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In this paper, image fusion method based on a new class of wavelet — non-separable wavelet with compactly supported, linear phase, orthogonal and dilation matrix [formula] is presented. We first construct a non-separable wavelet filter bank. Using these filters, the images involved are decomposed into wavelet pyramids. Then the following fusion algorithm was proposed: for low-frequency part, the average value is selected for new pixel value, For the three high-frequency parts of each level, the standard deviation of each image patch over 3×3 window in the high-frequency sub-images is computed as activity measurement. If the standard deviation of the area 3×3 window is bigger than the standard deviation of the corresponding 3×3 window in the other high-frequency sub-image. The center pixel values of the area window that the weighted area energy is bigger are selected. Otherwise the weighted value of the pixel is computed. Then a new fused image is reconstructed. The performance of the method is evaluated using the entropy, cross-entropy, fusion symmetry, root mean square error and peak-to-peak signal-to-noise ratio. The experiment results show that the non-separable wavelet fusion method proposed in this paper is very close to the performance of the Haar separable wavelet fusion method. [ABSTRACT FROM AUTHOR]

Time series change point detection can identify the locations of abrupt points in many dynamic processes. It can help us to find anomaly data in an early stage. At the same time, detecting change points for long, periodic, and multiple input series data has received a lot of attention recently, and is universally applicable in many fields including power, environment, finance, and medicine. However, the performance of classical methods typically scales poorly for such time series. In this paper, we propose CPMAN, a novel prediction-based change point detection approach via multi-stage attention networks. Our model consists of two key modules. First, in the time series prediction module, we employ the multi-stage attention-based networks and integrate the multi-series fusion mechanism. This module can adaptively extract features from the relevant input series and capture the long-term temporal dependencies. Secondly, in the change point detection module, we use the wavelet analysis-based algorithm to detect change points efficiently and identify the change points and outliers. Extensive experiments are conducted on various real-world datasets and synthetic datasets, proving the superiority and effectiveness of CPMAN. Our approach outperforms the state-of-the-art methods by up to 12.1% on the F1 Score. [ABSTRACT FROM AUTHOR]

Trajectory representation model has been proposed to describe non-rigid deformation. An optimal trajectory space finding algorithm for 3D non-rigid structure from motion (OTSF-NRSFM) based on this model also has been proposed. However, the influence of the wavelet basis selection on the OTSF-NRSFM algorithm has still not been studied. To help OTSF-NRSFM researchers select wavelet basis properly, we investigated the influences of wavelet basis selection. Two typical wavelet bases, DCT basis and WHT basis, are discussed in this paper. The spectrum properties of wavelet basis and feature point trajectory, trajectory representation results on synthetic shark data, OTSF-NRSFM reconstruction results on synthetic data and real data are analyzed. The results show that the wavelet selection has much influence on OTSF-NRSFM reconstruction results of some non-rigid feature points, which have complicated trajectory. This paper gives researchers some inspiration about wavelet basis selection in OTSF-NRSFM algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we develop a new constrained artificial-neural-network (ANN) formulation and the associated learning algorithm for predicting stock prices, a difficult time-series prediction problem. We characterize daily stock prices as a noisy non-stationary time series and identify its predictable low-frequency components. Using a recurrent finite-impulse-response ANN, we formulate the learning problem as a constrained optimization problem, develop constraints for incorporating cross validations, and solve the learning problem using algorithms based on the theory of extended saddle points for nonlinear constrained optimization. Finally, we illustrate our prediction results on ten stock-price time series. Our main contributions in this paper are the channel-specific low-pass filtering of noisy time series obtained by wavelet decomposition, the transformation of the low-pass signals to improve their stationarity, and the incorporation of constraints on cross validation that can improve the accuracy of predictions. Our experimental results demonstrate good prediction accuracy and annual returns. [ABSTRACT FROM AUTHOR]

This paper presents a wavelet-based computationally efficient implementation of the Linear Minimum Mean Square Error (LMMSE) algorithm in image super-resolution. The image super-resolution reconstruction problem is well-known to be an ill-posed inverse problem of large dimensions. The LMMSE estimator to be implemented in the image super-resolution reconstruction problem requires an inversion of a very large dimension matrix, which is practically impossible. Our suggested implementation is based on breaking the problem into four consecutive steps, a registration step, a multi-channel LMMSE restoration step, a wavelet-based image fusion step and an LMMSE image interpolation step. The objective of the wavelet fusion step is to integrate the data obtained from each observation into a single image, which is then interpolated to give a high-resolution image. The paper explains the implementation of each step. The proposed implementation has succeeded in obtaining a high-resolution image from multiple degraded observations with a high PSNR. The computation time of the suggested implementation is small when compared to traditional iterative image super-resolution algorithms. [ABSTRACT FROM AUTHOR]

