theory and lattice structure of complex paraunitary filterbanks with filters of hermitian symmetry antisymmetry properties the theory of the real coefficient linear phase filterbank lpfb is extended to the complex case in two ways leading to two generalized classes of m channel filterbanks one is the symmetric antisymmetric filterbank safb where all filters are symmetric or antisymmetric the other is the complex linear phase filterbank clpfb where all filters are hermitian symmetric or hermitian antisymmetric and hence have the linear phase property necessary conditions on the filter symmetry polarity and lengths for the existence of permissible solutions are investigated complete and minimal lattice structures are developed for the paraunitary safb and paraunitary clpfb where the channel number m is arbitrary even or odd and the subband filters could have different lengths with the elementary unitary matrices in the structure of the paraunitary safb constrained to be real and orthogonal the structure covers the most general real coefficient paraunitary lpfbs compared with the existing results the number of parameters is reduced significantly

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

error inhomogeneity in wavelet based compression despite the popularity of wavelet based image compression its shortcoming of having error inhomogeneity ei namely the error that is different for even and odd pixel location has not been previously analyzed and formally addressed the difference can be substantial up to 3 4 db peak signal to noise ratio psnr for some images and compression ratios in this paper we show that the ei is caused by asymmetrical filtering of quantization errors after the upsampling step in wavelet synthesis process nonuniformity and correlation of quantization errors can also contribute to this ei albeit to a smaller degree in addition to explaining the source of ei the model we developed in this paper also allows predicting its amount for a given wavelet furthermore we show how to redesign wavelet filters to reduce this ei at a cost of a small reduction in the overall psnr performance for applications that are sensitive to psnr degradation we also show how to design wavelet filters that can gradually tradeoff psnr performance for reduced ei

extension of the certain generalized stresses method for the stochastic analysis of homogeneous and laminated shells abstract the paper presents an extension of the certain generalized stresses method cgsm for the static finite element analysis of homogeneous and laminated shells with variability the basic assumption is that the generalized stresses do not depend on input parameters perturbation the cgsm is a non intrusive method that requires only one finite element analysis with some load cases to calculate the variability of mechanical quantities of interest the uncertain input parameters are material and physical properties uniform random parameters as well as random fields are considered the displacements statistical results mean value standard deviation and distribution are obtained by monte carlo simulations using a semi analytical formula two examples are treated the scordelis lo shell roof and an automotive windscreen the method provides results of good quality and is very economical from a computational time point of view

general embedded quantization for wavelet based lossy image coding embedded quantization is a mechanism employed by many lossy image codecs to progressively refine the distortion of a transformed image currently the most common approach to do so in the context of wavelet based image coding is to couple uniform scalar deadzone quantization usdq with bitplane coding bpc usdq bpc is convenient for its practicality and has proved to achieve competitive coding performance but the quantizer established by this scheme does not allow major variations this paper introduces a multistage quantization scheme named general embedded quantization geq that provides more flexibility to the quantizer geq schemes can be devised for specific decoding rates achieving optimal coding performance practical approaches of geq schemes achieve coding performance similar to that of usdq bpc while requiring fewer quantization stages the performance achieved by geq is evaluated in this paper through experimental results carried out in the framework of modern image coding systems

dynamic response analysis of stochastic truss structures under non stationary random excitation using the random factor method abstract the dynamic characteristics and responses of stochastic truss structures under non stationary random excitation are investigated using a new method called the random factor method rfm using the rfm the structural physical parameters and geometry can be considered as random variables based on the assumption that the randomness on each element is the same for all elements the structural stiffness and mass matrices can then respectively be described by the product of two parts corresponding to the random factor and the deterministic matrix from the expressions of structural random response in the frequency domain computational expressions for the mean value standard deviation and variation coefficient of the mean square value of the non stationary random displacement and stress response are developed by means of the random variable s functional moment method and the algebra synthesis method the influences of the randomness of the structural parameters on the dynamic characteristics structural displacement and stress responses are demonstrated using a truss structure

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

embedded image coding using zerotrees of wavelet coefficients the embedded zerotree wavelet algorithm ezw is a simple yet remarkably effective image compression algorithm having the property that the bits in the bit stream are generated in order of importance yielding a fully embedded code the embedded code represents a sequence of binary decisions that distinguish an image from the null image using an embedded coding algorithm an encoder can terminate the encoding at any point thereby allowing a target rate or target distortion metric to be met exactly also given a bit stream the decoder can cease decoding at any point in the bit stream and still produce exactly the same image that would have been encoded at the bit rate corresponding to the truncated bit stream in addition to producing a fully embedded bit stream the ezw consistently produces compression results that are competitive with virtually all known compression algorithms on standard test images yet this performance is achieved with a technique that requires absolutely no training no pre stored tables or codebooks and requires no prior knowledge of the image source the ezw algorithm is based on four key concepts 1 a discrete wavelet transform or hierarchical subband decomposition 2 prediction of the absence of significant information across scales by exploiting the self similarity inherent in images 3 entropy coded successive approximation quantization and 4 universal lossless data compression which is achieved via adaptive arithmetic coding

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

an mcmc approach to universal lossy compression of analog sources motivated by the markov chain monte carlo mcmc approach to the compression of discrete sources developed by jalali and weissman we propose a lossy compression algorithm for analog sources that relies on a finite reproduction alphabet which grows with the input length the algorithm achieves in an appropriate asymptotic sense the optimum shannon theoretic tradeoff between rate and distortion universally for stationary ergodic continuous amplitude sources we further propose an mcmc based algorithm that resorts to a reduced reproduction alphabet when such reduction does not prevent achieving the shannon limit the latter algorithm is advantageous due to its reduced complexity and improved rates of convergence when employed on sources with a finite and small optimum reproduction alphabet

fuzzy stochastic fem based homogenization framework for materials with polymorphic uncertainties in the microstructure uncertainties in the macroscopic response of heterogeneous materials result from two sources the natural variability in the microstructure s geometry and the lack of sufficient knowledge regarding the microstructure the first type of uncertainty is denoted aleatoric uncertainty and may be characterized by a known probability density function the second type of uncertainty is denoted epistemic uncertainty this kind of uncertainty cannot be described using probabilistic methods models considering both sources of uncertainties are called polymorphic in the case of polymorphic uncertainties some combination of stochastic methods and fuzzy arithmetic should be used thus in the current work we examine a fuzzy stochastic finite element method based homogenization framework for materials with random inclusion sizes we analyze an experimental radii distribution of inclusions and develop a stochastic representative volume element the stochastic finite element method is used to obtain the material response in the case of random inclusion radii due to unavoidable noise in experimental data an insufficient number of samples and limited accuracy of the fitting procedure the radii distribution density cannot be obtained exactly thus it is described in terms of fuzzy location and scale parameters the influence of fuzzy input on the homogenized stress measures is analyzed

