Showing papers on "Wavelet packet decomposition published in 2010"

Digital Image Watermarking Using Discrete Wavelet Transform and Singular Value Decomposition

Abstract: The main objective of developing an image-watermarking technique is to satisfy both imperceptibility and robustness requirements. To achieve this objective, a hybrid image-watermarking scheme based on discrete wavelet transform (DWT) and singular value decomposition (SVD) is proposed in this paper. In our approach, the watermark is not embedded directly on the wavelet coefficients but rather than on the elements of singular values of the cover image's DWT subbands. Experimental results are provided to illustrate that the proposed approach is able to withstand a variety of image-processing attacks.

Wavelets: Theory and Applications for Manufacturing

Abstract: Why wavelets.- From fourier transform to wavelet transform.- Wavelet integrated with fourier transform: a spectral post-processing technique.- Wavelet-based multi-sensor data fusion.- Integration of wavelet with fuzzy logic for machine defect severity classification.- Wavelet-based multi-fractal singularity spectrum.- Wavelet-based ultrasonic pulse detection and differentiation.- Wavelet-based multi-scale enveloping spectrogram.- Wavelet packet decomposition for cross-term interference suppression in wigner-ville distribution.- Optimal wavelet packet transform for discriminable feature extraction.- Wavelet selection criteria.- Customized wavelet design.

Detection and classification of power quality disturbances using discrete wavelet transform and wavelet networks

Abstract: A novel approach for detection and classification of power quality (PQ) disturbances is proposed. The distorted waveforms (PQ events) are generated based on the IEEE 1159 standard, captured with a sampling rate of 20 kHz and de-noised using discrete wavelet transform (DWT) to obtain signals with higher signal-to-noise ratio. The DWT is also used to decompose the signal of PQ events and to extract its useful information. Proper feature vectors are selected and applied in training the wavelet network classifier. The effectiveness of the proposed method is tested using a wide spectrum of PQ disturbances including dc offset, harmonics, flicker, interrupt, sag, swell, notching, transient and combinations of these events. Comparison of test results with those generated by other existing methods shows enhanced performance with a classification accuracy of 98.18%. The main contribution of the paper is an accurate (because of proper selection of feature vectors), fast (e.g. a new de-noising approach with proposed identification criterion) and robust (at different signal-to-noise ratios) wavelet network-based algorithm (as compared to the conventional wavelet-based algorithms) for detection/classification of individual, as well as combined PQ disturbances.

A multidimensional hybrid intelligent method for gear fault diagnosis

Abstract: Identifying gear damage categories, especially for early faults and combined faults, is a challenging task in gear fault diagnosis. This paper proposes a new multidimensional hybrid intelligent diagnosis method to identify different categories and levels of gear damage automatically. In this method, Hilbert transform, wavelet packet transform (WPT) and empirical mode decomposition (EMD) are performed on gear vibration signals to extract additional fault characteristic information. Then, multidimensional feature sets including time-domain, frequency-domain and time-frequency-domain features are generated to reveal gear health conditions. Multiple classifiers based on several classification algorithms and input features are combined with genetic algorithm (GA). Because of the use of multidimensional features and the combination of multiple classifiers, more accurate diagnosis results are expected with the proposed method. Experiments with different gear damage categories and damage levels were conducted, and the vibration signals were captured under different loads and motor speeds. The proposed method is applied to the collected signals to identify the gear damage categories and damage levels. The diagnosis results show it can reliably recognize single damage modes, combined damage modes, and damage levels.

Haar Wavelet Based Approach for Image Compression and Quality Assessment of Compressed Image

Abstract: With the increasing growth of technology and the entrance into the digital age, we have to handle a vast amount of information every time which often presents difficulties. So, the digital information must be stored and retrieved in an efficient and effective manner, in order for it to be put to practical use. Wavelets provide a mathematical way of encoding information in such a way that it is layered according to level of detail. This layering facilitates approximations at various intermediate stages. These approximations can be stored using a lot less space than the original data. Here a low complex 2D image compression method using wavelets as the basis functions and the approach to measure the quality of the compressed image are presented. The particular wavelet chosen and used here is the simplest wavelet form namely the Haar Wavelet. The 2D discrete wavelet transform (DWT) has been applied and the detail matrices from the information matrix of the image have been estimated. The reconstructed image is synthesized using the estimated detail matrices and information matrix provided by the Wavelet transform. The quality of the compressed images has been evaluated using some factors like Compression Ratio (CR), Peak Signal to Noise Ratio (PSNR), Mean Opinion Score (MOS), Picture Quality Scale (PQS) etc.

