Variance Of Wavelet Coefficients Research Articles

A landscape pattern gradient analysis method coupling wavelet algorithm for balancing development and protection activities of the coastal zone: A case study

Due to the economic importance and ecological vulnerability of coastal areas, the optimization of spatial patterns is important for the sustainable development of coastal zones. In this study, a new landscape pattern index gradient analysis method coupled with wavelet algorithm (GA-WA) was explored to balance the development and protection activities in the coastal zone. First, based on the classification results of remote sensing images, the gradient detection of the coastal zone was carried out using the cumulative moving window method, and the calculation of the landscape pattern index was carried out using Fragstats software to obtain the gradient change curve of the landscape pattern index. Secondly, the wavelet algorithm was applied to micro-analyze the above gradient change curves, and the results of multiscale analysis of the landscape pattern index in the study area were obtained. Finally, it is demonstrated how this method can help in practical decision making. It was found that:(1) The landscape pattern index gradient analysis method coupled with wavelet algorithms offers a new approach to balance the development and protection of coastal zones. This approach presents an innovative method for optimizing the ecological pattern of coastal zone landscapes from the perspective of macro–micro combination, which is not only applicable to coastal zones but also can be extended to other strip corridor landscapes.(2) The gradient analysis of the coastal zone landscape pattern index provides results at multiple spatial scales, which is superior to the analysis at a single spatial scale. The results of the gradient analysis method are finer and more stable, which solves the uncertainty problem of traditional landscape pattern index analysis. There is a significant difference between the landscape indices of the overall landscape and the gradient landscape, in which the AREA_MN index of the ecological land has the largest difference, reaching 110.18%.(3) Wavelet coefficient variance diagrams, real component contour diagrams, and modulus squared diagrams reveal the characteristics, cycles, and patterns of landscape dynamics changes, as well as the distribution at different gradient window scales. These tools help to identify the driving factors and development trends of landscape dynamics changes and solve problems of functional positioning in undeveloped areas, as well as the transformation of microscopic small parcels within developed areas. By analyzing regular cycles of landscape index changes, it is possible to determine the functional positioning of land and to position human intervention through peaks to guard against risky gradient windows.

Displacement Monitoring of a Bridge Based on BDS Measurement by CEEMDAN-Adaptive Threshold Wavelet Method.

From the viewpoint of BDS bridge displacement monitoring, which is easily affected by background noise and the calculation of a fixed threshold value in the wavelet filtering algorithm, which is often related to the data length. In this paper, a data processing method of Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN), combined with adaptive threshold wavelet de-noising is proposed. The adaptive threshold wavelet filtering method composed of the mean and variance of wavelet coefficients of each layer is used to de-noise the BDS displacement monitoring data. CEEMDAN was used to decompose the displacement response data of the bridge to obtain the intrinsic mode function (IMF). Correlation coefficients were used to distinguish the noisy component from the effective component, and the adaptive threshold wavelet de-noising occurred on the noisy component. Finally, all IMF were restructured. The simulation experiment and the BDS displacement monitoring data of Nanmao Bridge were verified. The results demonstrated that the proposed method could effectively suppress random noise and multipath noise, and effectively obtain the real response of bridge displacement.

The profile and fluttering characteristics of a codend with different mesh sizes and catch by fast Fourier transform and Morlet wavelet methods

The codend is the end and an essential part of the trawl, which plays a vital role in the selectivity and the storage of fish catches. Thus, to improve the trawl selectivity and control the probability of the fish escaping, it is essential to understand its hydrodynamic performance, fluttering motions, and spatial form of the codend structure. This study investigates the effects of the mesh size and simulated catch on hydrodynamic characteristics, net cross-section, and fluttering motions of the codend in the flume tank. Thus, three codends models were designed using polyethylene material with three different mesh sizes (60 mm, 80 mm, and 100 mm). Fourier analysis was performed via the Morlet wavelet analysis and the fast Fourier transform (FFT) method to observe the content of the wavelet coefficient variance and amplitude of the codend fluttering motions and time evolution of the drag forces. The results showed that at the empty stage, the decrease in mesh size led to an increase in drag force by 6.6%− 25.1%, an increase of the codend length by 2.6%− 4.3%, and a decrease in cross-sectional area by 14.9%− 51.7% of the codend. In addition, the time evolution was oscillatory quasi-periodic and related to the low-frequency activity. The codend drag oscillation frequency was mainly 0.30–0.45 Hz and decreased with the mesh size, and the amplitude and wavelet coefficient of the drag force increased with decreasing mesh size. For the codend with simulated catch, the shape of each codend was closed at the front of the mesh and bulging atthe rear contour, with the middle part of each codend being the most closed, and the cross-sectional area was about 15.1% of the empty codend (X = 104 cm). The codend position oscillates frequency was 0.30–0.45 Hz in X and Z directions. The drag oscillation frequency was mainly 0.30–0.45 Hz and synchronized with the position motion. The dominant frequencies of these codend motions and the associated drag showed low-frequency activities, with a small wavelet spectrum shifting from small-scale to large-scale motions. In addition, the codend with a greater mesh size showed a more stable behavior with a lower frequency and oscillatory motions than the codend with a small mesh size led to a decrease in drag on this codend. In addition, we recommend that the FFT can be used to obtain the amplitude and frequency directly for codend steady oscillation.

