Generation Wavelet Research Articles

Pan‐sharpening based on weighted red black wavelets

Pan-sharpening is a technique which provides an efficient and economical solution to generate multi-spectral (MS) images with high-spatial resolution by fusing spectral information in MS images and spatial information in panchromatic (PAN) image. In this study, the authors propose a new pan-sharpening method based on weighted red-black (WRB) wavelets and adaptive principal component analysis (PCA), where the usage of WRB wavelet decomposition is to extract the spatial details in PAN image and the adaptive PCA is used to select the adequate principal component for injecting spatial details. WRB wavelets are data-dependent second generation wavelets. Multi-resolution analysis (MRA) based on WRB wavelet transform shows a better de-correlation of the data compared with common linear translation-invariant MRA, which makes it suitable for applications requiring manipulating image details. A local processing strategy is introduced to reduce the artefact effects and spectral distortions in the pan-sharpened images. The proposed method is evaluated on the datasets acquired by QuickBird, IKONOS and Landsat-7 ETM + satellites and compared with existing methods. Experimental results demonstrate that the authors method can provide promising fused MS images with high-spatial resolution.

Image Denoising Algorithm Using Second Generation Wavelet Transformation and Principle Component Analysis

This study proposes novel image denoising algorithm using combination method. This method combines both Wavelet Based Denoising (WBD) and Principle Component Analysis (PCA) to increase the superiority of the observed image, subjectively and objectively. We exploit the important property of second generation WBD and PCA to increase the performance of our designed filter. One of the main advantages of the second generation wavelet transformation in noise reduction is its ability to keep the signal energy in small amount of coefficients in the wavelet domain. On the other hand, one of the main features of PCA is that the energy of the signal concentrates on a very few subclasses in PCA domain, while the noise’s energy equally spreads over the entire signal; this characteristic helps us to isolate the noise perfectly. Our algorithm compares favorably against several state-of-the- art filtering systems algorithms, such as Contourlet soft thresholding, Scale mixture by WT, Sparse 3D transformation and Normal shrink. In addition, the combined algorithm achieves very competitive performance compared with the traditional algorithms, especially when it comes to investigating the problem of how to preserve the fine structure of the tested image and in terms of the computational complexity reduction as well.

The Navel Orange Sugar and Acidity Quantitative Prediction Model Optimization Research by Second Generation Wavelet Transform

The author researches the impact of the second generation wavelet transform spectrometer data preprocessing navel orange sugar content and acidity Partial Least Squares (PLS) quantitative accuracy of the prediction model. This paper also collects the spectral date of one hundred navel oranges by visible/near-infrared diffuse reflectance detection technology and establishes the navel orange sugar content and acidity PLS prediction model using the sixty navel oranges as the establishing samples. The author contrasts changes of navel orange sugar content and acidity PLS prediction model because the spectral date of navel oranges are processed by the second generation wavelet transform, Finally conclusion: the second generation wavelet transform processing navel orange spectral data can improve the predictive ability of the sugar content and acidity PLS quantitative analysis models. Full Text: PDF DOI: http://dx.doi.org/10.11591/telkomnika.v12i7.5371

State recognition of the viscoelastic sandwich structure based on the adaptive redundant second generation wavelet packet transform, permutation entropy and the wavelet support vector machine

The viscoelastic sandwich structure is widely used in mechanical equipment, yet the structure always suffers from damage during long-term service. Therefore, state recognition of the viscoelastic sandwich structure is very necessary for monitoring structural health states and keeping the equipment running with high reliability. Through the analysis of vibration response signals, this paper presents a novel method for this task based on the adaptive redundant second generation wavelet packet transform (ARSGWPT), permutation entropy (PE) and the wavelet support vector machine (WSVM). In order to tackle the non-linearity existing in the structure vibration response, the PE is introduced to reveal the state changes of the structure. In the case of complex non-stationary vibration response signals, in order to obtain more effective information regarding the structural health states, the ARSGWPT, which can adaptively match the characteristics of a given signal, is proposed to process the vibration response signals, and then multiple PE features are extracted from the resultant wavelet packet coefficients. The WSVM, which can benefit from the conventional SVM as well as wavelet theory, is applied to classify the various structural states automatically. In this study, to achieve accurate and automated state recognition, the ARSGWPT, PE and WSVM are combined for signal processing, feature extraction and state classification, respectively. To demonstrate the effectiveness of the proposed method, a typical viscoelastic sandwich structure is designed, and the different degrees of preload on the structure are used to characterize the various looseness states. The test results show that the proposed method can reliably recognize the different looseness states of the viscoelastic sandwich structure, and the WSVM can achieve a better classification performance than the conventional SVM. Moreover, the superiority of the proposed ARSGWPT in processing the complex vibration response signals and the powerful ability of the PE in revealing the structural state changes are also demonstrated by the test results.

