Showing papers on "Wavelet published in 2013"

Discrete Signal Processing on Graphs

Abstract: In social settings, individuals interact through webs of relationships. Each individual is a node in a complex network (or graph) of interdependencies and generates data, lots of data. We label the data by its source, or formally stated, we index the data by the nodes of the graph. The resulting signals (data indexed by the nodes) are far removed from time or image signals indexed by well ordered time samples or pixels. DSP, discrete signal processing, provides a comprehensive, elegant, and efficient methodology to describe, represent, transform, analyze, process, or synthesize these well ordered time or image signals. This paper extends to signals on graphs DSP and its basic tenets, including filters, convolution, z-transform, impulse response, spectral representation, Fourier transform, frequency response, and illustrates DSP on graphs by classifying blogs, linear predicting and compressing data from irregularly located weather stations, or predicting behavior of customers of a mobile service provider.

Empirical Wavelet Transform

Abstract: Some recent methods, like the empirical mode decomposition (EMD), propose to decompose a signal accordingly to its contained information. Even though its adaptability seems useful for many applications, the main issue with this approach is its lack of theory. This paper presents a new approach to build adaptive wavelets. The main idea is to extract the different modes of a signal by designing an appropriate wavelet filter bank. This construction leads us to a new wavelet transform, called the empirical wavelet transform. Many experiments are presented showing the usefulness of this method compared to the classic EMD.

Invariant Scattering Convolution Networks

Abstract: A wavelet scattering network computes a translation invariant image representation which is stable to deformations and preserves high-frequency information for classification. It cascades wavelet transform convolutions with nonlinear modulus and averaging operators. The first network layer outputs SIFT-type descriptors, whereas the next layers provide complementary invariant information that improves classification. The mathematical analysis of wavelet scattering networks explains important properties of deep convolution networks for classification. A scattering representation of stationary processes incorporates higher order moments and can thus discriminate textures having the same Fourier power spectrum. State-of-the-art classification results are obtained for handwritten digits and texture discrimination, with a Gaussian kernel SVM and a generative PCA classifier.

Rotation, Scaling and Deformation Invariant Scattering for Texture Discrimination

Abstract: An affine invariant representation is constructed with a cascade of invariants, which preserves information for classification. A joint translation and rotation invariant representation of image patches is calculated with a scattering transform. It is implemented with a deep convolution network, which computes successive wavelet transforms and modulus non-linearities. Invariants to scaling, shearing and small deformations are calculated with linear operators in the scattering domain. State-of-the-art classification results are obtained over texture databases with uncontrolled viewing conditions.

Learning Sparsifying Transforms

Abstract: The sparsity of signals and images in a certain transform domain or dictionary has been exploited in many applications in signal and image processing. Analytical sparsifying transforms such as Wavelets and DCT have been widely used in compression standards. Recently, synthesis sparsifying dictionaries that are directly adapted to the data have become popular especially in applications such as image denoising, inpainting, and medical image reconstruction. While there has been extensive research on learning synthesis dictionaries and some recent work on learning analysis dictionaries, the idea of learning sparsifying transforms has received no attention. In this work, we propose novel problem formulations for learning sparsifying transforms from data. The proposed alternating minimization algorithms give rise to well-conditioned square transforms. We show the superiority of our approach over analytical sparsifying transforms such as the DCT for signal and image representation. We also show promising performance in signal denoising using the learnt sparsifying transforms. The proposed approach is much faster than previous approaches involving learnt synthesis, or analysis dictionaries.

Empirical Mode Decomposition-Based Time-Frequency Analysis of Multivariate Signals: The Power of Adaptive Data Analysis

Abstract: This article addresses data-driven time-frequency (T-F) analysis of multivariate signals, which is achieved through the empirical mode decomposition (EMD) algorithm and its noise assisted and multivariate extensions, the ensemble EMD (EEMD) and multivariate EMD (MEMD). Unlike standard approaches that project data onto predefined basis functions (harmonic, wavelet) thus coloring the representation and blurring the interpretation, the bases for EMD are derived from the data and can be nonlinear and nonstationary. For multivariate data, we show how the MEMD aligns intrinsic joint rotational modes across the intermittent, drifting, and noisy data channels, facilitating advanced synchrony and data fusion analyses. Simulations using real-world case studies illuminate several practical aspects, such as the role of noise in T-F localization, dealing with unbalanced multichannel data, and nonuniform sampling for computational efficiency.