Specific Recognition Technology of Infrared Absorption Spectra Based on Continuous Wavelet Decomposition

Because infrared (IR) absorption spectroscopy technology can offer high sensitivity and strong anti-interference capabilities, it is widely used in gas detection. To solve the problem of spectrum line aliasing in gas detection, this study examined the application of IR absorption spectroscopy technology based on time-frequency analysis in component identification. The second derivative spectrum of the IR absorption spectroscopy was processed by continuous wavelet transform to obtain the time-frequency characteristic matrix. The appropriate scale range was selected through the variance of wavelet coefficients. The correlation analysis of time and frequency on the time-frequency characteristic matrix was used for component identification. The experimental results showed that the correlation analysis of the time dimension can extract the characteristic absorption position of the gas to be measured in the gas mixture. The frequency correlation analysis at the characteristic absorption position can improve the recognition accuracy compared with the frequency correlation analysis in the entire spectral interval. The research in this article provides new ideas for the quantitative detection of gases.

Wavelet denoising with generalized bivariate prior model

This paper presents a novel wavelet method based on a prior model of wavelet coefficient with a generalized bivariate distribution function. The generalized bivariate prior model extends the isotropic bivariate prior model and anisotropic prior model, and can well characterize the joint parent-child statistical properties of many categories of images. Owing to the fact that the variance of wavelet coefficients are quite different for different scales and positions, we propose a local adaptive marginal variance estimation method based on this newly generalized prior model to improve the accuracy of marginal variance by considering the distribution of wavelet coefficients as the combination of Gaussian distribution and Laplacian distribution. By simulation experiments from three aspects, the results of the proposed method outperform the mainstream isotropic wavelet methods and anisotropic wavelet methods, and the practicality of the proposed method is verified by real noise image experiments.

Diagnosis and normalization of gridpoint background‐error variances induced by a block‐diagonal wavelet covariance matrix

A wavelet block‐diagonal approach can be used in order to specify 3D background‐error covariances from ensemble data. In this study, it is first formally demonstrated how resulting variances in grid‐point space can be expressed and diagnosed from variances of wavelet coefficients of background errors. In particular, it is shown that grid‐point variances can be seen as resulting from the application of scale‐dependent spatial filters to wavelet variance fields. In the context of correlation modelling, these formal results can be used for computing normalization coefficients in an accurate and efficient way, in order to ensure that diagonal elements of the resulting correlation matrix are effectively equal to one. The links between these normalization coefficients and correlation length‐scales are illustrated and discussed. The impact of this normalization approach is also examined in analysis and forecast experiments with the Météo‐France ARPEGE 4D‐Var system.

A Spectral Exponent-Based Feature of RR Interval Data for Congestive Heart Failure Discrimination Using a Wavelet-Based Approach

Congestive heart failure (CHF) is a common chronic condition which affects several millions of people around the world. Heart rate data which are crucial information needed for diagnosis and classification of CHF are similar to several physiological signals that exhibit an extraordinary range of patterns and behaviors. In this study, the spectral exponents of RR interval data of two groups of subjects, i.e., subjects with CHF and subjects with normal sinus rhythm, obtained using a wavelet-based approach are examined where the second order Daubechies wavelets are used. The spectral exponent of RR interval data is determined from a slope of logarithm of variance of wavelet coefficients (log2var(d m,n )) versus levels of wavelet-based decomposition (m) graph. In particular, the spectral exponent is estimated from the levels of wavelet-based decomposition ranges between m = 1 and m = 3 corresponding to finer-scale components of RR interval data. The minimum of spectral exponents of epochs of RR interval data is proposed as a quantitative feature for discriminating a subject with CHF. The computational results show that the subjects with CHF can be perfectly discriminated from the subjects with normal sinus rhythm using the spectral exponent-based feature. Furthermore, the perfect CHF discrimination can be achieved using the RR interval data with epoch size as short as 128 beats (approximately 2 min).