ordering for embedded coding of wavelet image data based on arbitrary scalar quantization schemes many modern wavelet quantization schemes specify wavelet coefficient step sizes as continuous functions of an input step size selection criterion rate control is achieved by selecting an appropriate set of step sizes in embedded wavelet coders however rate control is achieved simply by truncating the coded bit stream at the desired rate the order in which wavelet data are coded implicitly controls quantization step sizes applied to create the reconstructed image since these step sizes are effectively discontinuous piecewise constant functions of rate this paper examines the problem of designing a coding order for such a coder guided by a quantization scheme where step sizes evolve continuously with rate in particular it formulates an optimization problem that minimizes the average relative difference between the piecewise constant implicit step sizes associated with a layered coding strategy and the smooth step sizes given by a quantization scheme the solution to this problem implies a coding order elegant near optimal solutions are presented to optimize step sizes over a variety of regions of rates either continuous or discrete this method can be used to create layers of coded data using any scalar quantization scheme combined with any wavelet bit plane coder it is illustrated using a variety of state of the art coders and quantization schemes in addition the proposed method is verified with objective and subjective testing

a new family of nonredundant transforms using hybrid wavelets and directional filter banks we propose a new family of nonredundant geometrical image transforms that are based on wavelets and directional filter banks we convert the wavelet basis functions in the finest scales to a flexible and rich set of directional basis elements by employing directional filter banks where we form a nonredundant transform family which exhibits both directional and nondirectional basis functions we demonstrate the potential of the proposed transforms using nonlinear approximation in addition we employ the proposed family in two key image processing applications image coding and denoising and show its efficiency for these applications

the tric shell element theoretical and numerical investigation the tric facet triangular shell element which is based on the natural mode method is seen under the light of the non consistent formulation proposed by bergan and co workers under this formulation the convergence requirements are fulfilled even with relaxed conditions on the conformity demands of the displacement shape functions the intrinsic connection between the non consistent formulation and the natural mode method is demonstrated establishing thus a rigorous theoretical foundation for the tric element under the perspective of the non consistent formulation tric s convergence characteristics are established by satisfying apriori the patch test due to its inherent properties and thus guaranteeing convergence to the exact solution furthermore the element s accuracy robustness and efficiency are tested in a number of judiciously selected numerical examples on benchmark plate and shell problems while a cpu time comparison with a pure displacement based isoparametric shell element demonstrates its computational merits

adaptive entropy coded subband coding of images the authors describe a design approach called 2 d entropy constrained subband coding ecsbc based upon recently developed 2 d entropy constrained vector quantization ecvq schemes the output indexes of the embedded quantizers are further compressed by use of noiseless entropy coding schemes such as huffman or arithmetic codes resulting in variable rate outputs depending upon the specific configurations of the ecvq and the ecpvq over the subbands many different types of sbc schemes can be derived within the generic 2 d ecsbc framework among these the authors concentrate on three representative types of 2 d ecsbc schemes and provide relative performance evaluations they also describe an adaptive buffer instrumented version of 2 d ecsbc called 2 d ecsbc aec for use with fixed rate channels which completely eliminates buffer overflow underflow problems this adaptive scheme achieves performance quite close to the corresponding ideal 2 d ecsbc system

nonlinear dynamic analysis of shells with the triangular element tric abstract tric is a facet triangular shell element which is based on the natural mode method it has been shown that the tric shell element satisfies the individual element test and in the framework of the nonconsistent formulation the convergence requirements are fulfilled while it has been proved to be very efficient in linear and nonlinear static problems moreover another major advantage in the formulation of this element is the incorporation of the transverse shear deformations in a way that defies the shear locking phenomenon in this work the derivation of the consistent and lumped mass matrices of the tric element is presented so that it can be used in linear and nonlinear dynamic problems both translational and rotational inertia are included in the consistent mass matrix which is conceived using kinematical and geometrical arguments consistent with the assumed natural rigid body and straining modes of the element all the kinematical and geometrical arguments that are invoked for the derivation of the consistent mass matrix are briefly presented moreover two formulations of the lumped mass matrix of tric are derived the first formulation is based entirely on geometrical considerations whereas the second is based on lumping the consistent mass matrix of tric finally the element s robustness and accuracy will be shown by applying it to properly selected benchmark examples of nonlinear shell dynamics while its computational efficiency will be demonstrated by comparing the cpu performance of the element with the other available shell elements

directionlets anisotropic multidirectional representation with separable filtering in spite of the success of the standard wavelet transform wt in image processing in recent years the efficiency of its representation is limited by the spatial isotropy of its basis functions built in the horizontal and vertical directions one dimensional 1 d discontinuities in images edges and contours that are very important elements in visual perception intersect too many wavelet basis functions and lead to a nonsparse representation to efficiently capture these anisotropic geometrical structures characterized by many more than the horizontal and vertical directions a more complex multidirectional m dir and anisotropic transform is required we present a new lattice based perfect reconstruction and critically sampled anisotropic m dir wt the transform retains the separable filtering and subsampling and the simplicity of computations and filter design from the standard two dimensional wt unlike in the case of some other directional transform constructions e g curvelets contourlets or edgelets the corresponding anisotropic basis functions directionlets have directional vanishing moments along any two directions with rational slopes furthermore we show that this novel transform provides an efficient tool for nonlinear approximation of images achieving the approximation power o n sup 1 55 which while slower than the optimal rate o n sup 2 is much better than o n sup 1 achieved with wavelets but at similar complexity

adaptive transforms for image coding using spatially varying wavelet packets we introduce a novel adaptive image representation using spatially varying wavelet packets wps our adaptive representation uses the fast double tree algorithm introduced previously herley et al 1993 to optimize an operational rate distortion r d cost function as is appropriate for the lossy image compression framework this involves jointly determining which filter bank tree wp frequency decomposition to use and when to change the filter bank tree spatial segmentation for optimality the spatial and frequency segmentations must be done jointly not sequentially due to computational complexity constraints we consider quadtree spatial segmentations and binary wp frequency decompositions corresponding to two channel filter banks for application to image coding we present results verifying the usefulness and versatility of this adaptive representation for image coding using both a first order entropy rate measure based coder as well as a powerful space frequency quantization based spq based wavelet coder introduced by xiong et al 1993

modular categories and hopf algebras abstract the modularity of a ribbon hopf algebra is characterized by the drinfeld map an elementary approach to etingof and gelaki s 1998 math res lett 5 119 197 result on the dimensions of irreducible modules is given by deducing the necessary identities involving the matrix s ij from the well known orthogonal relations of hopf algebra characters

