a new parity space approach for fault detection based on stationary wavelet transform in the traditional parity relation based fault detection approach a lower order parity vector means a simpler online realization but a poorer performance index while a higher order parity vector brings a better performance index but leads to a higher computational load and a higher rate of misdetection in this note by introducing the so called stationary wavelet transform into the residual signal a new kind of parity relation based residual generator and the corresponding optimization approach are proposed the residual generator of the new approach can ensure a good performance index a satisfactory low misdetection rate and a suitable response speed to faults with a low order parity vector and a simple online implementation form the method is compared with three existing parity relation based approaches

numerical investigation on the obliquely incident water wave passing through the submerged breakwater by singular boundary method this short communication presents the singular boundary method sbm to solve the obliquely incident water wave passing through the submerged breakwater the sbm is a recent boundary type collocation method with the merits of being meshless integration free mathematically simple easy to program well suited for unbounded domain problems the accuracy and efficiency of the sbm is first verified in several benchmark examples in comparison with the boundary element method then the effects of the position size and geometry of the breakwater on water wave propagation are investigated through numerical experiments and some new observations are concluded

ideal spatial adaptation by wavelet shrinkage summary with ideal spatial adaptation an oracle furnishes information about how best to adapt a spatially variable estimator whether piecewise constant piecewise polynomial variable knot spline or variable bandwidth kernel to the unknown function estimation with the aid of an oracle offers dramatic advantages over traditional linear estimation by nonadaptive kernels however it is a priori unclear whether such performance can be obtained by a procedure relying on the data alone we describe a new principle for spatially adaptive estimation selective wavelet reconstruction we show that variable knot spline fits and piecewise polynomial fits when equipped with an oracle to select the knots are not dramatically more powerful than selective wavelet reconstruction with an oracle we develop a practical spatially adaptive method riskshrink which works by shrinkage of empirical wavelet coefficients riskshrink mimics the performance of an oracle for selective wavelet reconstruction as well as it is possible to do so a new inequality in multivariate normal decision theory which we call the oracle inequality shows that attained performance differs from ideal performance by at most a factor of approximately 2 log n where n is the sample size moreover no estimator can give a better guarantee than this within the class of spatially adaptive procedures riskshrink is essentially optimal relying only on the data it comes within a factor log 2 n of the performance of piecewise polynomial and variableknot spline methods equipped with an oracle in contrast it is unknown how or if piecewise polynomial methods could be made to function this well when denied access to an oracle and forced to rely on data alone

multiscale modeling and estimation of poisson processes with application to photon limited imaging many important problems in engineering and science are well modeled by poisson processes in many applications it is of great interest to accurately estimate the intensities underlying observed poisson data in particular this work is motivated by photon limited imaging problems this paper studies a new bayesian approach to poisson intensity estimation based on the haar wavelet transform it is shown that the haar transform provides a very natural and powerful framework for this problem using this framework a novel multiscale bayesian prior to model intensity functions is devised the new prior leads to a simple bayesian intensity estimation procedure furthermore we characterize the correlation behavior of the new prior and show that it has 1 f spectral characteristics the new framework is applied to photon limited image estimation and its potential to improve nuclear medicine imaging is examined

applying property testing to an image partitioning problem property testing is a rapidly growing field of research typically a property testing algorithm proceeds by quickly determining whether an input can satisfy some condition under the assumption that most inputs do not satisfy it if the input is far from satisfying the condition the algorithm is guaranteed to reject it with high probability applying this paradigm to image detection is desirable since images are large objects and a lot of time can be saved by quickly rejecting images which are far from satisfying a certain condition the user is interested in further typically most inputs are indeed far from the sought images we demonstrate this by analyzing the problem of deciding whether a binary image can be partitioned according to a template represented by a rectangular grid and introduce a quick rejector which tests an image extracted from the input image but whose size as well as the time required to construct it are constants which are independent of the input image size with high probability the rejector dismisses the inputs which are far from the template

performance analysis of transient detectors based on a class of linear data transforms the problem of detecting short duration nonstationary signals which are commonly referred to as transients is addressed transients are characterized by a signal model containing some unknown parameters and by a model mismatch representing the difference between the model and the actual signal both linear and nonlinear signal models are considered the transients are assumed to undergo a noninvertible linear transformation prior to the application of the detection algorithm examples of such transforms include the short time fourier transform the gabor transform and the wavelet transform closed form expressions are derived for the worst case detection performance for all possible mismatch signals of a given energy these expressions make it possible to evaluate and compare the performance of various transient detection algorithms for both single channel and multichannel data numerical examples comparing the performance of detectors based on the wavelet transform and the short time fourier transform are presented

shift variance and nonstationarity of linear periodically shift variant systems and applications to generalized sampling reconstruction processes we present a systematic analysis on shift variance of linear t periodically shift variant t lpsv systems with continuous time input and output we first determine how far a t lpsv system h is away from being shift invariant in terms of two measures namely the distance and the angle between h and the subspace of linear shift invariant systems we then consider the level and the index of shift variance svi of h via commutator of h and the shift operator and examine the amount of shift variance of h under particular input all these quantities are characterized in terms of the so called shift variant part and the shift variance kernel of h moreover we study nonstationarity of wide sense cyclostationary random processes possibly induced by t lpsv systems we define and calculate a measure of nonstationarity nst of the output as the svi of the autocorrelation operator the nst can be used to characterize performance loss when the output is treated with a wss approach the expected shift variance of h subject to particular wss random process is also calculated we apply the above results to generalized sampling reconstruction processes gsrps in addition we consider the approximation error of the gsrp and relate it to the shift variance measures three sampling schemes namely the orthogonal the consistent and the minimax regret sampling are examined in detail we show that for both deterministic and wss random inputs the minimax regret gsrp always introduces less shift variance than the consistent counterparts numerical results for the gsrps of b splines of various orders are provided

on the representation of operators in bases of compactly supported wavelets this paper describes exact and explicit representations of the differential operators d n dx n n 1 2 cdots in orthonormal bases of compactly supported wavelets as well as the representations of the hilbert transform and fractional derivatives the method of computing these representations is directly applicable to multidimensional convolution operators also sparse representations of shift operators in orthonormal bases of compactly supported wavelets are discussed and a fast algorithm requiring o n log n operations for computing the wavelet coefficients of all n circulant shifts of a vector of the length n 2 n is constructed as an example of an application of this algorithm it is shown that the storage requirements of the fast algorithm for applying the standard form of a pseudodifferential operator to a vector see g beylkin r r coifman and v rokhlin comm pure appl math 44 1991 pp 141 183 may be reduced from o n to o log 2 n significant entries