A constructive algorithm based on the theory of spectral pairs for constructing nonuniform wavelet basis in was considered by Gabardo and Nashed [Nonuniform multiresolution analysis and spectral pairs, J. Funct. Anal. 158 (1998) 209-241]. In this setting, the associated translation set is a spectrum which is not necessarily a group nor a uniform discrete set, given where (an integer) and is an odd integer with such that and are relatively prime and is the set of all integers. The objective of this paper is to construct nonuniform wavelet frame on local fields. A necessary condition and four sufficient conditions for nonuniform wavelet frame on local fields are given. [ABSTRACT FROM AUTHOR]

This paper presents a new approach of face recognition based on wavelet network using 2D fast wavelet transform and multiresolution analysis. This approach is divided in two stages: the training stage and the recognition stage. The first consists to approximate every training face image by a wavelet network. The second consists in recognition of a new test image by comparing it to all the training faces, the distances between this test face and all images from the training set are calculated in order to identify the searched person. The usual training algorithms presents some disadvantages when the weights of the wavelet network are computed by applying the back-propagation algorithm or by direct solution which requires computing an inversion of matrix, this computation may be intensive when the learning data is too large. We present in this paper our solutions to overcome these limitations. We propose a novel learning algorithm based on the 2D Fast Wavelet Transform. Furthermore, we have increased the performances of our algorithm by introducing the Levenberg-Marquardt method to optimize the learning functions and using the Beta wavelet which has at both an analytical expression and wavelet filter bank. Extensive empirical experiments are performed to compare the proposed method with other approaches as PCA, LDA, EBGM and RBF neural network using the ORL and FERET benchmarks. [ABSTRACT FROM AUTHOR]

This paper investigates the scope of wavelets for performance improvement in spread spectrum image watermarking. Performance of a digital image watermarking algorithm, in general, is determined by the visual invisibility of the hidden data (imperceptibility), reliability in the detection of the hidden information after various common and deliberate signal processing operations (robustness) applied on the watermarked signals and the amount of data to be hidden (payload) without affecting the imperceptibility and robustness properties. In this paper, we propose a few spread spectrum (SS) image watermarking schemes using discrete wavelet transform (DWT), biorthogonal DWT and M-band wavelets coupled with various modulation, multiplexing and signaling techniques. The performance of the watermarking methods are also reported along with the relative merits and demerits. [ABSTRACT FROM AUTHOR]

In this paper, we examine the wavelet characterization of Hardy space H1, and show that the H1-norm is a good choice for modelizing the oscillating patterns. Furthermore, we give the discrete representation of H1-norm by using wavelet coefficients, and apply it to the variational image decomposition models. Finally, we give the iterative algorithm, and present various numerical results on images to demonstrate the potential of our methods. [ABSTRACT FROM AUTHOR]

In this paper a novel color image segmentation algorithm based on homogeneity histogram is proposed. The proposed approach uses intermediate features of maximum overlap wavelet transform (IMOWT). The IMOWT, which is the efficient transform, has been applied to color image segmentation for its time effectiveness, flexibility and translation invariance which are required for good segmentation results. The set of transform coefficients derived from wavelet domain are subjected to an efficient peak finding algorithm (PFA). PFA is employed to identify the most significant peaks of the homogeneity histogram. While we process the homogeneity histogram, both local and global information are taken into account. This is particularly helpful in taking care of small objects and local variations of the image. This method provides better segmentation results when compared to the direct application of PFA and Mean shift algorithm. [ABSTRACT FROM AUTHOR]

In recent years, image coding based on wavelet transform has made rapid progress. In this paper, quincunx lifting scheme in wavelet transform is introduced and all phase interpolation filter banks which can be used in the lifting scheme for prediction and update are designed. Based on the basic idea of set partitioning in hierarchical trees (SPIHT) algorithm, the binary tree image coding algorithm is proposed. Just like SPIHT, the encoding algorithms can be stopped at any compressed file size or let run until the compressed file is a representation of a nearly lossless image. The experimental results on test images show that compared with SPIHT algorithm, the PSNRs of the proposed algorithm are superior by about 0.5 dB at the same bit rates and the subjective quality of reconstructed images is also better. [ABSTRACT FROM AUTHOR]

While in the process of decomposition of the Mallat discrete wavelet transform (DWT) fast algorithm, the algorithm has a drawback, that is, there is frequency distortion in the high frequency subband. In this paper, a new algorithm of decomposition and reconstruction in the discrete wavelet is presented. The algorithm can solve the frequency distortion in the high frequency subband in the process of decimation in each level. The simulation of numerical value example tests the validity of the algorithm. [ABSTRACT FROM AUTHOR]

