wavelets and filter banks theory and design the wavelet transform is compared with the more classical short time fourier transform approach to signal analysis then the relations between wavelets filter banks and multiresolution signal processing are explored a brief review is given of perfect reconstruction filter banks which can be used both for computing the discrete wavelet transform and for deriving continuous wavelet bases provided that the filters meet a constraint known as regularity given a low pass filter necessary and sufficient conditions for the existence of a complementary high pass filter that will permit perfect reconstruction are derived the perfect reconstruction condition is posed as a bezout identity and it is shown how it is possible to find all higher degree complementary filters based on an analogy with the theory of diophantine equations an alternative approach based on the theory of continued fractions is also given these results are used to design highly regular filter banks which generate biorthogonal continuous wavelet bases with symmetries

efficient scalar quantization of exponential and laplacian random variables this paper presents solutions to the entropy constrained scalar quantizer ecsq design problem for two sources commonly encountered in image and speech compression applications sources having the exponential and laplacian probability density functions we use the memoryless property of the exponential distribution to develop a new noniterative algorithm for obtaining the optimal quantizer design we show how to obtain the optimal ecsq either with or without an additional constraint on the number of levels in the quantizer in contrast to prior methods which require a multidimensional iterative solution of a large number of nonlinear equations the new method needs only a single sequence of solutions to one dimensional nonlinear equations in some laplacian cases one additional two dimensional solution is needed as a result the new method is orders of magnitude faster than prior ones we show that as the constraint on the number of levels in the quantizer is relaxed the optimal ecsq becomes a uniform threshold quantizer utq for exponential but not for laplacian sources we then further examine the performance of the utq and optimal ecsq and also investigate some interesting alternatives to the utq including a uniform reconstruction quantizer urq and a constant dead zone ratio quantizer cdzrq

on a general framework for q particles paraparticles and q paraparticles through deformations the authors propose a unification of deformations associated with the descriptions of q para and q para bosons and fermions for complex values of q

boundary integral equation methods for the elastic and thermoelastic waves in three dimensions in this paper we consider the boundary integral equation bie methods for solving the exterior neumann boundary value problems of elastic and thermoelastic waves in three dimensions based on the fredholm integral equations of the first kind the innovative contribution of this work lies in the proposal of the new regularized formulations for the hyper singular boundary integral operators bio associated with the time harmonic elastic and thermoelastic wave equations with the help of the new regularized formulations we only need to compute the integrals with weak singularities at most in the corresponding variational forms of the boundary integral equations the accuracy of the regularized formulations is demonstrated through numerical examples using the galerkin boundary element method bem

classified vector quantization of images vector quantization vq provides many attractive features for image coding with high compression ratios however initial studies of image coding with vq have revealed several difficulties most notably edge degradation and high computational complexity we address these two problems and propose a new coding method classified vector quantization cvq which is based on a composite source model blocks with distinct perceptual features such as edges are generated from different subsources i e belong to different classes in cvq a classifier determines the class for each block and the block is then coded with a vector quantizer designed specifically for that class we obtain better perceptual quality with significantly lower complexity with cvq when compared to ordinary vq we demonstrate with cvq visual quality which is comparable to that produced by existing coders of similar complexity for rates in the range 0 6 1 0 bits pixel

on quantization of simple harmonic oscillators a general framework is presented of quantizing the system of a simple harmonic oscillator various methods of quantization so far proposed are accommodated here in a unified form some remarks are also made on quantization for the case of more than one oscillator

q analogues of the parabose and parafermi oscillators and representations of quantum algebras deformations of the one dimensional parabose oscillators are presented they are shown to provide fock representations of the quantum sp q 2 algebra and ospq 1 2 superalgebra the representations of suq 2 are used to define the q analogues of the parafermi oscillators

regression modeling in back propagation and projection pursuit learning we study and compare two types of connectionist learning methods for model free regression problems 1 the backpropagation learning bpl and 2 the projection pursuit learning ppl emerged in recent years in the statistical estimation literature both the bpl and the ppl are based on projections of the data in directions determined from interconnection weights however unlike the use of fixed nonlinear activations usually sigmoidal for the hidden neurons in bpl the ppl systematically approximates the unknown nonlinear activations moreover the bpl estimates all the weights simultaneously at each iteration while the ppl estimates the weights cyclically neuron by neuron and layer by layer at each iteration although the bpl and the ppl have comparable training speed when based on a gauss newton optimization algorithm the ppl proves more parsimonious in that the ppl requires a fewer hidden neurons to approximate the true function to further improve the statistical performance of the ppl an orthogonal polynomial approximation is used in place of the supersmoother method originally proposed for nonlinear activation approximation in the ppl