a primal dual proximal algorithm for sparse template based adaptive filtering application to seismic multiple removal unveiling meaningful geophysical information from seismic data requires to deal with both random and structured noises as their amplitude may be greater than signals of interest primaries additional prior information is especially important in performing efficient signal separation we address here the problem of multiple reflections caused by wave field bouncing between layers since only approximate models of these phenomena are available we propose a flexible framework for time varying adaptive filtering of seismic signals using sparse representations based on inaccurate templates we recast the joint estimation of adaptive filters and primaries in a new convex variational formulation this approach allows us to incorporate plausible knowledge about noise statistics data sparsity and slow filter variation in parsimony promoting wavelet frames the designed primal dual algorithm solves a constrained minimization problem that alleviates standard regularization issues in finding hyperparameters the approach demonstrates significantly good performance in low signal to noise ratio conditions both for simulated and real field data

on the boundary element method for the signorini problem of the laplacian for the laplace equation with signorini boundary conditions two equivalent boundary variational inequality formulations are deduced we investigate the discretization by a boundary element galerkin method and obtain quasi optimal asymptotic error estimates in the underlying sobolev spaces an algorithm based on the decomposition coordination method is used to solve the discretized problems numerical examples confirm the predicted rate of convergence

guided wavelet shrinkage for edge aware smoothing edge aware smoothing has been extensively studied due to its wide range of applications in computer vision and graphics most published works have been focused on formulating the smoothing problem in the spatial domain in this paper we propose a new edge aware smoothing framework called guided wavelet shrinkage gws which is formulated in the wavelet domain as a maximum a posterior estimation problem we impose a number of desirable properties on the statistical models and the associated parameters in order to derive an effective and computationally efficient algorithm we compare the proposed gws with classical image denoising in the wavelet domain we have also compared different wavelet representations and found that the double density dual tree wavelet transform is the best choice we show that the gws can be configured as either self guidance or external guidance it can also be configured to operate in an iterative or non iterative way experimental results and comparison with many state of the algorithms demonstrate that the gws based algorithm can produce competitive results with mathcal o n computational complexity

block median pyramidal transform analysis and denoising applications a nonlinear multiscale pyramidal transform based on nonoverlapping block decompositions using the median operation and a polynomial approximation is considered it is shown that this structure can be useful for denoising of oneand two dimensional 1 d and 2 d signals various denoising techniques are analyzed including methods based on spatially adaptive thresholding and partial cycle spinning algorithms an analytical method for deriving the distribution function of the transform coefficients is also presented this in turn can be used for the selection of thresholds for denoising applications

multiresolution analysis of a class of nonstationary processes processing nonstationary signals is an important and challenging problem we focus on the class of nonstationary processes with stationary increments of an arbitrary order and place them in a multiscale framework unlike other related studies we concentrate on the discrete time analysis and derive a number of new results in addition to placing the related existing ones in the same framework we extend the study to various parametric models for which we derive the resulting multiresolution description we show that wide sense stationarity may be achieved by adequately selecting the analysis wavelet after generalizing the study to wavelet packet analysis we show that the latter possesses additional properties which are useful in the presence of other types of nonstationarities

an analysis of finite volume element method for solving the signorini problem we propose and analyze the finite volume element method for solving the signorini problem the stability and the optimal h1 convergence rate are given particularly we establish a superclose interpolation estimate for the bilinear form of this method based on this estimate and the interpolation post processing technique we derive an o h 3 2 order superconvergence in the h1 norm under a proper regularity condition finally an asymptotically exact a posteriori error estimator also is given for the error u u h 1

real time pattern matching using projection kernels a novel approach to pattern matching is presented in which time complexity is reduced by two orders of magnitude compared to traditional approaches the suggested approach uses an efficient projection scheme which bounds the distance between a pattern and an image window using very few operations on average the projection framework is combined with a rejection scheme which allows rapid rejection of image windows that are distant from the pattern experiments show that the approach is effective even under very noisy conditions the approach described here can also be used in classification schemes where the projection values serve as input features that are informative and fast to extract

wavelet frame accelerated reduced support vector machines in this paper a novel method for reducing the runtime complexity of a support vector machine classifier is presented the new training algorithm is fast and simple this is achieved by an over complete wavelet transform that finds the optimal approximation of the support vectors the presented derivation shows that the wavelet theory provides an upper bound on the distance between the decision function of the support vector machine and our classifier the obtained classifier is fast since a haar wavelet approximation of the support vectors is used enabling efficient integral image based kernel evaluations this provides a set of cascaded classifiers of increasing complexity for an early rejection of vectors easy to discriminate this excellent runtime performance is achieved by using a hierarchical evaluation over the number of incorporated and additional over the approximation accuracy of the reduced set vectors here this algorithm is applied to the problem of face detection but it can also be used for other image based classifications the algorithm presented provides a 530 fold speedup over the support vector machine enabling face detection at more than 25 fps on a standard pc

property testing and its connection to learning and approximation in this paper we consider the question of determining whether a function f has property p or is e far from any function with property p a property testing algorithm is given a sample of the value of f on instances drawn according to some distribution in some cases it is also allowed to query f on instances of its choice we study this question for different properties and establish some connections to problems in learning theory and approximation in particular we focus our attention on testing graph properties given access to a graph g in the form of being able to query whether an edge exists or not between a pair of vertices we devise algorithms to test whether the underlying graph has properties such as being bipartite k colorable or having a p clique clique of density p with respect to the vertex set our graph property testing algorithms are probabilistic and make assertions that are correct with high probability while making a number of queries that is independent of the size of the graph moreover the property testing algorithms can be used to efficiently i e in time linear in the number of vertices construct partitions of the graph that correspond to the property being tested if it holds for the input graph

