Stationary Wavelet Research Articles

Stationary Wavelet with Double Generalised Rayleigh Distribution

Statistics are mathematical tools applying scientific investigations, such as engineering and medical and biological analyses. However, statistical methods are often improved. Nowadays, statisticians try to find an accurate way to solve a problem. One of these problems is estimation parameters, which can be expressed as an inverse problem when independent variables are highly correlated. This paper’s significant goal is to interpret the parameter estimates of double generalized Rayleigh distribution in a regression model using a wavelet basis. It is difficult to use the standard version of the regression methods in practical terms, which is obtained using the likelihood. Since a noise level usually makes the result of estimation unstable, multicollinearity leads to various estimates. This kind of problem estimates that features of the truth are complicated. So it is reasonable to use a mixed method that combines a fully Bayesian approach and a wavelet basis. The usual rule for wavelet approaches is to choose a wavelet basis, where it helps to compute the wavelet coefficients, and then, these coefficients are used to remove Gaussian noise. Recovering data is typically calculated by inverting the wavelet coefficients. Some wavelet bases have been considered, which provide a shift-invariant wavelet transform, simultaneously providing improvements in smoothness, in recovering, and in squared-error performance. The proposed method uses combining a penalized maximum likelihood approach, a penalty term, and wavelet tools. In this paper, real data are involved and modeled using double generalized Rayleigh distributions, as they are used to estimate the wavelet coefficients of the sample using numerical tools. In practical applications, wavelet approaches are recommended. They reduce noise levels. This process may be useful since the noise level is often corrupted in real data, as a significant cause of most numerical estimation problems. A simulation investigation is studied using the MCMC tool to estimate the underlying features as an essential task statistics.

Selection of statistical wavelet features using a wrapper approach for electrical appliances identification based on a KNN classifier combined with voting rules method

This work is an extended version of a paper presented in the International Conference on Intelligent Systems and Patterns Recognition where the authors have proposed a compact features representation based on the estimation of statistical features using discrete wavelet transform for electrical appliances identification based on a K nearest neighbour classifier combined with voting rule strategy. The results have shown that the wavelet cepstral coefficients (WCC) descriptor presents highest performance with 98.13% classification rate (CR). In this work, we propose many extensions: 1) The logarithm energy (LOG_E) is used as additional descriptor; 2) The relevance of the wavelet-based features combined with LOG_E descriptor is investigated using feature selection based on wrappers approach; 3) Deep performances evaluation is carried out using five additional metrics. The results show that the selection of four features of WCC combined with LOG_E improves the CR at 98.51%.

Selection of statistical wavelet features using a wrapper approach for electrical appliances identification based on a KNN classifier combined with voting rules method

Selection of statistical wavelet features using a wrapper approach for electrical appliances identification based on a KNN classifier combined with voting rules method

Automated Cognitive Workload Assessment Using Logical Teaching Learning-Based Optimization and PROMETHEE Multi-Criteria Decision Making Approach

Cognitive workload assessment plays an important role to examine the mental status of brain for emergency situations faced by air traffic controllers, military personals and many more. It is also significant for brain disorder diagnosis and psychological health monitoring. Mental workload induced by various factors needs to be critically examined for better decisions. This paper presents an automated model for cognitive workload assessment to provide accurate categorization on intensity of workload induced by multitasking situations. Statistical wavelets corresponding to brain frequencies act as features for categorization task. The brain analysis needs technical expertise to identify the relevant information but, due to lack of sufficient number of experts, feature selection model helps to identify the relevant features responsible to categorize cognitive workload. Teaching Learning based Optimization (TLBO) method has been modified using ‘Logical Operators’ for binary feature selection problem in the current study and evaluated based on different parameters. Results on Logical TLBO reached upto 100% for binary and multiclass classification of cognitive workload. The results also show the proposed method is converging in minimum iteration for multiclass cognitive workload. PROMETHEE based multi-criteria decision-making approach has adopted for ranking of algorithm to select the best algorithm when multiple alternatives are available. Based on study of current literature, this approach appears to be first time implemented to provide ranking of optimization algorithms. The PROMETHEE method also suggests that the Logical TLBO is best among all the other compared approaches.

