession fears play a pivotal role in investment decision making and policy development aimed at reducing the likelihood of a recession and managing its impact. Using machine learning, we develop an economic agent-determined daily recession fear index using Google searches that isolates recession-related fears from overall stock market uncertainty. We study the evolving impact of recent recession fears on stock markets using directional wavelet coherence that distinguishes between positive and negative associations. Recession fears negatively impact world and G7 stock markets and trigger heightened volatility, with Japan being the most resilient. Monetary policy tightening in response to record inflation levels significantly contributes to persistent recession fears, suggesting that policymakers should consider co-ordinating responses to avoid an excessive global economic slowdown. Our methodology offers a high frequency monitoring tool that can be applied to analyse evolving relationships between variables and can be generalised to study the influence of specific events on financial markets by isolating topic-specific components from general proxies for uncertainty, attention or sentiment.

Wavelet-based statistics for enhanced 21cm EoR parameter constraints

We propose a new approach to improve the precision of astrophysical parameter constraints for the 21cm signal from the epoch of reionisation (EoR). Our method introduces new sets of summary statistics, hereafter ‘evolution compressed’ statistics, which quantify the spectral evolution of the 2D spatial statistics computed at fixed redshift. We defined such compressed statistics for power spectrum (PS), wavelet scattering transforms (WST), and wavelet moments (WM), which also characterise non-Gaussian features. To compare these different statistics, along with the 3D power spectrum, we estimated their Fisher information on three cosmological parameters from an ensemble of simulations of 21cm EoR data, both in noiseless and noisy scenarios using Square Kilometre Array (SKA) noise levels equivalent to 100 and 1000 h of observations. We also compare wavelet statistics, in particular WST, built from standard directional Morlet wavelets, as well as from a set of isotropic wavelets derived from the binning window function of the 2D power spectrum. For the noiseless case, the compressed wavelet statistics give constraints that are up to five times more precise than those obtained from the 3D isotropic power spectrum. At the same time, for 100 h SKA noise, from which it is difficult to extract non-Gaussian features, compressed wavelet statistics still give over 30% tighter constraints. We find that the wavelet statistics with wavelets derived from the power-spectrum binning window function provide the tightest constraints of all the statistics, with the WSTs seemingly performing better than the WMs, in particular when working with noisy data. The findings of this study demonstrate that evolution-compressed statistics extract more information than usual 3D isotropic power-spectra approaches and that our wavelet-based statistics can consistently outmatch power-spectrum-based statistics. When constructing such wavelet-based statistics, we also emphasise the need to choose a set of wavelets with an appropriate spectral resolution concerning the astrophysical process studied.

Enhancing RABASAR for Multi-Temporal SAR Image Despeckling through Directional Filtering and Wavelet Transform.

The presence of speckle noise severely hampers the interpretability of synthetic aperture radar (SAR) images. While research on despeckling single-temporal SAR images is well-established, there remains a significant gap in the study of despeckling multi-temporal SAR images. Addressing the limitations in the acquisition of the "superimage" and the generation of ratio images within the RABASAR despeckling framework, this paper proposes an enhanced framework. This enhanced framework proposes a direction-based segmentation approach for multi-temporal SAR non-local means filtering (DSMT-NLM) to obtain the "superimage". The DSMT-NLM incorporates the concept of directional segmentation and extends the application of the non-local means (NLM) algorithm to multi-temporal images. Simultaneously, the enhanced framework employs a weighted averaging method based on wavelet transform (WAMWT) to generate superimposed images, thereby enhancing the generation process of ratio images. Experimental results demonstrate that compared to RABASAR, Frost, and NLM, the proposed method exhibits outstanding performance. It not only effectively removes speckle noise from multi-temporal SAR images and reduces the generation of false details, but also successfully achieves the fusion of multi-temporal information, aligning with experimental expectations.