a modified multilevel algorithm for large scale scientific and engineering computing abstract a modified multilevel algorithm for solving the excessive storage requirements and ill conditioning encountered in the boundary type discretization method is proposed the modified multilevel algorithm is an extension of the modified dual level algorithm from dual levels to multiple levels the method is a kernel independent method the core idea is the layer by layer calculation and then layer by layer correction making use of a multilevel structure the original sparse matrix of the modified dual level algorithm breaks down into a series of smaller sparse matrices corresponding to different fine meshes the final matrix to be solved is hereby transformed to a series of smaller sparse matrices instead of a fully populated matrix the preconditioning effect originating from the recursive computations among the coarse mesh and fine meshes constitutes its core competitive attribute the method evaluates far field contributions only by the coarse mesh and uses a gradual approach to evaluate the near field contributions the storage requirements and computing complexity are hereby further reduced significantly

convergence and superconvergence analysis of a nonconforming finite element method for solving the signorini problem abstract in this paper we present the carey nonconforming finite element approximation of the variational inequality resulting from the signorini problem firstly we show that if the displacement field is of h 2 regularity the optimal convergence rate of o h can be obtained with respect to the energy norm secondly if stronger but reasonable h 5 2 regularity is available the superconvergence rate of o h 3 2 can be derived through the interpolated postprocessing technique finally numerical experiments are given which are consistent with our theoretical analysis

log polar wavelet energy signatures for rotation and scale invariant texture classification classification of texture images is important in image analysis and classification this paper proposes an effective scheme for rotation and scale invariant texture classification using log polar wavelet signatures the rotation and scale invariant feature extraction for a given image involves applying a log polar transform to eliminate the rotation and scale effects but at same time produce a row shifted log polar image which is then passed to an adaptive row shift invariant wavelet packet transform to eliminate the row shift effects so the output wavelet coefficients are rotation and scale invariant the adaptive row shift invariant wavelet packet transform is quite efficient with only o n spl middot log n complexity a feature vector of the most dominant log polar wavelet energy signatures extracted from each subband of wavelet coefficients is constructed for rotation and scale invariant texture classification in the experiments we employed a mahalanobis classifier to classify a set of 25 distinct natural textures selected from the brodatz album the experimental results based on different testing data sets for images with different orientations and scales show that the proposed classification scheme using log polar wavelet signatures outperforms two other texture classification methods its overall accuracy rate for joint rotation and scale invariance being 90 8 percent demonstrating that the extracted energy signatures are effective rotation and scale invariant features concerning its robustness to noise the classification scheme also performs better than the other methods

singularity detection and processing with wavelets the mathematical characterization of singularities with lipschitz exponents is reviewed theorems that estimate local lipschitz exponents of functions from the evolution across scales of their wavelet transform are reviewed it is then proven that the local maxima of the wavelet transform modulus detect the locations of irregular structures and provide numerical procedures to compute their lipschitz exponents the wavelet transform of singularities with fast oscillations has a particular behavior that is studied separately the local frequency of such oscillations is measured from the wavelet transform modulus maxima it has been shown numerically that one and two dimensional signals can be reconstructed with a good approximation from the local maxima of their wavelet transform modulus as an application an algorithm is developed that removes white noises from signals by analyzing the evolution of the wavelet transform maxima across scales in two dimensions the wavelet transform maxima indicate the location of edges in images

empirical bayes approach to improve wavelet thresholding for image noise reduction wavelet threshold algorithms replace small magnitude wavelet coefficients with zero and keep or shrink the other coefficients this is basically a local procedure because wavelet coefficients characterize the local regularity of a function although a wavelet transform has decorrelating properties structures in images like edges are never decorrelated completely and these structures appear in the wavelet coefficients a classification based on a local criterion like coefficient magnitude is not the perfect method to distinguish important uncorrupted coefficients from coefficients dominated by noise we therefore introduce a geometrical prior model for configurations of important wavelet coefficients and combine this with local characterization of a classical threshold procedure into a bayesian framework the local characterization is incorporated into the conditional model whereas the prior model describes only configurations not coefficient values more precisely local characterization favors co

biorthogonal bases of compactly supported wavelets orthonormal bases of compactly supported wavelet bases correspond to subband coding schemes with exact reconstruction in which the analysis and synthesis filters coincide we show here that under fairly general conditions exact reconstruction schemes with synthesis filters different from the analysis filters give rise to two dual riesz bases of compactly supported wavelets we give necessary and sufficient conditions for biorthogonality of the corresponding scaling functions and we present a sufficient condition for the decay of their fourier transforms we study the regularity of these biorthogonal bases we provide several families of examples all symmetric corresponding to linear phase filters in particular we can construct symmetric biorthogonal wavelet bases with arbitrarily high preassigned regularity we also show how to construct symmetric biorthogonal wavelet bases close to a nonsymmetric orthonormal basis

a nonlinear stein based estimator for multichannel image denoising the use of multicomponent images has become widespread with the improvement of multisensor systems having increased spatial and spectral resolutions however the observed images are often corrupted by an additive gaussian noise in this paper we are interested in multichannel image denoising based on a multiscale representation of the images a multivariate statistical approach is adopted to take into account both the spatial and the intercomponent correlations existing between the different wavelet subbands more precisely we propose a new parametric nonlinear estimator which generalizes many reported denoising methods the derivation of the optimal parameters is achieved by applying stein s principle in the multivariate case experiments performed on multispectral remote sensing images clearly indicate that our method outperforms conventional wavelet denoising techniques

entropy based algorithms for best basis selection adapted waveform analysis uses a library of orthonormal bases and an efficiency functional to match a basis to a given signal or family of signals it permits efficient compression of a variety of signals such as sound and images the predefined libraries of modulated waveforms include orthogonal wavelet packets and localized trigonometric functions and have reasonably well controlled time frequency localization properties the idea is to build out of the library functions an orthonormal basis relative to which the given signal or collection of signals has the lowest information cost the method relies heavily on the remarkable orthogonality properties of the new libraries all expansions in a given library conserve energy and are thus comparable several cost functionals are useful one of the most attractive is shannon entropy which has a geometric interpretation in this context

projection and self adaptive projection methods for the signorini problem with the bem abstract we propose two new projection methods for solving the signorini problem and study the relationship between them since the signorini boundary condition is equivalent to a projection fixed point problem the methods formulate the signorini boundary condition into a sequence of robin boundary conditions and only require solving a variational problem with simple boundary conditions at each iterative step the convergence speed of the first method depends on the parameter heavily and it is difficult to choose a proper for individual problems to improve the efficiency of the method we propose an adaptive projection method which adjusts the parameter automatically per iteration we establish the convergence analysis of the methods because the signorini boundary condition is given in an iterative form by the potential and its derivative on the boundary of the domain we can easily provide the boundary element approximation of the problem finally we present some numerical simulations which illustrate the performance of the methods