Statistical Wavelets With Harmony Search- Based Optimal Feature Selection of EEG Signals for Motor Imagery Classification

Brain Computer Interface (BCI) does not only help people of physical disability but also being used popularly in several other applications. Motor Imagery (MI) classification is one of the major contributions in BCI which works on segment of EEG signal within particular frequency band. Herein, feature selection plays important role in obtaining good classification results. In this article, Beta and Gamma frequency are considered with Statistical DWT (SDWT) based features for classification of EEG signals (MI classification) for patient monitoring, assistance healthcare services and daily living activities. Harmony search algorithm of feature selection is used to obtain the optimal feature set for classification of MI. The results show that frequency centric SDWT achieves average accuracy of 92.49% for weighted KNN (K-Nearest Neighbour) method. Comparison of accuracies before and after feature selection portrays that feature selection with harmony search improves the performance of proposed MI classification.

Deep transfer learning-based automated detection of COVID-19 from lung CT scan slices.

Lung abnormality is one of the common diseases in humans of all age group and this disease may arise due to various reasons. Recently, the lung infection due to SARS-CoV-2 has affected a larger human community globally, and due to its rapidity, the World-Health-Organisation (WHO) declared it as pandemic disease. The COVID-19 disease has adverse effects on the respiratory system, and the infection severity can be detected using a chosen imaging modality. In the proposed research work; the COVID-19 is detected using transfer learning from CT scan images decomposed to three-level using stationary wavelet. A three-phase detection model is proposed to improve the detection accuracy and the procedures are as follows; Phase1- data augmentation using stationary wavelets, Phase2- COVID-19 detection using pre-trained CNN model and Phase3- abnormality localization in CT scan images. This work has considered the well known pre-trained architectures, such as ResNet18, ResNet50, ResNet101, and SqueezeNet for the experimental evaluation. In this work, 70% of images are considered to train the network and 30% images are considered to validate the network. The performance of the considered architectures is evaluated by computing the common performance measures. The result of the experimental evaluation confirms that the ResNet18 pre-trained transfer learning-based model offered better classification accuracy (training = 99.82%, validation = 97.32%, and testing = 99.4%) on the considered image dataset compared with the alternatives.

RESERVOIR CHARACTERIZATION BY AVO ANALYSIS: A CASE STUDY OF PENYU BASIN, MALAYSIA

Amplitude variations with offset (AVO) method are applied in predicting hydrocarbon by interpreting the anomalies in terms of lithology and pore fluids using the AVO cross-plot of intercept, A, and gradient, B. The study was carried out and tested in the previously problematic field such as thick sand with non-commercial discovery in Penyu Basin, Malaysia. With limited prospect evaluation conducted in this basin, we aim to provide evidence of potential hydrocarbon accumulation exists in this region for further exploration development. The AVO response of the anomalies detected first executed in locating the potential hydrocarbon prospect before predicting shear wave velocity using the Greenberg-Castagna and Castagna equations. A statistical wavelet was then correlated with seismic data to optimize the depth-time conversion for synthetic derivation prior to fluid replacement modelling and Gassmann’s equations. It is concluded that the AVO class II anomalies on both seismic and synthetic seismogram generated by AVO modelling agreed on the presence of oil in the reservoir. The AVO and seismic attributes suggested that there are potential hydrocarbon prospects in the Penyu basin based on the interpretation of structural traps of faulted anticline and fault.Keywords: amplitude versus offset; hydrocarbon prediction; Penyu basin

On wavelet-based statistical process monitoring

This paper presents an overview of wavelet-based techniques for statistical process monitoring. The use of wavelet has already had an effective contribution to many applications. The increase of data availability has led to the use of wavelet analysis as a tool to reduce, denoise, and process the data before using statistical models for monitoring. The most recent review paper on wavelet-based methods for process monitoring had the goal to review the findings up to 2004. In this paper, we provide a recent reference for researchers and engineers with a different focus. We focus on: (i) wavelet statistical properties, (ii) control charts based on wavelet coefficients, and (iii) wavelet-based process monitoring methods within a machine learning framework. It is clear from the literature that wavelets are widely used with multivariate methods compared to univariate methods. We also found some potential research areas regarding the use of wavelet in image process monitoring and designing control charts based on wavelet statistics, and listed them in the paper.