基于提升小波变换的图像融合改进算法的研究

提出了一种基于提升小波变换的图像融合改进算法。针对提升小波分解后的低频和高频分量各自的特点，选用不同的规则进行融合，即低频系数采用选择法和加权平均相结合的策略，高频系数时，把小波系数的方差与绝对值综合起来考虑决定融合小波系数。实验结果表明，当采用平均梯度、信息熵、标准差、均方根误差和峰值信噪比作为客观评价准则，该算法的融合图像比拉普拉斯金字塔融合图像和传统的小波变换的融合图像具有更好的融合效果，较好地提高了图像融合精确度。 An improved algorithm is Proposed for image fusion based on lifting wavelet transform in the paper. According to the characteristics of lifting wavelet decomposition of the low and high frequency components of the respective, different fusion rules are adopted, namely low frequency coefficient selection method and the weighted average method, choosing the high frequency coefficient, the variance of wavelet coefficients and the absolute value of the wavelet coefficients are considered synthetically decision fusion. The experimental results show that, when we take the average gradient, the information entropy, the standard deviation, root mean square error and peak signal to noise ratio as the objective evaluation criteria of image fusion, image fusion algorithm has better fusion effect than Laplasse Pyramid fusion image and the traditional wavelet transform; it improves the accuracy of image fusion effectly.

A methodology for visually lossless JPEG2000 compression of monochrome stereo images.

A methodology for visually lossless compression of monochrome stereoscopic 3D images is proposed. Visibility thresholds are measured for quantization distortion in JPEG2000. These thresholds are found to be functions of not only spatial frequency, but also of wavelet coefficient variance, as well as the gray level in both the left and right images. To avoid a daunting number of measurements during subjective experiments, a model for visibility thresholds is developed. The left image and right image of a stereo pair are then compressed jointly using the visibility thresholds obtained from the proposed model to ensure that quantization errors in each image are imperceptible to both eyes. This methodology is then demonstrated via a particular 3D stereoscopic display system with an associated viewing condition. The resulting images are visually lossless when displayed individually as 2D images, and also when displayed in stereoscopic 3D mode.

Oscillatory neural activity associated with cognitive processes affected by spatial frequency

The spatial frequency contained in visual objects is known to affect human psychophysiology. In our previous study, we showed that event-related potentials are affected by spatial frequency during a simple calculation task. In that study, however, we did not investigate the contribution of oscillatory neural activities. The purpose of the present study is to characterize the changes in oscillatory neural activity associated with cognitive processes, and to investigate how these signals are affected by the spatial frequency of a visual stimulus during simple calculation tasks. We investigate these issues by analyzing our previously collected electroencephalography (EEG) dataset using the same visual stimulus, tasks, subjects, and EEG recordings. In that study, four types of vertically striped visual stimuli were used. The visual stimuli contained embedded numbers (from 0 to 9) that possessed the following frequency (f) characteristics: white noise, 1/f, 1/f2, and 1/f3. The subjects were instructed to perform two tasks: ‘add numbers’ (addition task) and ‘do not add numbers’ (reference task). EEG data were recorded, and event-related synchronization (ERS) and desynchronization (ERD) for each visual stimulus were analyzed on the basis of the intertrial variances of wavelet coefficients for theta, alpha, low-beta, and gamma band activity. Eight healthy men (21–23 years) were recruited to participate in the study. Our results suggest the presence of a frequency discrimination function in the theta band activity in the fronto-central area at the latency of 198 ms during the addition task. The alpha-band ERD during completion of the reference task also showed a spatial frequency dependency. This phenomenon was observed in the left temporal-parietal area at a latency of 376 ms, and is thought to be related to the perceptual filter. We conclude that the observed changes in oscillatory neural activity associated with cognitive processes are affected by spatial frequency. © 2014 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Image denoising with anisotropic bivariate shrinkage