Compressed Sensing for Energy-Efficient Wireless Telemonitoring of Noninvasive Fetal ECG Via Block Sparse Bayesian Learning

Abstract: Fetal ECG (FECG) telemonitoring is an important branch in telemedicine. The design of a telemonitoring system via a wireless body area network with low energy consumption for ambulatory use is highly desirable. As an emerging technique, compressed sensing (CS) shows great promise in compressing/reconstructing data with low energy consumption. However, due to some specific characteristics of raw FECG recordings such as nonsparsity and strong noise contamination, current CS algorithms generally fail in this application. This paper proposes to use the block sparse Bayesian learning framework to compress/reconstruct nonsparse raw FECG recordings. Experimental results show that the framework can reconstruct the raw recordings with high quality. Especially, the reconstruction does not destroy the interdependence relation among the multichannel recordings. This ensures that the independent component analysis decomposition of the reconstructed recordings has high fidelity. Furthermore, the framework allows the use of a sparse binary sensing matrix with much fewer nonzero entries to compress recordings. Particularly, each column of the matrix can contain only two nonzero entries. This shows that the framework, compared to other algorithms such as current CS algorithms and wavelet algorithms, can greatly reduce code execution in CPU in the data compression stage.

Compact Support Biorthogonal Wavelet Filterbanks for Arbitrary Undirected Graphs

Abstract: This paper extends previous results on wavelet filterbanks for data defined on graphs from the case of orthogonal transforms to more general and flexible biorthogonal transforms. As in the recent work, the construction proceeds in two steps: first we design “one-dimensional” two-channel filterbanks on bipartite graphs, and then extend them to “multi-dimensional” separable two-channel filterbanks for arbitrary graphs via a bipartite subgraph decomposition. We specifically design wavelet filters based on the spectral decomposition of the graph, and state sufficient conditions for the filterbanks to be perfect reconstruction and orthogonal. While our previous designs, referred to as graph-QMF filterbanks, are perfect reconstruction and orthogonal, they are not exactly k-hop localized, i.e., the computation at each node is not localized to a small k-hop neighborhood around the node. In this paper, we relax the condition of orthogonality to design a biorthogonal pair of graph-wavelets that are k-hop localized with compact spectral spread and still satisfy the perfect reconstruction conditions. The design is analogous to the standard Cohen-Daubechies-Feauveau's (CDF) construction of factorizing a maximally-flat Daubechies half-band filter. Preliminary results demonstrate that the proposed filterbanks can be useful for both standard signal processing applications as well as for signals defined on arbitrary graphs.

Multifocus and multispectral image fusion based on pixel significance using discrete cosine harmonic wavelet transform

Abstract: The energy compaction and multiresolution properties of wavelets have made the image fusion successful in combining important features such as edges and textures from source images without introducing any artifacts for context enhancement and situational awareness. The wavelet transform is visualized as a convolution of wavelet filter coefficients with the image under consideration and is computationally intensive. The advent of lifting-based wavelets has reduced the computations but at the cost of visual quality and performance of the fused image. To retain the visual quality and performance of the fused image with reduced computations, a discrete cosine harmonic wavelet (DCHWT)-based image fusion is proposed. The performance of DCHWT is compared with both convolution and lifting-based image fusion approaches. It is found that the performance of DCHWT is similar to convolution-based wavelets and superior/similar to lifting-based wavelets. Also, the computational complexity (in terms of additions and multiplications) of the proposed method scores over convolution-based wavelets and is competitive to lifting-based wavelets.