An efficient feature extraction scheme for classification of mental tasks based on inter-channel correlation in wavelet domain utilizing EEG signal

In this paper, an efficient scheme of extracting features from EEG signal is proposed for mental task classification based on inter-channel relationship in wavelet domain. It is shown that use of wavelet domain inter-channel relationship can drastically improve the classification performance obtained by conventional wavelet statistics. Both multi-level wavelet decomposition and node reconstruction are utilized for proposed inter-channel correlation feature extraction. It is expected that the correlation obtained from different combination of channels will be different for various mental tasks depending on the nature of the stimulus generated in the brain and thus can provide distinctive features. Support vector machine (SVM) classifier is used to carry out classification of five different mental tasks obtained from an openly accessible EEG dataset. It is found that the proposed scheme can classify mental tasks with a very high level of accuracy compared to that obtained by some existing methods.

New approach of ECG denoising based on 1-D double-density complex DWT and SBWT

ABSTRACT In this paper we propose a new ECG denoising approach based on the application of double-density complex denoising method in the stationary bionic wavelet transform () domain. This approach consists at the first step in applying the to the noisy ECG signal in order to obtain two noisy coefficients and . The latter is an approximation coefficient and is a detail one. The latter is then denoised using Soft thresholding for obtaining a denoised coefficient, . The double-density complex denoising method is applied to and we obtain a denoised coefficient, . The denoised ECG signal is finally obtained from the application of the inverse of the , to and . This proposed technique is evaluated and compared to the double-density complex denoising one, the denoising technique based on Wavelets and Hidden Markov Models, the technique based on Non-Local Means and our previous proposed approach based on and (translation invariant forward wavelet transform). The simulation results obtained from the computations of SNR (ratio), MAE (mean absolute error), PSNR (peak SNR) and CC (cross-correlation), show that the proposed technique outperforms the other techniques used in our evaluation

Analysing the Main Belt asteroid distributions by wavelets

We perform statistical wavelet analysis of the Main Belt asteroids, seeking statistically significant asteroid families. The goal is to test the new wavelet analysis algorithm and to compare its results with more traditional methods like the hierarchic clustering. We first consider several 1D distributions for various physical and orbital parameters of asteroids. Then we consider three bivariate distributions for the three orbital parameters (a,e,i) taken pairwisely. The full 3D analysis of this space is not available here, but based on the 2D results we perform a disentangling of overlapped 2D families and derive total of 44 3D families with confirmed statistical significance.

Gas Saturated Sandstone Reservoir Modeling Using Bayesian Stochastic Seismic Inversion

This study has been done to map the distribution of gas saturated sandstone reservoir by using stochastic seismic inversion in the “X” field, Bonaparte basin. Bayesian stochastic inversion seismic method is an inversion method that utilizes the principle of geostatistics so that later it will get a better subsurface picture with high resolution. The stages in conducting this stochastic inversion technique are as follows, (i) sensitivity analysis, (ii) well to seismic tie, (iii) picking horizon, (iv) picking fault, (v) fault modeling, (vi) pillar gridding, ( vii) making time structure maps, (viii) scale up well logs, (ix) trend modeling, (x) variogram analysis, (xi) stochastic seismic inversion (SSI). In the process of well to seismic tie, statistical wavelets are used because they can produce good correlation values. Then, the stochastic seismic inversion results show that the reservoir in the study area is a reservoir with tight sandstone lithology which has a low porosity value and a value of High acoustic impedance ranging from 30,000 to 40,000 ft /s*g/cc.

Discrete Wavelet Transform and Bird Swarm Optimized Bayesian Multimodal Medical Image Fusion

A novel Bayesian image fusion scheme using bird swarm optimization algorithm (BSA) is being proposed here.The medical Image fusion is progressed using the MRI brain images taken from the BRATS database and thesource images of different modalities are fused effectively to present an information rich fused image. The sourceimages are subjected to the Haar discrete wavelet transform (DWT) and the Bayesian fusion is performed usingthe Bayesian parameter, which is determined optimally using the BSA optimization. The analysis reveals that themethod outperformed the three existing methods of fusion that is nonsubsampled contourlet transform (NSCT),cascaded static wavelet (SWT) and NSCT ,that is (SWT-NSCT) and Holoentropy and SP-Whale Optimizationmethod (HW Fusion) with improved values of mutual information(1.4764),peak signal-to-noise ratio (37.2114)and root mean square error (9.9341) .