The construction of second generation wavelet-based multivariable finite elements for multiscale analysis of beam problems

A design method of second generation wavelet (SGW)-based multivariable finite elements is proposed for static and vibration beam analysis. An important property of SGWs is that they can be custom designed by selecting appropriate lifting coefficients depending on the application. The SGW-based multivariable finite element equations of static and vibration analysis of beam problems with two and three kinds of variables are derived based on the generalized variational principles. Compared to classical finite element method (FEM), the second generation wavelet-based multivariable finite element method (SGW-MFEM) combines the advantages of high approximation performance of the SGW method and independent solution of field functions of the MFEM. A multiscale algorithm for SGW-MFEM is presented to solve structural engineering problems. Numerical examples demonstrate the proposed method is a flexible and accurate method in static and vibration beam analysis.

The Fusion Algorithm of Infrared and Visible Images Based on Computer Vision

Directionlet transform is a lattice-based skewed discrete wavelet transform. It has advantages of multi-directional and anisotropy compared with standard two-dimensional wavelet transform, thus, it is better at describing the characteristics of images. For the research focus of different-source image fusion, a novel fusion algorithm based on Directionlet transform was proposed, and the fusion speed was improved efficiently by combing the transform with a lifting scheme. Firstly, between transform direction and alignment direction, two registered source images were decomposed by using lifting Directionlet transform respectively in different times, thus anisotropic sub images were obtained. Then, the low frequency components were combined averagely and the selection principle of high frequency sub images were based on which has stronger anisotropic edge information. Finally, the fused image was obtained by using inverse Directionlet transform. Experimental results show that the fusion effect and speed are both better than standard wavelet transform and other second generation wavelet transform.

Rolling Bearing Fault Diagnosis Based on Second Generation Wavelet Denoising and Improved EEMD

A new rolling bearing fault diagnosis approach is proposed. The original vibration signal is purified using the second generation wavelet denoising. The purified signal is further decomposed by an improved ensemble empirical mode decomposition (EEMD) method. A new selection criterion, including correlation analysis and the first two intrinsic mode functions (IMFs) with the maximum energy, is put forward to eliminate the pseudo low-frequency components. Experimental investigation show that the rolling bearing fault features can be effectively extracted.

Quantitative damage detection and sparse sensor array optimization of carbon fiber reinforced resin composite laminates for wind turbine blade structural health monitoring.

The active structural health monitoring (SHM) approach for the complex composite laminate structures of wind turbine blades (WTBs), addresses the important and complicated problem of signal noise. After illustrating the wind energy industry's development perspectives and its crucial requirement for SHM, an improved redundant second generation wavelet transform (IRSGWT) pre-processing algorithm based on neighboring coefficients is introduced for feeble signal denoising. The method can avoid the drawbacks of conventional wavelet methods that lose information in transforms and the shortcomings of redundant second generation wavelet (RSGWT) denoising that can lead to error propagation. For large scale WTB composites, how to minimize the number of sensors while ensuring accuracy is also a key issue. A sparse sensor array optimization of composites for WTB applications is proposed that can reduce the number of transducers that must be used. Compared to a full sixteen transducer array, the optimized eight transducer configuration displays better accuracy in identifying the correct position of simulated damage (mass of load) on composite laminates with anisotropic characteristics than a non-optimized array. It can help to guarantee more flexible and qualified monitoring of the areas that more frequently suffer damage. The proposed methods are verified experimentally on specimens of carbon fiber reinforced resin composite laminates.

An Adaptive De-Noising Method via the Lifting Scheme

The wavelet transform de-noising method based on the threshold shrinkage is widely used, however, the classical threshold shrinkage method maybe exists constant deviation or appears additional concussion after reconfiguration. If the threshold value is chosen too large, part of useful signal points will be eliminated; if chosen too small, part of the noise will be kept. In addition, the “first generation wavelet” de-noising method only can choose one type of wavelet base, and can't be changed during the de-noising process. Due to the different wavelet has its own characteristics and applicable signal, It can achieve local optimum then overall optimization that choosing wavelet in a small wave focus according to the partial feature of the signal, namely using the multiwavelets to comprehensively decompose signal. This paper puts forward a new threshold function, then improves the selection scheme of threshold value, achieves that it can select dynamically according to the wavelet decomposition levels; Finally, on the basis of the lifting theory, this paper puts forward an adaptive method, which can select wavelet dynamically according to the partial feature of the signal, comprehensively making use of the advantages of each wavelet, to achieve better de-noising effect and a certain degree of adaptability. Experiments show the effectiveness of our optimization.

