Wavelet Decomposition Level Research Articles

A wavelet-based baseline drift correction method for grounded electrical source airborne transient electromagnetic signals

A grounded electrical source airborne transient electromagnetic (GREATEM) system on an airship enjoys high depth of prospecting and spatial resolution, as well as outstanding detection efficiency and easy flight control. However, the movement and swing of the front-fixed receiving coil can cause severe baseline drift, leading to inferior resistivity image formation. Consequently, the reduction of baseline drift of GREATEM is of vital importance to inversion explanation. To correct the baseline drift, a traditional interpolation method estimates the baseline ‘envelope’ using the linear interpolation between the calculated start and end points of all cycles, and obtains the corrected signal by subtracting the envelope from the original signal. However, the effectiveness and efficiency of the removal is found to be low. Considering the characteristics of the baseline drift in GREATEM data, this study proposes a wavelet-based method based on multi-resolution analysis. The optimal wavelet basis and decomposition levels are determined through the iterative comparison of trial and error. This application uses the sym8 wavelet with 10 decomposition levels, and obtains the approximation at level-10 as the baseline drift, then gets the corrected signal by removing the estimated baseline drift from the original signal. To examine the performance of our proposed method, we establish a dipping sheet model and calculate the theoretical response. Through simulations, we compare the signal-to-noise ratio, signal distortion, and processing speed of the wavelet-based method and those of the interpolation method. Simulation results show that the wavelet-based method outperforms the interpolation method. We also use field data to evaluate the methods, compare the depth section images of apparent resistivity using the original signal, the interpolation-corrected signal and the wavelet-corrected signal, respectively. The results confirm that our proposed wavelet-based method is an effective, practical method to remove the baseline drift of GREATEM signals and its performance is significantly superior to the interpolation method.

Pavement macro-texture analysis using wavelets

This paper utilises a wavelet approach to interpret the macro-texture data collected on asphalt and concrete pavement surfaces with a wide range of macro-texture properties. The experimental data were obtained using a circular track meter (CTMeter) device on pavements built at the Virginia's Smart Road test facility. The size of the data-set allowed nine levels of wavelet decomposition with wavelengths ranging from 1.7 to 435 mm. The extent of macro-texture variation was summarised using the normalised wavelet energy metric defined as the sum of the squares of the detailed wavelet coefficients for the sub-bands that correspond to the macro-texture range of wavelengths divided by the length of the test section expressed in mm2/m. This metric was found highly correlated with the empirical mean profile depth measurements. Hence, the wavelet approach can be used to objectively analyse CTMeter measurements of pavement texture.

Lossy Image Compression Using Discrete Wavelet Transform and Thresholding Techniques

Results of lossy image compression using wavelet transforms and several thresholding techniques are presented here. The analyzed image was divided into little sub-images and each one was decomposed in a vector following a Hilbert fractal curve. The wavelet transform was applied to each vector and some of the high frequency components were suppressed based on some threshold criteria. Different levels of wavelet decomposition and wavelet mother functions were assessed. The Huffman coding algorithm was then applied in order to reduce image weight. Simulation results have revealed that high compression ratios were obtained with the mean and the standard deviation thresholding algorithms at different levels of wavelet decomposition.

Sequential Multiple Signature Scheme Based on Wavelet Domain Digital Watermarking

With wavelet transform multiresolution characteristics, using wavelet domain digital watermarking algorithm, we embed signed information in in the intermediate frequency subband picture which is processed by three level wavelet decomposition. Signed information not only have a good invisibility and robustness, but also enhance security. The practice shows that the scheme can effectively hide signature information in the seal picture, if attacked, the receiver can discriminate from seal image, and has better safety.