Carbon, water and energy fluxes in agricultural systems of Australia and New Zealand

A comprehensive understanding of the effects of agricultural management on climate–crop interactions has yet to emerge. Using a novel wavelet–statistics conjunction approach, we analysed the synchronisation amongst fluxes (net ecosystem exchange NEE, evapotranspiration and sensible heat flux) and seven environmental factors (e.g., air temperature, soil water content) on 19 farm sites across Australia and New Zealand. Irrigation and fertilisation practices improved positive coupling between net ecosystem productivity (NEP = −NEE) and evapotranspiration, as hypothesised. Highly intense management tended to protect against heat stress, especially for irrigated crops in dry climates. By contrast, stress avoidance in the vegetation of tropical and hot desert climates was identified by reverse coupling between NEP and sensible heat flux (i.e., increases in NEP were synchronised with decreases in sensible heat flux). Some environmental factors were found to be under management control, whereas others were fixed as constraints at a given location. Irrigated crops in dry climates (e.g., maize, almonds) showed high predictability of fluxes given only knowledge of fluctuations in climate (R2 > 0.78), and fluxes were nearly as predictable across strongly energy- or water-limited environments (0.60 < R2 < 0.89). However, wavelet regression of environmental conditions on fluxes showed much smaller predictability in response to precipitation pulses (0.15 < R2 < 0.55), where mowing or grazing affected crop phenology (0.28 < R2 < 0.59), and where water and energy limitations were balanced (0.7 < net radiation ∕ precipitation < 1.3; 0.27 < R2 < 0.36). By incorporating a temporal component to regression, wavelet–statistics conjunction provides an important step forward for understanding direct ecosystem responses to environmental change, for modelling that understanding, and for quantifying nonstationary, nonlinear processes such as precipitation pulses, which have previously defied quantitative analysis.

Blind image quality assessment using natural scene statistics of stationary wavelet transform

Image quality assessment (IQA) by human observers, who are the ultimate users, is of utmost importance. Since IQA performed by human observers could be time consuming therefore, computational models are required that can assess the quality of images using objective metrics. Blind image quality assessment (BIQA) methods could predicts the perceived quality of distorted images without requiring information regarding the pristine version of the image. The natural scene statistics (NSS) based BIQA methods predict the quality score by extracting features either in spatial or transform domain. We propose a new BIQA technique that extracts features both in spatial and transform domain. The NSS of stationary wavelet transform (SWT), morphological gradient, and discrete Laplacian are known to be similar to human visual system, and hence can be used for BIQA. Morphological gradient has the advantage that it is easy to generalize for any type of feature space and discrete Laplacian has the property to retain key structural information inherent in the image. SWT provides edge and high frequency information while preserving the scale of the image. We remove the redundancies between the extracted features from spatial and transform domain using an adaptive joint normalization framework. Our proposed BIQA technique is tested on five publicly available databases (i.e., TID2008, TID2013, LIVE, CSIQ, and LIVE from the wild image quality challenge). Our experimental results have shown that our proposed BIQA technique achieves higher accuracy in terms of image quality prediction in comparison to the state-of-the-art BIQA and full reference IQA techniques.

Industrial Pollution Areas Detection and Location via Satellite-Based IIOT

Industrial advancement has introduced a significant impact on ecological balance and natural resources; thus, pollution monitoring using smart sensors in the industrial Internet of Things (IIoT) has recently attracted growing interests in the era of Industry 4.0. However, the effective detection and location of polluted areas remains a major challenge for collecting and processing a massive amount of sensor data in the IIoT especially in far sea, danger zone, and mountain zone, where there is no communication infrastructure. In this article, we establish a satellite-terrestrial framework to detect and locate industrial pollution areas by integrating the satellite with the IIoT, and the massive amount of sensor data can be delivered to the satellite via a ground base station. Local attribute detection inspired by recent advances in graph signal processing provides a promising way for solving this problem. A subgraph can be formed by grouping the vertices with identical attributes, and these vertices can be easily separated from other vertices based on local attribute detection. In this article, new methods based on local attribute detection are proposed to detect and locate pollution areas. First, a stable wavelet statistic (SWS) is proposed by modeling the classical wavelet basis as a graph-based wavelet basis. To improve the generalization ability of the SWS, a new cluster center discovery method is proposed to minimize the distance between any vertex and the remaining vertices of the same cluster. Second, a smooth scan statistic is proposed by introducing a new constraint to simplify the problem formulation of the likelihood ratio test. The effectiveness of the two graph-based statistical methods is evaluated using real datasets for detecting and locating industrial pollution.