asymptotically optimal model estimation for quantization using high rate theory approximations we introduce flexible practical quantizers based on possibly non gaussian models in both the constrained resolution cr and the constrained entropy cases we derive model estimation criteria optimizing asymptotic with increasing rate quantizer performance we show that in the cr case the optimal criterion is different from the maximum likelihood criterion commonly used for that purpose and introduce a new criterion that we call constrained resolution minimum description length cr mdl we apply these principles to the generalized gaussian scaled mixture model which is accurate for many real world signals we provide an explanation of the reason why the cr mdl improves quantization performance in the cr case and show that cr mdl can compensate for a possible mismatch between model and data distribution thus this criterion is of a great interest for practical applications our experiments apply the new quantization method to controllable artificial data and to the commonly used modulated lapped transform representation of audio signals we show that both the cr mdl criterion and a non gaussian modeling have significant advantages

design of regular nonseparable bidimensional wavelets using grobner basis techniques the design of two dimensional 2 d filter banks yielding orthogonality and linear phase filters and generating regular wavelet bases is a difficult task involving the algebraic properties of multivariate polynomials using cascade forms implies dealing with nonlinear optimization we turn the issue of optimizing the orthogonal linear phase cascade from kovacevic and vetterli 1992 into a polynomial problem and solve it using grobner basis techniques and computer algebra this leads to a complete description of maximally flat wavelets among the orthogonal linear phase family proposed by kovacevic and vetterli we obtain up to five degrees of flatness for a 16 spl times 16 filter bank whose sobolev exponent is 2 11 making this wavelet the most regular orthogonal linear phase nonseparable wavelet to the authors knowledge

fast matching pursuit with a multiscale dictionary of gaussian chirps we introduce a modified matching pursuit algorithm called fast ridge pursuit to approximate n dimensional signals with m gaussian chirps at a computational cost o mn instead of the expected o mn sup 2 logn at each iteration of the pursuit the best gabor atom is first selected and then its scale and chirp rate are locally optimized so as to get a good chirp atom i e one for which the correlation with the residual is locally maximized a ridge theorem of the gaussian chirp dictionary is proved from which an estimate of the locally optimal scale and chirp is built the procedure is restricted to a sub dictionary of local maxima of the gaussian gabor dictionary to accelerate the pursuit further the efficiency and speed of the method is demonstrated on a sound signal

a semiparametric approach to canonical analysis summary classical canonical correlation analysis is one of the fundamental tools in statistics to investigate the linear association between two sets of variables we propose a method called semiparametric canonical analysis to generalize canonical correlation analysis to incorporate the important non linear association semiparametric canonical analysis is easy to implement and interpret statistical properties are proved a consistent estimation method is developed selection of significant semiparametric canonical analysis components is discussed simulations suggest that the methods proposed have satisfactory performance in finite samples one environmental data set and one data set in social science are investigated in which non linear canonical associations are observed and interpreted

the quantum group suq 2 and a q analogue of the boson operators a new realisation of the quantum group suq 2 is constructed by means of a q analogue to the jordan schwinger mapping determining thereby both the complete representation structure and q analogues to the wigner and racah operators to achieve this realisation a new elementary object is defined a q analogue to the harmonic oscillator the uncertainty relation for position and momentum in a q harmonic oscillator is quite unusual

a simple lemma on greedy approximation in hilbert space and convergence rates for projection pursuit regression and neural network training a general convergence criterion for certain iterative sequences in hilbert space is presented for an important subclass of these sequences estimates of the rate of convergence are given under very mild assumptions these results establish an 0 1 f4n nonsampling convergence rate for projection pursuit regression and neural network training where n represents the number of ridge functions neurons or coefficients in a greedy basis expansion

