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

functions analytic on the half plane as quantum mechanical states a transform between the state space of one dimensional quantum mechanical systems and a direct sum of two spaces of square integrable functions analytic on the open upper half plane is constructed it gives a representation of usual quantum mechanics on which the free evolution is trivial and the representation of canonical transformation very simple generalizations to higher dimensions are also discussed

a wavelet or lifting scheme based imputation method summary the paper proposes a new approach to imputation using the expected sparse representation of a surface in a wavelet or lifting scheme basis our method incorporates a bayesian mixture prior for these wavelet coefficients into a gibbs sampler to generate a complete posterior distribution for the variable of interest intuitively the estimator operates by borrowing strength from those observed neighbouring values to impute at the unobserved sites we demonstrate the strong performance of our estimator in both one and two dimensional imputation problems where we also compare its application with the standard imputation techniques of kriging and thin plate splines

optimized wavelet denoising for self similar alpha stable processes we investigate the performance of wavelet shrinkage methods for the denoising of symmetric alpha stable text s alpha text s self similar stochastic processes corrupted by additive white gaussian noise awgn where alpha is tied to the sparsity of the process the wavelet transform is assumed to be orthonormal and the shrinkage function minimizes the mean square approximation error mmse estimator we derive the corresponding formula for the expected value of the averaged estimation error we show that the predicted mmse is a monotone function of a simple criterion that depends on the wavelet and the statistical parameters of the process using the calculus of variations we then optimize this criterion to find the best performing wavelet within the extended family of meyer wavelets which are bandlimited these are compared with the daubechies wavelets which are compactly supported in time we find that the wavelets that are shorter in time in particular the haar basis are better suited to denoise the sparser processes say alpha while the bandlimited ones including the held and shannon wavelets offer the best performance for alpha 1 6 the limit corresponding to the gaussian case fbm with alpha 2

joint space frequency segmentation using balanced wavelet packet trees for least cost image representation we examine the question of how to choose a space varying filterbank tree representation that minimizes some additive cost function for an image the idea is that for a particular cost function e g energy compaction or quantization distortion some tree structures perform better than others while the wavelet tree represents a good choice for many signals it is generally outperformed by the best tree from the library of wavelet packet frequency selective trees the double tree library of bases performs better still by allowing different wavelet packet trees over all binary spatial segments of the image we build on this foundation and present efficient new pruning algorithms for both one and two dimensional 1 d and 2 d trees that will find the best basis from a library that is many times larger than the library of the single tree or double tree algorithms the augmentation of the library of bases overcomes the constrained nature of the spatial variation in the double tree bases and is a significant enhancement in practice use of these algorithms to select the least cost expansion for images with a rate distortion cost function gives a very effective signal adaptive compression scheme this scheme is universal in the sense that without assuming a model for the signal or making use of training data it performs very well over a large class of signal types in experiments it achieves compression rates that are competitive with the best training based schemes

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

low entropy image pyramids for efficient lossless coding an efficient image source coding technique gives good compression performance at low computational complexity this research introduces an efficient coding technique based on pyramid coding that involves transforming an image into an equivalent lower entropy form prior to lossless coding the proposed method is also a multiresolution technique that facilitates progressive image transmission

painless nonorthogonal expansions in a hilbert space h discrete families of vectors hj with the property that f j hj f hj for every f in h are considered this expansion formula is obviously true if the family is an orthonormal basis of h but also can hold in situations where the hj are not mutually orthogonal and are overcomplete the two classes of examples studied here are i appropriate sets of weyl heisenberg coherent states based on certain non gaussian fiducial vectors and ii analogous families of affine coherent states it is believed that such quasiorthogonal expansions will be a useful tool in many areas of theoretical physics and applied mathematics

superposition frames for adaptive time frequency analysis and fast reconstruction in this paper we introduce a broad family of adaptive linear time frequency representations termed superposition frames and show that they admit desirable fast overlap add reconstruction properties akin to standard short time fourier techniques this approach stands in contrast to many adaptive time frequency representations in the existing literature which while more flexible than standard fixed resolution approaches typically fail to provide for efficient reconstruction and often lack the regular structure necessary for precise frame theoretic analysis our main technical contributions come through the development of properties which ensure that our superposition construction provides for a numerically stable invertible signal representation our primary algorithmic contributions come via the introduction and discussion of two signal adaptation schemes based on greedy selection and dynamic programming respectively we conclude with two short enhancement examples that serve to highlight potential applications of our approach

