Showing papers on "Wavelet published in 2010"

Dictionaries for Sparse Representation Modeling

Abstract: Sparse and redundant representation modeling of data assumes an ability to describe signals as linear combinations of a few atoms from a pre-specified dictionary. As such, the choice of the dictionary that sparsifies the signals is crucial for the success of this model. In general, the choice of a proper dictionary can be done using one of two ways: i) building a sparsifying dictionary based on a mathematical model of the data, or ii) learning a dictionary to perform best on a training set. In this paper we describe the evolution of these two paradigms. As manifestations of the first approach, we cover topics such as wavelets, wavelet packets, contourlets, and curvelets, all aiming to exploit 1-D and 2-D mathematical models for constructing effective dictionaries for signals and images. Dictionary learning takes a different route, attaching the dictionary to a set of examples it is supposed to serve. From the seminal work of Field and Olshausen, through the MOD, the K-SVD, the Generalized PCA and others, this paper surveys the various options such training has to offer, up to the most recent contributions and structures.

EEG signal classification using PCA, ICA, LDA and support vector machines

Abstract: In this work, we proposed a versatile signal processing and analysis framework for Electroencephalogram (EEG). Within this framework the signals were decomposed into the frequency sub-bands using DWT and a set of statistical features was extracted from the sub-bands to represent the distribution of wavelet coefficients. Principal components analysis (PCA), independent components analysis (ICA) and linear discriminant analysis (LDA) is used to reduce the dimension of data. Then these features were used as an input to a support vector machine (SVM) with two discrete outputs: epileptic seizure or not. The performance of classification process due to different methods is presented and compared to show the excellent of classification process. These findings are presented as an example of a method for training, and testing a seizure prediction method on data from individual petit mal epileptic patients. Given the heterogeneity of epilepsy, it is likely that methods of this type will be required to configure intelligent devices for treating epilepsy to each individual's neurophysiology prior to clinical operation.

A Novel Multiresolution Spatiotemporal Saliency Detection Model and Its Applications in Image and Video Compression

Abstract: Salient areas in natural scenes are generally regarded as areas which the human eye will typically focus on, and finding these areas is the key step in object detection. In computer vision, many models have been proposed to simulate the behavior of eyes such as SaliencyToolBox (STB), Neuromorphic Vision Toolkit (NVT), and others, but they demand high computational cost and computing useful results mostly relies on their choice of parameters. Although some region-based approaches were proposed to reduce the computational complexity of feature maps, these approaches still were not able to work in real time. Recently, a simple and fast approach called spectral residual (SR) was proposed, which uses the SR of the amplitude spectrum to calculate the image's saliency map. However, in our previous work, we pointed out that it is the phase spectrum, not the amplitude spectrum, of an image's Fourier transform that is key to calculating the location of salient areas, and proposed the phase spectrum of Fourier transform (PFT) model. In this paper, we present a quaternion representation of an image which is composed of intensity, color, and motion features. Based on the principle of PFT, a novel multiresolution spatiotemporal saliency detection model called phase spectrum of quaternion Fourier transform (PQFT) is proposed in this paper to calculate the spatiotemporal saliency map of an image by its quaternion representation. Distinct from other models, the added motion dimension allows the phase spectrum to represent spatiotemporal saliency in order to perform attention selection not only for images but also for videos. In addition, the PQFT model can compute the saliency map of an image under various resolutions from coarse to fine. Therefore, the hierarchical selectivity (HS) framework based on the PQFT model is introduced here to construct the tree structure representation of an image. With the help of HS, a model called multiresolution wavelet domain foveation (MWDF) is proposed in this paper to improve coding efficiency in image and video compression. Extensive tests of videos, natural images, and psychological patterns show that the proposed PQFT model is more effective in saliency detection and can predict eye fixations better than other state-of-the-art models in previous literature. Moreover, our model requires low computational cost and, therefore, can work in real time. Additional experiments on image and video compression show that the HS-MWDF model can achieve higher compression rate than the traditional model.

Spectral methods for uncertainty quantification : with applications to computational fluid dynamics

Abstract: Introduction: Uncertainty Quantification and Propagation.- Basic Formulations.- Spectral Expansions.- Non-intrusive Methods.- Galerkin Methods.- Detailed Elementary Applications.- Application to Navier-Stokes Equations.- Advanced topics.- Solvers for Stochastic Galerkin Problems.- Wavelet and Multiresolution Analysis Schemes.- Adaptive Methods.- Epilogue.