an integrated model for evaluating the amount of data required for reliable recognition many recognition procedures rely on the consistency of a subset of data features with a hypothesis as the sufficient evidence to the presence of the corresponding object we analyze here the performance of such procedures using a probabilistic model and provide expressions for the sufficient size of such data subsets that if consistent guarantee the validity of the hypotheses with arbitrary confidence we focus on 2d objects and the affine transformation class and provide for the first time an integrated model which takes into account the shape of the objects involved the accuracy of the data collected the clutter present in the scene the class of the transformations involved the accuracy of the localization and the confidence we would like to have in our hypotheses increasingly it turns out that most of these factors can be quantified cumulatively by one parameter denoted effective similarity which largely determines the sufficient subset size the analysis is based on representing the class of instances corresponding to a model object and a group of transformations as members of a metric space and quantifying the variation of the instances by a metric cover

robust mel frequency cepstral coefficients feature detection and dual tree complex wavelet transform for digital audio watermarking a novel digital audio watermarking scheme based on robust mel frequency cepstral coefficients feature detection and dual tree complex wavelet transform is proposed in this paper which is similar as patchwork based methods that several segments are extracted from the host audio clip for watermarking use the robust mel frequency cepstral coefficients feature detection method is proposed to extract the feature segments which should be relocated when the host audio signal attacked by various distortions including both the common audio signal processing and the conventional geometric distortions with the robust feature segments the approximate shift invariant transform dual tree complex wavelet transform based watermarking method is proposed to embed the watermark into the dt cwt real low pass coefficients of each segment using the spread spectrum techniques the linear correlation is calculated to judge the existence of the watermark during the watermark detection experimental results show that the proposed digital audio watermarking scheme based on robust mel frequency cepstral coefficients feature detection and dual tree complex wavelet transform can achieve high robustness against the common audio signal processing such as low pass filtering mp3 compression echo addition volume change and normalization and geometric distortions such as resample time scale modification tsm pitch invariant tsm and tempo invariant pitch shifting in addition the proposed audio watermarking scheme is resilient to stir mark for audio and it performs much better comparing with the existing state of the art methods

analysis of the element free galerkin method for signorini problems abstract an efficient element free galerkin efg method is developed to solve signorini boundary value problems the nonlinear inequality signorini boundary conditions are reduced to a sequence of linear boundary conditions by using a projection iterative scheme then the efg method is used to deduce discrete system equations convergence of the proposed method is discussed numerical examples are finally provided to verify the convergence and high computational accuracy of the method

wavelet thresholding techniques for power spectrum estimation estimation of the power spectrum s f of a stationary random process can be viewed as a nonparametric statistical estimation problem we introduce a nonparametric approach based on a wavelet representation for the logarithm of the unknown s f this approach offers the ability to capture statistically significant components of ln s f at different resolution levels and guarantees nonnegativity of the spectrum estimator the spectrum estimation problem is set up as a problem of inference on the wavelet coefficients of a signal corrupted by additive non gaussian noise we propose a wavelet thresholding technique to solve this problem under specified noise resolution tradeoffs and show that the wavelet coefficients of the additive noise may be treated as independent random variables the thresholds are computed using a saddle point approximation to the distribution of the noise coefficients

a generalized element free galerkin method for stokes problem abstract a generalized element free galerkin gefg method is developed in this paper for solving stokes problem in primitive variable form to obtain stable numerical results for both velocity and pressure extended terms are only introduced into the approximate space of velocity in a special way as that in the generalized finite element method theoretical analysis shows that the gefg method implies a stabilized formulation similar to that in the variational multiscale element free galerkin vmefg method numerical results show the efficiency of the present method and reveal that both computational errors and cpu times of the present method are less than those of the vmefg and the finite element methods

two projection methods for the solution of signorini problems abstract two iterative methods based on projection and boundary element methods are considered for signorini problems the regularized problem with the projection boundary condition is first deduced from the signorini problem by using the equivalence between the signorini boundary condition and the projection fixed point problem our methods formulate the signorini boundary condition into a sequence of robin boundary conditions in the new boundary condition there is a penalty parameter the convergence speed of the first method is greatly influenced by the value of which is difficult to choose for individual problems to improve the performance of this method we present a self adaptive projection method which adjusts the parameter automatically per iteration based on the iterative data the main result of this work is to provide the convergence of the methods under mild assumptions as the iteration process is given by the potential and its derivative on the boundary of the domain the unknowns of the problem are computed explicitly by using the boundary element method both theoretical results and numerical experiments indicate efficiency of the methods proposed

wavelet shrinkage using cross validation summary wavelets are orthonormal basis functions with special properties that show potential in many areas of mathematics and statistics this paper concentrates on the estimation of functions and images from noisy data by using wavelet shrinkage a modified form of twofold cross validation is introduced to choose a threshold for wavelet shrinkage estimators operating on data sets of length a power of 2 the cross validation algorithm is then extended to data sets of any length and to multidimensional data sets the algorithms are compared with established threshold choosers by using simulation an application to a real data set arising from anaesthesia is presented

extraction of shift invariant wavelet features for classification of images with different sizes an effective shift invariant wavelet feature extraction method for classification of images with different sizes is proposed the feature extraction process involves a normalization followed by an adaptive shift invariant wavelet packet transform an energy signature is computed for each subband of these invariant wavelet coefficients a reduced subset of energy signatures is selected as the feature vector for classification of images with different sizes experimental results show that the proposed method can achieve high classification accuracy of 98 5 percent and outperforms the other two image classification methods

error estimate for the numerical solution of fractional reaction subdiffusion process based on a meshless method in this paper a numerical technique based on a meshless method is proposed for solving the time fractional reaction subdiffusion equation firstly we obtain a time discrete scheme based on a finite difference scheme then we use the meshless galerkin method to approximate the spatial derivatives and obtain a full discrete scheme in the proposed scheme some integrals appear over the boundary and the domain of problem which will be approximated using gauss legendre quadrature rule then we prove that the time discrete scheme is unconditionally stable and convergent using the energy method we show convergence order of the time discrete scheme is o the aim of this paper is to obtain an error estimate and to show convergence for the meshless galerkin method based on the radial basis functions numerical examples confirm the efficiency and accuracy of the proposed scheme