In Global Positioning System (GPS), receivers use FFT-based convolvers to acquire the signals. This paper shows a robust substitute algorithm for calculating the convolution that is less sensitive to additive noise. [ABSTRACT FROM AUTHOR]

This paper proposes two techniques for the enhancement of the performance of the Linear Minimum Mean Square Error (LMMSE) or Wiener restoration algorithm. The first approach relies on adaptively merging the Wiener restoration algorithm with a regularized restoration algorithm that is implemented iteratively. The merging process allows the capturing of edges regions from the Wiener restoration result and the capturing of flat areas from the regularized restoration result. The second approach is a smoothing technique to reduce noise in flat areas in the restored images. The decision that is used for selecting the regions in the restored image, in which either the regularization or the smoothing algorithm can be used, is dependent on the 2D Haar wavelet transform. [ABSTRACT FROM AUTHOR]

A multiresolution analysis (MRA) on local fields of positive characteristic was defined by Shah and Abdullah for which the translation set is a discrete set which is not a group. In this paper, we continue the study based on this nonstandard setting and introduce vector-valued nonuniform multiresolution analysis (VNUMRA) where the associated subspace V0 of L2(K, ℂM) has an orthonormal basis of the form {Φ (x - λ)}λ∈Λ where Λ = {0, r/N} + 풵, N ≥ 1 is an integer and r is an odd integer such that r and N are relatively prime and 풵 = {u(n) : n ∈ ℕ0}. We establish a necessary and sufficient condition for the existence of associated wavelets and derive an algorithm for the construction of VNUMRA on local fields starting from a vector refinement mask G(ξ) with appropriate conditions. Further, these results also hold for Cantor and Vilenkin groups. [ABSTRACT FROM AUTHOR]

In real time surveillance video applications, it is often required to identify a region of interest in a degraded low resolution (LR) image. State-of-the-art super-resolution (SR) techniques produce images with poor illumination and degraded high frequency details. In this paper, we present a different approach for SISR by correcting the dual-tree complex wavelet transform (DT-CWT) subbands using the multi-stage cascaded joint bilateral filter (MSCJBF) and singular value decomposition (SVD). The proposed method exploits geometric regularity for implementing the covariance-based interpolation in the spatial domain. We decompose the interpolated LR image into different image and wavelet coefficients by employing DT-CWT. To preserve edges, we alter the wavelet sub-bands with the high frequency details obtained from the MSCJBF. Simultaneously, we retain uniform illumination by improving the image coefficients using SVD. In addition, the wavelet sub-bands undergo lanczos interpolation prior to the subband refinement. Experimental results demonstrate the effectiveness of our method. [ABSTRACT FROM AUTHOR]

In this paper, an efficient multi-scale image disparity estimation algorithm is proposed which estimates the local displacements needed to align different regions between a pair of images. This phase-based approach is based on fractional dual-tree complex wavelet transform (FrDTCWT). In the proposed FrDTCWT, initially we obtained the fractional Fourier transform of the image. We decomposed the fractional transformed image by dual-tree complex wavelet transform into real and imaginary parts. The complex analytic signal is obtained from the real-valued function which is obtained from this FrDTCWT. The FRDTCWT inherits the excellent mathematical properties of DTCWT and FrFT. Phase and amplitude of the image are computed from the complex analytic signal. The disparity is estimated as the optical flow using the phase difference method. The efficiency of the proposed algorithm is carried out by different experiments on synthetic as well as on realistic image sequences. [ABSTRACT FROM AUTHOR]

In this paper, an orthogonal wavelet transform of signal based on complex B-spline bases is given. The new wavelet transform realizes accurate computation of coefficients of complex B-spline base functions. It integrates good properties of orthogonality, symmetry and continuity, and offers better approximations to continuous signal than do the Haar wavelet and Daubechies wavelets. All algorithms of the new orthogonal wavelet transform are based on explicit formulas and easy to be implemented. [ABSTRACT FROM AUTHOR]

In this paper, orthogonal multiwavelets on interval [0, 1] with arbitrary compact support γ and integer dilation factor a are studied. Firstly, the concept of multiwavelets on the interval [0, 1] is generalized to the arbitrary integer dilation factor a, a ≥ 2, a ∈ ℤ, and an algorithm for constructing orthogonal multiscaling function and multiwavelets on interval [0, 1] with dilation factor a is presented. Secondly, the decomposition and reconstruction formulas of multiwavelets on interval [0, 1] are deduced. Finally, the "balancing" concept of multiwavelets on the interval [0, 1] with dilation factor a is defined, and the algorithm of balancing the unbalanced multiwavelets on the interval [0, 1] is also given. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel approach to frequency segmentation using wavelet decomposition of pseudo-motion image. In this way, a fixed image is translated such that a sequence of moving images is produced, which are called the 0 pseudo-motion images. In fact, we can consider the translation of a function to be a motion of eyeshot. When a function is translated, its wavelet coefficients will oscillate. From this property, we can detect the special areas of the image. Some experiments were conducted, which are used to find the position of license plates of vehicles in digital images. The experimental results demonstrate the performance of the method. [ABSTRACT FROM AUTHOR]