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

approximation and compression with sparse orthonormal transforms we propose a new transform design method that targets the generation of compression optimized transforms for next generation multimedia applications the fundamental idea behind transform compression is to exploit regularity within signals such that redundancy is minimized subject to a fidelity cost multimedia signals in particular images and video are well known to contain a diverse set of localized structures leading to many different types of regularity and to nonstationary signal statistics the proposed method designs sparse orthonormal transforms sots that automatically exploit regularity over different signal structures and provides an adaptation method that determines the best representation over localized regions unlike earlier work that is motivated by linear approximation constructs and model based designs that are limited to specific types of signal regularity our work uses general nonlinear approximation ideas and a data driven setup to significantly broaden its reach we show that our sot designs provide a safe and principled extension of the karhunen loeve transform klt by reducing to the klt on gaussian processes and by automatically exploiting non gaussian statistics to significantly improve over the klt on more general processes we provide an algebraic optimization framework that generates optimized designs for any desired transform structure multiresolution block lapped and so on with significantly better n term approximation performance for each structure we propose a new prototype codec and test over a database of images simulation results show consistent increase in compression and approximation performance compared with conventional methods

an hvs based adaptive coder for perceptually lossy image compression abstract in this paper a locally adaptive wavelet image coder is presented it is based on an embedded human visual system model that exploits the space and frequency localization properties of wavelet decompositions for tuning the quantization step for each discrete wavelet transforms coefficient according to the local properties of the image a coarser quantization is performed in the areas of the image where the visibility of errors is reduced thus decreasing the total bit rate without affecting the resulting visual quality the size of the quantization step for each dwt coefficient is computed by taking into account the multiresolution structure of wavelet decompositions so that there is no need for any side information to be sent to the decoder or for prediction mechanisms perceptually lossless as well as perceptually lossy compression is supported the desired visual quality of the compressed image is set by means of a quality factor moreover the technique for tuning the target visual quality allows the user to define arbitrarily shaped regions of interest and to set for each one a different quality factor

image coding based on a morphological representation of wavelet data an experimental study of the statistical properties of wavelet coefficients of image data is presented as well as the design of two different morphology based image coding algorithms that make use of these statistics a salient feature of the proposed methods is that by a simple change of quantizers the same basic algorithm yields high performance embedded or fixed rate coders another important feature is that the shape information of morphological sets used in this coder is encoded implicitly by the values of wavelet coefficients thus avoiding the use of explicit and rate expensive shape descriptors these proposed algorithms while achieving nearly the same objective performance of state of the art zerotree based methods are able to produce reconstructions of a somewhat superior perceptual quality due to a property of joint compression and noise reduction they exhibit

tric a simple but sophisticated 3 node triangular element based on 6 rigid body and 12 straining modes for fast computational simulations of arbitrary isotropic and laminated composite shells tric is a simple but sophisticated 3 node shear deformable isotropic and composite flat shell element suitable for large scale linear and nonlinear engineering computations of thin and thick anisotropic plate and complex shell structures its stiffness matrix is based on 12 straining modes but essentially requires the computation of a sparse 9 by 9 matrix the element formulation departs from conventional cartesian mechanics as well as previously adopted physical lumping procedures and contains a completely new implementation of the transverse shear deformation it naturally circumvents all previously imposed constraints the methodology is based on physical inspirations of the natural mode finite element method nm fem formalized through appropriate geometrical trigonometrical and engineering mathematical relations and it involves only exact integrations its stiffness mass and geometrical matrices are all explicitly derived the kinematics of the element are hierarchically decomposed into 6 rigid body and 12 straining modes of deformation a simple congruent matrix operation transforms the elemental natural stiffness matrix to the local and global cartesian coordinates the modes show explicitly how the element deforms in axial straining symmetrical and antisymmetrical bending as well as in transverse shearing the latter has only become clear in the formulation presented here and has brought about a completion of the understanding of natural modes as they apply to the triangular shell element a wide range of numerical examples substantiate the conception and purpose of the element tric fast convergence is observed in many examples

image coding using wavelet transform a scheme for image compression that takes into account psychovisual features both in the space and frequency domains is proposed this method involves two steps first a wavelet transform used in order to obtain a set of biorthogonal subclasses of images the original image is decomposed at different scales using a pyramidal algorithm architecture the decomposition is along the vertical and horizontal directions and maintains constant the number of pixels required to describe the image second according to shannon s rate distortion theory the wavelet coefficients are vector quantized using a multiresolution codebook to encode the wavelet coefficients a noise shaping bit allocation procedure which assumes that details at high resolution are less visible to the human eye is proposed in order to allow the receiver to recognize a picture as quickly as possible at minimum cost a progressive transmission scheme is presented it is shown that the wavelet transform is particularly well adapted to progressive transmission

a low memory zerotree coding for arbitrarily shaped objects the set partitioning in hierarchical trees spiht algorithm is a computationally simple and efficient zerotree coding technique for image compression however the high working memory requirement is its main drawback for hardware realization we present a low memory zerotree coder lmzc which requires much less working memory than spiht the lmzc coding algorithm abandons the use of lists defines a different tree structure and merges the sorting pass and the refinement pass together the main techniques of lmzc are the recursive programming and a top bit scheme tbs in tbs the top bits of transformed coefficients are used to store the coding status of coefficients instead of the lists used in spiht in order to achieve high coding efficiency shape adaptive discrete wavelet transforms are used to transformation arbitrarily shaped objects a compact emplacement of the transformed coefficients is also proposed to further reduce working memory the lmzc carefully treats don t care nodes in the wavelet tree and does not use bits to code such nodes comparison of lmzc with spiht shows that for coding a 768 spl times 512 color image lmzc saves at least 5 3 mbytes of memory but only increases a little execution time and reduces minor peak signal to noise ratio psnr values thereby making it highly promising for some memory limited applications

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

new image compression techniques using multiwavelets and multiwavelet packets advances in wavelet transforms and quantization methods have produced algorithms capable of surpassing the existing image compression standards like the joint photographic experts group jpeg algorithm for best performance in image compression wavelet transforms require filters that combine a number of desirable properties such as orthogonality and symmetry however the design possibilities for wavelets are limited because they cannot simultaneously possess all of the desirable properties the relatively new field of multiwavelets shows promise in obviating some of the limitations of wavelets multiwavelets offer more design options and are able to combine several desirable transform features the few previously published results of multiwavelet based image compression have mostly fallen short of the performance enjoyed by the current wavelet algorithms this paper presents new multiwavelet transform and quantization methods and introduces multiwavelet packets extensive experimental results demonstrate that our techniques exhibit performance equal to or in several cases superior to the current wavelet filters