fast search for best representations in multitree dictionaries we address the best basis problem or more generally the best representation problem given a signal a dictionary of representations and an additive cost function the aim is to select the representation from the dictionary which minimizes the cost for the given signal we develop a new framework of multitree dictionaries which includes some previously proposed dictionaries as special cases we show how to efficiently find the best representation in a multitree dictionary using a recursive tree pruning algorithm we illustrate our framework through several examples including a novel block image coder which significantly outperforms both the standard jpeg and quadtree based methods and is comparable to embedded coders such as jpeg2000 and spiht

a unifying framework for lossless and progressive image coding progressive coding is a desirable feature for image database telebrowsing or image transmissions over low bandwidth channels furthermore for some applications exact image reconstruction is required in this paper we show that most of the lossless and progressive coders can be described by a common nonlinear subband decomposition scheme this unifying framework provides useful guidelines for the analysis and improvement of the considered decomposition methods finally we compare the respective performances of these methods in terms of shannon entropy for several images and also evaluate their compression ability when combined with a hierarchical coding technique

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

transforms associated to square integrable group representations i general results let g be a locally compact group which need not be unimodular let x u x x g be an irreducible unitary representation of g in a hilbert space h u assume that u is square integrable i e that there exists in h u at least one nonzero vector g such that u x g g 2 dx we give here a reasonably self contained analysis of the correspondence associating to every vector f h u the function u x g f on g discussing its isometry characterization of the range inversion and simplest interpolation properties this correspondence underlies many properties of generalized coherent states

time varying filter banks and wavelets time varying filter banks and wavelets are studied and a design procedure is presented in the resulting analysis synthesis structures the analysis filters and the corresponding synthesis filters the number of bands and the decimation rates can be changed with time such structures can be considered as time frequency overlapping block transforms from this viewpoint the tiling of the time frequency plane and the corresponding basis functions are changed in time the time varying discrete wavelet transforms can be considered a special case of time varying overlapping block transforms and are studied in detail the formulation is based on the time domain formulation of time varying analysis synthesis structures the design procedure can be used to design time varying perfectly invertible transformations with a finite number of distinct analysis structures for adaptive filter bank application a least squares design method is also studied

optimum quantizer performance for a class of non gaussian memoryless sources the performance of optimum quantizers subject to an entropy constraint is studied for a wide class of memoryless sources for a general distortion criterion necessary conditions are developed for optimality and a recursive algorithm is described for obtaining the optimum quantizer under a mean square error criterion the performance of entropy encoded uniform quantization of memoryless gaussian sources is well known to be within 0 255 bits sample of the rate distortion bound at relatively high rates despite claims to the contrary it is demonstrated that similar performance can be expected for a wide range of memoryless sources indeed for the cases considered the worst case performance is observed to be less than 0 3 bits sample from the rate distortion bound and in most cases this disparity is less at iow rates

a new class of biorthogonal wavelet systems for image transform coding we construct general biorthogonal coifman wavelet systems a new class of compactly supported biorthogonal wavelet systems with vanishing moments equally distributed for a scaling function and wavelet pair a time domain design method is employed and closed form expressions for the impulse responses and the frequency responses of the corresponding dual filters are derived the resulting filter coefficients are all dyadic fractions which is an attractive feature in the realization of multiplication free discrete wavelet transform even ordered systems in this family are symmetric which correspond to linear phase dual filters in particular three filterbanks fbs in this family are systematically verified to have competitive compression potential to the 9 7 tap biorthogonal wavelet fb by cohen et al 1992 which is currently the most widely used one in the field of wavelet transform coding in addition the proposed fb s have much smaller computational complexity in terms of floating point operations required in transformation and therefore indicate a better tradeoff between compression performance and computational complexity