Spoofing Mitigation Using Double Stationary Wavelet Transform in Civil GPS Receivers

In this paper, the Wavelet Transform (WT) is used to eliminate the influence of spoofing on the stationary Global Positioning System (GPS) receivers. Having no access to the authentic data, signal processing is only applied to the received spoofing signals. Pseudo-range is one of the most important influenced parameters under spoofing attack. Therefore, by reducing its deviations, spoofing reduction is possible. In this way, the pseudo-range difference between two observations is passed to the Statistic Wavelet Transform (SWT) at the first level. By de-noising in the next step and omission of noise, pseudo-range deviations due to a spoofing attack can be extracted. After that, measured pseudo-range of received signal is corrected. In the next step, the SWT is applied to the position coordinates. In this point, other irrational deviations because of spoofing threat can be compensated. For validation of the suggested algorithm, four different data sets are investigated. By applying bior 3.7 at level 3 and rbio 4.4 at level 9 as the first and the second WT respectively, we could mitigate spoofing more than 81% within a tolerance of 10% and an average of 86%. The test results show that the proposed technique supremely improves the performance of the GPS receiver and attenuates the effects of spoofing.

Across-scale process similarity based interpolation for image super-resolution

A pivotal step in image super-resolution techniques is interpolation, which aims at generating high resolution images without introducing artifacts such as blurring and ringing. In this paper, we propose a technique that performs interpolation through an infusion of high frequency signal components computed by exploiting ‘process similarity’. By ‘process similarity’, we refer to the resemblance between a decomposition of the image at a resolution to the decomposition of the image at another resolution. In our approach, the decompositions generating image details and approximations are obtained through the discrete wavelet (DWT) and stationary wavelet (SWT) transforms. The complementary nature of DWT and SWT is leveraged to get the structural relation between the input image and its low resolution approximation. The structural relation is represented by optimal model parameters obtained through particle swarm optimization (PSO). Owing to process similarity, these parameters are used to generate the high resolution output image from the input image. The proposed approach is compared with six existing techniques qualitatively and in terms of PSNR, SSIM, and FSIM measures, along with computation time (CPU time). It is found that our approach is the fastest in terms of CPU time and produces comparable results.

The determination of the constant phase of seismic wavelet using automatic seismic-well tying

ABSTRACTSeismic wavelet estimation is the bedrock of seismic-well tying and seismic inversion but remains a challenge. Huge amounts of effort have been expended on seismic wavelet estimation and determining the amplitude and phase spectrum is a time-consuming task. In this article, we develop a workflow to determine automatically the constant phase of an estimated wavelet. This workflow begins with statistical wavelet estimation and seismic-well tying. We then extract a new seismic wavelet with a constant phase by using the well and seismic data together. To obtain the best phase for the extracted wavelet using well and seismic data, we rotate the phase of the wavelet by a user-defined increment and perform automatic seismic-well tying for each phase-rotated wavelet. The phase that reaches the maximum correlation coefficient between the synthetic and seismic data is regarded as the best phase for wavelets in each iteration. We next update the time–depth relation using the best seismic-well tie (the maximum correlation coefficient). We repeat the wavelet estimation using well and seismic data, phase rotation, automatic seismic-well tying and time–depth updating until the difference between wavelets, and time–depth relationships, in the current and previous iterations is below a user-defined threshold.

Comparison of inversion method of maize leaf area index based on UAV hyperspectral remote sensing

The current inversion method of maize leaf area index has the problems of long time-consuming inversion, high energy consumption, and low fitting coefficient between the prediction result and the actual result. For these problems, an inversion method of maize leaf area index based on UAV hyperspectral remote sensing is proposed in this paper. Acquisition of spectral image of maize leaf using ASD Field SpecPro FR Field Hyperspectral instrument and CCD Array detector in UAV remote Sensing system. Denoising and segmentation of corn leaf images using stationary wavelets, improved Snake and PSO methods.. The improved Snake model is used to achieve coarse convergence of target image contour after denoising. Through particle swarm optimization iterative algorithm, the optimal image segmentation point is found and the image segmentation is achieved. Based on the results of image denoising segmentation, the expressions of modified chlorophyll absorption ratio, normalized difference spectral index, and ratio-type spectral index are obtained. The correlation between the three indices and the maize leaf area index was analyzed. Finally, the maize leaf area index was obtained by using ratio-type spectral index. Experiments show that the proposed method has a comprehensive performance, and has a strong advantage over the current method.