This paper presents a novel image denoising algorithm based on the modeling of wavelet coefficients with an anisotropic bivariate Laplacian distribution function. The anisotropic bivariate Laplacian model not only captures the child–parent dependency between wavelet coefficients, but also fits the anisotropic property of the variances of wavelet coefficients in different scales of natural images. With this statistical model, we derive a closed-form anisotropic bivariate shrinkage function in the framework of Bayesian denoising and a new image denoising approach with local marginal variance estimation based on this newly derived shrinkage function is proposed in the discrete wavelet transform (DWT) domain. The proposed anisotropic bivariate shrinkage approach is also extended to the dual-tree complex wavelet transform (DT-CWT) domain to further improve the performance of image denoising. To take full advantage of DT-CWT, a more accurate noise variance estimator is proposed and the way the anisotropic bivariate shrinkage function applied to the magnitudes of DT-CWT coefficients is presented. Experiments were carried out in both the DWT and the DT-CWT domain to validate the effectiveness of the proposed method. Using a representative set of standard test images corrupted by additive white Gaussian noise, the simulation results show that the proposed method provides promising results and is competitive with the best wavelet-based denoising results reported in the literature both in terms of peak signal-to-noise ratio (PSNR) and in visual quality.

Reversible Data Hiding Based on Two-level HDWT Coefficient Histograms

In recent years, reversible data hiding has attracted much more attention than before. Reversibility signifies that the original media can be recovered without any loss from the marked media after extracting the embedded message. This paper presents a new method that adopts two-level wavelet transform and exploits the feature of large wavelet coefficient variance to achieve the goal of high capacity with imperceptibility. Our method differs from those of previous ones in which the wavelet coefficients histogram not gray-level histogram is manipulated. Besides, clever shifting rules are introduced into histogram to avoid the decimal problem in pixel values after recovery to achieve reversibility. With small alteration of the wavelet coefficients in the embedding process, and therefore low visual distortion is obtained in the marked image. In addition, an important feature of our design is that the use of threshold is much different from previous studies. The results indicate that our design is superior to many other state-of-the-art reversible data hiding schemes.

Reversible Data Hiding Based on Two-level HDWT Coefficient Histograms

In recent years, reversible data hiding has attracted much more attention than before. Reversibility signifies that the original media can be recovered without any loss from the marked media after extracting the embedded message. This paper presents a new method that adopts two-level wavelet transform and exploits the feature of large wavelet coefficient variance to achieve the goal of high capacity with imperceptibility. Our method differs from those of previous ones in which the wavelet coefficients histogram not gray-level histogram is manipulated. Besides, clever shifting rules are introduced into histogram to avoid the decimal problem in pixel values after recovery to achieve reversibility. With small alteration of the wavelet coefficients in the embedding process, and therefore low visual distortion is obtained in the marked image. In addition, an important feature of our design is that the use of threshold is much different from previous studies. The results indicate that our design is superior to many other state-of-the-art reversible data hiding schemes.

Multilevel adaptive thresholding and shrinkage technique for denoising using Daubechies complex wavelet transform

In this paper, we have proposed a multilevel soft thresholding technique for noise removal in Daubechies complex wavelet transform domain. Two useful properties of Daubechies complex wavelet transform, approximate shift invariance and strong edge representation, have been explored. Most of the uncorrelated noise gets removed by shrinking complex wavelet coefficients at the lowest level, while correlated noise gets removed by only a fraction at lower levels, so we used multilevel thresholding and shrinkage on complex wavelet coefficients. The proposed method firstly detects strong edges using imaginary components of complex coefficients and then applies multilevel thresholding and shrinkage on complex wavelet coefficients in the wavelet domain at non-edge points. The proposed threshold depends on the variance of wavelet coefficients, the mean and the median of absolute wavelet coefficients at a particular level. Dependence of these parameters makes this method adaptive in nature. Results obtained for one-dimensional signals and two-dimensional images demonstrate an improved denoising performance over other related methods available in the literature.

신경회로망 기반 고장 진단 시스템을 위한 고장 신호별 특징 벡터 결정 방법

As rotating machines play an important role in industrial applications such as aeronautical, naval and automotive industries, many researchers have developed various condition monitoring system and fault diagnosis system by applying various techniques such as signal processing and pattern recognition. Recently, fault diagnosis systems using artificial neural network have been proposed. For effective fault diagnosis, this paper used MLP(multi-layer perceptron) network which is widely used in pattern classification. Since using obtained signals without preprocessing as inputs of neural network can decrease performance of fault classification, it is very important to extract significant features of captured signals and to apply suitable features into diagnosis system according to the kinds of obtained signals. Therefore, this paper proposes the decision method of the proper feature vectors about each fault signal for neural-network-based fault diagnosis system. We applied LPC coefficients, maximum magnitudes of each spectral section in FFT and RMS(root mean square) and variance of wavelet coefficients as feature vectors and selected appropriate feature vectors as comparing error ratios of fault diagnosis for sound, vibration and current fault signals. From experiment results, LPC coefficients and maximum magnitudes of each spectral section showed 100 % diagnosis ratios for each fault and the method using wavelet coefficients had noise-robust characteristic.