orthogonal time varying filter banks and wavelet packets considers the construction of orthogonal time varying filter banks by examining the time domain description of the two channel orthogonal filter bank the authors find it possible to construct a set of orthogonal boundary filters which allows to apply the filter bank to one sided or finite length signals without redundancy or distortion the method is constructive and complete there is a whole space of orthogonal boundary solutions and there is considerable freedom for optimization this may be used to generate subband tree structures where the tree varies over time and to change between different filter sets the authors also show that the iteration of discrete time time varying filter banks gives continuous time bases just as in the stationary case this gives rise to wavelet or wavelet packet bases for half line and interval regions

flexible tree structured signal expansions using time varying wavelet packets addresses the problem of finding the best time varying filter bank tree structured representation for a signal the tree is allowed to vary at regular intervals and the spacing of these changes can be arbitrarily short the question of how to choose tree structured representations of signals based on filter banks is considered wavelets and their adaptive version known as wavelet packets represent one approach that is popular wavelet packets are subband trees where the tree is chosen to match the characteristics of the signal variations where the tree varies over time have been proposed as the double tree and the time frequency tree algorithms time variation adds a further level of adaptivity in all of the approaches proposed so far the tree must be either fixed for the whole duration of the signal or fixed for its dyadic subintervals the solution that we propose as it allows more flexible variation is an advance on the wavelet packet algorithm the double tree algorithm and the recently proposed time frequency tree algorithm our solution is based on casting it in a dynamic programming dp setting focusing on compression applications we use a lagrangian cost of distortion spl lambda spl times rate as the objective function and explain our algorithm in detail pointing out its relation to existing approaches to the problem we demonstrate that the new algorithm indeed searches a larger library of representations than previously possible and that overcoming the constraint of dyadic time segmentations gives a significant improvement in practice

lossless image compression by quantization feedback in a content driven enhanced laplacian pyramid in this paper the effects of quantization noise feedback on the entropy of laplacian pyramids are investigated this technique makes it possible for the maximum absolute reconstruction error to be easily and strongly upper bounded near lossless coding and therefore allows reversible compression the entropy minimizing optimum quantizer is obtained by modeling the first order distributions of the differential signals as laplacian densities and by deriving a model for the equivalent memoryless entropy a novel approach based on an enhanced laplacian pyramid is proposed for the compression either lossless or lossy of gray scale images major details are prioritized through a content driven decision rule embedded in a uniform threshold quantizer with noise feedback lossless coding shows improvements over reversible joint photographers expert group jpeg and the reduced difference pyramid schemes while lossy coding outperforms jpeg with a significant peak signal to noise ratio psnr gain also subjective quality is higher even at very low bit rates due to the absence of the annoying impairments typical of jpeg moreover image versions having resolution and snr that are both progressively increasing are made available at the receiving end from the earliest retrieval stage on as intermediate steps of the decoding procedure without any additional cost

the isomorphism problem for universal enveloping algebras of nilpotent lie algebras in this paper we study the isomorphism problem for the universal enveloping algebras of nilpotent lie algebras we prove that if the characteristic of the underlying field is not 2 or 3 then the isomorphism type of a nilpotent lie algebra of dimension at most 6 is determined by the isomorphism type of its universal enveloping algebra examples show that the restriction on the characteristic is necessary

progressive image transmission using vector quantization on images in pyramid form a progressive image transmission scheme in which vector quantization is applied to images represented by pyramids is proposed a mean pyramid representation of an image is first built up by forming a sequence of reduced size images by averaging over blocks of 2 2 pixels a difference pyramid is then built up by taking the differences between successive levels in the mean pyramid progressive transmission is achieved by sending all the nodes in the difference pyramid starting from the top level and ending at the bottom level the kth approximate image can be formed by adding the information of level k to the previously reproduced k 1 st approximation to gain efficiency vector quantization is applied to the difference pyramid of the image on a level by level basis if the errors due to quantization at level k are properly delivered and included in the next level k 1 then it is demonstrated that the original image can be reconstructed an entropy coder is used to encode the final residual error image losslessly thus ensuring perfect reproduction of the original image the experiments demonstrate that it is possible to achieve simultaneously lossless and progressive transmission with compression at the intermediate level the use of vector quantization results in a coding gain over that obtained using only a huffman coder excellent reproduction is achieved at a bit rate of only 0 06 bits pixel

on the least asymmetric wavelets the asymmetry of daubechies 1988 1992 scaling functions and wavelets can be diminished by minimizing a special second moment in time for the wavelet generating discrete time filter the moment is involved in an uncertainty relation for discrete time signals other measures of asymmetry are addressed as well and corresponding results are compared