Analytic and directional wavelet packets in the space of periodic signals

Analytic and directional wavelet packets in the space of periodic signals

The Atacama Cosmology Telescope: map-based noise simulations for DR6

The increasing statistical power of cosmic microwave background (CMB) datasets requires a commensurate effort in understanding their noise properties. The noise in maps from ground-based instruments is dominated by large-scale correlations, which poses a modeling challenge. This paper develops novel models of the complex noise covariance structure in the Atacama Cosmology Telescope Data Release 6 (ACT DR6) maps. We first enumerate the noise properties that arise from the combination of the atmosphere and the ACT scan strategy. We then prescribe a class of Gaussian, map-based noise models, including a new wavelet-based approach that uses directional wavelet kernels for modeling correlated instrumental noise. The models are empirical, whose only inputs are a small number of independent realizations of the same region of sky. We evaluate the performance of these models against the ACT DR6 data by drawing ensembles of noise realizations. Applying these simulations to the ACT DR6 power spectrum pipeline reveals a ∼ 20% excess in the covariance matrix diagonal when compared to an analytic expression that assumes noise properties are uniquely described by their power spectrum. Along with our public code, mnms, this work establishes a necessary element in the science pipelines of both ACT DR6 and future ground-based CMB experiments such as the Simons Observatory (SO).

Directional lifting wavelet transform for image edge analysis

In this paper, we propose a new two-dimensional directional discrete wavelet transform that can decompose an image into 12 multiscale directional edge components. The proposed transform is designed in a fully discrete setting and thus is easy to implement in actual computations. The proposed transform is viewed as a category of redundant discrete wavelet transforms implemented by fast in-place computational algorithms by a lifting scheme that has been modified to incorporate redundancy. The redundancy is limited to (N×J+1)/4, where N=12 is the directional selectivity and J is a decomposition level of the multiscale transform. Numerical experiments in edge analysis using various images demonstrate the advantages of the proposed method over some conventional standard methods. The proposed method outperforms several conventional edge detection methods in identifying both the location and orientation of edges, and well captures the directional and geometrical features of images.

Directional lifting wavelet transform domain image steganography with deep-based compressive sensing

Directional lifting wavelet transform domain image steganography with deep-based compressive sensing

Direction sensitive analysis of higher order jump discontinuities along circles on the sphere

In recent years, scale-discretized directional wavelets and second-generation curvelets have been introduced on the unit sphere, yielding directional and localized polynomial frames for band-limited signals. In this paper, we show that these functions are able to detect the positions and orientations of all higher order jump discontinuities which lie along circles on the 2-sphere. Specifically, we prove upper and lower estimates for the magnitude of the corresponding inner products when the analysis function is concentrated in the neighborhood of such a singularity. Although similar results already exist in certain two-dimensional settings, this paper is the first one to consider frames and signals that are given on the 2-sphere. As a side product of our investigations, we also develop a new localization bound as well as an explicit formula for the auto-correlation function for second-generation curvelets.

Evaluation of a correlation phase recovery method to be used in temporal speckle pattern interferometry with noise contaminated specklegrams

When a phase distribution is evaluated in temporal speckle pattern interferometry, the accuracy of the retrieved phase distribution depends on how the different phase recovery methods deal with the influence of low-frequency noise and intensity bias. In this paper, we show that the proposed correlation method can effectively recover the phase distribution in time series of speckle interferograms that are affected by sets of adjacent non-modulated pixels, combined with very small phase changes between successive frames. The performance of the proposed method is analyzed when the retrieved optical phase distributions are coded in noisy temporal speckle pattern interferometry signals presenting large regions of adjacent low-modulated pixels. It is also compared with the data measured with the well-known one-dimensional Fourier transform technique, and the three-dimensional directional wavelet transform method. The performance of the proposed phase retrieval technique is compared with these last two methods using computer-simulated speckle interferograms, and the advantages and limitations of the proposed method are discussed. Finally, the performance of the proposed correlation technique to process real data is illustrated.