Automated Real-Time Epileptic Seizure Detection in Scalp EEG Recordings Using an Algorithm Based on Wavelet Packet Transform

Abstract: A novel wavelet-based algorithm for real-time detection of epileptic seizures using scalp EEG is proposed. In a moving-window analysis, the EEG from each channel is decomposed by wavelet packet transform. Using wavelet coefficients from seizure and nonseizure references, a patient-specific measure is developed to quantify the separation between seizure and nonseizure states for the frequency range of 1-30 Hz. Utilizing this measure, a frequency band representing the maximum separation between the two states is determined and employed to develop a normalized index, called combined seizure index (CSI). CSI is derived for each epoch of every EEG channel based on both rhythmicity and relative energy of that epoch as well as consistency among different channels. Increasing significantly during ictal states, CSI is inspected using one-sided cumulative sum test to generate proper channel alarms. Analyzing alarms from all channels, a seizure alarm is finally generated. The algorithm was tested on scalp EEG recordings from 14 patients, totaling 75.8 h with 63 seizures. Results revealed a high sensitivity of 90.5% , a false detection rate of 0.51 h-1 and a median detection delay of 7 s. The algorithm could also lateralize the focus side for patients with temporal lobe epilepsy.

Medical image fusion via an effective wavelet-based approach

Abstract: A novel wavelet-based approach for medical image fusion is presented, which is developed by taking into not only account the characteristics of human visual system (HVS) but also the physical meaning of the wavelet coefficients. After the medical images to be fused are decomposed by the wavelet transform, different-fusion schemes for combining the coefficients are proposed: coefficients in low-frequency band are selected with a visibility-based scheme, and coefficients in high-frequency bands are selected with a variance based method. To overcome the presence of noise and guarantee the homogeneity of the fused image, all the coefficients are subsequently performed by a window-based consistency verification process. The fused image is finally constructed by the inverse wavelet transform with all composite coefficients. To quantitatively evaluate and prove the performance of the proposed method, series of experiments and comparisons with some existing fusion methods are carried out in the paper. Experimental results on simulated and real medical images indicate that the proposed method is effective and can get satisfactory fusion results.

On the Analytic Wavelet Transform

Abstract: An exact and general expression for the analytic wavelet transform of a real-valued signal is constructed, resolving the time-dependent effects of nonnegligible amplitude and frequency modulation. The analytic signal is first locally represented as a modulated oscillation, demodulated by its own instantaneous frequency, and then Taylor-expanded at each point in time. The terms in this expansion, called the instantaneous modulation functions, are time-varying functions which quantify, at increasingly higher orders, the local departures of the signal from a uniform sinusoidal oscillation. Closed-form expressions for these functions are found in terms of Bell polynomials and derivatives of the signal's instantaneous frequency and bandwidth. The analytic wavelet transform is shown to depend upon the interaction between the signal's instantaneous modulation functions and frequency-domain derivatives of the wavelet, inducing a hierarchy of departures of the transform away from a perfect representation of the signal. The form of these deviation terms suggests a set of conditions for matching the wavelet properties to suit the variability of the signal, in which case our expressions simplify considerably. One may then quantify the time-varying bias associated with signal estimation via wavelet ridge analysis, and choose wavelets to minimize this bias.

Time-Frequency Analysis of Power-Quality Disturbances via the Gabor–Wigner Transform

Abstract: Recently, many signal-processing techniques, such as fast Fourier transform, short-time Fourier transform, wavelet transform (WT), and wavelet packet transform (WPT), have been applied to detect, identify, and classify power-quality (PQ) disturbances. For research on PQ analysis, it is critical to apply the appropriate signal-processing techniques to solve PQ problems. In this paper, a new time-frequency analysis method, namely, the Gabor-Wigner transform (GWT), is introduced and applied to detect and identify PQ disturbances. Since GWT is an operational combination of the Gabor transform (GT) and the Wigner distribution function (WDF), it can overcome the disadvantages of both. GWT has two advantages which are that it has fewer cross-term problems than the WDF and higher clarity than the GT. Studies are presented which verify that the merits of GWT make it adequate for PQ analysis. In the case studies considered here, the various PQ disturbances, including voltage swell, voltage sag, harmonics, interharmonics, transients, voltage changes with multiple frequencies and voltage fluctuation, or flicker, will be thoroughly investigated by using this new time-frequency analysis method.

Detection of Motor Bearing Outer Raceway Defect by Wavelet Packet Transformed Motor Current Signature Analysis

Abstract: Motor current signature analysis (MCSA) is a method of sampling the running current through a data logger at high sampling speed, followed by using mathematical tools such as fast Fourier transform (FFT) to identify relevant motor signature changes in the frequency spectrum for motor fault identification. Although there are numerous types of motor fault, research conducted by Electric Power Research Institute (EPRI) indicated that motor bearing fault accounted for more than 40% of all types of motor fault. The main aim of this paper is to evaluate the use of MCSA for detecting bearing outer raceway defect. Stage-by-stage experimental verification shows that the method of MCSA is effective in detecting bearing fault with the use of wavelet packet transformation (WPT). In addition, a novel linear application of linear regression for wavelet data analysis is applied and presented in this paper.