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

feature oriented multiple description wavelet based image coding we address the problem of resilient image coding over error prone networks where packet losses occur recent literature highlights the multiple description coding mdc as a promising approach to solve this problem in this paper we introduce a novel wavelet based multiple description image coder referred to as the feature oriented mdc fo mdc the proposed multiple description md coder exploits the statistics of the wavelet coefficients and identifies the subsets of samples that are sensitive to packet loss a joint optimization between tree pruning and quantizer selection in the rate distortion sense is used in order to allocate more bits to these sensitive coefficients when compared with the state of the art md scalar quantization coder the proposed fo mdc yields a more efficient central side distortion tradeoff control mechanism furthermore it proves to be more robust for image transmission even with high packet loss ratios which makes it suitable for protecting multimedia streams over packet erasure channels

space frequency quantization for wavelet image coding a new class of image coding algorithms coupling standard scalar quantization of frequency coefficients with tree structured quantization related to spatial structures has attracted wide attention because its good performance appears to confirm the promised efficiencies of hierarchical representation this paper addresses the problem of how spatial quantization modes and standard scalar quantization can be applied in a jointly optimal fashion in an image coder we consider zerotree quantization zeroing out tree structured sets of wavelet coefficients and the simplest form of scalar quantization a single common uniform scalar quantizer applied to all nonzeroed coefficients and we formalize the problem of optimizing their joint application we develop an image coding algorithm for solving the resulting optimization problem despite the basic form of the two quantizers considered the resulting algorithm demonstrates coding performance that is competitive often outperforming the very best coding algorithms in the literature

curved wavelet transform for image coding the conventional two dimensional wavelet transform used in existing image coders is usually performed through one dimensional 1 d filtering in the vertical and horizontal directions which cannot efficiently represent edges and lines in images the curved wavelet transform presented in this paper is carried out by applying 1 d filters along curves rather than being restricted to vertical and horizontal straight lines the curves are determined based on image content and are usually parallel to edges and lines in the image to be coded the pixels along these curves can be well represented by a small number of wavelet coefficients the curved wavelet transform is used to construct a new image coder the code stream syntax of the new coder is the same as that of jpeg2000 except that a new marker segment is added to the tile headers results of image coding and subjective quality assessment show that the new image coder performs better than or as well as jpeg2000 it is particularly efficient for images that contain sharp edges and can provide a psnr gain of up to 1 67 db for natural images compared with jpeg2000

representation and compression of multidimensional piecewise functions using surflets we study the representation approximation and compression of functions in m dimensions that consist of constant or smooth regions separated by smooth m 1 dimensional discontinuities examples include images containing edges video sequences of moving objects and seismic data containing geological horizons for both function classes we derive the optimal asymptotic approximation and compression rates based on kolmogorov metric entropy for piecewise constant functions we develop a multiresolution predictive coder that achieves the optimal rate distortion performance for piecewise smooth functions our coder has near optimal rate distortion performance our coder for piecewise constant functions employs surflets a new multiscale geometric tiling consisting of m dimensional piecewise constant atoms containing polynomial discontinuities our coder for piecewise smooth functions uses surfprints which wed surflets to wavelets for piecewise smooth approximation both of these schemes achieve the optimal asymptotic approximation performance key features of our algorithms are that they carefully control the potential growth in surflet parameters at higher smoothness and do not require explicit estimation of the discontinuity we also extend our results to the corresponding discrete function spaces for sampled data we provide asymptotic performance results for both discrete function spaces and relate this asymptotic performance to the sampling rate and smoothness orders of the underlying functions and discontinuities for approximation of discrete data we propose a new scale adaptive dictionary that contains few elements at coarse and fine scales but many elements at medium scales simulation results on synthetic signals provide a comparison between surflet based coders and previously studied approximation schemes based on wedgelets and wavelets

nonlinear free vibration analysis of composite plates with material uncertainties a monte carlo simulation approach abstract in this paper the effects of dispersion in material properties on free vibration response of composite plates with geometric nonlinearity in von karman sense are investigated the higher order shear deformation theory is employed for the study reported here an efficient c0 finite element formulation is developed for the analysis using monte carlo simulation the second order statistics i e mean and standard deviation of the nonlinear free vibration response of the composite laminates are obtained for different thickness and amplitude ratios the input statistics mean and variance of the material property are assumed to be known as a priori the computed results demonstrate the influence of the variations in the material properties and amplitudes on the nonlinear free vibration response of the composite plates the results are compared with those available in the literature

on the importance of combining wavelet based nonlinear approximation with coding strategies this paper provides a mathematical analysis of transform compression in its relationship to linear and nonlinear approximation theory contrasting linear and nonlinear approximation spaces we show that there are interesting classes of functions random processes which are much more compactly represented by wavelet based nonlinear approximation these classes include locally smooth signals that have singularities and provide a model for many signals encountered in practice in particular for images however we also show that nonlinear approximation results do not always translate to efficient compress on strategies in a rate distortion sense based on this observation we construct compression techniques and formulate the family of functions stochastic processes for which they provide efficient descriptions in a rate distortion sense we show that this family invariably leads to besov spaces yielding a natural relationship among besov smoothness linear nonlinear approximation order and compression performance in a rate distortion sense the designed compression techniques show similarities to modern high performance transform codecs allowing us to establish relevant rate distortion estimates and identify performance limits

spherical coding algorithm for wavelet image compression in recent literature there exist many high performance wavelet coders that use different spatially adaptive coding techniques in order to exploit the spatial energy compaction property of the wavelet transform two crucial issues in adaptive methods are the level of flexibility and the coding efficiency achieved while modeling different image regions and allocating bitrate within the wavelet subbands in this paper we introduce the ldquospherical coder rdquo which provides a new adaptive framework for handling these issues in a simple and effective manner the coder uses local energy as a direct measure to differentiate between parts of the wavelet subband and to decide how to allocate the available bitrate as local energy becomes available at finer resolutions i e in smaller size windows the coder automatically updates its decisions about how to spend the bitrate we use a hierarchical set of variables to specify and code the local energy up to the highest resolution i e the energy of individual wavelet coefficients the overall scheme is nonredundant meaning that the subband information is conveyed using this equivalent set of variables without the need for any side parameters despite its simplicity the algorithm produces psnr results that are competitive with the state of art coders in literature

multiple description wavelet based image coding we consider the problem of coding images for transmission over error prone channels the impairments we target are transient channel shutdowns as would occur in a packet network when a packet is lost or in a wireless system during a deep fade when data is delivered it is assumed to be error free but some of the data may never reach the receiver the proposed algorithms are based on a combination of multiple description scalar quantizers with techniques successfully applied to the construction of some of the most efficient subband coders a given image is encoded into multiple independent packets of roughly equal length when packets are lost the quality of the approximation computed at the receiver depends only on the number of packets received but does not depend on exactly which packets are actually received when compared with previously reported results on the performance of robust image coders based on multiple descriptions on standard test images our coders attain similar psnr values using typically about 50 60 of the bit rate required by these other state of the art coders while at the same time providing significantly more freedom in the mechanism for allocation of redundancy among descriptions

fast variable run length coding for embedded progressive wavelet based image compression run length coding has attracted much attention in wavelet based image compression because of its simplicity and potentially low complexity the main drawback is the inferior rd performance compared to the state of the art coder spiht in this paper we concentrate on the embedded progressive run length code of tian and wells 1996 1998 we consider significance sequences drawn from the scan in the dominant pass it turns out that self similar curves for scanning the dominant pass increase the compression efficiency significantly this is a consequence of the correlation of direct neighbors in the wavelet domain this dependence can be better exploited by using groups of coefficients similar to the spiht algorithm this results in a new and very fast coding algorithm which shows performance similar to the state of the art coder spiht but with lower complexity and small and fixed memory overhead