use of bias term in projection pursuit learning improves approximation and convergence properties in a regression problem one is given a multidimensional random vector x the components of which are called predictor variables and a random variable y called response a regression surface describes a general relationship between x and y a nonparametric regression technique that has been successfully applied to high dimensional data is projection pursuit regression ppr the regression surface is approximated by a sum of empirically determined univariate functions of linear combinations of the predictors projection pursuit learning ppl formulates ppr using a 2 layer feedforward neural network the smoothers in ppr are nonparametric whereas those in ppl are based on hermite functions of some predefined highest order r we demonstrate that ppl networks in the original form do not have the universal approximation property for any finite r and thus cannot converge to the desired function even with an arbitrarily large number of hidden units but by including a bias term in each linear projection of the predictor variables ppl networks can regain these capabilities independent of the exact choice of r experimentally it is shown in this paper that this modification increases the rate of convergence with respect to the number of hidden units improves the generalization performance and makes it less sensitive to the setting of r finally we apply ppl to chaotic time series prediction and obtain superior results compared with the cascade correlation architecture

optimal bit allocation via the generalized bfos algorithm p h westerink et al 1988 developed an optimal bit allocation algorithm that is simplified when all operational distortion rate functions which are referred to as quantizer functions are convex this algorithm is restated using the generalized breiman friedman olshen and stone bfos algorithm a recently developed technique for variable rate vector quantizer design for both cases of convex and nonconvex quantizer functions qfs and its complexity is analyzed the use of the generalized bfos algorithm for optimal bit allocation is analysed it is shown that if each source has a convex quantizer function then the complexity of the algorithm is low

optimal pruning with applications to tree structured source coding and modeling an algorithm introduced by l breiman et al 1984 in the context of classification and regression trees is reinterpreted and extended to cover a variety of applications in source coding and modeling in which trees are involved these include variable rate and minimum entropy tree structured vector quantization minimum expected cost decision trees variable order markov modeling optimum bit allocation and computer graphics and image processing using quadtrees a concentration on the first of these and a detailed analysis of variable rate tree structured vector quantization are provided it is found that variable rate tree structured vector quantization outperforms not only the fixed rate variety but also full search vector quantization the successive approximation character of variable rate tree structured vector quantization permits it to degrade gracefully if the rate is reduced at the encoder this has applications to the problem of buffer overflow

an optimal quadtree based motion estimation and motion compensated interpolation scheme for video compression we propose an optimal quadtree qt based motion estimator for video compression it is optimal in the sense that for a given bit budget for encoding the displacement vector field dvf and the qt segmentation the scheme finds a dvf and a qt segmentation which minimizes the energy of the resulting displaced frame difference dfd we find the optimal qt decomposition and the optimal dvf jointly using the lagrangian multiplier method and a multilevel dynamic program we introduce a new very fast convex search for the optimal lagrangian multiplier spl lambda which results in a very fast convergence of the lagrangian multiplier method the resulting dvf is spatially inhomogeneous since large blocks are used in areas with simple motion and small blocks in areas with complex motion we also propose a novel motion compensated interpolation scheme which uses the same mathematical tools developed for the qt based motion estimator one of the advantages of this scheme is the globally optimal control of the tradeoff between the interpolation error energy and the dvf smoothness another advantage is that no interpolation of the dvf is required since we directly estimate the dvf and the qt segmentation for the frame which needs to be interpolated we present results with the proposed qt based motion estimator which show that for the same dfd energy the proposed estimator uses about 25 fewer bits than the commonly used block matching algorithm we also experimentally compare the interpolated frames using the proposed motion compensated interpolation scheme with the reconstructed original frames

a piecewise single index model for dimension reduction in this article we propose to use different single index models for observations in different regions of the sample space this approach inherits the estimation efficiency of the single index model in each region and at the same time allows the global model to have multidimensionality in the sense of conventional dimension reduction on the other hand the model can be seen as an extension of cart and a piecewise linear model proposed modeling procedures including identifying the region for every single index model and estimation of the single index models are developed simulation studies and real data analysis are employed to demonstrate the usefulness of the approach computer code and technical details of the method are provided as supplementary material online