Robust blind image watermarking scheme based on Redundant Discrete Wavelet Transform and Singular Value Decomposition

Abstract: Copyright protection and proof of ownership are two of the main important applications of the digital image watermarking. The challenges faced by researchers interested in digital image watermarking applications lie in the creation of new algorithms to serve those applications and to be resistant to most types of attacks, especially the geometrical attacks. Robustness, high imperceptibility, security, and large capacity are four essential requirements in any watermarking scheme. This paper presents a new image watermarking scheme based on the Redundant Discrete Wavelet Transform (RDWT) and the Singular Value Decomposition (SVD). The gray scale image watermark was embedded directly in the singular values of the RDWT sub-bands of the host image. The scheme achieved a large capacity due to the redundancy in the RDWT domain and at the same time preserved high imperceptibility due to SVD properties. Embedding the watermarking pixel's values without any modification inside the wavelet coefficient of the host image overcomes the security issue. Furthermore, the experimental results of the proposed scheme showed a high level of robustness not only against the image processing attacks but also against the geometrical attacks which are considered as difficult attacks to resist.

Automatic Defect Detection on Hot-Rolled Flat Steel Products

Abstract: Automatic defect detection on hot-rolled steel surface is challenging owing to its localization on a large surface, variation in appearance, and their rare occurrences. It is difficult to detect these defects either by physics-based models or by small-sample statistics using a single threshold. As a result, this problem is focused to derive a set of good-quality defect descriptors from the surface images. These descriptors should discriminate the various surface defects when fed to suitable machine learning algorithms. This research work has evaluated the performance of a number of different wavelet feature sets, namely, Haar, Daubechies 2 (DB2), Daubechies 4 (DB4), biorthogonal spline, and multiwavelet in different decomposition levels derived from 32 × 32 contiguous (nonoverlapping) pixel blocks of steel surface images. We have developed an automated visual inspection system for an integrated steel plant to capture surface images in real time. It localizes defects employing kernel classifiers, such as support vector machine and recently proposed vector-valued regularized kernel function approximation. Test results on 1000 defect-free and 432 defective images comprising of 24 types of defect classes reveal that three-level Haar feature set is more promising to address this problem than the other wavelet feature sets as well as texture-based segmentation or thresholding technique of defect detection.

Monthly Rainfall Prediction Using Wavelet Neural Network Analysis

Abstract: Rainfall is one of the most significant parameters in a hydrological model. Several models have been developed to analyze and predict the rainfall forecast. In recent years, wavelet techniques have been widely applied to various water resources research because of their time-frequency representation. In this paper an attempt has been made to find an alternative method for rainfall prediction by combining the wavelet technique with Artificial Neural Network (ANN). The wavelet and ANN models have been applied to monthly rainfall data of Darjeeling rain gauge station. The calibration and validation performance of the models is evaluated with appropriate statistical methods. The results of monthly rainfall series modeling indicate that the performances of wavelet neural network models are more effective than the ANN models.

An Automated Parallel Image Registration Technique Based on the Correlation of Wavelet Features

Abstract: With the increasing importance of multiple multiplatform remote sensing missions, fast and automatic integration of digital data from disparate sources has become critical to the success of these endeavors. Our work utilizes maxima of wavelet coefficients to form the basic features of a correlation-based automatic registration algorithm. Our wavelet-based registration algorithm is tested successfully with data from the National Oceanic and Atmospheric Administration (NOAA) Advanced Very High Resolution Radiometer (AVHRR) and the Landsat Thematic Mapper (TM), which differ by translation and/or rotation. By the choice of high-frequency wavelet features, this method is similar to an edge-based correlation method, but by exploiting the multiresolution nature of a wavelet decomposition, our method achieves higher computational speeds for comparable accuracies. This algorithm has been implemented on a single-instruction multiple-data (SIMD) massively parallel computer, the MasPar MP-2, as well as on the CrayT3D, the Cray T3E, and a Beowulf cluster of Pentium workstations.