Multifocus Image Fusion and Restoration With Sparse Representation

Abstract: To obtain an image with every object in focus, we always need to fuse images taken from the same view point with different focal settings. Multiresolution transforms, such as pyramid decomposition and wavelet, are usually used to solve this problem. In this paper, a sparse representation-based multifocus image fusion method is proposed. In the method, first, the source image is represented with sparse coefficients using an overcomplete dictionary. Second, the coefficients are combined with the choose-max fusion rule. Finally, the fused image is reconstructed from the combined sparse coefficients and the dictionary. Furthermore, the proposed fusion scheme can simultaneously resolve the image restoration and fusion problem by changing the approximate criterion in the sparse representation algorithm. The proposed method is compared with spatial gradient (SG)-, morphological wavelet transform (MWT)-, discrete wavelet transform (DWT)-, stationary wavelet transform (SWT)-, curvelet transform (CVT)-, and nonsubsampling contourlet transform (NSCT)-based methods on several pairs of multifocus images. The experimental results demonstrate that the proposed approach performs better in both subjective and objective qualities.

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.

The Curvelet Transform

Abstract: Multiresolution methods are deeply related to image processing, biological and computer vision, and scientific computing. The curvelet transform is a multiscale directional transform that allows an almost optimal nonadaptive sparse representation of objects with edges. It has generated increasing interest in the community of applied mathematics and signal processing over the years. In this article, we present a review on the curvelet transform, including its history beginning from wavelets, its logical relationship to other multiresolution multidirectional methods like contourlets and shearlets, its basic theory and discrete algorithm. Further, we consider recent applications in image/video processing, seismic exploration, fluid mechanics, simulation of partial different equations, and compressed sensing.

Classification of human emotion from EEG using discrete wavelet transform

Abstract: In this paper, we summarize the human emotion recognition using different set of electroencephalogram (EEG) channels using discrete wavelet transform. An audio-visual induction based protocol has been designed with more dynamic emotional content for inducing discrete emotions (disgust, happy, surprise, fear and neutral). EEG signals are collected using 64 electrodes from 20 subjects and are placed over the entire scalp using International 10-10 system. The raw EEG signals are preprocessed using Surface Laplacian (SL) filtering method and decomposed into three different frequency bands (alpha, beta and gamma) using Discrete Wavelet Transform (DWT). We have used “db4” wavelet function for deriving a set of conventional and modified energy based features from the EEG signals for classifying emotions. Two simple pattern classification methods, K Nearest Neighbor (KNN) and Linear Discriminant Analysis (LDA) methods are used and their performances are compared for emotional states classification. The experimental results indicate that, one of the proposed features (ALREE) gives the maximum average classification rate of 83.26% using KNN and 75.21% using LDA compared to those of conventional features. Finally, we present the average classification rate and subsets of emotions classification rate of these two different classifiers for justifying the performance of our emotion recognition system.

Block Compressed Sensing of Images Using Directional Transforms

Abstract: Recent years have seen significant interest in the paradigm of compressed sensing (CS) which permits, under certain conditions, signals to be sampled at sub-Nyquist rates via linear projection onto a random basis while still enabling exact reconstruction of the original signal. As applied to 2D images, however, CS faces several challenges including a computationally expensive reconstruction process and huge memory required to store the random sampling operator. Recently, several fast algorithms have been developed for CS reconstruction, while the latter challenge was addressed by Gan using a block-based sampling operation as well as projection-based Landweber iterations to accomplish fast CS reconstruction while simultaneously imposing smoothing with the goal of improving the reconstructed-image quality by eliminating blocking artifacts. In this technique, smoothing is achieved by interleaving Wiener filtering with the Landweber iterations, a process facilitated by the relative simple implementation of the Landweber algorithm. In this work, we adopt Gan's basic framework of block-based CS sampling of images coupled with iterative projection-based reconstruction with smoothing. Our contribution lies in that we cast the reconstruction in the domain of recent transforms that feature a highly directional decomposition. These transforms---specifically, contourlets and complex-valued dual-tree wavelets---have shown promise to overcome deficiencies of widely-used wavelet transforms in several application areas. In their application to iterative projection-based CS recovery, we adapt bivariate shrinkage to their directional decomposition structure to provide sparsity-enforcing thresholding, while a Wiener-filter step encourages smoothness of the result. In experimental simulations, we find that the proposed CS reconstruction based on directional transforms outperforms equivalent reconstruction using common wavelet and cosine transforms. Additionally, the proposed technique usually matches or exceeds the quality of total-variation (TV) reconstruction, a popular approach to CS recovery for images whose gradient-based operation also promotes smoothing but runs several orders of magnitude slower than our proposed algorithm.