multiple wavelet threshold estimation by generalized cross validation for images with correlated noise denoising algorithms based on wavelet thresholding replace small wavelet coefficients by zero and keep or shrink the coefficients with absolute value above the threshold the optimal threshold minimizes the error of the result as compared to the unknown exact data to estimate this optimal threshold we use generalized cross validation this procedure does not require an estimation for the noise energy originally this method assumes uncorrelated noise in this paper we describe how we can extend it to images with correlated noise

the element free galerkin method for the nonlinear p laplacian equation abstract the element free galerkin efg method is developed in this paper for solving the nonlinear p laplacian equation the moving least squares approximation is used to generate meshless shape functions the penalty approach is adopted to enforce the dirichlet boundary condition the galerkin weak form is employed to obtain the system of discrete equations and two iterative procedures are developed to deal with the strong nonlinearity then the computational formulas of the efg method for the p laplacian equation are established numerical results are finally given to verify the convergence and high computational precision of the method

noise covariance properties in dual tree wavelet decompositions dual tree wavelet decompositions have recently gained much popularity mainly due to their ability to provide an accurate directional analysis of images combined with a reduced redundancy when the decomposition of a random process is performed which occurs in particular when an additive noise is corrupting the signal to be analyzed it is useful to characterize the statistical properties of the dual tree wavelet coefficients of this process as dual tree decompositions constitute over complete frame expansions correlation structures are introduced among the coefficients even when a white noise is analyzed in this paper we show that it is possible to provide an accurate description of the covariance properties of the dual tree coefficients of a wide sense stationary process the expressions of the cross covariance sequences of the coefficients are derived in the one and two dimensional cases asymptotic results are also provided allowing to predict the behavior of the second order moments for large lag values or at coarse resolution in addition the cross correlations between the primal and dual wavelets which play a primary role in our theoretical analysis are calculated for a number of classical wavelet families simulation results are finally provided to validate these results

meshless projection iterative analysis of signorini problems using a boundary element free method this paper presents a meshless method based on coupling a boundary element free method befm with a new projection iterative scheme for signorini problems using the new iterative scheme the nonlinear complementary signorini boundary conditions are transformed into neumann boundary conditions then mixed elliptic problems are formed and are solved by the befm in this method only a nodal data structure on the boundary is required and the coefficient matrices of the discrete system equations only have to be computed once in the whole iterative process convergence of the iterative scheme is discussed theoretically numerical examples involving beach percolation and an electropaint process are given to illustrate the convergence rate and high computational efficiency of the method

hybrid finite element methods for the signorini problem we study three mixed linear finite element methods for the numerical simulation of the two dimensional signorini problem applying falk s lemma and saddle point theory to the resulting discrete mixed variational inequality allows us to state the convergence rate of each of them two of these finite elements provide optimal results under reasonable regularity assumptions on the signorini solution and the numerical investigation shows that the third method also provides optimal accuracy

relaxing tight frame condition in parallel proximal methods for signal restoration a fruitful approach for solving signal deconvolution problems consists of resorting to a frame based convex variational formulation in this context parallel proximal algorithms and related alternating direction methods of multipliers have become popular optimization techniques to approximate iteratively the desired solution until now in most of these methods either lipschitz differentiability properties or tight frame representations were assumed in this paper it is shown that it is possible to relax these assumptions by considering a class of non necessarily tight frame representations thus offering the possibility of addressing a broader class of signal restoration problems in particular it is possible to use non necessarily maximally decimated filter banks with perfect reconstruction which are common tools in digital signal processing the proposed approach allows us to solve both frame analysis and frame synthesis problems for various noise distributions in our simulations it is applied to the deconvolution of data corrupted with poisson noise or laplacian noise by using non tight discrete dual tree wavelet representations and filter bank structures

a sure approach for digital signal image deconvolution problems in this paper we are interested in the classical problem of restoring data degraded by a convolution and the addition of a white gaussian noise the originality of the proposed approach is twofold first we formulate the restoration problem as a nonlinear estimation problem leading to the minimization of a criterion derived from stein s unbiased quadratic risk estimate secondly the deconvolution procedure is performed using any analysis and synthesis frames that can be overcomplete or not new theoretical results concerning the calculation of the variance of the stein s risk estimate are also provided in this work simulations carried out on natural images show the good performance of our method with respect to conventional wavelet based restoration methods

the phase corrected undecimated discrete wavelet packet transform and its application to interpreting the timing of events this paper is concerned with the development and application of the phase corrected maximal overlap discrete wavelet packet transform modwpt the discrete cyclic filtering steps of the modwpt are fully explained energy preservation is proven with filter coefficients chosen from daubechie s least asymmetric class the optimum time shifts to apply to ensure approximate zero phase filtering at every level of the modwpt are studied and applied to the wavelet packet coefficients to give phase corrections which ensure alignment with the original time series also the time series values at each time are decomposed into details associated with each frequency band and these line up perfectly with features in the original time series since the details are shown to arise through exact zero phase filtering the phase corrected modwpt is applied to a non stationary time series of hourly averaged southern hemisphere solar magnetic field magnitude data acquired by the ulysses spacecraft the occurrence times of the shock waves previously determined via manual pattern matching on the raw data match those times in the time frequency plot where a broadband spectrum is obtained in other words the phase corrected modwpt provides an approach to picking the location of complicated events we demonstrate the superiority of the modwpt in interpreting timing information over two competing methods namely the cosine packet transform or local cosine transform and the short time fourier transform

the discrete wavelet transform wedding the a trous and mallat algorithms two separately motivated implementations of the wavelet transform are brought together it is observed that these algorithms are both special cases of a single filter bank structure the discrete wavelet transform the behavior of which is governed by the choice of filters in fact the a trous algorithm is more properly viewed as a nonorthonormal multiresolution algorithm for which the discrete wavelet transform is exact moreover it is shown that the commonly used lagrange a trous filters are in one to one correspondence with the convolutional squares of the daubechies filters for orthonormal wavelets of compact support a systematic framework for the discrete wavelet transform is provided and conditions are derived under which it computes the continuous wavelet transform exactly suitable filter constraints for finite energy and boundedness of the discrete transform are also derived relevant signal processing parameters are examined and it is observed that orthonormality is balanced by restrictions on resolution