A Blind Watermarking Scheme Using New Nontensor Product Wavelet Filter Banks

Abstract: As an effective method for copyright protection of digital products against illegal usage, watermarking in wavelet domain has recently received considerable attention due to the desirable multiresolution property of wavelet transform. In general, images can be represented with different resolutions by the wavelet decomposition, analogous to the human visual system (HVS). Usually, human eyes are insensitive to image singularities revealed by different high frequency subbands of wavelet decomposed images. Hence, adding watermarks into these singularities will improve the imperceptibility that is a desired property of a watermarking scheme. That is, the capability for revealing singularities of images plays a key role in designing wavelet-based watermarking algorithms. Unfortunately, the existing wavelets have a limited ability in revealing singularities in different directions. This motivates us to construct new wavelet filter banks that can reveal singularities in all directions. In this paper, we utilize special symmetric matrices to construct the new nontensor product wavelet filter banks, which can capture the singularities in all directions. Empirical studies will show their advantages of revealing singularities in comparison with the existing wavelets. Based upon these new wavelet filter banks, we, therefore, propose a modified significant difference watermarking algorithm. Experimental results show its promising results.

Feature extraction of partial discharge signals using the wavelet packet transform and classification with a probabilistic neural network

Abstract: Partial discharge (PD) classification in power cable accessories and high voltage equipment in general is essential in evaluating the severity of the damage in the insulation. In this article, the PD classification was realised as a two-fold process. Firstly, measurements taken from a high-frequency current transformer (HFCT) sensor were represented as features by means of a transformation to the classifier and secondly, the probabilistic neural network (PNN) classifier itself was capable of effectively recognising features coming from different types of discharges. The feature that was used as a fingerprint for PD characterisation was extracted from the moments of the probability density function (PDF) of the wavelet coefficients at various scales, obtained through the wavelet packets transformation. The PNN classifier was used to classify the PDs and assess the suitability of this feature vector in PD classification. Four types of artificial PDs were created in a high voltage laboratory, namely corona discharge in air, floating discharge in oil, internal discharge in oil and surface discharge in air, at different applied voltages, and were used to train the PNN algorithm. The results obtained here (97.49, 91.9, 100 and 99.8% for the corona, the floating, the internal and the surface discharges, respectively) are very encouraging for the use of PNN in PD classification with this particular feature vector. This article suggests a feature extraction and classification algorithm for PD classification, which when combined together reduced the dimensionality of the feature space to a manageable dimension, and achieved very high levels of classification.

Exploring Duplicated Regions in Natural Images

Abstract: Duplication of image regions is a common method for manipulating original images, using typical software like Adobe Photoshop, 3DS MAX, etc In this study, we propose a duplication detection approach that can adopt two robust features based on discrete wavelet transform (DWT) and kernel principal component analysis (KPCA) Both schemes provide excellent representations of the image data for robust block matching Multiresolution wavelet coefficients and KPCA-based projected vectors corresponding to image-blocks are arranged into a matrix for lexicographic sorting Sorted blocks are used for making a list of similar point-pairs and for computing their offset frequencies Duplicated regions are then segmented by an automatic technique that refines the list of corresponding point-pairs and eliminates the minimum offset-frequency threshold parameter in the usual detection method A new technique that extends the basic algorithm for detecting Flip and Rotation types of forgeries is also proposed This method uses global geometric transformation and the labeling technique to indentify the mentioned forgeries Experiments with a good number of natural images show very promising results, when compared with the conventional PCA-based approach A quantitative analysis indicate that the wavelet-based feature outperforms PCA- or KPCA-based features in terms of average precision and recall in the noiseless, or uncompressed domain, while KPCA-based feature obtains excellent performance in the additive noise and lossy JPEG compression environments

Adaptive Nonseparable Wavelet Transform via Lifting and its Application to Content-Based Image Retrieval

Abstract: We present in this paper a novel way to adapt a multidimensional wavelet filter bank, based on the nonseparable lifting scheme framework, to any specific problem. It allows the design of filter banks with a desired number of degrees of freedom, while controlling the number of vanishing moments of the primal wavelet (\mathtilde N? moments) and of the dual wavelet ( N? moments). The prediction and update filters, in the lifting scheme based filter banks, are defined as Neville filters of order \mathtilde N? and N? , respectively. However, in order to introduce some degrees of freedom in the design, these filters are not defined as the simplest Neville filters. The proposed method is convenient: the same algorithm is used whatever the dimensionality of the signal, and whatever the lattice used. The method is applied to content-based image retrieval (CBIR): an image signature is derived from this new adaptive nonseparable wavelet transform. The method is evaluated on four image databases and compared to a similar CBIR system, based on an adaptive separable wavelet transform. The mean precision at five of the nonseparable wavelet based system is notably higher on three out of the four databases, and comparable on the other one. The proposed method also compares favorably with the dual-tree complex wavelet transform, an overcomplete nonseparable wavelet transform.