In this paper, we present an efficient biorthogonal wavelet construction for the ternary Loop subdivision based on the lifting scheme, and give the corresponding decomposition and reconstruction formulas. We apply the proposed algorithm to the progressive transmission and the denoising of 3D graphics, and show its sufficient stability and good performance by some numerical experiments. Since the usual input mesh does not possess the property of subdivision connectivity, while the multiresolution analysis based on subdivision surface requires the processed initial mesh to be semi-regular, we further propose a new rapid algorithm of constructing the initial mesh which not only possesses ternary subdivision connectivity but also approximates the given input mesh. [ABSTRACT FROM AUTHOR]

Currently, two-dimensional dyadic wavelet transform (2D-DWT) is habitually considered as the one presented by Mallat, which is defined by an approximation component, two detail components in horizontal and vertical directions. This paper is to introduce a new type of two-dimensional dyadic wavelet transform and its application so that dyadic wavelet can be studied and used widely furthermore. (1) Two-dimensional stationary dyadic wavelet transform (2D-SDWT) is proposed, it is defined by approximation coefficients, detail coefficients in horizontal, vertical and diagonal directions, which is essentially the extension of two-dimensional stationary wavelet transform for orthogonal/biorthogonal wavelet filters. (2) ε-decimated dyadic discrete wavelet transform (DDWT) is introduced and its relation with 2D-SDWT is given, where ε is a sequence of 0's and 1's. (3) Mallat decomposition algorithm based on dyadic wavelet is introduced as a special case of ε-decimated DDWT, and so a face recognition algorithm based on dyadic wavelet is proposed, and experimental results are given to show its effectiveness. [ABSTRACT FROM AUTHOR]

In this paper, we describe an algorithm for computing biorthogonal compactly supported dyadic wavelets related to the Walsh functions on the positive half-line ℝ+. It is noted that a similar technique can be applied in very general situations, e.g., in the case of Cantor and Vilenkin groups. Using the feedback-based approach, some numerical experiments comparing orthogonal and biorthogonal dyadic wavelets with the Haar, Daubechies, and biorthogonal 9/7 wavelets are prepared. [ABSTRACT FROM AUTHOR]

Taking advantage of both the scaling property of wavelets and the high learning ability of neural networks, wavelet networks have recently emerged as a powerful tool in many applications in the field of signal processing such as data compression, function approximation as well as image recognition and classification. A novel wavelet network-based method for image classification is presented in this paper. The method combines the Orthogonal Least Squares algorithm (OLS) with the Pyramidal Beta Wavelet Network architecture (PBWN). First, the structure of the Pyramidal Beta Wavelet Network is proposed and the OLS method is used to design it by presetting the widths of the hidden units in PBWN. Then, to enhance the performance of the obtained PBWN, a novel learning algorithm based on orthogonal least squares and frames theory is proposed, in which we use OLS to select the hidden nodes. In the simulation part, the proposed method is employed to classify colour images. Comparisons with some typical wavelet networks are presented and discussed. Simulations also show that the PBWN-orthogonal least squares (PBWN-OLS) algorithm, which combines PBWN with the OLS algorithm, results in better performance for colour image classification. [ABSTRACT FROM AUTHOR]

This paper presents a study on wavelets and their characteristics for the specific purpose of serving as a feature extraction tool for speaker verification (SV), considering a Radial Basis Function (RBF) classifier, which is a particular type of Artificial Neural Network (ANN). Examining characteristics such as support-size, frequency and phase responses, amongst others, we show how Discrete Wavelet Transforms (DWTs), particularly the ones which derive from Finite Impulse Response (FIR) filters, can be used to extract important features from a speech signal which are useful for SV. Lastly, an SV algorithm based on the concepts presented is described. [ABSTRACT FROM AUTHOR]

Rate control plays an essential role in video coding and transmission to provide the best video quality at the receiver's end given the constraint of certain network conditions. In this paper, a rate control algorithm using the Quality Factor (QF) optimization method is proposed for the wavelet-based video codec and implemented on an open source Dirac video encoder. A mathematical model which we call Rate-QF (R - QF) model is derived to generate the optimum QF for the current coding frame according to the target bitrate. The proposed algorithm is a complete one pass process and does not require complex mathematical calculation. The process of calculating the QF is quite simple and further calculation is not required for each coded frame. The experimental results show that the proposed algorithm can control the bitrate precisely (within 1% of target bitrate in average). Moreover, the variation of bitrate over each Group of Pictures (GOPs) is lower than that of H.264. This is an advantage in preventing the buffer overflow and underflow for real-time multimedia data streaming. [ABSTRACT FROM AUTHOR]