improved transient signal detection using a wavepacket based detector with an extended translation invariant wavelet transform this paper presents the theory of m band extended translation invariant eti wavelet transforms the eti generalizes the translation invariant wavelet transform of weiss 1933 it is shown that iteration of the eti in a tree structure provides a signal decomposition into an orthonormal wavepacket basis other properties such as translation invariance and invertibility of the transform are proven the theory is then applied to transient signal detection through development of a family of translation invariant wavepacket based detectors this family of detectors provides improved the performance over previously defined wavepacket based detectors a performance analysis is conducted roc curves generated by monte carlo simulation are presented indicating the detector performance the detector performance is demonstrated to be independent of the signal translation

maximum principle satisfying and positivity preserving high order central discontinuous galerkin methods for hyperbolic conservation laws maximum principle or positivity preserving property holds for many mathematical models when the models are approximated numerically it is preferred that these important properties can be preserved by numerical discretizations for the robustness and the physical relevance of the approximate solutions in this paper we investigate such discretizations of high order accuracy within the central discontinuous galerkin framework more specifically we design and analyze high order maximum principle satisfying central discontinuous galerkin methods for scalar conservation laws and high order positivity preserving central discontinuous galerkin for compressible euler systems the performance of the proposed methods will be demonstrated through a set of numerical experiments

rotation invariant multiresolution texture analysis using radon and wavelet transforms a new rotation invariant texture analysis technique using radon and wavelet transforms is proposed this technique utilizes the radon transform to convert the rotation to translation and then applies a translation invariant wavelet transform to the result to extract texture features a k nearest neighbors classifier is employed to classify texture patterns a method to find the optimal number of projections for the radon transform is proposed it is shown that the extracted features generate an efficient orthogonal feature space it is also shown that the proposed features extract both of the local and directional information of the texture patterns the proposed method is robust to additive white noise as a result of summing pixel values to generate projections in the radon transform step to test and evaluate the method we employed several sets of textures along with different wavelet bases experimental results show the superiority of the proposed method and its robustness to additive white noise in comparison with some recent texture analysis methods

the nonlinear statistics of high contrast patches in natural images recently there has been a great deal of interest in modeling the non gaussian structures of natural images however despite the many advances in the direction of sparse coding and multi resolution analysis the full probability distribution of pixels values in a neighborhood has not yet been described in this study we explore the space of data points representing the values of 3 3 high contrast patches from optical and 3d range images we find that the distribution of data is extremely sparse with the majority of the data points concentrated in clusters and non linear low dimensional manifolds furthermore a detailed study of probability densities allows us to systematically distinguish between images of different modalities optical versus range which otherwise display similar marginal distributions our work indicates the importance of studying the full probability distribution of natural images not just marginals and the need to understand the intrinsic dimensionality and nature of the data we believe that object like structures in the world and the sensor properties of the probing device generate observations that are concentrated along predictable shapes in state space our study of natural image statistics accounts for local geometries such as edges in natural scenes but does not impose such strong assumptions on the data as independent components or sparse coding by linear change of bases

error analysis of the meshless finite point method abstract the finite point method fpm is a notable truly meshless method based on the moving least squares mls approximation and the point collocation technique in this paper the error of the fpm is analyzed theoretically theoretical results show that the present error bound is directly related to the nodal spacing and the order of basis functions used in the mls approximation the present error estimation is independent of the condition number of the coefficient matrix and improves the previously reported estimations numerical examples with more than 160000 nodes are given to confirm the theoretical result

efficient face detection by a cascaded support vector machine expansion we describe a fast system for the detection and localization of human faces in images using a nonlinear supportvector machine we approximate the decision surface in terms of a reduced set of expan

the near shift invariance of the dual tree complex wavelet transform revisited abstract the dual tree complex wavelet transform dt c wt is an enhancement of the conventional discrete wavelet transform dwt due to a higher degree of shift invariance and a greater directional selectivity finding its applications in signal and image processing this paper presents a quantitative proof of the superiority of the dt c wt over the dwt in case of modulated wavelets

m band nonlinear subband decompositions with perfect reconstruction we investigate nonlinear multirate filterbanks with maximal decimation and perfect reconstruction definitions of the desired properties of such structures are given for general nonlinear filterbanks we then consider a triangular representation of linear filterbanks and see that it may be easily extended to the nonlinear case furthermore general nonlinear filterbanks are presented for which perfect reconstruction is either inherently guaranteed or ensured subject to an easily verified condition extensions to bidimensional filters are also discussed and an application for nonlinear multiresolution schemes to feature sieves is shown

on the stability of the moving least squares approximation and the element free galerkin method in this paper the stability of the moving least squares mls approximation and a stabilized mls approximation is analyzed theoretically and verified numerically it is shown that the stability of the mls approximation deteriorates severely as the nodal spacing decreases while the stability of the stabilized mls approximation is not affected by the nodal spacing the stabilized mls approximation is introduced into the element free galerkin efg method to produce a stabilized efg method theoretical error analysis of the stabilized efg method is provided for boundary value problems with mixed boundary conditions of dirichlet and robin type numerical examples confirm the theoretical results and show that the stabilized efg method has higher computational precision and better stability than the original efg method

time invariant orthonormal wavelet representations a simple construction of an orthonormal basis starting with a so called mother wavelet together with an efficient implementation gained the wavelet decomposition easy acceptance and generated a great research interest in its applications an orthonormal basis may not however always be a suitable representation of a signal particularly when time or space invariance is a required property the conventional way around this problem is to use a redundant decomposition we address the time invariance problem for orthonormal wavelet transforms and propose an extension to wavelet packet decompositions we show that it is possible to achieve time invariance and preserve the orthonormality we subsequently propose an efficient approach to obtain such a decomposition we demonstrate the importance of our method by considering some application examples in signal reconstruction and time delay estimation

variational multiscale interpolating element free galerkin method for the nonlinear darcy forchheimer model abstract in this paper the variational multiscale interpolating element free galerkin vmiefg method is developed to obtain the numerical solution of the nonlinear darcy forchheimer model we use the interpolating moving least squares method instead of the moving least squares approximation to construct meshless shape functions with delta function properties then the flux boundary condition of the darcy forchheimer model can be handled easily hughes variational multiscale hvm method is applied to overcome the numerical oscillation caused by equal order basis for the velocity and pressure moreover the hvm ensures that the resultant formulation in the vmiefg method is consistent and the stabilization parameter or tensor appears naturally consequently the stabilization parameter is free of user defined the fixed point iteration method is used to deal with the nonlinear term some numerical examples are provided to illustrate the stability and performance of the proposed method for solving the nonlinear darcy forchheimer model