application of projection pursuit learning to boundary detection and deblurring in images abstract projection pursuit learning networks pplns have been used in many fields of research but have not been widely used in image processing in this paper we demonstrate how this highly promising technique may be used to connect edges and produce continuous boundaries we also propose the application of ppln to deblurring a degraded image when little or no a priori information about the blur is available the ppln was successful at developing an inverse blur filter to enhance blurry images theory and background information on projection pursuit regression ppr and ppln are also presented

progressive coding of a gaussian source using matching pursuit in this paper the application of matching pursuit mp in progressive coding of memoryless gaussian sources is studied in addition a detailed analysis of the rate distortion performance of our proposed mp encoder is presented and the distortion of the mp encoder is derived in terms of dictionary size and number of quantization levels and the optimum parameters are calculated our analysis is based on a probabilistic model for matching pursuit residual vectors our simulation results verify the accuracy of our analysis and show that matching pursuit can produce an embedded bitstream with comparable quality to existing quantizers the mp encoder outperforms quantizers that are capable of producing embedded bitstreams

adaptive rate distortion optimal in loop quantization for matching pursuit in this paper an adaptive in loop quantization technique is proposed for quantizing inner product coefficients in matching pursuit for each matching pursuit mp stage a different quantizer is used based on the probability distribution of mp coefficients the quantizers are optimized for a given rate budget constraint additionally our proposed adaptive quantization scheme finds the optimal quantizers for each stage based on the already encoded inner product coefficients experimental results show that our proposed adaptive quantization scheme outperforms existing quantization methods used in matching pursuit image coding

tilings of the time frequency plane construction of arbitrary orthogonal bases and fast tiling algorithms the authors consider expansions which give arbitrary orthonormal tilings of the time frequency plane these differ from the short time fourier transform wavelet transform and wavelet packets tilings in that they change over time they show how this can be achieved using time varying orthogonal tree structures which preserve orthogonality even across transitions the method is based on the construction of boundary and transition filters these allow us to construct essentially arbitrary tilings time varying modulated lapped transforms are a special case where both boundary and overlapping solutions are possible with filters obtained by modulation they present a double tree algorithm which for a given signal decides on the best binary segmentation in both time and frequency that is it is a joint optimization of time and frequency splitting the algorithm is optimal for additive cost functions e g rate distortion and results in time varying best bases the main application of which is for compression of nonstationary signals experiments on test signals are presented

transformation of hypersingular integrals and black box cubature in this paper we will consider hypersingular integrals as they arise by transforming elliptic boundary value problems into boundary integral equations first local representations of these integrals will be derived these representations contain so called finite part integrals in the second step these integrals are reformulated as improper integrals we will show that these integrals can be treated by cubature methods for weakly singular integrals as they exist in the literature

the weak chebyshev x greedy algorithm in the unweighted bergman space we study a greedy algorithm called the weak chebyshev x greedy algorithm wcxga and investigate its application to unweighted bergman spaces we first show that the wcxga converges for a wide class of real and complex banach spaces and dictionaries we then prove that certain bergman spaces and their holomorphic monomial dictionaries belong to the class of banach spaces for which the wcxga converges

sparse identification of nonlinear functions and parametric set membership optimality analysis sparse identification can be relevant in the automatic control field to solve several problems for nonlinear systems such as identification control filtering fault detection however identifying a maximally sparse approximation of a nonlinear function is in general an np hard problem the common approach is to use relaxed or greedy algorithms that under certain conditions can provide sparsest solutions in this technical note a combined l1 relaxed greedy algorithm is proposed and conditions are given under which the approximation derived by the algorithm is a sparsest one differently from other conditions available in the literature the ones provided here can be actually verified for any choice of the basis functions defining the sparse approximation a set membership analysis is also carried out assuming that the function to approximate is a linear combination of unknown basis functions belonging to a known set of functions it is shown that the algorithm is able to exactly select the basis functions which define the unknown function and to provide an optimal estimate of their coefficients

q deformed paracommutation relations the representations of an algebra of q deformed paracommutation relations are discussed the bose quantization is shown to be exceptional among all possible para bose quantizations also it is demonstrated that the ignatiev and kuzmin oscillator 1987 is a particular case of the q deformed paraoscillator