Nonlocal Hierarchical Dictionary Learning Using Wavelets for Image Denoising

Abstract: Exploiting the sparsity within representation models for images is critical for image denoising. The best currently available denoising methods take advantage of the sparsity from image self-similarity, pre-learned, and fixed representations. Most of these methods, however, still have difficulties in tackling high noise levels or noise models other than Gaussian. In this paper, the multiresolution structure and sparsity of wavelets are employed by nonlocal dictionary learning in each decomposition level of the wavelets. Experimental results show that our proposed method outperforms two state-of-the-art image denoising algorithms on higher noise levels. Furthermore, our approach is more adaptive to the less extensively researched uniform noise.

Wavelet-Based Capacity Configuration and Coordinated Control of Hybrid Energy Storage System for Smoothing Out Wind Power Fluctuations

Abstract: Stochastically fluctuating wind power has a negative impact on power grid operations. This paper presents a wind power filtering approach to mitigate short- and long-term fluctuations using a hybrid energy storage system (HESS), and a novel wavelet-based capacity configuration algorithm to properly size the HESS. A frequency distribution allocates wind power fluctuations to the different HESS components to more easily satisfy 1-min and 30-min fluctuation mitigation requirements (FMR). An ultra-capacitor bank (UC) mitigates short-term fluctuations. In the HESS, and a lithium-ion battery bank (LB) minimizes long-term fluctuations. This paper also proposes a novel online-wavelet based coordination control scheme for the HESS, consisting of primary filtering (PF) and secondary filtering (SF) stages. The PF stage obtains a combined power output that fully satisfies the FMRs, while the SF stage provides additional smoothing of the wind power output fluctuations after the PF stage. A remaining energy level (REL) feedback control maintains the REL of the battery bank within its proper range. Case studies demonstrate that the proposed wavelet-based algorithm is more efficient than other published algorithms, and needs a lower energy storage capacity to satisfy 1-min and 30-min FMRs.

A Wavelet-ANFIS Hybrid Model for Groundwater Level Forecasting for Different Prediction Periods

Abstract: Artificial neural network (ANN) and Adaptive Neuro-Fuzzy Inference System (ANFIS) have an extensive range of applications in water resources management. Wavelet transformation as a preprocessing approach can improve the ability of a forecasting model by capturing useful information on various resolution levels. The objective of this research is to compare several data-driven models for forecasting groundwater level for different prediction periods. In this study, a number of model structures for Artificial Neural Network (ANN), Adaptive Neuro-Fuzzy Inference System (ANFIS), Wavelet-ANN and Wavelet-ANFIS models have been compared to evaluate their performances to forecast groundwater level with 1, 2, 3 and 4 months ahead under two case studies in two sub-basins. It was demonstrated that wavelet transform can improve accuracy of groundwater level forecasting. It has been also shown that the forecasts made by Wavelet-ANFIS models are more accurate than those by ANN, ANFIS and Wavelet-ANN models. This study confirms that the optimum number of neurons in the hidden layer cannot be always determined by using a specific formula but trial-and-error method. The decomposition level in wavelet transform should be determined according to the periodicity and seasonality of data series. The prediction of these models is more accurate for 1 and 2 months ahead (for example RMSE = 0.12, E = 0.93 and R 2 = 0.99 for wavelet-ANFIS model for 1 month ahead) than for 3 and 4 months ahead (for example RMSE = 2.07, E = 0.63 and R 2 = 0.91 for wavelet-ANFIS model for 4 months ahead).

Chatter identification in end milling process using wavelet packets and Hilbert–Huang transform

Abstract: Chatter detection is an important task to improve productivity and part quality in the machining process. Since measured signals from sensors are usually contaminated by background noise and other disturbances, it is necessary to find efficient signal processing algorithms to identify the chatter as soon as possible. This paper presents an effective chatter identification method for the end milling process based on the study of two advanced signal processing techniques, i.e., wavelet package transform (WPT) and Hilbert–Huang transform (HHT). The WPT works as a preprocessor to denoise the measured signals and hence the performance of the HHT is enhanced. The proposed method consists of four steps. First, the measured signals are decomposed by the WPT, so that the chatter signals are allocated in a certain frequency band. Secondly, wavelet packets with rich chatter information are selected and are used to reconstruct new signals. Thirdly, the reconstructed signals are analyzed with HHT to obtain a Hilbert–Huang spectrum, which is a full time–frequency–energy distribution of the signals. Finally, the mean value and standard deviation of the Hilbert–Huang spectrum are calculated to detect the chatter and identify its levels as well. The proposed method is applied to the end milling process and the experimental results prove that the method can identify the chatter effectively.