shift variance analysis of generalized sampling processes this paper is concerned with quantifying shift variance of linear systems with continuous time input and discrete time output we first introduce a notion of shift invariance for the system it specifies how the system should respond when the input signal is shifted for generalized sampling processes the property is characterized by the sampling kernel and is shown to be equivalent to lack of aliasing and to shiftability we then define a shift variance level which describes how far the system can be possibly away from the set of systems that are shift invariant the level is defined to be the maximum of the induced norms of the commutators of the system and the shift operators both continuous time or discrete time are necessarily involved a shift variance measure is then defined to be the ratio of the shift variance level to the system norm further divided by two so that the measure is between zero and unity for generalized sampling we obtain analytical formulas for the shift variance level and the shift variance measure the results allow us to analyze the shift variance of among others the discrete time wavelet transform dwt and the short time fourier transform stft we obtain a simple relation between the shift variance levels at all scales of the dwt and show that the shift variance measures are identical at all scales we calculate the shift variance level and the shift variance measure of some typical dwts and the stfts

gradient schemes for the signorini and the obstacle problems and application to hybrid mimetic mixed methods gradient schemes is a framework which enables the unified convergence analysis of many different methods such as finite elements conforming non conforming and mixed and finite volumes methods for 2nd order diffusion equations we show in this work that the gradient schemes framework can be extended to variational inequalities involving mixed dirichlet neumann and signorini boundary conditions this extension allows us to provide error estimates for numerical approximations of such models recovering known convergence rates for some methods and establishing new convergence rates for schemes not previously studied for variational inequalities the general framework we develop also enables us to design a new numerical method for the obstacle and signorini problems based on hybrid mimetic mixed schemes we provide numerical results that demonstrate the accuracy of these schemes and confirm our theoretical rates of convergence

orthonormal bases of compactly supported wavelets we construct orthonormal bases of compactly supported wavelets with arbitrarily high regularity the order of regularity increases linearly with the support width we start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction the construction then follows from a synthesis of these different approaches

shiftable multiscale transforms one of the major drawbacks of orthogonal wavelet transforms is their lack of translation invariance the content of wavelet subbands is unstable under translations of the input signal wavelet transforms are also unstable with respect to dilations of the input signal and in two dimensions rotations of the input signal the authors formalize these problems by defining a type of translation invariance called shiftability in the spatial domain shiftability corresponds to a lack of aliasing thus the conditions under which the property holds are specified by the sampling theorem shiftability may also be applied in the context of other domains particularly orientation and scale jointly shiftable transforms that are simultaneously shiftable in more than one domain are explored two examples of jointly shiftable transforms are designed and implemented a 1 d transform that is jointly shiftable in position and scale and a 2 d transform that is jointly shiftable in position and orientation the usefulness of these image representations for scale space analysis stereo disparity measurement and image enhancement is demonstrated

a hierarchy of support vector machines for pattern detection we introduce a computational design for pattern detection based on a tree structured network of support vector machines svms an svm is associated with each cell in a recursive partitioning of the space of patterns hypotheses into increasingly finer subsets the hierarchy is traversed coarse to fine and each chain of positive responses from the root to a leaf constitutes a detection our objective is to design and build a network which balances overall error and computation initially svms are constructed for each cell with no constraints this free network is then perturbed cell by cell into another network which is graded in two ways first the number of support vectors of each svm is reduced by clustering in order to adjust to a pre determined increasing function of cell depth second the decision boundaries are shifted to preserve all positive responses from the original set of training data the limits on the numbers of clusters virtual support vectors result from minimizing the mean computational cost of collecting all detections subject to a bound on the expected number of false positives when applied to detecting faces in cluttered scenes the patterns correspond to poses and the free network is already faster and more accurate than applying a single pose specific svm many times the graded network promotes very rapid processing of background regions while maintaining the discriminatory power of the free network

image analysis using a dual tree m band wavelet transform we propose a two dimensional generalization to the m band case of the dual tree decomposition structure initially proposed by kingsbury and further investigated by selesnick based on a hilbert pair of wavelets we particularly address 1 the construction of the dual basis and 2 the resulting directional analysis we also revisit the necessary pre processing stage in the m band case while several reconstructions are possible because of the redundancy of the representation we propose a new optimal signal reconstruction technique which minimizes potential estimation errors the effectiveness of the proposed m band decomposition is demonstrated via denoising comparisons on several image types natural texture seismics with various m band wavelets and thresholding strategies significant improvements in terms of both overall noise reduction and direction preservation are observed

a boundary type meshless solver for transient heat conduction analysis of slender functionally graded materials with exponential variations abstract this study presents a parallel meshless solver for transient heat conduction analysis of slender functionally graded materials fgms with exponential variations in the present parallel meshless solver a strong form boundary collocation method the boundary knot method bkm in conjunction with laplace transform is implemented to solve the heat conduction equations of slender fgms with exponential variations this method is mathematically simple easy to parallel meshless and without domain discretization however two ill posed issues the ill conditioning dense bkm matrix and numerical inverse laplace transform process may lead to incorrect numerical results here the extended precision arithmetic epa and the domain decomposition method ddm have been adopted to alleviate the effect of these two ill posed issues on numerical efficiency of the present method then the parallel algorithm has been employed to significantly reduce the computational cost and enhance the computational capacity for the fgm structures with larger length width ratio to demonstrate the effectiveness of the present parallel meshless solver for transient heat conduction analysis several benchmark examples are considered under slender fgms with exponential variations the present results are compared with the analytical solutions the conventional boundary knot method and comsol simulation

fast simulation of multi dimensional wave problems by the sparse scheme of the method of fundamental solutions in this work a meshless scheme is presented for the fast simulation of multi dimensional wave problems the present method is rather simple and straightforward the houbolt method is used to eliminate the time dependence of spatial variables then the original wave problem is converted into equivalent systems of modified helmholtz equations the sparse scheme of the method of fundamental solutions in combination with the localized method of approximate particular solutions is employed for efficient implementation of spatial variables to demonstrate the effectiveness and simplicity of this new approach three numerical examples have been assessed with excellent performance

the wavelet transform time frequency localization and signal analysis two different procedures for effecting a frequency analysis of a time dependent signal locally in time are studied the first procedure is the short time or windowed fourier transform the second is the wavelet transform in which high frequency components are studied with sharper time resolution than low frequency components the similarities and the differences between these two methods are discussed for both schemes a detailed study is made of the reconstruction method and its stability as a function of the chosen time frequency density finally the notion of time frequency localization is made precise within this framework by two localization theorems