geometry based distributed scene representation with omnidirectional vision sensors this paper addresses the problem of efficient representation of scenes captured by distributed omnidirectional vision sensors we propose a novel geometric model to describe the correlation between different views of a 3 d scene we first approximate the camera images by sparse expansions over a dictionary of geometric atoms since the most important visual features are likely to be equivalently dominant in images from multiple cameras we model the correlation between corresponding features in different views by local geometric transforms for the particular case of omnidirectional images we define the multiview transforms between corresponding features based on shape and epipolar geometry constraints we apply this geometric framework in the design of a distributed coding scheme with side information which builds an efficient representation of the scene without communication between cameras the wyner ziv encoder partitions the dictionary into cosets of dissimilar atoms with respect to shape and position in the image the joint decoder then determines pairwise correspondences between atoms in the reference image and atoms in the cosets of the wyner ziv image in order to identify the most likely atoms to decode under epipolar geometry constraints experiments demonstrate that the proposed method leads to reliable estimation of the geometric transforms between views in particular the distributed coding scheme offers similar rate distortion performance as joint encoding at low bit rate and outperforms methods based on independent decoding of the different images

the boundary integro differential equations of three dimensional neumann problem in linear elasticity in this paper we mainly consider the three dimensional neumann problem in linear elasticity which is reduced to a system of integro differential equations on the boundary based on a new representation of the derivatives of the double layer potential furthermore a new boundary finite element method for this neumann problem is presented

best wavelet packet bases in a rate distortion sense a fast rate distortion r d optimal scheme for coding adaptive trees whose individual nodes spawn descendents forming a disjoint and complete basis cover for the space spanned by their parent nodes is presented the scheme guarantees operation on the convex hull of the operational r d curve and uses a fast dynamic programing pruning algorithm to markedly reduce computational complexity applications for this coding technique include r coefman et al s yale univ 1990 generalized multiresolution wavelet packet decomposition iterative subband coders and quadtree structures applications to image processing involving wavelet packets as well as discrete cosine transform dct quadtrees are presented

convolution quadrature method based symmetric galerkin boundary element method for 3 d elastodynamics the boundary integral equations in 3 d elastodynamics contain convolution integrals with respect to the time they can be performed analytically or with the convolution quadrature method the latter time stepping procedure s benefit is the usage of the laplace transformed fundamental solution therefore it is possible to apply this method also to problems where analytical time dependent fundamental solutions might not be known to obtain a symmetric formulation the second boundary integral equation has to be used which unfortunately requires special care in the numerical implementation since it involves hypersingular kernel functions therefore a regularization for closed surfaces of the laplace transformed elastodynamic kernel functions is presented which transforms the bilinear form of the hypersingular integral operator to a weakly singular one supplementarily a weakly singular formulation of the laplace transformed elastodynamic double layer potential is presented this results in a time domain boundary element formulation involving at least only weakly singular integral kernels finally numerical studies validate this approach with respect to different spatial and time discretizations further a comparison with the wider used collocation method is presented it is shown numerically that the presented formulation exhibits a good convergence rate and a more stable behavior compared with collocation methods copyright 2008 john wiley sons ltd

matching wavelet packets to gaussian random processes we consider the problem of approximating a set of arbitrary discrete time gaussian random processes by a single representative wavelet based gaussian process we measure the similarity between the original processes and the wavelet based process with the bhattacharyya 1943 coefficient by manipulating the bhattacharyya coefficient we reduce the task of defining the representative process to finding an optimal unitary matrix of wavelet based eigenvectors an associated diagonal matrix of eigenvalues and a mean vector the matching algorithm we derive maximizes the nonadditive bhattacharyya coefficient in three steps a migration algorithm that determines the best basis by searching through a wavelet packet tree for the optimal unitary matrix of wavelet based eigenvectors and two separate fixed point algorithms that derive an appropriate set of eigenvalues and a mean vector we illustrate the method with two different classes of processes first order markov and bandlimited the technique is also applied to the problem of robust terrain classification in polarimetric sar images

harmonic decomposition of audio signals with matching pursuit we introduce a dictionary of elementary waveforms called harmonic atoms that extends the gabor dictionary and fits well the natural harmonic structures of audio signals by modifying the standard matching pursuit we define a new pursuit along with a fast algorithm namely the fast harmonic matching pursuit to approximate n dimensional audio signals with a linear combination of m harmonic atoms our algorithm has a computational complexity of o mkn where k is the number of partials in a given harmonic atom the decomposition method is demonstrated on musical recordings and we describe a simple note detection algorithm that shows how one could use a harmonic matching pursuit to detect notes even in difficult situations e g very different note durations lots of reverberation and overlapping notes