Linear Discriminant Analysis (LDA) is a popular statistical method for both feature extraction and dimensionality reduction in face recognition. The major drawback of LDA is the so-called small sample size (3S) problem. This problem always occurs when the total number of training samples is smaller than the dimension of feature space. Under this situation, the within-class scatter matrix Sw becomes singular and LDA approach cannot be implemented directly. To overcome the 3S problem, this paper proposes a novel wavelet-face based subspace LDA algorithm. Wavelet-face feature extraction and dimensionality reduction are based on two-level D4-filter wavelet transform and discarding the null space of total class scatter matrix St. It is shown that our obtained projection matrix satisfies the uncorrelated constraint conditions. Hence in the sense of statistical uncorrelation, this projection matrix is optimal. The proposed method for face recognition has been evaluated with two public available databases, namely ORL and FERET databases. Comparing with existing LDA-based methods to solve the 3S problem, our method gives the best performance. [ABSTRACT FROM AUTHOR]

In recent years, significant advances in vibration control of structures have been achieved due greatly to the emergent technologies based on smart materials, such as mangnetorheological (MR) fluids. This paper develops a computational algorithm for the modeling and identification of the MR dampers by using wavelet systems to handle the nonlinear terms. By taking into account the Haar wavelets, the properties of integral operational matrix and of product operational matrix are introduced and utilized to find an algebraic representation form instead of the differential equations of the dynamical system. It is shown that MR damper parameters can be estimated easily by considering only the algebraic equations obtained. [ABSTRACT FROM AUTHOR]

In this paper, an algorithm for constructing a class of orthogonal two-direction refinable functions and the corresponding orthogonal two-direction wavelets is obtained. In addition, the relation of both two-direction refinable functions and multiwavelets is discussed. We discover that Chui–Lian's orthogonal symmetric/antisymmetric multiscaling functions and the corresponding multiwavelets can be recovered by using an orthogonal two-direction refinable function and the corresponding two-direction wavelets, respectively. Finally, some construction examples are given. [ABSTRACT FROM AUTHOR]

Recently, several wavelet-based algorithms have been proposed for feature extraction in non-stationary signals such as ECG. These methods, however, have mainly used general purpose (unmatched) wavelet bases such as Daubechies and Quadratic Spline. In this paper, five new matched wavelet bases, with minimum approximation error and maximum coding gain criteria, are designed and applied to ECG signal analysis. To study the effect of using different wavelet bases for this application, two different wavelet-based R peak detection algorithms are implemented: (1) a conventional wavelet-based method; and (2) a modified wavelet-based R peak detection algorithm. Both algorithms are evaluated using the MIT-BIH Arrhythmia database. Experimental results show lower computational complexity (up to 76%) of the proposed R peak detection method compared to the conventional method. They also show considerable decrease in the number of failed detections (up to 55%) for both the conventional and the proposed algorithms when using matched wavelets instead of Quadratic Spline wavelet which, according to the literature, has generated the best detection results among all conventional wavelet bases studied previously for ECG signal analysis. [ABSTRACT FROM AUTHOR]

A new method by combining wavelet packet transform with kernel learning algorithms is proposed to estimate the mental fatigue state in this paper. The first step of this method is to investigate the impact of long term mental arithmetic task on psychology and physiology of subjects by subjective self-reporting measures, action performance test, power spectral indices of HRV and wavelet packet parameters of EEG. The second step is to calculate the wavelet packet features of all EEG data segments, including relative wavelet packet energy parameters in four frequency bands, wavelet packet entropy and three ratio indices. Finally, kernel principal component analysis (KPCA) and support vector machine (SVM) are jointly applied to differentiate two mental fatigue states. The investigation suggests that the joint KPCA-SVM method is able to effectively reduce the dimensionality of the feature vectors, speed up the convergence in the training of SVM and achieve higher classification accuracy (88%) of the mental fatigue state. Hence KPCA-SVM could be a promising model for the estimation of mental fatigue. [ABSTRACT FROM AUTHOR]

Stationary wavelet transform is an efficient algorithm for remote sensing image fusion. In this paper, we investigate the effects of orthogonal/biorthogonal filters and decomposition depth on using stationary wavelet analysis for fusion. Spectral discrepancy and spatial distortion are used as quality measures. Empirical results lead to some recommendations on the wavelet filter parameters for use in remote sensing image fusion applications. [ABSTRACT FROM AUTHOR]