2 step scalar deadzone quantization for bitplane image coding modern lossy image coding systems generate a quality progressive codestream that truncated at increasing rates produces an image with decreasing distortion quality progressivity is commonly provided by an embedded quantizer that employs uniform scalar deadzone quantization usdq together with a bitplane coding strategy this paper introduces a 2 step scalar deadzone quantization 2sdq scheme that achieves same coding performance as that of usdq while reducing the coding passes and the emitted symbols of the bitplane coding engine this serves to reduce the computational costs of the codec and or to code high dynamic range images the main insights behind 2sdq are the use of two quantization step sizes that approximate wavelet coefficients with more or less precision depending on their density and a rate distortion optimization technique that adjusts the distortion decreases produced when coding 2sdq indexes the integration of 2sdq in current codecs is straightforward the applicability and efficiency of 2sdq are demonstrated within the framework of jpeg2000

an investigation of wavelet based image coding using an entropy constrained quantization framework wavelet image decompositions generate a tree structured set of coefficients providing an hierarchical data structure for representing images a new class of previously proposed image compression algorithms has focused on new ways for exploiting dependencies between this hierarchy of wavelet coefficients using zero tree data structures this paper presents a new framework for understanding the efficiency of one specific algorithm in this class we introduced previously and dubbed the space frequency quantization sfq based coder it describes at a higher level how the sfq based image coder of our earlier work can be construed as a simplified attempt to design a global entropy constrained vector quantizer ecvq with two noteworthy features i it uses an image sized codebook dimension departing from conventional small dimensional codebooks that are applied to small image blocks and ii it uses an on line image adaptive application of constrained ecvq which typically uses off line training data in its codebook design phase the principal insight offered by the new framework is that improved performance is achieved by more accurately characterizing the joint probabilities of arbitrary sets of wavelet coefficients we also present an empirical statistical study of the distribution of the wavelet coefficients of high frequency bands which are responsible for most of the performance gain of the new class of algorithms this study verifies that the improved performance achieved by the new class of algorithms like the sfq based coder can be attributed to its being designed around one conveniently structured and efficient collection of such sets namely the zero tree data structure the results of this study further inspire the design of alternative novel data structures based on nonlinear morphological operators

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

subband coding of images subband coding has become quite popular for the source encoding of speech this paper presents a simple yet efficient extension of this concept to the source coding of images we specify the constraints for a set of two dimensional quadrature mirror filters qmf s for a particular frequency domain partition and show that these constraints are satisfied by a separable combination of one dimensional qmf s bits are then optimally allocated among the subbands to minimize the mean squared error for dpcm coding of the subbands also an adaptive technique is developed to allocate the bits within each subband by means of a local variance mask optimum quantization is employed with quantizers matched to the laplacian distribution subband coded images are presented along with their signal to noise ratios snr s the snr performance of the subband coder is compared to that of the adaptive discrete cosine transform dct vector quantization and differential vector quantization for bit rates of 0 67 1 0 and 2 0 bits per pixel for 256 256 monochrome images the adaptive subband coder has the best snr performance

fast adaptive wavelet packet image compression wavelets are ill suited to represent oscillatory patterns rapid variations of intensity can only be described by the small scale wavelet coefficients which are often quantized to zero even at high bit rates our goal is to provide a fast numerical implementation of the best wavelet packet algorithm in order to demonstrate that an advantage can be gained by constructing a basis adapted to a target image emphasis is placed on developing algorithms that are computationally efficient we developed a new fast two dimensional 2 d convolution decimation algorithm with factorized nonseparable 2 d filters the algorithm is four times faster than a standard convolution decimation an extensive evaluation of the algorithm was performed on a large class of textured images because of its ability to reproduce textures so well the wavelet packet coder significantly out performs one of the best wavelet coder on images such as barbara and fingerprints both visually and in term of psnr

integer wavelet transform for embedded lossy to lossless image compression the use of the discrete wavelet transform dwt for embedded lossy image compression is now well established one of the possible implementations of the dwt is the lifting scheme ls because perfect reconstruction is granted by the structure of the ls nonlinear transforms can be used allowing efficient lossless compression as well the integer wavelet transform iwt is one of them this is an interesting alternative to the dwt because its rate distortion performance is similar and the differences can be predicted this topic is investigated in a theoretical framework a model of the degradations caused by the use of the iwt instead of the dwt for lossy compression is presented the rounding operations are modeled as additive noise the noise are then propagated through the ls structure to measure their impact on the reconstructed pixels this methodology is verified using simulations with random noise as input it predicts accurately the results obtained using images compressed by the well known ezw algorithm experiment are also performed to measure the difference in terms of bit rate and visual quality this allows to a better understanding of the impact of the iwt when applied to lossy image compression

mutual information based analysis of jpeg2000 contexts context based arithmetic coding has been widely adopted in image and video compression and is a key component of the new jpeg2000 image compression standard in this paper the contexts used in jpeg2000 are analyzed using the mutual information which is closely related to the compression performance we first show that when combining the contexts the mutual information between the contexts and the encoded data will decrease unless the conditional probability distributions of the combined contexts are the same given i the initial number of contexts and f the final desired number of contexts there are s i f possible context classification schemes where s i f is called the stirling number of the second kind the optimal classification scheme is the one that gives the maximum mutual information instead of using an exhaustive search the optimal classification scheme can be obtained through a modified generalized lloyd algorithm with the relative entropy as the distortion metric for binary arithmetic coding the search complexity can be reduced by using dynamic programming our experimental results show that the jpeg2000 contexts capture the correlations among the wavelet coefficients very well at the same time the number of contexts used as part of the standard can be reduced without loss in the coding performance