A Novel Method for Recognition of Bioradiolocation Signal Breathing Patterns for Noncontact Screening of Sleep Apnea Syndrome

A novel method for recognition of breathing patterns of bioradiolocation signals breathing patterns (BSBP) in the task of noncontact screening of sleep apnea syndrome (SAS) is proposed and implemented on the base of wavelet transform (WT) and neural network (NNW) applications. Selection of the optimal parameters of WT includes determination of the proper level of wavelet decomposition and the best basis for feature extraction using modified entropy criterion. Selection of the optimal properties of NNW includes defining the best number of hidden neurons and learning algorithm for the chosen NNW topology. The effectiveness of the proposed approach is tested on clinically verified database of BRL signals corresponding to the three classes of breathing patterns: obstructive sleep apnea (OSA); central sleep apnea (CSA); normal calm sleeping (NCS) without sleep-disordered breathing (SDB) episodes.

Wavelet domain compounding for speckle reduction in optical coherence tomography

Visibility of optical coherence tomography (OCT) images can be severely degraded by speckle noise. A computationally efficient despeckling approach that strongly reduces the speckle noise is reported. It is based on discrete wavelet transform (DWT), but eliminates the conventional process of threshold estimation. By decomposing an image into different levels, a set of sub-band images are generated, where speckle noise is additive. These sub-band images can be compounded to suppress the additive speckle noise, as DWT coefficients resulting from speckle noise tend to be approximately decorrelated. The final despeckled image is reconstructed by taking the inverse wavelet transform of the new compounded sub-band images. The performance of speckle reduction and edge preservation is controlled by a single parameter: the level of wavelet decomposition. The proposed technique is applied to intravascular OCT imaging of porcine carotid arterial wall and ophthalmic OCT images. Results demonstrate the effectiveness of this technique for speckle noise reduction and simultaneous edge preservation. The presented method is fast and easy to implement and to improve the quality of OCT images.

Theoretical Basis for Optical Granulometry by Wavelet Transformation

A theoretical framework for optical granulometry of sands by a wavelet transformation method is presented. The Haar wavelet transformation is explained by using simple mathematics with comparisons drawn to the use of wavelet decomposition in image compression and image enhancement. The use of seven wavelet decomposition levels on thousands of 128×128 pixel areas of a much larger image of a soil specimen presorted by size yields the soil’s particle-size distribution. The method employs previously developed calibration curves of a wavelet index (CA) versus the average number of pixels per particle diameter (PPD). The curves are nonlinear in CA versus log10(PPD) space. This paper demonstrates that the nonlinearity stems from having to use a relatively low number of decomposition levels. With future advances in camera technology, a linear CA versus log10(PPD) calibration curve could be developed requiring a single soil texture index (T) parameter.

Fusion Method of Infrared and Visible Images Based on Wavelet Packet Transform

The multi-sensor image fusion is the effective practices to increase the image information, highlight the detection superiority, reduce fuzzy understanding and to reduce data redundancy. Image fusion based on wavelet transform, the image wavelet decomposition processing only exists in the low-frequency, when the image contains high-frequency information, such as a large number of small edge or texture, which can not extract the feature information of the image, so resulting in the fusion is ineffective. In response to these problems, the use of image fusion algorithm based on wavelet packet transform, continue to break down, while the low-frequency further decomposition of the high-frequency of the image, extracts image feature information more effectively. In the same conditions of wavelet function, decomposition level, the fusion policy, comparative analysis has been researched on wavelet transform and wavelet packet transform on the same parameters of the information entropy, average gradient, standard deviation, spatial frequency, the results show that, image fusion of the algorithm based on wavelet packet transform are the highest and the better. In the other hand, in order to investigate the fusion effectiveness of the decomposition level on the same wavelet function conditions, fusion image parameters, such as entropy, average gradient, standard deviation, and spatial frequency, have been calculated using the db3 wavelet function corresponding to the decomposition level 1-5. The results show that the fusion effectiveness should achieve the best with wavelet decomposition level of 3 or 2.

