Wavelet Detail Coefficients Research Articles

Chaotic and statistical tests on fiber optic dynamic data taken from the riser section of a circulating fluidized bed

Dynamical tests have been applied to fiber optic data taken from a cold-flow circulating fluidized bed to characterize flow conditions, identify three characteristic scales (macro, meso, and micro), and understand the contribution these scales have on the raw data. The characteristic variable analyzed is the raw voltage signal obtained from a fiber-optic probe taken at various axial and radial positions under different loading conditions. These experiments were carried out with the bed material of cork particles with a medium particle size of 812μm. The characterization was accomplished through analysis of the distribution of the signal through the third and fourth moments of skewness and excess kurtosis. A generalization of the autocorrelation function known as the average mutual information function was analyzed by examining the function's first minimum, identifying the point at which successive elements are no longer correlated. Further characterization was accomplished through the correlation dimension, a measure of the complexity of the chaotic attractor in deterministic chaos theory. Lastly, the amount of disorder of the system is described by a Kolmogorov-type entropy estimate. All six aforementioned tests were also implemented on ten levels of detail coefficients resulting from a discrete wavelet transformation of the same signal as used above. Through this analysis it is possible to identify and describe micro (particle level), meso (clustering or turbulence level), and macro (physical or dimensional level) length scales even though some literature considers these scales inseparable as is discussed. This investigation also used detail wavelet coefficients in conjunction with ANOVA to show which scales have the most impact on the raw signal resulting from local hydrodynamic conditions.

Chaotic and statistical tests on fiber optic dynamic data taken from the riser section of a circulating fluidized bed

Dynamical tests have been applied to fiber optic data taken from a cold-flow circulating fluidized bed to characterize flow conditions, identify three characteristic scales (macro, meso, and micro), and understand the contribution these scales have on the raw data. The characteristic variable analyzed is the raw voltage signal obtained from a fiber-optic probe taken at various axial and radial positions under different loading conditions. These experiments were carried out with the bed material of cork particles with a medium particle size of 812 μm. The characterization was accomplished through analysis of the distribution of the signal through the third and fourth moments of skewness and excess kurtosis. A generalization of the autocorrelation function known as the average mutual information function was analyzed by examining the function's first minimum, identifying the point at which successive elements are no longer correlated. Further characterization was accomplished through the correlation dimension, a measure of the complexity of the chaotic attractor in deterministic chaos theory. Lastly, the amount of disorder of the system is described by a Kolmogorov-type entropy estimate. All six aforementioned tests were also implemented on ten levels of detail coefficients resulting from a discrete wavelet transformation of the same signal as used above. Through this analysis it is possible to identify and describe micro (particle level), meso (clustering or turbulence level), and macro (physical or dimensional level) length scales even though some literature considers these scales inseparable as is discussed. This investigation also used detail wavelet coefficients in conjunction with ANOVA to show which scales have the most impact on the raw signal resulting from local hydrodynamic conditions.

Gunturk-Altunbasak-Mersereau Alternating Projections Image Demosaicking

The problem of image demosaicking (or demosaicing) is where an image has been captured through a color filter array (CFA), and the goal is to estimate complete color information at every pixel. This IPOL article describes the image demosaicking method proposed by Gunturk, Altunbasak, and Mersereau in "Color Plane Interpolation Using Alternating Projections." Given an initial demosaicking, the method improves the result by alternatingly applying two different projections. One projection copies the green channel's wavelet detail coefficients to the red and blue channels while the other projection constrains the solution to agree with the observed data.

Gunturk-Altunbasak-Mersereau Alternating Projections Image Demosaicking

The problem of image demosaicking (or demosaicing) is where an image has been captured through a color filter array (CFA), and the goal is to estimate complete color information at every pixel. This IPOL article describes the image demosaicking method proposed by Gunturk, Altunbasak, and Mersereau in "Color Plane Interpolation Using Alternating Projections." Given an initial demosaicking, the method improves the result by alternatingly applying two different projections. One projection copies the green channel's wavelet detail coefficients to the red and blue channels while the other projection constrains the solution to agree with the observed data.