vector valued nonstationary gabor frames abstract as an extension of gabor frames nonstationary gabor nsg frames were recently introduced in adaptive signal analysis they allow for efficient reconstruction with flexible sampling and varying window functions in this paper we generalize the notion of nsg frames from l 2 r to the vector valued hilbert space l 2 r c l and investigate the resulting vector valued nsg frames we derive a walnut s representation of the mixed frame operator and provide some necessary sufficient conditions for a vector valued nsg system to be a frame for l 2 r c l furthermore we show the existence of painless vector valued nsg frames and of vector valued nsg frames with fast decaying window functions

multiscale poisson data smoothing summary the paper introduces a framework for non linear multiscale decompositions of poisson data that have piecewise smooth intensity curves the key concept is conditioning on the sum of the observations that are involved in the computation of a given multiscale coefficient within this framework most classical wavelet thresholding schemes for data with additive homoscedastic noise can be used any family of wavelet transforms orthogonal biorthogonal or second generation can be incorporated in this framework our second contribution is to propose a bayesian shrinkage approach with an original prior for coefficients of this decomposition as such the method combines the advantages of the haar fisz transform with wavelet smoothing and bayesian multiscale likelihood models with additional benefits such as extendability towards arbitrary wavelet families simulations show an important reduction in average squared error of the output compared with the present techniques of anscombe or fisz variance stabilization or multiscale likelihood modelling

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

nonlocal image restoration with bilateral variance estimation a low rank approach simultaneous sparse coding ssc or nonlocal image representation has shown great potential in various low level vision tasks leading to several state of the art image restoration techniques including bm3d and lssc however it still lacks a physically plausible explanation about why ssc is a better model than conventional sparse coding for the class of natural images meanwhile the problem of sparsity optimization especially when tangled with dictionary learning is computationally difficult to solve in this paper we take a low rank approach toward ssc and provide a conceptually simple interpretation from a bilateral variance estimation perspective namely that singular value decomposition of similar packed patches can be viewed as pooling both local and nonlocal information for estimating signal variances such perspective inspires us to develop a new class of image restoration algorithms called spatially adaptive iterative singular value thresholding saist for noise data saist generalizes the celebrated bayesshrink from local to nonlocal models for incomplete data saist extends previous deterministic annealing based solution to sparsity optimization through incorporating the idea of dictionary learning in addition to conceptual simplicity and computational efficiency saist has achieved highly competent often better objective performance compared to several state of the art methods in image denoising and completion experiments our subjective quality results compare favorably with those obtained by existing techniques especially at high noise levels and with a large amount of missing data

enveloping algebras of simple three dimensional lie algebras abstract the killing form of a simple three dimensional lie algebra is shown to classify the lie algebra and its enveloping algebra the lie algebra is isomorphic to the two by two trace zero matrices the so called split case if and only if the form is isotropic in the sense of quadratic form theory in characteristic zero the skew field of quotients of the enveloping algebra is shown to be isomorphic to a weyl skew field if and only if the lie algebra is split automorphisms of the lie algebra and its enveloping algebra are induced by isometries of the killing form in the nonsplit case

wavelet packet image coding using space frequency quantization we extend our previous work on space frequency quantization sfq for image coding from wavelet transforms to the more general wavelet packet transforms the resulting wavelet packet coder offers a universal transform coding framework within the constraints of filterbank structures by allowing joint transform and quantizer design without assuming a priori statistics of the input image in other words the new coder adaptively chooses the representation to suit the image and the quantization to suit the representation experimental results show that for some image classes our new coder gives excellent coding performance

best basis search in lapped dictionaries this paper proposes analyzes and illustrates several best basis search algorithms for dictionaries consisting of lapped orthogonal bases it improves upon the best local cosine basis selection based on a dyadic tree by considering larger dictionaries of bases it is shown that this can result in sparser representations and approximate shift invariance an algorithm that is strictly shift invariant is also provided the experiments in this paper suggest that the new dictionaries can be advantageous for time frequency analysis compression and noise removal accelerated versions of the basic algorithm are provided that explore various tradeoffs between computational efficiency and adaptability it is shown that the proposed algorithms are in fact applicable to any finite dictionary comprised of lapped orthogonal bases one such novel dictionary is proposed that constructs the best local cosine representation in the frequency domain and it is shown that the new dictionary is better suited for representing certain types of signals