Directional wavelet packets originating from polynomial splines

Directional wavelet packets originating from polynomial splines

Simultaneous source separation by shot collocation and strength variation

Simultaneous shooting offers opportunities for significant cost savings in seismic data acquisitions. The most common strategy uses random delay shots where source separation is achieved during the processing stage, thereby doubling source densities. We have determined that the creation of a collocated source survey, where shots are repeated simultaneously at multiple positions, is a viable alternative strategy, with the additional benefit that it may increase source density even further while keeping the acquisition duration unchanged. Source separation is achieved using overcomplete independent component analysis by first by applying a directional wavelet transform to separate source signals with different slowness, then estimating the mixing matrix, followed by solving an optimization problem with an energy constraint combined with a sparseness inducing prior and obtaining the required waveforms. Synthetic tests find average reconstruction quality on the order of 22.1, 15.4, and 8.4 dB if, respectively, three, four, or five shots are acquired in two mixtures. Examination of the true versus obtained zero-offset sections also demonstrates the robustness of our signal recovery strategy. The advantage of shot collocation over conventional acquisitions is that it may triple or even quadruple the source density for unchanged acquisition durations with superior reconstruction results compared with dithered acquisitions using similar blending factors.

An hybrid denoising algorithm based on directional wavelet packets

An hybrid denoising algorithm based on directional wavelet packets

Directional Stockwell transform in L 2(ℝ n )

In the present article, we propose a directionally tuned variant of the continuous Stockwell transform in the context of multi-dimensional signal analysis. Owing to the directional selectivity coupled with a frequency adaptable window, the proposed transform serves as a bridge between the directional short-time Fourier and wavelet transforms. Besides the formulation of all the fundamental results, including the orthogonality relation and reconstruction formula, we also obtain several uncertainty inequalities associated with the directional Stockwell transform.

Directional wavelet modal curvature method for damage detection in plates

Abstract Vibration-based damage detection using the 2D modal curvature has become a research focus. However, the traditional methods based on modal curvature lack the sensitivity to direction of the damage. To address this problem, a directional 2D Morlet wavelet modal curvature is proposed in this paper. The directional wavelet modal curvatures show the following merits: robust to noise interference and sensitive to direction of damage. By the numerical simulation, the efficiency of the proposed method is demonstrated in the plate-like structure.

Feature enhancement method of rolling bearing acoustic signal based on RLS-RSSD

The bearing acoustic signal is interfered by reflected sounds and background noises, resulting in a low signal-to-noise ratio (SNR). To address this problem, this paper proposes a feature enhancement method that combines recursive least squares (RLS) with resonance-based sparse signal decomposition (RSSD) into the RLS-RSSD method. First, the RLS method is used as the inverse filter to remove the reverberation as well as reduce the interference of the late reflected sound on the direct signal, then RSSD and wavelet denoising are used to eliminate aperiodic component in the low and high frequency bands. The signals are synthesized based on the amplitudes of different frequency signals, and finally, the bearing fault is determined by envelope spectrum analysis. The results of the simulation data, experimental data, and field application data analysis indicate that the frequency of bearing defects can be accurately extracted by the proposed method.

A directional continuous wavelet transform of mode shape for line-type damage detection in plate-type structures

Line-type damage is abundant in engineering structures that have been in service for a long time. Vibration-based nondestructive testing as a global method has been extensively used in structural damage identification. In this study, a two-dimensional directional continuous wavelet transform (2D-DCWT)-based damage identification algorithm using “Morlet2d” wavelet for line-type damage detection in plate structures is presented. An analytical long narrow notch-type damage model of simply-supported plates is proposed to evaluate line-type damage effect on plate vibration performance. Based on the proposed model, the biggest challenge in parameter selection of wavelet analysis is solved. The fundamental aspects of 2D-DCWT algorithm in term of notch location and orientation are assessed. A multi-mode shape fusion approach is presented to make the 2D-DCWT algorithm apply to the high-order mode shapes. A comparative study with isotropic “Mexcan-hat2d” wavelet-based damage identification is performed, and it demonstrates that the proposed 2D-DCWT algorithm is superior in noise immunity. The efficiency and practicability of the 2D-DCWT algorithm are certified by an experimental modal test on damage detection of an artificially-induced notched aluminum alloy clamped plate using excitation-response system of the Piezoelectric Leadzirconate-Titanate (PZT) and Scanning laser Doppler Vibrometers (SLDV). As demonstrated in both the analytical and experimental investigation, the suggested approach may successfully identify line-type damage in plate-type structures.