Scale dependent wavelet selection for de-noising of partial discharge detection

Abstract: Wavelet shrinkage methods are effective for de-noising of partial discharge (PD) detection. Base wavelets are related to distortion of PD signals de-noised by wavelet shrinkage methods. This paper presents a scale dependent wavelet selection scheme for de-noising of PD detection. The scale dependent wavelet selection scheme is called the energy based wavelet selection (EBWS) because an energy criterion is proposed for the scheme. In the proposed energy criterion, a base wavelet is selected as an optimal base wavelet if it can generate an approximation with the largest energy among all base wavelets for selection at each scale. PD high-frequency signals are simulated and PD ultra-high-frequency signals are obtained by experiments in laboratory for de-noising experiments and analysis. In comparison with the correlation-based wavelet selection (CBWS) scheme, the wavelet shrinkage, based on the EBWS, generates significantly smaller waveform distortion and magnitude errors of de-noised PD signals.

Dual-Tree Complex Wavelet Transform Based SAR Despeckling Using Interscale Dependence

Abstract: In this paper, a dual-tree complex wavelet transform (DTCWT) based despeckling algorithm is proposed for synthetic aperture radar (SAR) images, considering the significant dependences of the wavelet coefficients across different scales. The DTCWT has the advantage of improved directional selectivity, approximate shift invariance, and perfect reconstruction over the discrete wavelet transform. The wavelet coefficients in each subband are modeled with a bivariate Cauchy probability density function (PDF) which takes into account the statistical dependence among the wavelet coefficients. Mellin transform of two dependent random variables is utilized to estimate the dispersion parameter of the bivariate Cauchy PDF from the noisy observations. This method is faster and effective when compared to that of the earlier techniques on numerical integration. Within this framework, we propose a new method for despeckling SAR images employing a maximum a posteriori estimator. Experimental results show that the proposed method based on bivariate Cauchy prior achieves better performance in terms of equivalent number of looks, peak signal-to-noise ratio, and Pratt's figure of merit.

p-Adic Multiresolution Analysis and Wavelet Frames

Abstract: We study p-adic multiresolution analyses (MRAs). A complete characterization of test functions generating an MRA (scaling functions) is given. We prove that only 1-periodic test functions may be taken as orthogonal scaling functions and that all such scaling functions generate the Haar MRA. We also suggest a method for constructing sets of wavelet functions and prove that any set of wavelet functions generates a p-adic wavelet frame.

Steerable Wavelet Frames Based on the Riesz Transform

Abstract: We consider an extension of the 1-D concept of analytical wavelet to n-D which is by construction compatible with rotations. This extension, called a monogenic wavelet, yields a decomposition of the wavelet coefficients into amplitude, phase, and phase direction. The monogenic wavelet is based on the hypercomplex monogenic signal which is defined using Riesz transforms and perfectly isotropic wavelets frames. Employing the new concept of Clifford frames, we can show that the monogenic wavelet generates a wavelet frame. Furthermore, this approach yields wavelet frames that are steerable with respect to direction. Applications to descreening and contrast enhancement illustrate the versatility of this approach to image analysis and reconstruction.

Time Domain Signal Analysis Using Wavelet Packet Decomposition Approach

Abstract: This paper explains a study conducted based on wavelet packet transform techniques. In this paper the key idea underlying the construction of wavelet packet analysis (WPA) with various wavelet basis sets is elaborated. Since wavelet packet decomposition can provide more precise frequency resolution than wavelet decomposition the implementation of one dimensional wavelet packet transform and their usefulness in time signal analysis and synthesis is illustrated. A mother or basis wavelet is first chosen for five wavelet filter families such as Haar, Daubechies (Db4), Coiflet, Symlet and dmey. The signal is then decomposed to a set of scaled and translated versions of the mother wavelet also known as time and frequency parameters. Analysis and synthesis of the time signal is performed around 8 seconds to 25 seconds. This was conducted to determine the effect of the choice of mother wavelet on the time signals. Results are also prepared for the comparison of the signal at each decomposition level. The physical changes that are occurred during each decomposition level can be observed from the results. The results show that wavelet filter with WPA are useful for analysis and synthesis purpose. In terms of signal quality and the time required for the analysis and synthesis, the Haar wavelet has been seen to be the best mother wavelet. This is taken from the analysis of the signal to noise ratio (SNR) value which is around 300 dB to 315 dB for the four decomposition levels.