Robustness Analysis of QIM Watermarking against Additional Noise

A mutual information function was defined as a criterion measuring the robustness of watermarking algorithm. Considering QIM scheme, error probability of watermarking can be calculated to validate the measurement of mutual information function. By mean of numerical computation, mutual information under Gaussian noise and uniform noise is calculated with change of noise standard deviation. In the experiment, an audio section is selected as the host and their third lever wavelet detail coefficients are quantified according to watermark bit series. Experiment results show that statistic Bit Error Rate (BER) is matched with evaluation conclusion of mutual information method when step is on the small side. Mutual information function can be selected as a cost function to evaluate the robustness of watermarking algorithm, and predict the BER.

Technologies for Pattern Recognition of Late Potentials atria: classification approaches

In this paper the problem of atrial late potentials (ALP) recognition is solved by the formation of their signs in the basis of eigenvectors. Covariance matrix is formed for an ensemble of wavelet detail coefficients obtained by multi-level wavelet decomposition of electrocardiosignals (ECS). The results of cluster analysis in a model experiment on the classification of ECS with and without ALP on the background noise are presented.

Quantisation-based video watermarking in the wavelet domain with spatial and temporal redundancy

In this article we introduce a new public digital watermarking technique for video copyright protection working in the discrete wavelet transform domain. The scheme uses binary images as watermarks. These are embedded in the detail wavelet coefficients of the middle wavelet sub-bands. The method is a combination of spread spectrum and quantisation-based watermarking. Every bit of the watermark is spread over a number of wavelet coefficients with the use of a secret key. The resilience of the watermarking algorithm was tested against a series of eight different attacks using different videos. To improve the resilience of the algorithm we use error correction codes and embed the watermark with spatial and temporal redundancy. The proposed method achieves a very good perceptual quality with mean peak signal-to-noise ratio values of the watermarked videos of more than 40 dB and high resistance to a large spectrum of attacks.

Application of two-dimensional spatial wavelet transform in the detection of an obstructed crack on a thin plate

SUMMARY This paper reports a feasibility study on the use of the two-dimensional spatial wavelet transform for the crack detection of partially obstructed plates and the use of Bayesian statistical system identification framework in quantifying the reliability of the crack-detection results. The value of the proposed methodology lies in its ability to detect obstructed cracks when measurement at or close to the cracked region is not possible. Under such a situation, most of the non-model-based crack-detection methods in the literature, which rely heavily on the crack-induced changes of certain indicators (e.g. displacement or curvature mode shapes) at or close to the cracks, become inapplicable. This paper reveals for the first time that it is possible to use one of the detail coefficients of the two-dimensional spatial wavelet transform to identify crack characteristics even when the crack is obstructed. The main objective of the paper is to report the development of a model-based crack-detection method to identify such characteristics as the crack location, length and depth of an obstructed crack in plate-type structures. A comprehensive series of numerical case studies using a rectangular cracked plate with covers of different dimensions is employed to verify the proposed wavelet-based crack-detection method. The case study results are encouraging implying that the proposed methodology is feasible not only for estimating crack characteristics, but also for quantifying the uncertainties associated with the identification results. The important factors that affect these uncertainties are discussed based on the results from the numerical case study. Copyright © 2011 John Wiley & Sons, Ltd.

Discrete wavelet and modified PCA decompositions for postural stability analysis in biometric applications

The aim of this study is to compare the Discrete wavelet decomposition and the modified Principal Analysis Component (PCA) decomposition to analyze the stabilogram for the purpose to provide a new insight about human postural stability. Discrete wavelet analysis is used to decompose the stabilogram into several timescale components (i.e. detail wavelet coefficients and approximation wavelet coefficients). Whereas, the modified PCA decomposition is applied to decompose the stabilogram into three components, namely: trend, rambling and trembling. Based on the modified PCA analysis, the trace of analytic trembling and rambling in the complex plan highlights a unique rotation center. The same property is found when considering the detail wavelet coefficients. Based on this property, the area of the circle in which 95% of the trace’s data points are located, is extracted to provide important information about the postural equilibrium status of healthy subjects (average age 31 ± 11 years). Based on experimental results, this parameter seems to be a valuable parameter in order to highlight the effect of visual entries, stabilogram direction, gender and age on the postural stability. Obtained results show also that wavelets and the modified PCA decomposition can discriminate the subjects by gender which is particularly interesting in biometric applications and human stability simulation. Moreover, both techniques highlight the fact that male are less stable than female and the fact that there is no correlation between human stability and his age (under 60).