Cascade algorithms play an important role in wavelet analysis and computer graphics. The paper considers the convergence of cascade algorithms in Sobolev spaces. With the help of the factorization of matrix masks, we give a sufficient condition for the convergence. The condition is expressed in the time domain. More importantly, an algorithm for the construction of convergent cascade algorithms in Sobolev space starting from any matrix mask satisfying a mild condition is presented. Examples are given to illustrate our theorems. [ABSTRACT FROM AUTHOR]

Multivariate wavelets analysis is a powerful tool for multi-dimensional signal processing, but tensor product wavelets have a number of drawbacks. In this paper, we give an algorithm of parametric representation compactly supported trivariate orthogonal wavelet filter, which simplifies the study of trivariate orthogonal wavelet. Four examples are also given to demonstrate the method. [ABSTRACT FROM AUTHOR]

Structure distortion evaluation allows us to directly measure the similarity between signature patterns without classification using feature vectors, which usually suffers from limited training samples. In this paper, we incorporate the merits of both global and local alignment algorithms to define structure distortion using signature skeletons identified by a robust wavelet thinning technique. A weak affine model is employed to globally register two signature skeletons and structure distortion between two signature patterns, which are determined by applying an elastic local alignment algorithm. Similarity measurement is evaluated in the form of Euclidean distance of all found corresponding feature points. Experimental results showed that the proposed similarity measurement was able to provide sufficient discriminatory information in terms of equal error rate being 18.6% with four training samples. [ABSTRACT FROM AUTHOR]

A new algorithm for modeling of chaotic systems is presented in this paper. First, more information is acquired utilizing the reconstructed embedding phase space, and the multiwavelets transform provides a sensible decomposition of the data so that the underlying temporal structures of the original time series become more tractable. Second, based on the Recurrent Least Squares Support Vector Machines (RLS-SVM), modeling of the chaotic system is realized. To demonstrate the effectiveness of our algorithm, we use the power spectrum and dynamic invariants involving the Lyapunov exponents and the correlation dimension as criterions, and then apply our method to Chua's circuit time series. The similarity of dynamic invariants between the original and generated time series shows that the proposed method can capture the dynamics of the chaotic time series more effectively. [ABSTRACT FROM AUTHOR]

This paper presents a new reference trajectory and a fuzzy wavelet neural network controller to synthesize the gait of a five-link biped robot when walking on the level ground. Both the single support phase (SSP) and the double support phase (DSP) are considered. The gait of the biped can be determined when the trajectories of the hip and the swing limb are designed. The trajectories of the hip and the swing limb are approximated with the time polynomial functions. The coefficients of the functions are determined by the constraint equations cast in terms of coherent physical characteristics, such as repeatability, continuity, stability, and minimization of the effect of impact. The fuzzy wavelet neural network controller is trained by error back-propagation algorithm. Given the certain gait parameters such as the step length, maximum step height, walking speed, and so on, the control scheme can generate the smooth gait profiles. The simulation results show that the designed controller can follow the reference trajectories well. [ABSTRACT FROM AUTHOR]

As we know, a polarimetric whitening filter can efficiently reduce speckle under the circumstances of keeping the same resolution, but it is not self-adaptive. Although it can be transformed to be self-adaptive by adding a window, the blur is serious on the heterogeneous areas or brightness. In this paper, we present a new algorithm. First, fully polarimetric measurements (HH, HV, VV) are processed by polarimetric whitening filters (PWF) method. Second, the PWF result is de-noised by stationary wavelet transform thresholding. Experimental result shows that this method not only suppresses the speckle noise effectively, but also preserves as many target characteristics of original images as possible. The final visual effect of the recovery SAR image is satisfying. [ABSTRACT FROM AUTHOR]

An essential step in character recognition is to extract the skeleton characteristics of the character. In this paper, an efficient algorithm is proposed to extract visually satisfactory skeleton from printed and handwritten characters, which overcomes fundamental shortcomings of our previous skeletonization technique based on the maximum modulus symmetry of wavelet transform (WT). The proposed method is motivated from some desirable properties of the WT with constructed wavelet functions: namely, the local modulus minima of the WT are scale-independent at different level scales and are located at the medial axis of the symmetrical contours of character stroke. Thus the modulus minima of the WT are computed as the intrinsic skeletons of character strokes. To achieve faster implementation, a multiscale processing technique is employed. Thus major structures of the skeleton are extracted using the coarse scale, while fine structures are extracted using the fine scale. We have tested the algorithm on handwritten and printed character images. Experimental results show that the proposed algorithm is applicable to not only binary image but also gray-level image where it can be impractical to use other skeletonization techniques, such as thinning and distance transforms. Further, it can effectively remove unwanted artifacts and branches from the extracted skeletons at the intersections and junctions of character strokes and is robust against noises while most existing methods perform poorly. [ABSTRACT FROM AUTHOR]