SU‐E‐J‐108: Texture Segmentation in Magnetic Resonance Images Using Discrete Wavelet Transform Combined with Gabor Wavelets

Purpose: Edge detection improves image readability and plays an important role in images preprocessing aimed to their segmentation and automatic recognition of their contents. The purpose of this study was to describe methods of edge detection in magnetic resonance images, with the emphasis on the use of discrete wavelet transform (DWT) combined with Gabor wavelets. Methods: Modulus maxima method by Mallat S (A Wavelet Tour of Signal Processing. Academic Press, 1998), provides the method for edge detection using wavelet transform. This method is based on finding local maxima of horizontal and vertical wavelet coefficients in the first level of wavelet decomposition because it is supposed that this level represents edges. This method was tested with various wavelet functions both on simulated and real medical images. A multiresolution approach using undecimated wavelet transform is also employed which allows the low‐low (LL), low‐high (LH), high‐low (HL), and high‐high (HH) sub‐bands to remain at full size. A simple peak finding algorithm is used to determine the peaks out of array of these texture features. Results: Using wavelet transform method, the decomposition was performed up to two levels. Gabor filters are then applied to the wavelet approximations at all levels to obtain the characteristic texture features such as entropy, second to fourth central moments and coefficient of variation. High values of the second central variance and fourth central variance signify images in which regions can be clearly differentiated. The corresponding filter outputs are compared to obtain an image containing minimum pixel values. Conclusion: A complex wavelet function could help to improve results of edge detection in real images. A comparison of basic edge detection methods including simple gradient operators and Gabor wavelets, and their combination with wavelet transform was presented. Mathematical principals were studied, as well as application of these methods.

Wavelet-based distortion measure for binary images

This paper proposes an objective distortion measure for binary images. Whereas most previously proposed measures decide the distortion weight of a distorted pixel based on the relationship with the neighbouring pixels in the spatial domain, we observe the characteristics of distorted pixels in multi-spectral spatial-frequency bands. Similarities between the binary wavelet transform and the human visual system are utilised to obtain the distortion weight. When we decide the distortion weight of a distorted pixel, we consider flatness, edge orientation and texture complexity of the distorted pixel at each level of binary wavelet decomposition. Experimental results on various sample images show that the proposed measure is more adequate to human than previously proposed measures.

Wavelet de‐noising techniques with power spectral density to vibration signal

PurposeDenoising of the vibration signal is crucial to identify a structure's damage. Based on noise frequency character, the “real” vibration signal can be gotten. The purpose of this paper is to propose a novel method for denoising a signal based on the wavelet transform.Design/methodology/approachThe vibration signal with noise which can be collected by wireless network is decomposed by wavelet transform. In order to select optimal level of wavelet decomposition, based on noise's frequency, power spectral density is used. A soft thresholding method based on minimum mean‐variance is used for vibration signal de‐noising with Gaussian noise.FindingsA novel method has been described in his paper. Based on the relationship between vibration signal's character and noise frequency, the way to get rid of noise is combined wavelet transform with power spectral density.Originality/valueIn order to select optimal level of wavelet decomposition, based on noise's frequency, power spectral density is used. A soft thresholding method based on minimum mean‐variance is used for vibration signal denoising with Gaussian noise.

Experimental study of burn classification and prediction using indirect method in surface grinding of AISI 1045 steel

Grinding burn is a discoloration phenomenon according to the thickness of oxide layer on the ground surface. This study tries to establish an automatic grinding burn detection system with robust burn features that are caused by burn and not by the design parameters. To address this issue, a method based on acoustic emission sensor, accelerator, electric current transducers, and voltage transducers was proposed in an attempt to extract burn signatures. A trial-and-error experimental procedure was presented to find out burn threshold. Vitrified aluminum oxide grinding wheel and AISI 1045 steel workpiece were used in the grinding test, as they were the most commonly used wheel–workpiece combinations in conventional grinding process. With the help of fast Fourier transform and discrete wavelet transform, the spectral centroid of AE signal, the maximum value of power signal, and the RMS of the AE wavelet decomposition transform from wavelet decomposition levels d1 to d5 were extracted as burn features. The spectral centroid of AE signal was believed not to be affected by grinding parameters. A classification and prediction system based on support vector machine was established in order to identify grinding burn automatically. Results indicate that the classification system performs quite well on grinding burn classification and prediction.

An Adaptive Self-Configuration Scheme for Severity Invariant Machine Fault Diagnosis

Vibration signals, used for abnormality detection in machine health monitoring (MHM), exhibit significant variation with varying fault severity. This signal variation causes overlap among the features characterizing different types of faults, which results in severe performance degradation of the fault diagnostic model. In this paper, a wavelet based adaptive training set and feature selection (WATF) self-configuration scheme is presented, which selects the optimum wavelet decomposition level, and employs adaptive selection of the training set and features. Optimal wavelet decomposition level selection is such that the maximum fault signature-signal energy bands are achieved. The severity variant features, which could cause detrimental class overlap for MHM, are avoided using adaptive selection of the training set and features based on the location of a test data in feature space. WATF uses Support Vector Machines (SVM) to build the fault diagnostic model, and its performance and robustness has been tested with data having different severity levels. Comparative studies of WATF with eight existing fault diagnosis schemes show that, for publicly available data sets, WATF achieves higher fault detection accuracy, even when training and testing data sets belong to different severity levels.

Optimisation of wavelet-based image fusion for multi-focused images

Image fusion is a process of combining information from two or more images (multi–images) of the same scene to get a composite image, which is more suitable for human visual perception for further image processing tasks. In the present work, spatial–domain and transform domain image fusion techniques have been evaluated and compared. It was experimentally determined that wavelet–based image fusion provides the best fusion results. Further, the effect of wavelet–based decomposition level on fusion performance has also been determined and an optimal wavelet–based decomposition level for multi–focused image has been proposed. Two defocussed images were utilised to investigate the performance of image fusion scheme to select suitable wavelet family and wavelet decomposition level. The image quality was measured objectively for different wavelet filters of the fused image using Root Mean Square Error (RMSE) and an optimised level of decomposition was determined.

Multimodal Biometric System Using Finger Knuckle and Nail: A Neural Network Approach

Dorsum of the hand can be very useful in Personal identification but yet it has not that much extensive attention. Single scan of dorsum hand can give two biometric traits finger-knuckle and finger nail. This paper presents an approach to combine Finger-knuckle and finger-nail features. Finger nail biometric is considered as quite unique biometric trait hence we combine this trait with finger knuckle. We also developed an algorithm to extract ROI from Finger-knuckle and finger-nail. Finger- knuckle features are extracted using Mel Frequency Cepstral Coefficient (MFCC) technique and the features of finger-nail are extracted from second level wavelet decomposition. We combined these features using feature level fusion and feed forward back-propagation Neural Network for classification. The performance of the system has been tested on our own KVKR- knuckle database that includes 100 subject's dorsal hands. Evaluation results shows that increase in training set gives increased performance rate. The best performance of the proposed system reaches up to 97% with respective training of 90% of total dataset. 

Wavelet-based Identification of Time-Varying Shear-beam buildings using Incomplete and Noisy Measurement Data

Quite a lot of structural identification techniques assume that the complete state of the structure can be measured which unfortunately cannot be easily met in practice. In addition, measurement data are normally contaminated with noise which unavoidably affects the performance of these techniques. In this paper, two waveletbased identification techniques are developed to identify time-varying parameters in a shear-beam building using incomplete and noisy measurement data. By approximating the unknown time-varying parameters using wavelet multiresolution expressions, a parametric identification problem is transformed into a nonparametric coefficient optimization. As the wavelet multi-resolution expressions can accurately represent arbitrary functions, these wavelet-based techniques can be used to identify various forms of timevarying behavior that can occur to the building’s parameters. Depending on the availability of measurement data, two wavelet-based identification techniques, story-by-story and sub-structural, are proposed. To minimize the effect of measurement noise, a wavelet decomposition level selection scheme and a multi-rate Kalman data fusion technique are adopted. Numerical studies are conducted to illustrate the performance of the proposed wavelet-based timevarying structural identification techniques. Results show that the techniques can track the time-varying properties of shear-beam buildings quite accurately under incomplete and noisy measurement condition.

The Impacts of Decomposition Levels in Wavelet Transform on Anomaly Detection from Hyperspectral Imagery

In this paper, we analyzed the effect of wavelet decomposition levels in feature extraction for anomaly detection from hyperspectral imagery. After wavelet analysis, anomaly detection was experimentally performed using the RX detector algorithm to analyze the detecting capabilities. From the experiment for anomaly detection using CASI imagery, the characteristics of extracted features and the changes of their patterns showed that radiance curves were simplified as wavelet transform progresses and H bands did not show significant differences between target anomaly and background in the previous levels. The results of anomaly detection and their ROC curves showed the best performance when using the appropriate sub-band decided from the visual interpretation of wavelet analysis which was L band at the decomposition level where the overall shape of profile was preserved. The results of this study would be used as fundamental information or guidelines when applying wavelet transform to feature extraction and selection from hyperspectral imagery. However, further researches for various anomaly targets and the quantitative selection of optimal decomposition levels are needed for generalization.

MATHEMATICAL IMPLEMENTATION OF HYBRID FAST FOURIER TRANSFORM AND DISCRETE WAVELET TRANSFORM FOR DEVELOPING GRAPHICAL USER INTERFACE USING VISUAL BASIC FOR SIGNAL PROCESSING APPLICATIONS

In recent years, the application of discrete wavelet transform (DWT) on biosignal processing has made a significant impact on developing several applications. However, the existing user-friendly software based on graphical user interfaces (GUI) does not allow the freedom of saving the wavelet coefficients in .txt or .xls format and to analyze the frequency spectrum of wavelet coefficients at any desired wavelet decomposition level. This work describes the development of mathematical models for the implementation of DWT in a GUI environment. This proposed software based on GUI is developed under the visual basic (VB) platform. As a preliminary tool, the end user can perform "j" level of decomposition on a given input signal using the three most popular wavelet functions — Daubechies, Symlet, and Coiflet over "n" order. The end user can save the output of wavelet coefficients either in .txt or .xls file format for any further investigations. In addition, the users can gain insight into the most dominating frequency component of any given wavelet decomposition level through fast Fourier transform (FFT). This feature is highly essential in signal processing applications for the in-depth analysis on input signal components. Hence, this GUI has the hybrid features of FFT with DWT to derive the frequency spectrum of any level of wavelet coefficient. The novel feature of this software becomes more evident for any signal processing application. The proposed software is tested with three physiological signal — electroencephalogram (EEG), electrocardiogram (ECG), and electromyogram (EMG) — samples. Two statistical features such as mean and energy of wavelet coefficient are used as a performance measure for validating the proposed software over conventional software. The results of proposed software is compared and analyzed with MATLAB wavelet toolbox for performance verification. As a result, the proposed software gives the same results as the conventional toolbox and allows more freedom to the end user to investigate the input signal.

Simultaneous Least Squares Wavelet Decomposition for Multidimensional Irregularly Spaced Data

The multidimensional Discrete Wavelet Transform (DWT) has been widely used in signal and image processing for regularly sampled data. For irregularly sampled data, however, other techniques should be used including the Least Square Wavelet Decomposition (LSWD). The commonly used level by level (sequential) wavelet decomposition, which calculates the wavelet coefficients in each resolution separately, may result in a gross interpolation error. To overcome this drawback, a different approach called the Simultaneous Least Square Wavelet Decomposition, which computes all wavelet coefficients simultaneously, have been proposed by the authors. In this paper, we extend the simultaneous LSWD approach to the multidimensional case and show that this method has excellent reconstruction property for two dimensional irregularly spaced data.

Wavelet Based Separation for Synthetic Topographical Characterization of Surface Prepared by Abrasive Water Jet

To study the synthetic topographical characterization of surface created by abrasive water jet (AWJ) and carry out a detailed research for the process of surface creating, this paper researches the surface signals obtained both by contact profiler and a new developed optical instrument. Through wavelet decomposition and re-construction of surface signal, surface features, such as form error, waviness and roughness are separated rationally. Some fundamental issues, such as the selection of wavelet bases and the determination of wavelet decomposition level are discussed in detail.