Multiscale viscoacoustic waveform inversion with the second generation wavelet transform and adaptive time–space domain finite-difference method

Multiscale viscoacoustic waveform inversion with the second generation wavelet transform and adaptive time–space domain finite-difference method

Representation of Image Data by New Lifting based Biorthogonal Wavelets and Its Application to Lossless Compression

In this paper an attempt has been made to derive the lifting scheme for a set of new bi-orthogonal wavelets and apply on image compression. Four new bi-orthogonal wavelets are designed by taking different basis functions which are selected so as to capture the sharp edges which are common in images. For these classical wavelets, lifting versions are calculated and presented in this paper. The lifting step calculation is simplest among the schemes in related literature. From the designed wavelet filters, the poly-phase matrix is written and decomposed the matrix into a form from which lifting steps are directly available. To incorporate coding Set Partitioning In Hierarchical Trees (SPIHT) algorithm is used. The Peak Signal to Noise Ratio (PSNR), Compression Ratio (CR), Transforming Time (TT), Encoding Time (ET) and Decoding Times (DT) are calculated. It was found that the compression performance of new classical wavelets is a little better than that of existing classical/first generation wavelets and that of new lifting based wavelets is far better than that of existing classical wavelets and also existing lifting based wavelets.

Hierarchical graph Laplacian eigen transforms

Hierarchical graph Laplacian eigen transforms

Detection of the Dynamic Unbalance with Cardan Shaft Applying the Second Wavelet Transform and Singular Value Decomposition

A new method of detecting cardan shaft dynamic unbalance in high-speed train is proposed applying the combination between the second generation wavelet transform(SGWT) and singular value decomposition(SVD) contrary to the basic defect of overlap frequency existing in the SGWT. The vibration acceleration signals installed on gimbal next to gearbox are decomposed through the SGWT to get the different scale decomposition signal. The Hankel matrix, which is constructed throng the single scale approximate decomposition signal, is orthogonally decomposed by SVD, the key singular values are selected to reconstruct vibration sign on the base of key stacks of singular values. Fourier spectrum of the reconstructed signal through SVD is applied to detect cardan shaft dynamic unbalance in high-speed train, eliminate the effect of overlap frequency on submerging unbalance fault features and highlight the failure characteristics. The method is verified by test data in the condition of dynamic unbalance, the results show that the method can effectively seize the fault features caused by cardan shaft dynamic unbalance, such as fundamental, multiplier, divider frequency. With comparison to the traditional wavelet decomposition, the simple SGWT, the clarity and failure characterization force of Fourier spectrum are significantly improved.

Application of second generation wavelets to blind spherical deconvolution

We address the problem of spherical deconvolution in a non-parametric statistical framework, where both the signal and the operator kernel are subject to measurement errors. After a preliminary treatment of the kernel, we apply a thresholding procedure to the signal in a second generation wavelet basis. Under standard assumptions on the kernel, we study the minimax performances of the resulting algorithm in terms of Lp losses (p≥1) on Besov spaces on the sphere. We hereby extend the application of second generation spherical wavelets to the blind spherical deconvolution framework. It is important to stress that the procedure is adaptive with regard to both the target function sparsity and the kernel blurring effect. We end with the study of a concrete example, putting into evidence the improvement of our procedure on the recent blockwise SVD algorithm of Delattre et al. (2012).

A novel approach to machining condition monitoring of deep hole boring

In the optimization of deep hole boring processes, machining condition monitoring (MCM) plays an important role for efficient tool change policies, product quality control and lower tool costs. This paper proposes a novel approach to the MCM of deep hole boring on the basis of the pseudo non-dyadic second generation wavelet transform (PNSGWT). This approach is developed via constructing a valuable indicator, i.e., the wavelet energy ratio around the natural frequency of boring bar. Self-excited vibration occurs at the frequency of the most dominant mode of the machine tool structure. Via modeling dynamic cutting process and performing its simulation analysis during deep hole boring, it is found that the vibration amplitudes at the nature frequency of the machine tool rise with the tool wear. The PNSGWT that has relative adjustable dyadic time-frequency partition grids, good time-frequency localizability and exact shift-invariance is used to extract the wavelet energy in the specified frequency band. Accordingly, the MCM of deep hole boring can be implemented by means of normalizing the wavelet energy. Finally, a field experiment on deep hole boring machine tool is conducted, and the result shows that the proposed method is effective in the process of monitoring tool wear and surface finish quality for deep hole boring.