a posteriori quantization of progressive matching pursuit streams this paper proposes a rate distortion optimal a posteriori quantization scheme for matching pursuit mp coefficients the a posteriori quantization applies to an mp expansion that has been generated offline and cannot benefit of any feedback loop to the encoder in order to compensate for the quantization noise the redundancy of the mp dictionary provides an indicator of the relative importance of coefficients and atom indices and subsequently on the quantization error it is used to define a universal upper bound on the decay of the coefficients sorted in decreasing order of magnitude a new quantization scheme is then derived where this bound is used as an oracle for the design of an optimal a posteriori quantizer the latter turns the exponentially distributed coefficient entropy constrained quantization problem into a simple uniform quantization problem using simulations with random dictionaries we show that the proposed exponentially upper bounded quantization euq clearly outperforms classical schemes stepping on the ideal oracle based approach a suboptimal adaptive scheme is then designed that approximates the euq but still outperforms competing quantization methods in terms of rate distortion characteristics finally the proposed quantization method is studied in the context of image coding it performs similarly to state of the art coding methods and even better at low rates while interestingly providing a progressive stream that is very easy to transcode and adapt to changing rate constraints

sparse representations for image decompositions we are given an image i and a library of templates cal l such that cal l is an overcomplete basis for i the templates can represent objects faces features analytical functions or be single pixel templates canonical templates there are infinitely many ways to decompose i as a linear combination of the library templates each decomposition defines a representation for the image i given cal l what is an optimal representation for i given cal l and how to select it we are motivated to select a sparse compact representation for i and to account for occlusions and noise in the image we present a concave cost function criterion on the linear decomposition coefficients that satisfies our requirements more specifically we study a weighted l norm with 0 p 1 we prove a result that allows us to generate all local minima for the l norm and the global minimum is obtained by searching through the local ones due to the computational complexity i e the large number of local minima we also study a greedy and iterative weighted l matching pursuit strategy

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

optimized atom position and coefficient coding for matching pursuit based image compression in this paper we propose a new encoding algorithm for matching pursuit image coding we show that coding performance is improved when correlations between atom positions and atom coefficients are both used in encoding we find the optimum tradeoff between efficient atom position coding and efficient atom coefficient coding and optimize the encoder parameters our proposed algorithm outperforms the existing coding algorithms designed for matching pursuit image coding additionally we show that our algorithm results in better rate distortion performance than jpeg 2000 at low bit rates

local minimax learning of functions with best finite sample estimation error bounds applications to ridge and lasso regression boosting tree learning kernel machines and inverse problems optimal local estimation is formulated in the minimax sense for inverse problems and nonlinear regression this theory provides best mean squared finite sample error bounds for some popular statistical learning algorithms and also for several optimal improvements of other existing learning algorithms such as smoothing splines and kernel regularization the bounds and improved algorithms are not based on asymptotics or bayesian assumptions and are truly local for each query not depending on cross validating estimates at other queries to optimize modeling parameters results are given for optimal local learning of approximately linear functions with side information context using real algebraic geometry in particular finite sample error bounds are given for ridge regression and for a local version of lasso regression the new regression methods require only quadratic programming with linear or quadratic inequality constraints for implementation greedy additive expansions are then combined with local minimax learning via a change in metric an optimal strategy is presented for fusing the local minimax estimators of a class of experts providing optimal finite sample prediction error bounds from random forests local minimax learning is extended to kernel machines best local prediction error bounds for finite samples are given for tikhonov regularization the geometry of reproducing kernel hilbert space is used to derive improved estimators with finite sample mean squared error mse bounds for class membership probability in two class pattern classification problems a purely local cross validation free algorithm is proposed which uses fisher information with these bounds to determine best local kernel shape in vector machine learning finally a locally quadratic solution to the finite fourier moments problem is presented after reading the first three sections the reader may proceed directly to any of the subsequent applications sections