numerical solution of spectral stochastic finite element systems abstract this paper addresses the issues involved in solving systems of linear equations which arise in the context of the spectral stochastic finite element ssfem formulation two efficient solution procedures are presented that dramatically reduce the amount of computations involved in numerically solving these problems a brief review is first provided of the underlying spectral approach which highlights the peculiar structure of the matrices generated and how their properties are related to both the level of approximation involved as well as to the convergence behavior of the proposed solution procedure the differences between these matrices from their deterministic finite element counterparts are illustrated an iterative solution scheme is proposed which utilizes their specific properties for efficient memory management and enhanced convergence behavior results from numerical tests are presented comparisons with standard algorithms illustrate the efficiency of the proposed algorithm the second solution procedure presented in this paper is based on hierarchical basis concepts results from numerical tests are again provided and the limitations of this approach are assessed the performance of both proposed algorithms indicates that the linear algebraic systems from the underlying ssfem formulation can be solved with considerably less effort in memory and computation time than their size suggests furthermore the data structures and the hierarchical concept introduced in this study are found to have great potential for the future development of adaptive procedures in stochastic fem

stochastic finite element analysis of shells in the present paper the stochastic formulation of the triangular composite tric facet shell element is presented using the weighted integral and local average methods the elastic modulus of the structure is considered to be a two dimensional homogeneous stochastic field which is represented via the spectral representation method as a result of the proposed derivation and the special features of the element the stochastic stiffness matrix is calculated in terms of a minimum number of random variables of the stochastic field giving a cost effective stochastic matrix under the assumption of a pre specified power spectral density function of the stochastic field it is possible to compute the response variability of the shell structure numerical tests are provided to demonstrate the applicability of the proposed methodologies

robust design of structures using optimization methods the robust design of structures with stochastic parameters is studied using optimization techniques the first two statistical moments of the stochastic parameters including design variables are considered in conjunction with the second order perturbation method for the approximation of mean value and variance of the structural response in this framework the sensitivities of the mean values and variances of the structural performance function with respect to the design variables are calculated for use in the optimization task the robust design of structures is formulated as a multi criteria optimization problem in which both the expected value and the standard deviation of the objective function are to be minimized the robustness of the feasibility is also taken into account by involving the variability of the structural response in the constraints the two criteria optimization problem is converted into a scalar one and is then solved by a gradient based optimization algorithm to demonstrate the applicability of the presented method numerical examples are given involving static and dynamic response

stochastic finite element analysis of shells with combined random material and geometric properties abstract in this work an extended stochastic formulation of the triangular composite facet shell element tric is presented for the case of combined uncertain material young s modulus poisson s ratio and geometric thickness properties these properties are assumed to be described by uncorrelated two dimensional homogeneous stochastic fields the stochastic finite element analysis of shell structures is performed using the spectral representation method for the description of the random fields in conjunction with monte carlo simulation mcs for the computation of the response variability useful conclusions regarding the influence of each one of the structural parameters on the response variability are derived from the numerical tests examined

comparison of different methods of classification in subband coding of images this paper investigates various classification techniques applied to subband coding of images as a way of exploiting the nonstationary nature of image subbands the advantages of subband classification are characterized in a rate distortion framework in terms of classification gain and overall subband classification gain two algorithms maximum classification gain and equal mean normalized standard deviation classification which allow unequal number of blocks in each class are presented the dependence between the classification maps from different subbands is exploited either directly while encoding the classification maps or indirectly by constraining the classification maps the trade off between the classification gain and the amount of side information is explored coding results for a subband image coder based on classification are presented the simulation results demonstrate the value of classification in subband coding

wavelet domain approximation and compression of piecewise smooth images the wavelet transform provides a sparse representation for smooth images enabling efficient approximation and compression using techniques such as zerotrees unfortunately this sparsity does not extend to piecewise smooth images where edge discontinuities separating smooth regions persist along smooth contours this lack of sparsity hampers the efficiency of wavelet based approximation and compression on the class of images containing smooth c sup 2 regions separated by edges along smooth c sup 2 contours for example the asymptotic rate distortion r d performance of zerotree based wavelet coding is limited to d r spl lsim 1 r well below the optimal rate of 1 r sup 2 in this paper we develop a geometric modeling framework for wavelets that addresses this shortcoming the framework can be interpreted either as 1 an extension to the zerotree model for wavelet coefficients that explicitly accounts for edge structure at fine scales or as 2 a new atomic representation that synthesizes images using a sparse combination of wavelets and wedgeprints anisotropic atoms that are adapted to edge singularities our approach enables a new type of quadtree pruning for piecewise smooth images using zerotrees in uniformly smooth regions and wedgeprints in regions containing geometry using this framework we develop a prototype image coder that has near optimal asymptotic r d performance d r spl lsim logr sup 2 r sup 2 for piecewise smooth c sup 2 c sup 2 images in addition we extend the algorithm to compress natural images exploring the practical problems that arise and attaining promising results in terms of mean square error and visual quality

adaptive wavelet packet basis selection for zerotree image coding image coding methods based on adaptive wavelet transforms and those employing zerotree quantization have been shown to be successful we present a general zerotree structure for an arbitrary wavelet packet geometry in an image coding framework a fast basis selection algorithm is developed it uses a markov chain based cost estimate of encoding the image using this structure as a result our adaptive wavelet zerotree image coder has a relatively low computational complexity performs comparably to state of the art image coders and is capable of progressively encoding images

significance linked connected component analysis for wavelet image coding the success in wavelet image coding is mainly attributed to a recognition of the importance of data organization and representation there have been several very competitive wavelet coders developed namely shapiro s 1993 embedded zerotree wavelets ezw servetto et al s 1995 morphological representation of wavelet data mrwd and said and pearlman s see ieee trans circuits syst video technol vol 6 p 245 50 1996 set partitioning in hierarchical trees spiht we develop a novel wavelet image coder called significance linked connected component analysis slcca of wavelet coefficients that extends mrwd by exploiting both within subband clustering of significant coefficients and cross subband dependency in significant fields extensive computer experiments on both natural and texture images show convincingly that the proposed slcca outperforms ezw mrwd and spiht for example for the barbara image at 0 25 b pixel slcca outperforms ezw mrwd and spiht by 1 41 db 0 32 db and 0 60 db in psnr respectively it is also observed that slcca works extremely well for images with a large portion of texture for eight typical 256 spl times 256 grayscale texture images compressed at 0 40 b pixel slcca outperforms spiht by 0 16 db 0 63 db in psnr this performance is achieved without using any optimal bit allocation procedure thus both the encoding and decoding procedures are fast