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

wavelet based linear system modeling and adaptive filtering it is shown how linear time varying systems can be modeled in several different ways by discrete time wavelets or more generally by some set of functions interpretation of physical meanings possible efficiency and other characteristics of the modeling are considered system identification minimizing the mean square output error is studied optimal coefficients and the corresponding minimum mean square error are found and they are in general time varying least mean square adaptive filtering algorithms are derived for on line filtering and system identification theoretically and by simulations the advantages of using wavelet based filtering are shown separation of adaptation effects from unknown time varying system behavior and fast convergence adaptive coefficients estimated by a recursive least square algorithm can tend toward constants even in the case of time varying systems time invariant system identification and adaptive filtering is given as a special case of the general time varying setting

time varying lapped transforms and wavelet packets the perfect reconstruction conditions for a time varying lapped transform paraunitary filter bank are developed through the factorization of the transform matrix into sparse factors a general formulation is presented allowing one to switch between two paraunitary filter banks however the extended lapped transform elt is often used as an example furthermore an adaptive wavelet packet is developed employing a time varying tree association of elts in all cases perfect reconstruction is inherently assured

image interpolation for progressive transmission by using radial basis function networks investigates the application of a radial basis function network rbfn to hierarchical image coding for progressive transmission the rbfn is then used to generate an interpolated image from the subsampled version an efficient method of computing the network parameters is developed for reduction in computational and memory requirements the coding method does not suffer from problems of blocking effect and can produce the coarsest image quickly quantization error effects introduced at one stage are considered in decoding images at the following stages thus allowing lossless progressive transmission

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

a progressively predictive image pyramid for efficient lossless coding a low entropy pyramidal image data structure suited for lossless coding and progressive transmission is proposed in this work the new coder called the progressively predictive pyramid ppp is based on the well known laplacian pyramid by introducing inter resolution predictors into the original laplacian pyramid we show that the entropy level in the original pyramid can be reduced significantly to take full advantage of progressive transmission a scheme is introduced to create the predictor adaptively thus eliminating the need to transmit the predictor and reducing the coding overheads a method for designing the predictor is presented numerical results show that ppp is superior to traditional approaches to pyramid generation in the sense that the pyramids generated by ppp always have significantly lower entropy values

quantum field theory in ninety minutes on presente divers aspects de la theorie quantique des champs la theorie p 2 a 2 dimensions la theorie 3 4 a 3 dimensions la theorie de yang mills a 4 dimensions

adaptive transient solution of nonuniform multiconductor transmission lines using wavelets this paper presents a highly adaptive algorithm for the transient simulation of nonuniform interconnects loaded with arbitrary nonlinear and dynamic terminations the discretization of the governing equations is obtained through a weak formulation using biorthogonal wavelet bases as trial and test functions it is shown how the multiresolution properties of wavelets lead to very sparse approximations of the voltages and currents in typical transient analyzes a simple yet effective time space adaptive algorithm capable of selecting the minimal number of unknowns at each time iteration is described numerical results show the high degree of adaptivity of the proposed scheme

the laplacian pyramid as a compact image code we describe a technique for image encoding in which local operators of many scales but identical shape serve as the basis functions the representation differs from established techniques in that the code elements are localized in spatial frequency as well as in space pixel to pixel correlations are first removed by subtracting a lowpass filtered copy of the image from the image itself the result is a net data compression since the difference or error image has low variance and entropy and the low pass filtered image may represented at reduced sample density further data compression is achieved by quantizing the difference image these steps are then repeated to compress the low pass image iteration of the process at appropriately expanded scales generates a pyramid data structure the encoding process is equivalent to sampling the image with laplacian operators of many scales thus the code tends to enhance salient image features a further advantage of the present code is that it is well suited for many image analysis tasks as well as for image compression fast algorithms are described for coding and decoding