model checking in regression via dimension reduction lack of fit checking for parametric and semiparametric models is essential in reducing misspecification the efficiency of most existing model checking methods drops rapidly as the dimension of the covariates increases we propose to check a model by projecting the fitted residuals along a direction that adapts to the systematic departure of the residuals from the desired pattern consistency of the method is proved for parametric and semiparametric regression models a bootstrap implementation is also discussed simulation comparisons with several existing methods are made suggesting that the proposed methods are more efficient than the existing methods when the dimension increases air pollution data from chicago are used to illustrate the procedure

in loop atom modulus quantization for matching pursuit and its application to video coding this paper provides a precise analytical study of the selection and modulus quantization of matching pursuit mp coefficients we demonstrate that an optimal rate distortion trade off is achieved by selecting the atoms up to a quality dependent threshold and by defining the modulus quantizer in terms of that threshold in doing so we take into account quantization error re injection resulting from inserting the modulus quantizer inside the mp atom computation loop in loop quantization not only improves coding performance but also affects the optimal quantizer design for both uniform and nonuniform quantization we measure the impact of our work in the context of video coding for both uniform and nonuniform quantization the precise understanding of the relation between atom selection and quantization results in significant improvements in terms of coding efficiency at high bitrates the proposed nonuniform quantization scheme results in 0 5 to 2 db improvement over the previous method

filter design with low complexity coefficients we introduce a heuristic for designing filters that have low complexity coefficients as measured by the total number of nonzeros digits in the binary or canonic signed digit csd representations of the filter coefficients while still meeting a set of design specifications such as limits on frequency response magnitude phase and group delay numerical examples show that the method is able to attain very low complexity designs with only modest relaxation of the specifications

pattern classification using projection pursuit abstract this article discusses the adaptation of recently developed regression techniques to classifier design apart from finite sample effects projection pursuit pp regression may be used to model a desired response class as a sum of ridge functions according to a minimum expected squared error criterion this approach can be shown to furnish an optimal discriminant function which can satisfy the neyman pearson criterion over all possible thresholds basis function expansions are used instead of smoothed histograms to reduce computation since good approximation of a discriminant by a linear combination of moderate number of ridge functions may not be easy we introduce an improved method utilizing a nonlinear weighting function

on a conjecture of huber concerning the convergence of projection pursuit regression we generalize the projection pursuit procedure of friedman and stuetzle abstract version and prove strong convergence this answers a question of huber

wavelet footprints theory algorithms and applications wavelet based algorithms have been successful in different signal processing tasks the wavelet transform is a powerful tool because it manages to represent both transient and stationary behaviors of a signal with few transform coefficients discontinuities often carry relevant signal information and therefore they represent a critical part to analyze we study the dependency across scales of the wavelet coefficients generated by discontinuities we start by showing that any piecewise smooth signal can be expressed as a sum of a piecewise polynomial signal and a uniformly smooth residual theorem 1 we then introduce the notion of footprints which are scale space vectors that model discontinuities in piecewise polynomial signals exactly we show that footprints form an overcomplete dictionary and develop efficient and robust algorithms to find the exact representation of a piecewise polynomial function in terms of footprints this also leads to efficient approximation of piecewise smooth functions finally we focus on applications and show that algorithms based on footprints outperform standard wavelet methods in different applications such as denoising compression and nonblind deconvolution in the case of compression we also prove that at high rates footprint based algorithms attain optimal performance theorem 3

integration of singular integrals for the galerkin type boundary element method in 3d elasticity abstract the mixed boundary value problem in three dimensional linear elasticity is solved via a system of boundary integral equations the galerkin approximation of the singular and hypersingular integral equations leads to hyper singular and regular double integrals the numerical cubature of the singular integrals is discussed in the case of domains which have piecewise smooth surfaces with a riemann metric structure we give a method for reducing finite part integrals to at most cauchy singular integrals the presented integration method applied to cauchy singular integrals leads to explicitly given regular integrand functions which can be integrated by standard gaussian product quadrature rules the number of necessary gaussian knots depends on the shape of the boundary elements and on the curvature of the surface we give estimates of the quadrature error including constants which mark the properties of the boundary elements the error estimates can be taken to implement adaptive cubature methods the numerical example is a mixed boundary value problem with corner and edge singularities

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