Based on the DT-CWT Transformation Methods for 3D-Nanometer Roughness Rating Reference

This paper proposes the third generation wavelet--double tree complex wavelet (DT-CWT) transformation used in nanometer roughness rating, based on the explanation of the shortcomings of the current nanometer roughness rating reference and conventional three dimensional datum evaluations due to the insufficient study. The experiment got porous anodic alumina film as the object of surface roughness of nanotechnology study. Through the comparisons of the three generations of the wavelet reconstruction after the maximum reconstruction error, a conclusion can be made that the superiority of DT-CWT in application is very obvious, a result meeting the16% principle of the surface roughness rating on the bases of DT - CWT extracted datum to compute income parameters, which indicates the feasibility of this application to the extraction of the nano3-D roughness evaluation. Keywords: nanometer roughness;dual-tree complex wavelet;three dimensional datum

Wavelets for fault diagnosis of rotary machines: A review with applications

Over the last 20 years, particularly in last 10 years, great progress has been made in the theory and applications of wavelets and many publications have been seen in the field of fault diagnosis. This paper attempts to provide a review on recent applications of the wavelets with focus on rotary machine fault diagnosis. After brief introduction of the theoretical background on both classical wavelet transform and second generation wavelet transform, applications of wavelets in rotary machine fault diagnosis are summarized according to the following categories: continuous wavelet transform-based fault diagnosis, discrete wavelet transform-based fault diagnosis, wavelet packet transform-based fault diagnosis, and second generation wavelet transform-based fault diagnosis. In addition, some new research trends, including wavelet finite element method, dual-tree complex wavelet transform, wavelet function selection, new wavelet function design, and multi-wavelets that advance the development of wavelet-based fault diagnosis are also discussed.

Image Steganography Based on Wavelet Families

Image Steganography Based on Wavelet Families Wavelet transforms are considered to be an ideal domain for image compression and transmission. The new generation still image compression standard JPEG2000 uses the bi-orthogonal CDF 5/3 wavelet (also called the CDF (2, 2) wavelet) for lossless compression and a CDF 9/7 wavelet for lossy compression. There are several known wavelet families such as Daubechies, Coiflet, Symlet, CDF, etc. The problem of selecting a suitable wavelet for signal and image processing has always challenged the researchers. The conventional wavelet filters often have floating point coefficients and couldn’t realize the lossless reconstruction. The second generation wavelet transforms are based on lifting scheme and they map integers to integers. Thus they realize the lossless compression of image data with minimal memory usage and low computational complexity.

Digital Image Watermarking Based on Second Generation Wavelet Transform

Most of the watermarking techniques based on DWT technique embed watermarks into the detail (or middle frequency) coefficients of the host image for a good-trade-off between robustness and fidelity. But, in order to obtain the most robustness, the DC area (LL sub-band) may be a most suitable region for watermark embedding, as the signal energy of DC components is much bigger than that of high frequency sub-bands. A blind novel watermarking algorithm based on fast lifting wavelet transform, a kind of second generation wavelet transform, is proposed. Firstly, a multi-level discrete lifting wavelet transform is employed, and then the watermark is embedded into DC area of last level lifting wavelet transform according to amplitude modulation method with a secret key, lastly a watermarked image is obtained after lifting wavelet reconstruction to be applied. The results of experiments show that this algorithm is still effective after applying high compression ratio JPEG.

The Application of Multi-Wavelet in GPS Deformation Signal Processing

With wavelet technology used more widely in GPS deformation analysis, the paper will talk multi-wavelet (the second generation wavelet) theory used for GPS deformation monitoring data analysis. Due to multi-wavelet has a short branch set, orthogonal, symmetric (antisymmetric) and two order approximation characteristics, in the same filter length, using multiple wavelet on deformation monitoring signal can obtain better denoising effect than traditional wavelet. The paper studies signal adopting different preprocessing methods, makes a study of the selection problem in multi-wavelet preprocessing method. The GPS deformation monitoring signal is disposed using different multi-wavelet which adopts optima preprocessing method, and the paper makes a comparison to the conventional odd wavelet. The result confirms: multi-wavelet is more superiority than conventional wavelet, which decreases RMSE, advances SNR, obtains higher analytic precision, conforms the validity and practicability in physical problem, and offers a new road for deformation monitoring signal process