interpolating wavelet collocation method of time dependent maxwell s equations characterization of electrically large optical waveguide discontinuities biorthogonal interpolating wavelets have been applied to electromagnetic field modeling through the wavelet collocation method in time domain yielding a versatile first principle algorithm for the solution of time dependent maxwell s equations with inhomogeneous media the resulting scheme maintains high accuracy while by virtue of its sub gridding capability significant reduction of the computational expenditure has been obtained the proposed method has been applied to the analysis of two dimensional dielectric waveguide discontinuities particularly for the modeling of electrically large optical waveguides where the dimension of the analyzed structure is much larger than the wavelength of the highest frequency content of the transmitted signal the proposed method has been proven to be highly efficient compared to the standard finite difference method

ondelettes and phase cell cluster expansions a vindication y meyer has recently developed a particularly useful o n basis forl2 r d expansions using this basis i e expansions into ondelettes or wavelets have yielded important new results in soft and hard analysis the expansion into ondelettes of a boson scalar field naturally leads to phase cell cluster expansions a formalism already developed by the authors using other related bases adoption of ondelettes expansions into the phase cell program gives improvements of some extant results and excises an early error

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

recursive biorthogonal interpolating wavelets and signal adapted interpolating filter banks in this paper by combining the ideas of the recursive wavelets with second generation wavelets a family of recursive biorthogonal interpolating wavelets rbiws is developed the rbiws have simple shape parameter vectors on each level which allows a multichannel decomposition algorithm and provides a flexible structure for designing signal adapted interpolating filter banks in the single level case an efficient approach to design an optimum two channel biorthogonal interpolating filter bank is proposed which maximizes the coding gain under the traditional quantization noise assumption furthermore in the multilevel case using level wise optimization of the shape parameter vectors signal adapted tree structured recursive biorthogonal interpolating filter banks rbifbs are designed which are efficient in computation and can remarkedly improve the coding gain finally numerical results demonstrate the effectiveness of the proposed methods

a class of counterexamples to the gel fand kirillov conjecture limburgs univ centrum dept wni b 3500 diepenbeek belgium alev j univ reims ufr sci dept math moulin housse bp 347 f 51062 reims france

a block spin construction of ondelettes part i lemarie functions using block spin assignments we construct anl2 orthonormal basis consisting of dyadic scalings and translates of just a finite number of functions these functions have exponential localization and for even values of a construction parameterm one can make them classcm 1 with vanishing moments up to orderm inclusive such a basis has an important application to phase cell cluster expansions in quantum field theory

phase space localization theorem for ondelettes it is proven that an orthonormal basis of ondelettes can never have exponential localization in both position space and momentum space

lossless image compression and encryption using scan abstract this paper presents a new methodology which performs both lossless compression and encryption of binary and gray scale images the compression and encryption schemes are based on scan patterns generated by the scan methodology the scan is a formal language based two dimensional spatial accessing methodology which can efficiently specify and generate a wide range of scanning paths or space filling curves this paper presents a brief overview of scan compression and decompression algorithms encryption and decryption algorithms and test results of the methodology

theory implementation and applications of nonstationary gabor frames signal analysis with classical gabor frames leads to a fixed time frequency resolution over the whole time frequency plane to overcome the limitations imposed by this rigidity we propose an extension of gabor theory that leads to the construction of frames with time frequency resolution changing over time or frequency we describe the construction of the resulting nonstationary gabor frames and give the explicit formula for the canonical dual frame for a particular case the painless case we show that wavelet transforms constant q transforms and more general filter banks may be modeled in the framework of nonstationary gabor frames further we present the results in the finite dimensional case which provides a method for implementing the above mentioned transforms with perfect reconstruction finally we elaborate on two applications of nonstationary gabor frames in audio signal processing namely a method for automatic adaptation to transients and an algorithm for an invertible constant q transform

lattice structures for optimal design and robust implementation of two channel perfect reconstruction qmf banks a lattice structure and an algorithm are presented for the design of two channel qmf quadrature mirror filter banks satisfying a sufficient condition for perfect reconstruction the structure inherently has the perfect reconstruction property while the algorithm ensures a good stopband attenuation for each of the analysis filters implementations of such lattice structures are robust in the sense that the perfect reconstruction property is preserved in spite of coefficient quantization the lattice structure has the hierarchical property that a higher order perfect reconstruction qmf bank can be obtained from a lower order perfect reconstruction qmf bank simply by adding more lattice sections several numerical examples are provided in the form of design tables