Short-Term Load Forecasting: Similar Day-Based Wavelet Neural Networks

Abstract: In deregulated electricity markets, short-term load forecasting is important for reliable power system operation, and also significantly affects markets and their participants. Effective forecasting, however, is difficult in view of the complicated effects on load by a variety of factors. This paper presents a similar day-based wavelet neural network method to forecast tomorrow's load. The idea is to select similar day load as the input load based on correlation analysis, and use wavelet decomposition and separate neural networks to capture the features of load at low and high frequencies. Despite of its "noisy" nature, high frequency load is well predicted by including precipitation and high frequency component of similar day load as inputs. Numerical testing shows that this method provides accurate predictions.

Seislet transform and seislet frame

Abstract: We introduce a digital waveletlike transform, which is tailored specifically for representing seismic data. The transform provides a multiscale orthogonal basis with basis functions aligned along seismic events in the input data. It is defined with the help of the wavelet-lifting scheme combined with local plane-wave destruction. In the 1D case, the seislet transform is designed to follow locally sinusoidal components. In the 2D case, it is designed to follow local plane-wave components with smoothly variable slopes. If more than one component is present, the transform turns into an overcomplete representation or a tight frame. In these terms, the classic digital wavelet transform is simply a seislet transform for a zero frequency (in one dimension) or zero slope (in two dimensions). The main objective of the new transform is an effective seismic-data compression for designing efficient data-analysis algorithms. Traditional signal-processing tasks such as noise attenuation and trace interpolation become simply defined in the seislet domain. When applied in the offset direction on common-midpoint or common-image-point gathers, the seislet transform finds an additional application in optimal stacking of seismic records.

Sparse Image and Signal Processing: Wavelets, Curvelets, Morphological Diversity

Abstract: This book presents the state of the art in sparse and multiscale image and signal processing, covering linear multiscale transforms, such as wavelet, ridgelet, or curvelet transforms, and non-linear multiscale transforms based on the median and mathematical morphology operators Recent concepts of sparsity and morphological diversity are described and exploited for various problems such as denoising, inverse problem regularization, sparse signal decomposition, blind source separation, and compressed sensing This book weds theory and practice in examining applications in areas such as astronomy, biology, physics, digital media, and forensics A final chapter explores a paradigm shift in signal processing, showing that previous limits to information sampling and extraction can be overcome in very significant ways Matlab and IDL code accompany these methods and applications to reproduce the experiments and illustrate the reasoning and methodology of the research available for download at the associated Web site

Super-Resolution With Sparse Mixing Estimators

Abstract: We introduce a class of inverse problem estimators computed by mixing adaptively a family of linear estimators corresponding to different priors. Sparse mixing weights are calculated over blocks of coefficients in a frame providing a sparse signal representation. They minimize an l1 norm taking into account the signal regularity in each block. Adaptive directional image interpolations are computed over a wavelet frame with an O(N log N) algorithm, providing state-of-the-art numerical results.

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.

Incipient gear box fault diagnosis using discrete wavelet transform (DWT) for feature extraction and classification using artificial neural network (ANN)

Abstract: An efficient predictive plan is needed for any industry because it can optimize the resources management and improve the economy plant, by reducing unnecessary costs and increasing the level of safety. A great percentage of breakdowns in the productive processes are caused for gear box, they began its deterioration from early stages, also called incipient level. The extracted features from the DWT are used as inputs in a neural network for classification purposes. The results show that the developed method can reliably diagnose different conditions of the gear box. The wavelet transform is used to represent all possible types of transients in vibration signals generated by faults in a gear box. It is shown that the transform provides a powerful tool for condition monitoring and fault diagnosis. The vibration signal of a spur bevel gear box in different conditions is used to demonstrate the application of various wavelets in feature extraction. In this paper fault diagnostics of spur bevel gear box is treated as a pattern classification problem. The major steps in pattern classification are feature extraction, and classification. This paper investigates the use of discrete wavelets for feature extraction and artificial neural network for classification.

An intelligent background-correction algorithm for highly fluorescent samples in Raman spectroscopy

Abstract: Fluorescent background is a major problem in recoding the Raman spectra of many samples, which swamps or obscures the Raman signals. The background should be suppressed in order to perform further qualitative or quantitative analysis of the spectra. For this purpose, an intelligent background-correction algorithm is developed, which simulates manual background-correction procedure intelligently. It basically consists of three aspects: (1) accurate peak position detection in the Raman spectrum by continuous wavelet transform (CWT) with the Mexican Hat wavelet as the mother wavelet; (2) peak-width estimation by signal-to-noise ratio (SNR) enhancing derivative calculation based on CWT but with the Haar wavelet as the mother wavelet; and (3) background fitting using penalized least squares with binary masks. This algorithm does not require any preprocessing step for transforming the spectrum into the wavelet space and can suppress the fluorescent background of Raman spectra intelligently and validly. The algorithm is implemented in R language and available as open source software (http://code.google.com/p/baselinewavelet). Copyright © 2009 John Wiley & Sons, Ltd.