A Wavelet-Based Approach for Online External Leakage Diagnosis and Isolation from Internal Leakage in Hydraulic Actuators

This paper presents experimental evaluation of applying wavelet transform for on-line external leakage fault detection and isolation from internal leakage in hydraulic actuators. In this work, the more realistic case of an actuator that is driven to track pseudorandom position reference inputs against a load is considered. The wavelet-based method developed in this paper, decomposes a limited-duration pressure signal at either chamber of a hydraulic actuator into effective approximate and detail wavelet coefficients. The limited-duration pressure signal is collected using a sliding window technique. It is shown that the root mean square (RMS) value of the level four approximate wavelet coefficient collectively establishes a feature index that can effectively be used for on-line detection of external leakage. Once the external leakage occurs, this index value decreases proportionally. Therefore, one can report the faulty operating condition by monitoring this index. Additionally, built upon the previous work in which the level two detail coefficient was found to be sensitive to internal leakage fault, we further investigate the isolation of external leakage from internal leakage in an actuator. Extensive validation tests demonstrate the effectiveness of the proposed technique, given any position reference input, loading condition, and controller type or effectiveness. Experimental tests show promising results for detecting external leakage as low as 0.3 L/min and isolating it from internal leakage as low as 0.48 L/min, during an on-line testing procedure.

Sharing secret images using integer single or multiple wavelet transform

Integer wavelet transform or multiple wavelet transform has been found attractive in image and video applications where its scaling function(s) and wavelet(s) provide higher energy compaction in smooth (scaling) subband and smaller values of detail (wavelet) coefficients. This paper presents a study on an image sharing method applying the integer single or multiple wavelet transform and Shamir’s (r, m) threshold scheme that provide highly compact and easily manageable shadows for real time progressive transmission. Experimental results are given to illustrate the characteristics of this method.

Robust wavelet-based video watermarking scheme for copyright protection using the human visual system

The development of the information technology and computer networks facilitates easy duplication, manipulation, and distribution of digital data. Digital watermarking is one of the proposed solutions for effectively safeguarding the rightful ownership of digital images and video. We propose a public digital watermarking technique for video copyright protection in the discrete wavelet transform domain. The scheme uses binary images as watermarks. These are embedded in the detail wavelet coefficients of the middle wavelet subbands. The method is a combination of spread spectrum and quantization-based watermarking. Every bit of the watermark is spread over a number of wavelet coefficients with the use of a secret key by means of quantization. The selected wavelet detail coefficients from different subbands are quantized using an optimal quantization model, based on the characteristics of the human visual system (HVS). Our HVS-based scheme is compared to a non-HVS approach. The resilience of the watermarking algorithm is tested against a series of different spatial, temporal, and compression attacks. To improve the robustness of the algorithm, we use error correction codes and embed the watermark with spatial and temporal redundancy. The proposed method achieves a good perceptual quality and high resistance to a large spectrum of attacks.

Sferics noise reduction in time-domain electromagnetic systems: application to MegaTEMII signal enhancement

Two noise reduction techniques are proposed for the removal of sferics noise from airborne transient electromagnetic data. Both techniques use multi-resolution analysis via a stationary wavelet transform of the data. The analysed signal is divided into several successive lower resolution components. The transient character of the sferics can be seen as high amplitudes of the wavelet detail coefficients close to the time of the sferics event. The first noise reduction strategy, named the wavelet extraction technique, identifies sferics in the first detail coefficients using an energy detector. The corresponding detail coefficients are set to zero, and the electromagnetic signal is reconstructed by inverse transform. This technique is very robust and successful both for on-time and off-time data and even in the case where several sferics are present. However, when sferics occur near the switch on or the switch off times of the airborne electromagnetic transmitter signal, or if the low frequency components of the spheric are very high, this technique becomes less effective. To overcome this problem, the second strategy, named the wavelet stacking technique, uses the shift invariance and linearity of the stationary wavelet transform to perform data stacking in the wavelet domain. Tests on synthetic data results show that the wavelet stacking technique performs better than the mean and median stacking techniques. The wavelet extraction and median stacking present equivalent performance. On very noisy real data, the wavelet stacking technique makes the detection of weak anomalies more straightforward. After additional smoothing by filtering, wavelet extraction and median stacking can produce similar results to wavelet stacking. However, the amplitude and temporal decay of anomalies can be affected by high residual sferics noise. The wavelet extraction technique has the advantage that it can be used to extract sferics for an audio frequency magnetic-like method to map subsurface conductivity changes. When a large number of sferics are observed, the current practice is to stop data acquisition; these techniques allow data collection to continue.