rounding transform and its application for lossless pyramid structured coding a new transform called the rounding transform rt is introduced in this paper this transform maps an integer vector onto another integer vector by using weighted average and difference filters followed by a rounding operation the rt can be applied to lossless pyramid structured coding with various elementary block sizes and filters in addition it generalizes other mean based lossless pyramid structured coding schemes

wavelet transform based adaptive filters analysis and new results in this paper the wavelet transform is used in an adaptive filtering structure the coefficients of the adaptive filter are updated by the help of the least mean square lms algorithm first the wavelet transform based adaptive filter wtaf is described and it is analyzed for its wiener optimal solution then the performance of the wtaf is studied by the help of learning curves for three different convergence factors 1 constant convergence factor 2 time varying convergence factor and 3 exponentially weighted convergence factor the exponentially weighted convergence factor is proposed to introduce scale based variation to the weight update equation it is shown for two different sets of data that the rate of convergence increases significantly for all three wtaf structures as compared to that of time domain lms the high convergence rates of the wtaf give us reason to expect that it will perform well in tracking rapid changes in a signal

m band biorthogonal interpolating wavelets via lifting scheme recently the lifting scheme was generalized to the multidimensional and multiband cases and was used to design m band interpolating scaling filters and their duals based on this idea we develop a new lifting pattern namely the progressive lifting pattern this pattern allows us to pairwise generate m band interpolating filterbanks and wavelets by the order from lowpass to highpass filters a complete lifting procedure is divided into m 1 simple steps in each step a pair of filters the l th filter and its dual are generated in this way an m band biorthogonal interpolating filterbank wavelet is determined by m m 1 lifting filters the first 2 m 1 lifting filters completely characterize the two scaling filters as well as the vanishing moments of bandpass and highpass filters the residual m 1 m 2 lifting filters are used to pairwise optimize the bandpass and highpass filters in terms of the criterion of stopband energy minimization the obtained m band biorthogonal interpolating filterbanks and wavelets provide excellent frequency characteristics in particular low stopband sidelobes furthermore the pattern is also utilized to design signal adapted interpolating filterbanks and their rational coefficient counterparts in terms of subband coding gain the obtained filterbanks achieve large subband coding gains the rational coefficient filterbanks preserve the biorthogonality and allow wavelet transforms from integers to integers and a unifying lossy lossless coding framework at the cost of a slight degradation in subband coding gain

symmetry based scalable lossless compression of 3d medical image data we propose a novel symmetry based technique for scalable lossless compression of 3d medical image data the proposed method employs the 2d integer wavelet transform to decorrelate the data and an intraband prediction method to reduce the energy of the sub bands by exploiting the anatomical symmetries typically present in structural medical images a modified version of the embedded block coder with optimized truncation ebcot tailored according to the characteristics of the data encodes the residual data generated after prediction to provide resolution and quality scalability performance evaluations on a wide range of real 3d medical images show an average improvement of 15 in lossless compression ratios when compared to other state of the art lossless compression methods that also provide resolution and quality scalability including 3d jpeg2000 jpeg2000 and h 264 avc intra coding

numerical methods for the generalized zakharov system we present two numerical methods for the approximation of the generalized zakharov system zs the first one is the time splitting spectral tssp method which is explicit time reversible and time transverse in variant if the generalized zs is keeps the same decay rate of the wave energy as that in the generalized zs gives exact results for the plane wave solution and is of spectral order accuracy in space and second order accuracy in time the second one is to use a local spectral method the discrete singular convolution dsc for spatial derivatives and the fourth order runge kutta rk4 for time integration which is of high the same as spectral order accuracy in space and can be applied to deal with general boundary conditions in order to test accuracy and stability we compare these two methods with other existing methods fourier pseudospectral method fps and wavelet galerkin method wg for spatial derivatives combining with the rk4 for time integration as well as the standard finite difference method fd for solving the zs with a solitary wave solution furthermore extensive numerical tests are presented for plane waves solitary wave collisions in 1d as well as a 2d problem of the generalized zs numerical results show that tssp and dsc are spectralorder accuracy in space and much more accurate than fd and for stability tssp requires k o h dsc rk4 requires k o h2 for fixed acoustic speed where k is the time step and h is the spatial mesh size