Wavelet Methods in Computational Fluid Dynamics

Abstract: This article reviews state-of-the-art adaptive, multiresolution wavelet methodologies for modeling and simulation of turbulent flows with various examples. Different numerical methods for solving the Navier-Stokes equations in adaptive wavelet bases are described. We summarize coherent vortex extraction methodologies, which utilize the efficient wavelet decomposition of turbulent flows into space-scale contributions, and present a hierarchy of wavelet-based turbulence models. Perspectives for modeling and computing industrially relevant flows are also given.

Application of mother wavelet functions for automatic gear and bearing fault diagnosis

Abstract: This paper introduces an automatic feature extraction system for gear and bearing fault diagnosis using wavelet-based signal processing. Vibration signals recorded from two experimental set-ups were processed for gears and bearing conditions. Four statistical features were selected: standard deviation, variance, kurtosis, and fourth central moment of continuous wavelet coefficients of synchronized vibration signals (CWC-SVS). In this research, the mother wavelet selection is broadly discussed. 324 mother wavelet candidates were studied, and results show that Daubechies 44 (db44) has the most similar shape across both gear and bearing vibration signals. Next, an automatic feature extraction algorithm is introduced for gear and bearing defects. It also shows that the fourth central moment of CWC-SVS is a proper feature for both bearing and gear failure diagnosis. Standard deviation and variance of CWC-SVS demonstrated more appropriate outcome for bearings than gears. Kurtosis of CWC-SVS illustrated the acceptable performance for gears only. Results also show that although db44 is the most similar mother wavelet function across the vibration signals, it is not the proper function for all wavelet-based processing.

Multiscale Wavelets on Trees, Graphs and High Dimensional Data: Theory and Applications to Semi Supervised Learning

Abstract: Harmonic analysis, and in particular the relation between function smoothness and approximate sparsity of its wavelet coefficients, has played a key role in signal processing and statistical inference for low dimensional data. In contrast, harmonic analysis has thus far had little impact in modern problems involving high dimensional data, or data encoded as graphs or networks. The main contribution of this paper is the development of a harmonic analysis approach, including both learning algorithms and supporting theory, applicable to these more general settings. Given data (be it high dimensional, graph or network) that is represented by one or more hierarchical trees, we first construct multi-scale wavelet-like orthonormal bases on it. Second, we prove that in analogy to the Euclidean case, function smoothness with respect to a specific metric induced by the tree is equivalent to exponential rate of coefficient decay, that is, to approximate sparsity. These results readily translate to simple practical algorithms for various learning tasks. We present an application to transductive semi-supervised learning.

Compressive imaging using approximate message passing and a Markov-tree prior

Abstract: We propose a novel algorithm for compressive imaging that exploits both the sparsity and persistence across scales found in the 2D wavelet transform coefficients of natural images. Like other recent works, we model wavelet structure using a hidden Markov tree (HMT) but, unlike other works, ours is based on loopy belief propagation (LBP). For LBP, we adopt a recently proposed “turbo” message passing schedule that alternates between exploitation of HMT structure and exploitation of compressive-measurement structure. For the latter, we leverage Donoho, Maleki, and Montanari's recently proposed approximate message passing (AMP) algorithm. Experiments with a large image database suggest that, relative to existing schemes, our turbo LBP approach yields state-of-the-art reconstruction performance with substantial reduction in complexity.

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.

Image Super Resolution Based on Interpolation of Wavelet Domain High Frequency Subbands and the Spatial Domain Input Image

Abstract: In this paper, we propose a new super-resolution technique based on interpolation of the high-frequency subband images obtained by discrete wavelet transform (DWT) and the input image. The proposed technique uses DWT to decompose an image into different subband images. Then the high-frequency subband images and the input low-resolution image have been interpolated, followed by combining all these images to generate a new super-resolved image by using inverse DWT. The proposed technique has been tested on Lena, Elaine, Pepper, and Baboon. The quantitative peak signal-to-noise ratio (PSNR) and visual results show the superiority of the proposed technique over the conventional and state-of-art image resolution enhancement techniques. For Lena's image, the PSNR is 7.93 dB higher than the bicubic interpolation.