Properties of electric turbulence in the polar cap ionosphere

Small-scale (scales of ∼0.5–256 km) electric fields in the polar cap ionosphere are studied on the basis of measurements of the Dynamics Explorer 2 (DE-2) low-altitude satellite with a polar orbit. Nineteen DE-2 passes through the high-latitude ionosphere from the morning side to the evening side are considered when the IMF z component was southward. A rather extensive polar cap, which could be identified using the ɛ-t spectrograms of precipitating particles with auroral energies, was formed during the analyzed events. It is shown that the logarithmic diagrams (LDs), constructed using the discrete wavelet transform of electric fields in the polar cap, are power law (μ ∼ sα). Here, μ is the variance of the detail coefficients of the signal discrete wavelet transform, s is the wavelet scale, and index α characterizes the LD slope. The probability density functions P(δE, s) of the electric field fluctuations δE observed on different scales s are non-Gaussian and have intensified wings. When the probability density functions are renormalized, that is constructed of δE/sγ, where γ is the scaling exponent, they lie near a single curve, which indicates that the studied fields are statistically self-similar. In spite of the fact that the amplitude of electric fluctuations in the polar cap is much smaller than in the auroral zone, the quantitative characteristics of field scaling in the two regions are similar. Two possible causes of the observed turbulent structure of the electric field in the polar cap are considered: (1) the structure is transferred from the solar wind, which is known to have turbulent properties, and (2) the structure is generated by convection velocity shears in the region of open magnetic field lines. The detected dependence of the characteristic distribution of turbulent electric fields over the polar cap region on IMF By and the correlation of the rms amplitudes of δE fluctuations with IMF Bz and the solar wind transfer function (By2 + Bz2)1/2sin(θ/2), where θ is the angle between the geomagnetic field and IMF reconnecting on the dayside magnetopause when IMF Bz < 0, together with the absence of dependence on the IMF variability are arguments for the second mechanism.

Wavelet selection for disease classification by DNA microarray data

The microarrays report the measures of the expression levels of tens of thousands of genes, this high dimensional feature vector contains also irrelevant information for accurate classification. Moreover, only few training samples are available, hence for avoiding the curse of dimensionality problem a feature reduction should be performed before the classification step.Here, we proposed a set of orthogonal wavelet detail coefficients of different wavelet mothers to extract the features from the microarray data. We propose to use a multi-classifiers where each classifier, a support vector machine, is trained using a different set of detail coefficients, the classifiers are combined by “sum rule”. The detail coefficients set selection is performed by running Sequential Forward Floating Selection (SFFS).The goodness of the proposed method is validated using the area under the ROC curve as performance indicator, the experiments are carried out on four-datasets: Breast dataset; Ovarian dataset; Lung dataset; Prostate dataset.The results show that the proposed method outperforms the performance that can be obtained by a single set of detail coefficients.Moreover, we have shown that, also using as features the detail coefficients, a random subspace of classifiers outperforms the stand-alone classifiers.