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

lagrange wavelets for signal processing this paper deals with the design of interpolating wavelets based on a variety of lagrange functions combined with novel signal processing techniques for digital imaging halfband lagrange wavelets b spline lagrange wavelets and gaussian lagrange lagrange distributed approximating functional daf wavelets are presented as specific examples of the generalized lagrange wavelets our approach combines the perceptually dependent visual group normalization vgn technique and a softer logic masking slm method these are utilized to rescale the wavelet coefficients remove perceptual redundancy and obtain good visual performance for digital image processing

ne mcs technique for stochastic structural response sensitivity in structural sensitivity analysis deterministic procedure is insufficient to provide complete information stochastic analysis is a holistic approach for computing response sensitivity considering uncertainties in structural parameters present study focuses an efficient stochastic finite element method for random response sensitivity analysis randomness of design variables is modeled through local averaging technique followed by cholesky decomposition for digital simulation neumann expansion blended with monte carlo simulation ne mcs has been employed in finite element solution for response sensitivity numerical examples are presented to illustrate the ne mcs technique solution employing direct monte carlo simulation and perturbation are also presented to show the efficiency and accuracy of the proposed technique

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

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

buckling analysis of imperfect shells with stochastic non gaussian material and thickness properties in this paper the effect of material and thickness spatial variation on the buckling load of isotropic shells with random initial geometric imperfections is investigated to this purpose a random spatial variability of the elastic modulus as well as of the thickness of the shell is introduced in addition to the random initial geometric deviations of the shell structure from its perfect geometry the main novelty of this paper compared to previous works is that a non gaussian assumption is made for the distribution of the two aforementioned uncertain parameters i e the modulus of elasticity and the shell thickness which are described by two dimensional uni variate 2d 1v homogeneous non gaussian stochastic fields the initial geometric imperfections are described as a 2d 1v gaussian non homogeneous stochastic field with properties derived from corresponding experimental measurements numerical examples are presented focusing on the influence of the non gaussian assumption on the variability of the buckling load which is calculated by means of the monte carlo simulation method it is shown that the choice of the marginal probability distribution for the description of the material and thickness variability is crucial since it affects significantly the statistics of the buckling load of imperfection sensitive shell type structures

faster computation of the karhunen loeve expansion using its domain independence property the goal of this work is to reduce the cost of computing the coefficients in the karhunen loeve kl expansion the kl expansion serves as a useful and efficient tool for discretizing second order stochastic processes with known covariance function its applications in engineering mechanics include discretizing random field models for elastic moduli fluid properties and structural response the main computational cost of finding the coefficients of this expansion arises from numerically solving an integral eigenvalue problem with the covariance function as the integration kernel mathematically this is a homogeneous fredholm equation of second type one widely used method for solving this integral eigenvalue problem is to use finite element fe bases for discretizing the eigenfunctions followed by a galerkin projection this method is computationally expensive in the current work it is first shown that the shape of the physical domain in a random field does not affect the realizations of the field estimated using kl expansion although the individual kl terms are affected based on this domain independence property a numerical integration based scheme accompanied by a modification of the domain is proposed in addition to presenting mathematical arguments to establish the domain independence numerical studies are also conducted to demonstrate and test the proposed method numerically it is demonstrated that compared to the galerkin method the computational speed gain in the proposed method is of three to four orders of magnitude for a two dimensional example and of one to two orders of magnitude for a three dimensional example while retaining the same level of accuracy it is also shown that for separable covariance kernels a further cost reduction of three to four orders of magnitude can be achieved both normal and lognormal fields are considered in the numerical studies c 2014 elsevier b v all rights reserved

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

a progressive transmission image coder using linear phase uniform filterbanks as block transforms this paper presents a novel image coding scheme using m channel linear phase perfect reconstruction filterbanks lpprfbs in the embedded zerotree wavelet ezw framework introduced by shapiro 1993 the innovation here is to replace the ezws dyadic wavelet transform by m channel uniform band maximally decimated lpprfbs which offer finer frequency spectrum partitioning and higher energy compaction the transform stage can now be implemented as a block transform which supports parallel processing and facilitates region of interest coding decoding for hardware implementation the transform boasts efficient lattice structures which employ a minimal number of delay elements and are robust under the quantization of lattice coefficients the resulting compression algorithm also retains all the attractive properties of the ezw coder and its variations such as progressive image transmission embedded quantization exact bit rate control and idempotency despite its simplicity our new coder outperforms some of the best image coders published previously in the literature for almost all test images especially natural hard to code ones at almost all bit rates

a wavelet based analysis of fractal image compression why does fractal image compression work what is the implicit image model underlying fractal block coding how can we characterize the types of images for which fractal block coders will work well these are the central issues we address we introduce a new wavelet based framework for analyzing block based fractal compression schemes within this framework we are able to draw upon insights from the well established transform coder paradigm in order to address the issue of why fractal block coders work we show that fractal block coders of the form introduced by jacquin 1992 are haar wavelet subtree quantization schemes we examine a generalization of the schemes to smooth wavelets with additional vanishing moments the performance of our generalized coder is comparable to the best results in the literature for a jacquin style coding scheme our wavelet framework gives new insight into the convergence properties of fractal block coders and it leads us to develop an unconditionally convergent scheme with a fast decoding algorithm our experiments with this new algorithm indicate that fractal coders derive much of their effectiveness from their ability to efficiently represent wavelet zero trees finally our framework reveals some of the fundamental limitations of current fractal compression schemes

subband coding of images using vector quantization a novel two dimensional subband coding technique is presented that can be applied to images as well as speech a frequency band decomposition of the image is carried out by means of 2d separable quadrature mirror filters which split the image spectrum into 16 equal rate subbands these 16 parallel subband signals are regarded as a 16 dimensional vector source and coded as such using vector quantization in the asymptotic case of high bit rates a theoretical analysis yields that a lower bound to the gain is attainable by choosing this approach over scalar quantization of each subband with an optimal bit allocation it is shown that vector quantization in this scheme has several advantages over coding the subbands separately experimental results are given and it is shown the scheme has a performance that is comparable to that of more complex coding techniques

comparative study of projection schemes for stochastic finite element analysis we present a comparison of subspace projection schemes for stochastic finite element analysis in terms of accuracy and computational efficiency more specifically we compare the polynomial chaos projection scheme with reduced basis projection schemes based on the preconditioned stochastic krylov subspace numerical studies are presented for two problems 1 static analysis of a plate with random young s modulus and 2 settlement of a foundation supported on a randomly heterogeneous soil monte carlo simulation results based on exact structural analysis are used to generate benchmark results against which the projection schemes are compared we show that stochastic reduced basis methods require significantly less computer memory and execution time compared to the polynomial chaos approach particularly for large scale problems with many random variables for the class of problems considered we find that stochastic reduced basis methods can be up to orders of magnitude faster while providing results of comparable or better accuracy