A comparison between polynomial and wavelet expansions for the identification of coupled map lattice (CML) models for deterministic spatiotemporal dynamical systems is presented in this paper. The pattern dynamics generated by smooth and nonsmooth nonlinear maps in a well-known two-dimensional CML structure are analyzed. By using an orthogonal feedforward regression algorithm (OFR), polynomial and wavelet models are identified for the CML's in chaotic regimes. The quantitative dynamical invariants such as the largest Lyapunov exponents and correlation dimensions are estimated and used to evaluate the performance of the identified models. [ABSTRACT FROM AUTHOR]

As a global feature of fingerprints, the thinning of ridges, extraction of minutiae and computation of orientation field are very important for automatic fingerprint recognition. Many algorithms have been proposed for their computation and estimation, but their results are unsatisfactory, especially for poor quality fingerprint images. In this paper, a robust wavelet-based method to create thinned ridge map of fingerprint for automatic recognition is proposed. Properties of modulus minima based on the spline wavelet function are substantially investigated. Desirable characteristics show that this method is suitable to describe the skeleton of the ridge of the fingerprint image. A multi-scale thinning algorithm based on the modulus minima of wavelet transform is presented. The proposed algorithm is able to improve the skeleton representation of the ridge of the fingerprint without side-effects and limitations of the existing methods. The thinned ridge map can facilitate the extraction of the minutiae for matching in fingerprint recognition. Experiments have been conducted to validate the effectiveness and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

This paper presents an implementation of a wavelet analysis toolbox and its integration within Excel. The toolbox includes the discrete wavelet transform, inverse wavelet transform, wavelet-based de-noising, and an associated plotting utility. The transforms and the de-noising algorithms were implemented in a DLL using C++ while the user interfaces were developed using Visual Basic for Applications (VBA) forms. A simple technique was used to automate the transfer of data, associated properties, and user selections from the worksheet to the DLL, and the computed values from the DLL back to the worksheet. We show how the grouping and presentation of computed wavelet coefficients allow for multiresolution analysis and further processing within Excel. We highlight the benefits behind implementing the basic wavelet analysis functions in Excel with reference to MATLAB. [ABSTRACT FROM AUTHOR]

In stereo research the construction of a dense disparity map is a complicated task when the scene contains a lot of occlusions. In this case in the neighborhood of occlusions, we could consider that the images have a non-stationary behavior. In this paper we propose a new method for computing a dense disparity map using the decomposition of the 2D wavelet transform in four quarters allowing us to find a corresponding pixel in the case of occlusion as well. Our algorithm constructs in each pixel of two images four estimators corresponding to each quarter. The matching of the four wavelet coefficient estimators in the right image with the other four in the left image allow us to construct a dense map disparity map in each pixel of an image. [ABSTRACT FROM AUTHOR]

Two-Dimensional Wavelet Transforms have proven to be highly effective tools for image analysis. In this paper, we present a VLSI implementation of four- and six-coefficient Daubechies Wavelet Transforms using an algebraic integer encoding representation for the coefficients. The Daubechies filters (DAUB4 and DAUB6) provide excellent spatial and spectral locality, properties which make it useful in image compression. In our algorithm, the algebraic integer representation of the wavelet coefficients provides error-free calculations until the final reconstruction step. This also makes the VLSI architecture simple, multiplication-free and inherently parallel. Compared to other DWT algorithms found in the literature, such as embedded zero-tree, recursive or semi-recursive, linear systolic arrays and conventional fixed-point binary architectures, it has reduced hardware cost, lower power dissipation and optimized data-bus utilization. The architecture is also cascadable for computation of one- or multi-dimensional Daubechies Discrete Wavelet Transforms. [ABSTRACT FROM AUTHOR]

Spectroface is a face representation method using wavelet transform and Fourier transform and has been proved to be invariant to translation, on-the-plane rotation and scale. Two types of spectrofaces, namely first order and second order spectrofaces, have been proposed and successfully applied for face recognition. This paper reports a generalized spectroface, in which, we prove that any continuous and compact supported low-pass filters can be used to replace the wavelet transform. This feature provides a high flexibility of the spectroface representation. It is also proved that the generalized spectroface is translation invariant. A simple but effective feature selection algorithm is also proposed for the generalized spectroface in which the recognition is further increased. Three standard databases from Yale University, Olivette Research Laboratory and MIT, are used to evaluate the proposed method. The recognition accuracy is as high as 99.29%. If we consider the top three matches, the accuracy increases to 99.64%. [ABSTRACT FROM AUTHOR]