Detection and Classification of Voltage Swells Using Wavelet Transforms

Through this paper a novel technique for detecting and characterizing disturbances in power systems based on wavelet transforms is proposed. The voltage signal under investigation is often corrupted by noises, therefore the signal is first de-noised and then wavelet transform is applied. Using the first detail wavelet coefficients, voltage disturbance is detected and its duration is determined. The combination of an adaptive prediction filter based sub-band decomposition structure with a rule based histogram analysis block produce successful detection and classification results on our real life power system transient data. In this paper, voltage swell is considered for comparing both approaches. Proposed scheme is implemented using MATLAB, Simulink, DSP and Wavelet toolboxes. Transmission-Line relaying involves three major tasks: detection, classification, and location of the fault. It must be done as fast and accurate as possible to de-energize the faulted line and protecting the system from the harmful effects of the fault. With the wide application of high-power electronics switchgears, problems of Power Quality (PQ) are becoming more serious day by day. At the same time, the demand on power quality gets more critical. Thus it is essential to establish a power quality monitoring system to detect power quality disturbance (1)-(2). Practically, a power quality monitoring system should have the following functions: detect power quality disturbance, identify the type and duration of disturbance signals, calculate disturbance amplitude and other relevant parameters, etc. Thus the power quality monitoring system should be as precise and of real time as possible. In recent years, a lot of methods for detection and identification of power quality disturbance

A Class-Conditioned Lossless Wavelet-Based Predictive Multispectral Image Compressor

We present a nonlinear lossless compressor designed for multispectral images consisting of few bands and having greater spatial than spectral correlation. Our compressor is based on a 2-D integer wavelet transform that reduces spatial correlation. Different models for the statistical dependences of wavelet detail coefficients are analyzed and tested to perform linear inter/intraband predictions. Band, class, scale, and orientation are used as conditioning contexts to calculate predictions, as well as to encode prediction errors with an adaptive arithmetic coder. A new mechanism is proposed for band ordering, based on wavelet fine detail coefficients. Our compressor CLWP outperforms state-of-the-art lossless compressors. It has random access capability and can be applied to compress volumetric data having similar characteristics.

Identification of Listeria Species Using a Low-Cost Surface-Enhanced Raman Scattering System With Wavelet-Based Signal Processing

We investigated the ability to distinguish between six species within the Listeria genus (including the human pathogen Listeria monocytogenes ) based on a bacteria sample's surface-enhanced Raman scattering (SERS) spectrum. Our measurement system consists of a portable low-cost Raman spectral acquisition unit and associated signal processing and classification modules. First, Listeria was cultured and then adsorbed onto silver colloidal nanoparticles for SERS measurements. A total of 483 SERS spectra were collected and preprocessed (using a stationary wavelet transform decomposition) to remove noise and baseline artifact. Distinguishing features were extracted by retaining detail wavelet coefficients of significant value across multiple scales. Using a linear classifier in association with ldquoleave one outrdquo cross-validation, the system achieved maximum classification accuracies of 96.1% (six-category) and 97.9% (two-category, L. monocytogenes versus all others). Dimensionality reduction was used to decrease the number of features from 74 to 5 while maintaining similar classification accuracy. In the future, it is envisioned that a measurement system such as this, which is a combination of low-cost hardware with sophisticated signal processing, could play a complementary role with existing methods in realizing a rapid inexpensive means of identifying food-borne bacterial pathogens.

Prominent feature selection of microarray data

For wavelet transform, a set of orthogonal wavelet basis aims to detect the localized changing features contained in microarray data. In this research, we investigate the performance of the selected wavelet features based on wavelet detail coefficients at the second level and the third level. The genetic algorithm is performed to optimize wavelet detail coefficients to select the best discriminant features. Experiments are carried out on four microarray datasets to evaluate the performance of classification. Experimental results prove that wavelet features optimized from detail coefficients efficiently characterize the differences between normal tissues and cancer tissues.

Feature extraction and dimensionality reduction for mass spectrometry data

Mass spectrometry is being used to generate protein profiles from human serum, and proteomic data obtained from mass spectrometry have attracted great interest for the detection of early stage cancer. However, high dimensional mass spectrometry data cause considerable challenges. In this paper we propose a feature extraction algorithm based on wavelet analysis for high dimensional mass spectrometry data. A set of wavelet detail coefficients at different scale is used to detect the transient changes of mass spectrometry data. The experiments are performed on 2 datasets. A highly competitive accuracy, compared with the best performance of other kinds of classification models, is achieved. Experimental results show that the wavelet detail coefficients are efficient way to characterize features of high dimensional mass spectra and reduce the dimensionality of high dimensional mass spectra.