frequency shift invariant orthonormal wavelet packet representations it is commonly known that the dyadic structure of wavelet expansions results in both time and frequency translation sensitivity of an input signal we develop the first efficient method to reduce frequency alignment sensitivity by introducing a wavelet packet decomposition that is invariant to frequency shifts of a signal a frequency shifted wavelet packet library is presented and an efficient best basis algorithm is developed to determine the best signal representation among all frequency shifts of a signal the algorithm computes all frequency shifted coefficients in o n sup 2 operations followed by an efficient depth first tree search of the same complexity

a galerkin boundary node method and its convergence analysis the boundary node method bnm exploits the dimensionality of the boundary integral equation bie and the meshless attribute of the moving least square mls approximations however since mls shape functions lack the property of a delta function it is difficult to exactly satisfy boundary conditions in bnm besides the system matrices of bnm are non symmetric a galerkin boundary node method gbnm is proposed in this paper for solving boundary value problems in this approach an equivalent variational form of a bie is used for representing the governing equation and the trial and test functions of the variational formulation are generated by the mls approximation as a result boundary conditions can be implemented accurately and the system matrices are symmetric total details of numerical implementation and error analysis are given for a general bie taking the dirichlet problem of laplace equation as an example we set up a framework for error estimates of gbnm some numerical examples are also given to demonstrate the efficacity of the method

building robust wavelet estimators for multicomponent images using stein s principle multichannel imaging systems provide several observations of the same scene which are often corrupted by noise in this paper we are interested in multispectral image denoising in the wavelet domain we adopt a multivariate statistical approach in order to exploit the correlations existing between the different spectral components our main contribution is the application of stein s principle to build a new estimator for arbitrary multichannel images embedded in additive gaussian noise simulation tests carried out on optical satellite images show that the proposed method outperforms conventional wavelet shrinkage techniques

wavelet based multiresolution analysis of wivenhoe dam water temperatures 1 water temperature measurements from wivenhoe dam offer a unique opportunity for studying fluctuations of temperatures in a subtropical dam as a function of time and depth cursory examination of the data indicate a complicated structure across both time and depth we propose simplifying the task of describing these data by breaking the time series at each depth into physically meaningful components that individually capture daily subannual and annual dsa variations precise definitions for each component are formulated in terms of a wavelet based multiresolution analysis the dsa components are approximately pairwise uncorrelated within a given depth and between different depths they also satisfy an additive property in that their sum is exactly equal to the original time series each component is based upon a set of coefficients that decomposes the sample variance of each time series exactly across time and that can be used to study both time varying variances of water temperature at each depth and time varying correlations between temperatures at different depths each dsa component is amenable for studying a certain aspect of the relationship between the series at different depths the daily component in general is weakly correlated between depths including those that are adjacent to one another the subannual component quantifies seasonal effects and in particular isolates phenomena associated with the thermocline thus simplifying its study across time the annual component can be used for a trend analysis the descriptive analysis provided by the dsa decomposition is a useful precursor to a more formal statistical analysis

boundary integral equation methods for the two dimensional fluid solid interaction problem this paper is concerned with boundary integral equation methods for solving the two dimensional fluid solid interaction problem we reduce the problem to three different systems of boundary integral equations via direct and indirect approaches existence and uniqueness results for variational solutions of boundary integral equations are established since in all these variational formulations the hypersingular boundary integral operator associated with the time harmonic navier equation is a dominating integral operator we also include a new regularization formulation for this hypersingular operator which allows us to treat the hypersingular kernel by a weakly singular kernel numerical examples are presented to verify and validate the theoretical results

translation invariant contourlet transform and its application to image denoising most subsampled filter banks lack the feature of translation invariance which is an important characteristic in denoising applications in this paper we study and develop new methods to convert a general multichannel multidimensional filter bank to a corresponding translation invariant ti framework in particular we propose a generalized algorithme agrave trous which is an extension of the algorithme agrave trous introduced for 1 d wavelet transforms using the proposed algorithm as well as incorporating modified versions of directional filter banks we construct the ti contourlet transform tict to reduce the high redundancy and complexity of the tict we also introduce semi translation invariant contourlet transform stict then we employ an adapted bivariate shrinkage scheme to the stict to achieve an efficient image denoising approach our experimental results demonstrate the benefits and potential of the proposed denoising approach complexity analysis and efficient realization of the proposed ti schemes are also presented

superconvergence of finite element method for the signorini problem in this paper we study the superconvergence of the frictionless signorini problem when approximated by bilinear finite elements by virtue of the information on the contact zone we can derive a superconvergence rate of o h 3 2 under a proper regularity assumption finally a numerical test is given to verify our result

minimax description length for signal denoising and optimized representation approaches to wavelet based denoising or signal enhancement have generally relied on the assumption of normally distributed perturbations to relax this assumption which is often violated in practice we derive a robust wavelet thresholding technique based on the minimax description length mmdl principle we first determine the least favorable distribution in the spl epsiv contaminated normal family as the member that maximizes the entropy we show that this distribution and the best estimate based upon it namely the maximum likelihood estimate together constitute a saddle point the mmdl approach results in a thresholding scheme that is resistant to heavy tailed noise we further extend this framework and propose a novel approach to selecting an adapted or best basis bb that results in optimal signal reconstruction finally we address the practical case where the underlying signal is known to be bounded and derive a two sided thresholding technique that is resistant to outliers and has bounded error

investigating existence of chaos in short and long term dynamics of moroccan exchange rates abstract this paper proposes a new methodology to investigate presence of chaos in exchange rate time series by combining wavelet transform and lyapunov exponent estimation in particular stationary wavelet transform swt is applied to exchange rate original time series for decomposition purpose as a result approximation and details coefficients are extracted they are used to represent long and short term dynamics of the original exchange rate time series then largest lyapunov exponent is estimated for each type of dynamics to check for presence of chaos our methodology is applied to several moroccan exchange rate time series the empirical results show that in general the hypothesis of chaotic structure is accepted for currency levels but it is rejected for currency returns on both long and short dynamics in addition long and short dynamics exhibit different chaotic patterns in some exchange rate time series our approach may be useful to understand chaotic behaviour in original exchange rate time series

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed