Wavelet Detail Coefficients Research Articles

An Efficient Algorithm for Multimodal Medical Image Fusion based On Feature Selection and PCA Using DTCWT

Background: In the two past decades, medical image fusion has become an essential part of modern medicine due to the availability of numerous imaging modalities (MRI, CT, SPECT. etc). This paper presents a new medical image fusion algorithm based on DTCWT and uses different fusion rules in order to obtain a new image which contains more information than any of the input images. Methods: In order to improve the visual quality of the fused image, we propose a new image fusion algorithm based on Dual Tree Complex Wavelet Transform (DTCWT). Using different fusion rules in a single algorithm leads to a perfect reconstruction of the output (fused image).This combination will create a new method which exploits the advantages of each method separately. DTCWT present good directionality since it considers the edge information in six directions and provides approximate shift invariant. The goal of Principal Component Analysis (PCA) is to extract the most significant features (wavelet coefficients in our case) in order to improve the spatial resolution. The proposed algorithm fuses the detailed wavelet coefficients of input images using features selection rule. Results: We have conducted several experiments over different sets of multimodal medical images such as CT/MRI, MRA/T1-MRI; however, only results of two sets have been presented (due to pages-limit). The proposed fusion algorithm is compared to recent fusion methods presented in the literature (eight methods) in terms of visual quality and quantitatively using well known fusion performance metrics (five metrics). Results showed that the proposed algorithm outperforms the existing ones in terms of visual and quantitative evaluations. Conclusion: This paper focuses on image fusion of medical images obtained from different modalities. We have proposed a novel algorithm based on DTCWT in order to merge multimodal medical images. Experiments have been performed over two different sets of multimodal medical images. The results show that the proposed method significantly outperforms other techniques reported in the literature.

High-bandwidth and flexible tracking control for precision motion with application to a piezo nanopositioner.

For precision motion, high-bandwidth and flexible tracking are the two important issues for significant performance improvement. Iterative learning control (ILC) is an effective feedforward control method only for systems that operate strictly repetitively. Although projection ILC can track varying references, the performance is still limited by the fixed-bandwidth Q-filter, especially for triangular waves tracking commonly used in a piezo nanopositioner. In this paper, a wavelet transform-based linear time-varying (LTV) Q-filter design for projection ILC is proposed to compensate high-frequency errors and improve the ability to tracking varying references simultaneously. The LVT Q-filter is designed based on the modulus maximum of wavelet detail coefficients calculated by wavelet transform to determine the high-frequency locations of each iteration with the advantages of avoiding cross-terms and segmenting manually. The proposed approach was verified on a piezo nanopositioner. Experimental results indicate that the proposed approach can locate the high-frequency regions accurately and achieve the best performance under varying references compared with traditional frequency-domain and projection ILC with a fixed-bandwidth Q-filter, which validates that through implementing the LTV filter on projection ILC, high-bandwidth and flexible tracking can be achieved simultaneously by the proposed approach.

Application of well logs integration and wavelet transform to improve fracture zones detection in metamorphic rocks

The traditional approach to fracture zones detection is based on a visual inspection of core samples, or the application of special well logging program represented by imaging well logging. However, not all wells are fully cored, as the core description of fractures in laboratory is time consuming and expensive. Additionally, the interpretation of special well logging program in detecting fracture zones also needs the geologists' experience. This study provides a complete set of methodology for fracture zones detection and fracture numbers calculation in which wavelet analysis is utilized. For the sensitive well logs in fracture zones, we have made a contrast between well logs and imaging logging that shows up density, caliper, resistivity and acoustic logs are more or less suitable. To meet little changes with the same trends in one curve which indicates the present of fracture zones, we proposed a method that integrates the above four well logs into one, named fractured integrated index. Decomposing the integrated curve with discrete wavelet analysis shows that the detailed wavelet coefficients (cD1) energy are highly suitable for detection of fracture zones. In addition to the above four well logs, microsphere focusing logging is also used to enhance the accuracy of the detecting analysis. The method is applied to Chinese Continental Scientific Drilling Main Hole located about 17 km southwest of Donghai in the southern segment of the Sulu UHP terrane, and the results are promising in accordance with the imaging logging and cores information.

A wavelet-based Gaussian method for energy dispersive X-ray fluorescence spectrum.

This paper presents a wavelet-based Gaussian method (WGM) for the peak intensity estimation of energy dispersive X-ray fluorescence (EDXRF). The relationship between the parameters of Gaussian curve and the wavelet coefficients of Gaussian peak point is firstly established based on the Mexican hat wavelet. It is found that the Gaussian parameters can be accurately calculated by any two wavelet coefficients at the peak point which has to be known. This fact leads to a local Gaussian estimation method for spectral peaks, which estimates the Gaussian parameters based on the detail wavelet coefficients of Gaussian peak point. The proposed method is tested via simulated and measured spectra from an energy X-ray spectrometer, and compared with some existing methods. The results prove that the proposed method can directly estimate the peak intensity of EDXRF free from the background information, and also effectively distinguish overlap peaks in EDXRF spectrum.

Convolutional neural networks for wavelet domain super resolution

We present a single image super resolution technique in which we estimate wavelet detail coefficients of a desired high resolution (HR) image using a convolutional neural network (CNN) on the given low resolution (LR) image. Detail coefficients are necessarily sparse for natural images, unlike pixel intensities, and are thus better suited to be CNN output. This allows us to train a CNN with far fewer samples and lesser training time and yet achieve better reconstruction quality with lesser run time compared to a recent state-of-the-art technique that directly estimates the HR pixels using a CNN.

Online technique for insulation assessment of induction motor stator windings under different load conditions

This paper presents a new condition monitoring system which is able to evaluate and diagnose the stator winding insulation deterioration (SWID) at its initial stages. During the last few decades, considerable efforts have been made in condition monitoring of SWID in induction motors. Nevertheless, an effective diagnosis technique that can lead to a fast and accurate detection of SWID shortly after its occurrence remains a challenge. A new modelling technique is introduced using finite element method which enables detailed simulation (two turn-to-turn resolution) of insulation degradation in a stator slot. Experimental setup is then used to validate the proposed modelling technique. The detail and approximation coefficients of the discrete wavelet transform are shown to provide effective detection of SWID within a few seconds after its occurrence. The proposed system continuously monitors the status of the induction motor and is able to detect the insulation deterioration of only 1.2% turns of phase winding when it starts to take place. The proposed method is only applicable to turn insulation failure detection. Its viability under different load conditions is validated for a small-sized induction motor with simulated turn insulation fault.

Down-hole transient temperature, pressure and flow-rate data processing and integrated interpretation for nonlinearity diagnosis using wavelet transform

During oil and gas field development, continuous and real-time pressure, temperature and, occasionally, flow-rate data are available. Considering that the transient data acquisition process is relatively independent, integrating the analysis of the transient temperature, pressure and flow-rate data can include a large amount of useful information and can significantly reduce interpretation uncertainties.Typically, permanent down-hole gauge (PDG) data contain noise, outliers and other types of error signals that do not comport with known physical properties due to the uncontrolled collection conditions. For the purpose of correctly interpreting transient pressure and temperature data, data processing is an essential preliminary step. Several effective methods associated with pressure data processing have been applied in practice, but temperature data processing has not been discussed at length. In addition, the nonlinearities, which are caused by gas/multi-phase flow, non-Darcy flow or a change in well-reservoir parameters, may result in the erroneous application of pressure transient analysis (PTA) methods. As a result, an effective method for nonlinearity diagnosis needs to be developed.This paper describes how transient temperature, pressure and flow-rate data were processed and interpreted. First, the theory of wavelet transform was briefly introduced. Second, a workflow for the transient down-hole data processing was developed. Third, the simplest wavelet transform method, the Haar wavelet, was selected as the transient identification algorithm. In the pressure case and the temperature case, it was found that large amplitudes in the wavelet detail coefficients were caused by flow events. Fourth, the relationship between the wavelet transform amplitude and rate change (unit-rate change coefficient) was analysed, and an improved diagnostic method of nonlinearity from both transient pressure and temperature data was developed. According to the derived analytical solutions, the nonlinearities caused by a change in well-reservoir properties can be identified. Finally, the way in which the unit-rate change coefficients behave with the changes of different reservoir-well parameters was also researched by conducting sensitivity studies.As the errors that are caused by measurement technical problems or interpretation constraints in pressure data are not expected to appear in the transient temperature data, the applications of both synthetic datasets and real field datasets demonstrated that the temperature data can provide additional constraints for pressure data. Additionally, the reliability of the developed methods, which reveal complementary reservoir information from transient temperature data, was verified.

A wavelet filtering method for cumulative gamma spectroscopy used in wear measurements

Continuous ultra-mild wear quantification using radioactive isotopes involves measuring very low amounts of activity in limited time intervals. This results in gamma spectra with poor signal-to-noise ratio and hence very scattered wear data, especially during running-in, where wear is intrinsically low. Therefore, advanced filtering methods reducing the wear data scattering and making the calculation of the main peak area more accurate are mandatory. An energy-time dependent threshold for wavelet detail coefficients based on Poisson statistics and using a combined Barwell law for the estimation of the average photon counting rate is then introduced. In this manner, it was shown that the accuracy of running-in wear quantification is enhanced.

Genetic Fuzzy System (GFS) based wavelet co-occurrence feature selection in mammogram classification for breast cancer diagnosis

Summary Breast cancer is significant health problem diagnosed mostly in women worldwide. Therefore, early detection of breast cancer is performed with the help of digital mammography, which can reduce mortality rate. This paper presents wrapper based feature selection approach for wavelet co-occurrence feature (WCF) using Genetic Fuzzy System (GFS) in mammogram classification problem. The performance of GFS algorithm is explained using mini-MIAS database. WCF features are obtained from detail wavelet coefficients at each level of decomposition of mammogram image. At first level of decomposition, 18 features are applied to GFS algorithm, which selects 5 features with an average classification success rate of 39.64%. Subsequently, at second level it selects 9 features from 36 features and the classification success rate is improved to 56.75%. For third level, 16 features are selected from 54 features and average success rate is improved to 64.98%. Lastly, at fourth level 72 features are applied to GFS, which selects 16 features and thereby increasing average success rate to 89.47%. Hence, GFS algorithm is the effective way of obtaining optimal set of feature in breast cancer diagnosis.

ECG Signal Compression Using the High Frequency Components of Wavelet Transform

Electrocardiography (ECG) is the method of recording electrical activity of the heart by using electrodes. In ambulatory and continuous monitoring of ECG, the data that need to be handled is huge. Hence we require an efficient compression technique. The data also must retain the clinically important features after compression. For most of the signals, the low frequency component is considered as most important part of the signal. In wavelet analysis, the approximation coefficients are the low frequency components of the signal. The detail coefficients are the high frequency components of the signal. Most of the time the detail coefficients (high frequency components) are not considered. In this paper, we propose to use detail coefficients of Wavelet transform for ECG signal compression. The Compression Ratio (CR) of both the approximation and detail coefficients are compared. Threshold based technique is adopted. The Threshold value helps to remove the coefficients below the set threshold value of coefficients. Experiment is carried out using different types of Wavelet transforms. MIT BIH ECG data base is used for experimentation. MATLAB tool is used for simulation purpose. The novelty of the method is that the CR achieved by detail coefficients is better. CR of about 88% is achieved using Sym3 Wavelet. The performance measure of the reconstructed signal is carried out by PRD.

Denoising of X-ray pulsar observed profile in the undecimated wavelet domain

The low intensity of the X-ray pulsar signal and the strong X-ray background radiation lead to low signal-to-noise ratio (SNR) of the X-ray pulsar observed profile obtained through epoch folding, especially when the observation time is not long enough. This signifies the necessity of denoising of the observed profile. In this paper, the statistical characteristics of the X-ray pulsar signal are studied, and a signal-dependent noise model is established for the observed profile. Based on this, a profile noise reduction method by performing a local linear minimum mean square error filtering in the un-decimated wavelet domain is developed. The detail wavelet coefficients are rescaled by multiplying their amplitudes by a locally adaptive factor, which is the local variance ratio of the noiseless coefficients to the noisy ones. All the nonstationary statistics needed in the algorithm are calculated from the observed profile, without a priori information. The results of experiments, carried out on simulated data obtained by the ground-based simulation system and real data obtained by Rossi X-Ray Timing Explorer satellite, indicate that the proposed method is excellent in both noise suppression and preservation of peak sharpness, and it also clearly outperforms four widely accepted and used wavelet denoising methods, in terms of SNR, Pearson correlation coefficient and root mean square error.

Airborne hyperspectral discrimination of tree species with different ages using discrete wavelet transform

In this article, the capability of discrete wavelet transform (DWT) to discriminate tree species with different ages using airborne hyperspectral remote sensing is investigated. The performance of DWT is compared against commonly used traditional methods, i.e. original reflectance and first and second derivatives. The hyperspectral data are obtained from Thetford forest of the UK, which contains Corsican and Scots pines with different ages and broadleaved tree species. The discrimination is performed by employing three different spectral measurement techniques (SMTs) including Spectral Angle Mapper (SAM), Spectral Information Divergence (SID), and a combination of SAM and SID. Five different mother wavelets with a total of 50 different orders are tested. The wavelet detail coefficient (CD) from each decomposition level and combination of all CDs plus the approximation coefficient from the final decomposition level (C-All) are extracted from each mother wavelet. The results show the superiority of DWT against the reflectance and derivatives for all the three SMTs. In DWT, C-All provided the highest discrimination accuracy compared to other coefficients. An overall accuracy difference of about 20–30% is observed between the finest coefficient and C-All. Amongst the SMTs, SID provided the highest accuracy, while SAM showed the lowest accuracy. Using DWT in combination with SID, an overall accuracy up to around 71.4% is obtained, which is around 13.5%, 14.7%, and 27% higher than the accuracies achieved with reflectance and first and second derivatives, respectively.

Detection on Structural Sudden Damage Using Continuous Wavelet Transform and Lipschitz Exponent

The degradation of civil engineering structures may lead to a sudden stiffness reduction in a structure and such a sudden damage will cause a discontinuity in the dynamic responses. The detection on structural sudden damage has been actively carried out in this study. The signal singularity of the acceleration responses with sudden stiffness reduction is characterized by the coefficients of continuous wavelet transform with fine scales. A detection approach based on the CWT is proposed in terms of the decomposed detail coefficients of continuous wavelet transform to detect the damage time instant and location. The Lipschitz exponent is mathematically used to estimate the local properties of certain function and is applied to reflect the damage severity. Numerical simulation using a five-story shear building under different types of excitation is carried out to assess the validity of the proposed detection approach for the building at different damage levels. The sensitivity of the damage index to the intensity and frequency range of measurement noise is also investigated. The effects of both measurement noise intensity and frequency range on the damage detection are numerically investigated.

Damage identification using 2-D discrete wavelet transform on extended operational mode shapes

In this paper a new scheme of damage detection and localisation is presented by implementing frequency response functions (FRFs) of damaged structure only. First damage sensitive shape signals are generated by taking the second order derivatives of the operational mode shapes at each frequency coordinate and then the anti-symmetric extension of each shape signal at the beginning and at the end of the signal is created to avoid boundary distortion phenomenon. In order to highlight the damage influence on shape signals, the shape signals are normalised with respect to the maximum value to adjust the amplitude difference between shape signals at different frequencies. It is illustrated that normalisation of shape signals significantly improves the damage localisation results. After normalising the shape signals, a two-dimensional (2-D) map of all shape signals is created and then is analysed by employing 2-D discrete wavelet transform (DWT). By performing 2-D DWT, three sets of horizontal, vertical and diagonal detailed wavelet coefficients will be obtained. It is demonstrated that amongst these three sets, horizontal detail coefficients are the most sensitive ones to any perturbation in the shape signals due to damage occurrence and, thus, are utilised to localise damage in this study.

Wave Forecasting Using Neuro Wavelet Technique

In the present work a hybrid Neuro-Wavelet Technique is used for forecasting waves up to 6 hr, 12 hr, 18 hr and 24 hr in advance using hourly measured significant wave heights at an NDBC station 41004 near the east coast of USA. The NW Technique is employed by combining two methods, Discrete Wavelet Transform and Artificial Neural Networks. The hourly data of previously measured significant wave heights spanning over 2 years from 2010 and 2011 is used to calibrate and test the models. The discrete wavelet transform of NWT analyzes frequency of signal with respect to time at different scales. It decomposes time series into low (approximate) and high (detail) frequency components. The decomposition of approximate can be carried out up to desired multiple levels in order to provide more detail and approximate components which provides relatively smooth varying amplitude series. The neural network is trained with decorrelated approximate and detail wavelet coefficients. The outputs of networks during testing are reconstructed back using inverse DWT. The results were judged by drawing the wave plots, scatter plots and other error measures. The developed models show reasonable accuracy in prediction of significant wave heights from 6 to 24 hours. To compare the results traditional ANN models were also developed at the same location using the same data and for same time interval.

Removing prediction lag in wave height forecasting using Neuro - Wavelet modeling technique

Forecasting of waves using ANN has been done by many researchers since last two decades in which use of previous wave heights is done for forecasting the same for few hours to few days in advance. These wave forecasting models exhibit lag in prediction timing which makes the univariate time series forecasting a futile attempt. This can be attributed to high autocorrelation between the last two observed wave heights. In the present work a hybrid technique called multilevel neuro-wavelet transform is used for forecasting significant wave heights up to 36hr in advance at three locations around USA coastline using the previously measured SWHs at the same locations in order to remove the phase lag in prediction. The discrete wavelet transform (DWT) used in the present work for multiple times decomposes the time series into approximate (low) and detail (high) frequency components preventing any correlation between the sequentially observed wave heights. The neural network is then trained with these decorrelated approximate and detail wavelet coefficients. The outputs of networks during testing are reconstructed back using the inverse DWT. It was seen that the prediction lag in forecasting of significant wave height is completely removed by this hybrid multilevel neuro-wavelet technique.

Image denoising using local contrast and adaptive mean in wavelet transform domain

Images are often corrupted by noise due to the imperfection of image acquisition systems and transmission channels. Traditional algorithms perform image denoising in the pixel domain. However, the transform domain denoising methods have shown outstanding success over the last decades. There are many image denoising methods which are in existence over the last decades, originated from various disciplines such as probability theory, statistics, partial differential equations, linear and nonlinear filtering, spectral and multiresolution analysis due to the robustness of the systems. Recently, image denoising has been attracting much attention using the wavelet transform. Wavelet based approach provides a particularly useful method for image denoising when the preservation of contents in the scene is of importance because the local adaptivity is based explicitly on the values of the wavelet detail coefficients. In this paper, we have proposed a new thresholding technique based on local contrast and adaptive mean in the wavelet transform domain.

On-the-Fly Extraction of Polyhedral Buildings From Airborne LiDAR Data

This letter presents an on-the-fly method for extracting polyhedral buildings from airborne light detection and ranging (LiDAR) data. By using the gridding method, the planimetric position and elevation of laser footprints (normally treated as points) in the obtained scan line are mapped into a data sequence. Then, discrete stationary wavelet transform is applied to analyze the elevation variation in the sequence. Buildings in the scan line can be obtained from the detail wavelet coefficients of the sequence. Moreover, to improve precision of the extraction, the gradients of grid points in the geometric planes of building roofs along the direction of the scan line are calculated and remedied by using the corresponding gradients acquired from the adjacent scan lines. With the proposed on-the-fly method, polyhedral buildings in the scan area can be accurately extracted from laser points along the scan lines during the scanning process. The new method is validated by using a set of real airborne LiDAR data.

Application of Wavelet Analysis to Spectral Data for Categorization of Lamb Muscles

Application of wavelet analysis to near-infrared (NIR) hyperspectral imaging data was exploited for categorization of lamb muscles in this study. A variety of common wavelet transforms was investigated to identify the best wavelet features for categorization of lamb muscles. The fifth-order Daubechies wavelet (“db5”) was found to be the best wavelet function for decomposition of lamb spectral signal. Features of wavelet coefficients extracted from db5 wavelet at the fifth decomposition level were then used as the inputs of least-squares support vector machine (LS-SVM) for developing classification models. Principal component analysis (PCA) was used for dimensionality reduction. Classification performance of LS-SVM classifiers in tandem with wavelet transform and PCA was compared with the LS-SVM models based on original, first derivative, second derivative, smoothing, standard normal variate (SNV), and multiplicative scatter correction (MSC) spectral data; then, the overall correct classification performance for the training and test sets using combination with wavelet approximation and detail coefficients in fifth decomposition scale and PCA was 100 and 96.15 %, respectively. In addition, the developed classification models were successfully applied to the hyperspectral images for obtaining classification maps and the kappa coefficient of 0.83 was obtained for the visual classification. The results revealed that the application of wavelet analysis has a great potential for categorization of lamb muscles in tandem with multivariate analysis and image processing.

Multiscale Derivative Transform and Its Application to Image Watermarking

A transform that estimates the first and higher-order derivatives of images at multiple scales is proposed. The proposed transform, called Multi-Scale Derivative Transform (MSDT), is specially designed for image watermarking applications. To calculate the first and higher-order image derivatives, MSDT uses the detail wavelet coefficients of the image. Unlike traditional wavelet-based image derivative estimators that use only the horizontal and vertical wavelet coefficients, the proposed transform maps the diagonal as well as the horizontal and vertical wavelet coefficients to the horizontal and vertical derivatives of the image. The inverse transform is designed such that any change in the image derivative domain results in the minimum possible change in the wavelet coefficients. This renders a watermark, that is embedded in the derivative domain, less visible in the image domain. The application of this transform to image watermarking is discussed, and the results are compared with those obtained using traditional wavelet-based image derivative estimators.