Brain-computer interface technologies: from signal to action.

Abstract: Here, we present a state-of-the-art review of the research performed on the brain-computer interface (BCI) technologies with a focus on signal processing approaches. BCI can be divided into three main components: signal acquisition, signal processing, and effector device. The signal acquisition component is generally divided into two categories: noninvasive and invasive. For noninvasive, this review focuses on electroencephalogram. For the invasive, the review includes electrocorticography, local field potentials, multiple-unit activity, and single-unit action potentials. Signal processing techniques reviewed are divided into time-frequency methods such as Fourier transform, autoregressive models, wavelets, and Kalman filter and spatiotemporal techniques such as Laplacian filter and common spatial patterns. Additionally, various signal feature classification algorithms are discussed such as linear discriminant analysis, support vector machines, artificial neural networks, and Bayesian classifiers. The article ends with a discussion of challenges facing BCI and concluding remarks on the future of the technology.

Empirical Mode Decomposition vs. Wavelet Decomposition for the Extraction of Respiratory Signal From Single-Channel ECG: A Comparison

Abstract: The respiratory signal can be accurately evaluated by single-channel electrocardiogram (ECG) processing, as shown in recent literature. Indirect methods to derive the respiratory signal from ECG can benefit from a simultaneous study of both respiratory and cardiac activities. These methods lead to major advantages such as low cost, high efficiency, and continuous noninvasive respiratory monitoring. The aim of this paper is to reconstruct the waveform of the respiratory signal by processing single-channel ECG. To achieve these goals, two techniques of decomposition of the ECG signal into suitable bases of functions are proposed, such as the empirical mode decomposition (EMD) and the wavelet analysis. The results highlight the main differences between them in terms of both theoretical foundations, and performance achieved by applying these algorithms to extract the respiratory waveform shape from single-channel ECG are presented. The results also show that both algorithms are able to reconstruct the respiratory waveform, although the EMD is able to break down the original signal without a preselected basis function, as it is necessary for wavelet decomposition. The EMD outperforms the wavelet approach. Some results on experimental data are presented.

Detection of Driver Drowsiness Using Wavelet Analysis of Heart Rate Variability and a Support Vector Machine Classifier

Abstract: Driving while fatigued is just as dangerous as drunk driving and may result in car accidents. Heart rate variability (HRV) analysis has been studied recently for the detection of driver drowsiness. However, the detection reliability has been lower than anticipated, because the HRV signals of drivers were always regarded as stationary signals. The wavelet transform method is a method for analyzing non-stationary signals. The aim of this study is to classify alert and drowsy driving events using the wavelet transform of HRV signals over short time periods and to compare the classification performance of this method with the conventional method that uses fast Fourier transform (FFT)-based features. Based on the standard shortest duration for FFT-based short-term HRV evaluation, the wavelet decomposition is performed on 2-min HRV samples, as well as 1-min and 3-min samples for reference purposes. A receiver operation curve (ROC) analysis and a support vector machine (SVM) classifier are used for feature selection and classification, respectively. The ROC analysis results show that the wavelet-based method performs better than the FFT-based method regardless of the duration of the HRV sample that is used. Finally, based on the real-time requirements for driver drowsiness detection, the SVM classifier is trained using eighty FFT and wavelet-based features that are extracted from 1-min HRV signals from four subjects. The averaged leave-one-out (LOO) classification performance using wavelet-based feature is 95% accuracy, 95% sensitivity, and 95% specificity. This is better than the FFT-based results that have 68.8% accuracy, 62.5% sensitivity, and 75% specificity. In addition, the proposed hardware platform is inexpensive and easy-to-use.