Fusion of noisy infrared and visible images based on anisotropic bivariate shrinkage

The performance of wavelet-based image fusion can be improved by taking into account the statistical dependencies between wavelet coefficients. This paper focuses on the fusion of noisy infrared and visible images and presents a new image fusion approach based on the modeling of wavelet coefficients with an anisotropic bivariate Laplacian distribution function. The use of the anisotropic bivariate Laplacian model not only captures the dependencies between wavelet coefficients and their parents, but also fits the fact that the variances of wavelet coefficients of natural images are quite different from scale to scale. Based on this statistical model together with the assumption of additive white Gaussian noise, a closed-form anisotropic bivariate shrinkage function is derived within the framework of Bayesian denoising. Then an improved image fusion algorithm is proposed by incorporating the newly derived shrinkage approach into the fusion scheme. The performance of the proposed method was compared with three other methods and was found to perform the best in terms of both visual quality and objective metric Q AB / F n [17] when tested on four representative sets of infrared and visible images corrupted by additive white Gaussian noise.

DAUBECHIES COMPLEX WAVELET TRANSFORM BASED MULTILEVEL SHRINKAGE FOR DEBLURRING OF MEDICAL IMAGES IN PRESENCE OF NOISE

Deblurring in the presence of noise is a hard problem, especially in ultrasonic and CT images. In this paper, we propose a new method of image deblurring in presence of noise, using symmetric Daubechies complex wavelet transform. The proposed method is based on shrinkage of multilevel Daubechies complex wavelet coefficients, and is adaptive as it uses shrinkage function based on the variance of wavelet coefficients as well as the mean and the median of absolute wavelet coefficients at a particular level. The results obtained after the application of the proposed method demonstrate an improved performance over other related methods available in literature.

A Multi-Horizon Scale for Volatility

We decompose volatility of a stock market index both in time and scale using wavelet filters and design a probabilistic indicator for valatilities, analogous to the Richter scale in geophysics. The peak-over-threshold method is used to fit the generalized Pareto probability distribution for the extreme values in the realized variances of wavelet coefficients. The indicator is computed for the daily Dow Jones Industrial Averages index data from 1986 to 2007 and for the intraday CAC 40 data from 1995 to 2006. The results are used for comparison and structural multi-resolution analysis of extreme events on the stock market and for the detection of financial crises.

Decomposition of Surface Data into Fractal Signals Based on Mean Likelihood and Importance Sampling and Its Applications to Feature Extraction

This paper deals with the decomposition of surface data into several fractal signal based on the parameter estimation by the Mean Likelihood and Importance Sampling (IS) based on the Monte Carlo simulations. The method is applied to the feature extraction of surface data. Assuming the stochastic models for generating the surface, the likelihood function is defined by using wavelet coefficients and the parameter are estimated based on the mean likelihood by using the IS. The approximation of the wavelet coefficients is used for estimation as well as the statistics defined for the variances of wavelet coefficients, and the likelihood function is modified by the approximation. After completing the decomposition of underlying surface data into several fractal surface, the prediction method for the fractal signal is employed based on the scale expansion based on the self-similarity of fractal geometry. After discussing the effect of additive noise, the method is applied to the feature extraction of real distribution of surface data such as the cloud and earthquakes.

Wavelet-based detection of coherent structures and self-affinity in financial data

As a linear superposition of translated and dilated versions of a chosen analyzing wavelet function, the wavelet transform lends itself to the analysis of underlying multi-scale structure in nonstationary time series. In this work, we use the discrete wavelet transform (DWT) to investigate scaling and search for the presence of coherent structures in financial data. Quantitative measurements are given by the DWT of the original time series and wavelet coefficient variance. We find that variations and correlations in the transform coefficients are able to indicate the presence of structure and that measurements based on the DWT allow us to observe scaling directly in the nonstationary time series.