trellis coded quantization of memoryless and gauss markov sources trellis coded quantization tcq is developed and applied to the encoding of memoryless and gauss markov sources the theoretical justification for the approach is alphabet constrained rate distortion theory which is a dual to the channel capacity argument that motivates trellis coded modulation tcm the authors adopt the notions of signal set expansion set partitioning and branch labeling of tcm but modify the techniques to account for the source distribution to design tcq coders of low complexity with excellent mean squared error mse performance for a memoryless uniform source tcq provides an mse within 0 21 db of the distortion rate bound at all positive integral rates the performance is superior to that promised by the coefficient of quantization for all of the best lattices known in dimensions 24 or less for a memoryless gaussian source the tcq performance at rates of 0 5 1 and 2 b sample is superior to all previous results the authors found in the literature the encoding complexity of tcq is very modest tcq is incorporated into a predictive coding structure for the encoding of gauss markov sources simulation results for first second and third order gauss markov sources are presented

image subband coding using context based classification and adaptive quantization adaptive compression methods have been a key component of many proposed subband or wavelet image coding techniques this paper deals with a particular type of adaptive subband image coding where we focus on the image coder s ability to adjust itself on the fly to the spatially varying statistical nature of image contents this backward adaptation is distinguished from more frequently used forward adaptation in that forward adaptation selects the best operating parameters from a predesigned set and thus uses considerable amount of side information in order for the encoder and the decoder to operate with the same parameters specifically we present backward adaptive quantization using a new context based classification technique which classifies each subband coefficient based on the surrounding quantized coefficients we couple this classification with online parametric adaptation of the quantizer applied to each class a simple uniform threshold quantizer is employed as the baseline quantizer for which adaptation is achieved our subband image coder based on the proposed adaptive classification quantization idea exhibits excellent rate distortion performance in particular at very low rates for popular test images it is comparable or superior to most of the state of the art coders in the literature

modal approaches for the stochastic finite element analysis of structures with material and geometric uncertainties this paper presents two efficient modal approaches as an alternative to direct formulations for the time harmonic dynamic analysis of structures with random material and shape parameters in both approaches the structural eigenproblem is solved and complemented by a sensitivity analysis to the random parameters the modal perturbation stochastic finite element method sfem then condenses the response sensitivities to assess the response variability the mixed perturbation monte carlo sfem assesses the response statistics by sampling the structural eigenmodes according to the perturbation estimation of their probability distribution functions pdfs geometric uncertainties are handled through an appropriate shape parameterisation and a shape design sensitivity analysis two numerical applications examine both approaches in terms of accuracy variability level and computational requirements the applications involve a plate bending problem with random young modulus or edge length and a plate with a random flatness default particular observations related to the influence of the parameter pdfs in simulation based methods are also provided

scalable wavelet video coding using aliasing reduced hierarchical motion compensation we describe a spatially scalable video coding framework in which motion correspondences between successive video frames are exploited in the wavelet transform domain the basic motivation for our coder is that motion fields are typically smooth and therefore can be efficiently captured through a multiresolutional framework a wavelet decomposition is applied to each video frame and the coefficients at each level are predicted from the coarser level through backward motion compensation to remove the aliasing effects caused by downsampling in the transform a special interpolation filter is designed with the weighted aliasing energy as part of the optimization goal and motion estimation is carried out with low pass filtering and interpolation in the estimation loop further to achieve robust motion estimation against quantization noise we propose a novel backward forward hybrid motion compensation scheme and a tree structured dynamic programming algorithm to optimize the backward forward mode choices a novel adaptive quantization scheme is applied to code the motion predicted residue wavelet coefficients experimental results reveal 0 3 2 db increase in coded psnr at low bit rates over the state of the art h 263 standard with all enhancement modes enabled and similar improvements over mpeg 2 at high bit rates with a considerable improvement in subjective reconstruction quality while simultaneously supporting a scalable representation

space frequency quantization for image compression with directionlets the standard separable 2 d wavelet transform wt has recently achieved a great success in image processing because it provides a sparse representation of smooth images however it fails to efficiently capture 1 d discontinuities like edges or contours these features being elongated and characterized by geometrical regularity along different directions intersect and generate many large magnitude wavelet coefficients since contours are very important elements in the visual perception of images to provide a good visual quality of compressed images it is fundamental to preserve good reconstruction of these directional features in our previous work we proposed a construction of critically sampled perfect reconstruction transforms with directional vanishing moments imposed in the corresponding basis functions along different directions called directionlets in this paper we show how to design and implement a novel efficient space frequency quantization sfq compression algorithm using directionlets our new compression method outperforms the standard sfq in a rate distortion sense both in terms of mean square error and visual quality especially in the low rate compression regime we also show that our compression method does not increase the order of computational complexity as compared to the standard sfq algorithm

r d optimized tree structured compression algorithms with discrete directional wavelet transform a new image coding method based on discrete directional wavelet transform s wt and quad tree decomposition is proposed here the s wt is a kind of transform proposed in v velisavljevic b beferull lozano m vetterli p l dragotti directionlets anisotropic multidirectional representation with separable filtering ieee trans image process 15 7 2006 which is based on lattice theory and with the difference with the standard wavelet transform is that the former allows more transform directions because the directional property in a small region is more regular than in a big block generally in order to sufficiently make use of the multidirectionality and directional vanishing moment dvm of s wt the input image is divided into many small regions by means of the popular quad tree segmentation and the splitting criterion is on the rate distortion sense after the optimal quad tree is obtained by means of the embedded property of speck a resource bit allocation algorithm is fast implemented utilizing the model proposed in m rajpoot model based optimal bit allocation in ieee data compression conference 2004 proceedings dcc 2004 19 experiment results indicate that our algorithms perform better compared to some state of the art image coders

a new approach for the stochastic analysis of finite element modelled structures with uncertain parameters a method for evaluating the static response of uncertain finite element fe discretised structures is presented the method is comparable with the perturbation procedures from a computational point of view but it overcomes the drawbacks related to these procedures in fact the present method gives excellent level of accuracy even for high amount of uncertainties moreover it produces the exact solution for statically determinate structures the accuracy is remarkable even in the evaluation of high order statistics and probability density function of the response so that reliability consideration can be drawn

a formulation for stochastic finite element analysis of plate structures with uncertain poisson s ratio up to now the young s modulus is mainly dealt within the analysis of response variability however since the poisson s ratio is the other material constant which influences the behavior of structures the independent evaluation of the effects of this parameter on the response variability is of importance in this paper a formulation to determine the response variability in plate structure due to the randomness of poisson s ratio is given to filter out the independent contributions of randomness in poisson s ratio to the response variability the constitutive matrix has to be decomposed into several sub matrices in order to include the poisson s ratio in the constitutive relation as a non linear parameter a polynomial expansion of poisson s ratio is introduced to demonstrate the validity of the proposed formulation an example is chosen and the results are compared with those obtained by means of monte carlo simulation through the formulation proposed in this paper it becomes possible for the non statistical weighted integral stochastic approach to deal with all the uncertain material parameters in its application

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