With the fast evolution of Multimedia systems, Image compression algorithms are very much needed to achieve effective transmission and compact storage by removing the redundant information of the image data. Wavelet transforms have received significant attention, recently, due to their suitability for a number of important signal and image compression applications and the lapped nature of this transform and the computational simplicity, which comes in the form of filter bank implementations. In this paper, the implementation of image compression algorithms based on discrete wavelet transform such as embedded zero tree wavelet (EZW) coder, set partitioning in hierarchical trees coder without lists (SPIHT — No List) and packetizable zero tree wavelet (PZW) coder in DSP processor is dealt in detail and their performance analysis is carried out in terms of different compression ratios, execution timing and for different packet losses. PSNR is used as the criteria for the measurement of reconstructed image quality. [ABSTRACT FROM AUTHOR]

The multiscaling function of Alpert multiwavelet system and Chui–Lian multiwavelet system consist of one symmetric and one antisymmetric scaling functions. In its single level decomposition, only one of 16 subband blocks may be considered as a core part because the antisymmetric scaling function may play the high pass filter. We complete the Alpert multiwavelet system by determining the high pass filter using the algorithm of paraunitary extension principle. Taking the advantage of the symmetric/antisymmetric (SA) feature of Alpert and Chui–Lian multiscaling functions, our iteration (SA iteration) of multiwavelet decomposition continues to the core part (1/16 of subbands) for the image denoising problem while the traditional iteration applies to the one fourth of 16 subbands as core parts. The numerical results demonstrate that our method of symmetric/antisymmetric iteration exhibits performance superior to the traditional ways. [ABSTRACT FROM AUTHOR]

In this work, an improvement of the Complex Wavelet Additive Synthesis (CWAS) algorithm is presented. This algorithm is based on a discrete version of the Complex Continuous Wavelet Transform (CCWT) which analyzes the input signal in a frame-to-frame approach and under variable frequency resolution per octave. After summarizing several Time-Frequency Distributions (TFD), concretely the standard Short Time Fourier Transform (STFT), the Pseudo Wigner-Ville Distribution (PWVD), reassignment and complex wavelets, a comparative study of the accuracy in the instantaneous frequency (IF) estimation is shown. The comparative study includes three different signal processing tools (based on the summarized TFD): the Time-Frequency Toolbox (TFTB) of François Auger, the High Resolution Spectrographic Routines (HRSR) of Sean Fulop and the proposed CWAS algorithm. A set of eight synthetic signals have been analyzed using six different methods: the regular STFT spectrogram, the PWVD, their corresponding reassigned versions, the Nelson crossed spectrum method and finally the Complex Continuous Wavelet Transform (CCWT). Finally, two- and three-dimensional Time-Frequency representations of the IF provided by the CWAS algorithm are presented. [ABSTRACT FROM AUTHOR]

We present an algorithm that compresses two-dimensional data, which are piece-wise smooth in one direction and have oscillatory events in the other direction. Fine texture, seismic, hyper-spectral and fingerprints have this mixed structure. The transform part of the compression process is an algorithm that combines the application of the wavelet transform in one direction with the local cosine transform (LCT) in the other direction. This is why it is called hybrid compression. The quantization and the entropy coding parts in the compression process were taken from SPIHT codec but it can also be taken from any multiresolution based codec such as EZW. To efficiently apply the SPIHT codec to a mixed coefficients array, reordering of the LCT coefficients takes place. When oscillating events are present in different directions as in fingerprints or when the image comprises of a fine texture, a 2D LCT with coefficients reordering is applied. These algorithms outperform algorithms that are solely based on the the application of 2D wavelet transforms to each direction with either SPIHT or EZW coding including JPEG2000 compression standard. The proposed algorithms retain fine oscillating events including texture even at a low bitrate. Its compression capabilities are also demonstrated on multimedia images that have a fine texture. The wavelet part in the mixed transform of the hybrid algorithm utilizes the Butterworth wavelet transforms library that outperforms the 9/7 biorthogonal wavelet transform. [ABSTRACT FROM AUTHOR]

We present two strategies for detecting patterns and clusters in high-dimensional timedependent functional data. The use on wavelet-based similarity measures, since wavelets are well suited for identifying highly discriminant local time and scale features. The multiresolution aspect of the wavelet transform provides a time-scale decomposition of the signals allowing to visualize and to cluster the functional data into homogeneous groups. For each input function, through its empirical orthogonal wavelet transform the first strategy uses the distribution of energy across scales to generate a representation that can be sufficient to make the signals well distinguishable. Our new similarity measure combined with an efficient feature selection technique in the wavelet domain is then used within more or less classical clustering algorithms to effectively differentiate among high-dimensional populations. The second strategy uses a similarity measure between the whole time-scale representations that is based on wavelet-coherence tools. The clustering is then performed using a k-centroid algorithm starting from these similarities. Practical performance is illustrated through simulations as well as daily profiles of the French electricity power demand [ABSTRACT FROM AUTHOR]