Emboli detection using a wrapper-based feature selection algorithm with multiple classifiers

Traditionally, analyzing spectral recordings and Doppler shift sounds for detecting emboli is done by experts visually and aurally. These techniques for detecting emboli are both subjective and expensive. In the proposed study, an emboli detection system, which makes binary classification to decide whether a signal is emboli or not, is developed using Q-factor tuned Directional Dual-Tree Rational-Dilation Complex Wavelet Transform for feature extraction. A Doppler ultrasound signal dataset including 400 samples – 200 from embolic, 100 from speckles, and 100 from artifacts – is used. Besides feeding dataset to Support Vector Machines, Multilayer Perceptron, Logistic Regression algorithms for classification; the ensemble voting approach was also applied to obtain higher performance. The experiments including the feature selection and classification algorithms are conducted with an unbiased two-step cross-validation procedure. Firstly, grid-search was used for finding optimum hyper-parameters and features on the training and validation sets. Next, the optimal model was applied to the test set. Lastly, a wrapper-based feature selection algorithm called Boruta was applied to the dataset to overcome insufficient number of samples problem. This problem is very common in biomedical studies due to the difficulties occurring in their creation such as the high-dependency to well-trained human power to acquire meaningful data, and expensiveness in terms of money and time. The results showed that ensemble learning has higher performance than single classifiers when a limited number of training samples is available. Besides, the results point out that close prediction performance was obtained with fewer samples when the Boruta algorithm was applied.

Image inpainting using directional wavelet packets originating from polynomial splines

The paper presents a new algorithm for the image inpainting problem. The algorithm uses a recently designed versatile library of quasi-analytic complex-valued wavelet packets (qWPs) which originate from polynomial splines of arbitrary orders. Tensor products of 1D qWPs provide a diversity of 2D qWPs oriented in multiple directions. For example, a set of the fourth-level qWPs comprises 62 different directions. The properties of these qWPs such as refined frequency resolution, directionality of waveforms with unlimited number of orientations, (anti-)symmetry of waveforms and windowed oscillating structure of waveforms with a variety of frequencies, make them efficient in image processing applications, in particular, in dealing with the inpainting problem addressed in the paper. The obtained results for this problem are quite competitive with the best state-of-the-art algorithms. The inpainting is implemented by an iterative scheme, which expands the Split Bregman Iteration (SBI) procedure by supplying it with an adaptive variable soft thresholding based on the Bivariate Shrinkage algorithm. In the inpainting experiments, performance comparison between the qWP-based methods and the state-of-the-art algorithms is presented.

SH Wavelet Propagation Through the Random Distribution of Aligned Line Cracks Based on the Radiative Transfer Theory

This paper studies the propagation of SH wavelet intensity through the random distribution of aligned line cracks in a two-dimensional (2-D) homogeneous medium as the simplest mathematical model of the heterogeneous Earth medium. The scattering process of a single line crack is described by Mathieu functions. The random distribution of cracks is well represented by the scattering coefficient, that is, the scattering power per unit area. Two methods are proposed for the derivation of the space–time distribution of the intensity Green function for the unit isotropic radiation from a point source: one is the single scattering approximation and the other is the Monte Carlo simulation. The former and the latter are deterministic and stochastic methods, respectively. In the case that the wavenumber is larger than the reciprocal of the crack length, synthesized time traces show that direct wavelets near the ray direction parallel to the line cracks decrease according to the geometrical decay with increasing travel distance as if there exists a transparent channel along the crack line direction; however, those near the direction normal to the line cracks decrease more rapidly because of strong scattering attenuation. At large lapse times, multiple scattering produces a swelling around the source location, which is prolonged to the crack line direction. Those characteristics well reflect the anisotropy of the line crack scattering. The Monte Carlo simulation presented here could be a fundamental base for the study of more realistic crack scattering problems.