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

a generalized finite difference gfd ale scheme for incompressible flows around moving solid bodies on hybrid meshfree cartesian grids a scheme using the mesh free generalized finite differencing gfd on flows past moving bodies is proposed the aim is to devise a method to simulate flow past an immersed moving body that avoids the intensive remeshing of the computational domain and minimizes data interpolation associated with the established computational fluid methodologies as such procedures are time consuming and are a significant source of error in flow simulation in the present scheme the moving body is embedded and enveloped by a cloud of mesh free nodes which convects with the motion of the body against a background of cartesian nodes the generalized finite difference gfd method with weighted least squares wls approximation is used to discretize the two dimensional viscous incompressible navier stokes equations at the mesh free nodes while standard finite difference approximations are applied elsewhere the convecting motion of the mesh free nodes is treated by the arbitrary lagrangian eulerian ale formulation of the flow equations which are solved by a second order crank nicolson based projection method the proposed numerical scheme was tested on a number of problems including the decaying vortex flow external flows past moving bodies and body driven flows in enclosures

massively parallel finite element computation of incompressible flows involving fluid body interactions abstract we describe our massively parallel finite element computations of unsteady incompressible flows involving fluid body interactions these computations are based on the deforming spatial domain stabilized space time dsd sst finite element formulation unsteady flows past a stationary naca 0012 airfoil are computed for reynolds numbers 1000 5000 and 100 000 significantly different flow patterns are observed for these three cases the method is then applied to computation of the dynamics of an airfoil falling in a viscous fluid under the influence of gravity it is observed that the location of the center of gravity of the airfoil plays an important role in determining its pitch stability computations are reported also for simulation of the dynamics of a two dimensional projectile that has a certain initial velocity specially designed mesh moving schemes are employed to eliminate the need for remeshing all these computations were carried out on the thinking machines cm 200 and cm 5 supercomputers with major speed ups compared to traditional supercomputers the implicit equation systems arising from the finite element discretizations of these large scale problems are solved iteratively by using the gmres update technique with diagonal preconditioners the finite element formulations and their parallel implementations assume unstructured meshes

fast rates for support vector machines using gaussian kernels for binary classification we establish learning rates up to the order of n 1 for support vector machines svms with hinge loss and gaussian rbf kernels these rates are in terms of two assumptions on the considered distributions tsybakov s noise assumption to establish a small estimation error and a new geometric noise condition which is used to bound the approximation error unlike previously proposed concepts for bounding the approximation error the geometric noise assumption does not employ any smoothness assumption 1 introduction in recent years support vector machines svms have been the subject of many theoretical considerations despite this effort their learning performance on restricted classes of distributions is still widely unknown in particular it is unknown under which nontrivial circumstances svms can guarantee fast learning rates the aim of this work is to use concepts like tsybakov s noise assumption and local rademacher averages to establish learning rates up to the order of n 1 for nontrivial distributions in addition to these concepts that are used to deal with the stochastic part of the analysis we also introduce a geometric assumption for distributions that allows us to estimate the approximation properties of gaussian rbf kernels unlike many other concepts introduced for bounding the approximation error our geometric assumption is not in terms of smoothness but describes the concentration and the noisiness of the data generating distribution near the decision boundary let us formally introduce the statistical classification problem to this end let us fix a subset x r d we write y 1 1 given a finite training set

on the rate of convergence of regularized boosting classifiers a regularized boosting method is introduced for which regularization is obtained through a penalization function it is shown through oracle inequalities that this method is model adaptive the rate of convergence of the probability of misclassification is investigated it is shown that for quite a large class of distributions the probability of error converges to the bayes risk at a rate faster than n v 2 4 v 1 where v is the vc dimension of the base class whose elements are combined by boosting methods to obtain an aggregated classifier the dimension independent nature of the rates may partially explain the good behavior of these methods in practical problems under tsybakov s noise condition the rate of convergence is even faster we investigate the conditions necessary to obtain such rates for different base classes the special case of boosting using decision stumps is studied in detail we characterize the class of classifiers realizable by aggregating decision stumps it is shown that some versions of boosting work especially well in high dimensional logistic additive models it appears that adding a limited labelling noise to the training data may in certain cases improve the convergence as has been also suggested by other authors

the entire regularization path for the support vector machine the support vector machine svm is a widely used tool for classification many efficient implementations exist for fitting a two class svm model the user has to supply values for the tuning parameters the regularization cost parameter and the kernel parameters it seems a common practice is to use a default value for the cost parameter often leading to the least restrictive model in this paper we argue that the choice of the cost parameter can be critical we then derive an algorithm that can fit the entire path of svm solutions for every value of the cost parameter with essentially the same computational cost as fitting one svm model we illustrate our algorithm on some examples and use our representation to give further insight into the range of svm solutions

analysis of low bit rate image transform coding calculations based on high resolution quantizations prove that the distortion rate d r of an image transform coding is proportional to 2 sup 2r when r is large enough in wavelet and block cosine bases we show that if r 1 bit pixel then d r varies like r sup 1 2 spl gamma where spl gamma remains of the order of 1 for most natural images the improved performance of embedded codings in wavelet bases is analyzed at low bit rates we show that the compression performance of an orthonormal basis depends mostly on its ability to approximate images with a few nonzero vectors

an improved algorithm for the solution of the regularization path of support vector machine this paper describes an improved algorithm for the numerical solution to the support vector machine svm classification problem for all values of the regularization parameter c the algorithm is motivated by the work of hastie and follows the main idea of tracking the optimality conditions of the svm solution for ascending value of c it differs from hastie s approach in that the tracked path is not assumed to be 1 d instead a multidimensional feasible space for the optimality condition is used to solve the tracking problem such a treatment allows the algorithm to properly handle data sets which hastie s approach fails these data sets are characterized by the presence of linearly dependent points in the kernel space duplicate points or nearly duplicate points such data sets are quite common among many real world data especially those with nominal features other contributions of this paper include a unifying formulation of the tracking process in the form of a linear programming problem update formula for the linear programs considerations that guard against accumulation of errors resulting from the use of incremental updates and routines to speed up the algorithm the algorithm is implemented under the matlab environment and is available for download experiments with several data sets including data set having up to several thousand data points are reported

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

statistical performance of support vector machines the support vector machine svm algorithm is well known to the computer learning community for its very good practical results the goal of the present paper is to study this algorithm from a statistical perspective using tools of concentration theory and empirical processes our main result builds on the observation made by other authors that the svm can be viewed as a statistical regularization procedure from this point of view it can also be interpreted as a model selection principle using a penalized criterion it is then possible to adapt general methods related to model selection in this framework to study two important points 1 what is the minimum penalty and how does it compare to the penalty actually used in the svm algorithm 2 is it possible to obtain oracle inequalities in that setting for the specific loss function used in the svm algorithm we show that the answer to the latter question is positive and provides relevant insight to the former our result shows that it is possible to obtain fast rates of convergence for svms

solution path for pin svm classifiers with positive and negative tau values applying the pinball loss in a support vector machine svm classifier results in pin svm the pinball loss is characterized by a parameter tau its value is related to the quantile level and different tau values are suitable for different problems in this paper we establish an algorithm to find the entire solution path for pin svm with different tau values this algorithm is based on the fact that the optimal solution to pin svm is continuous and piecewise linear with respect to tau we also show that the nonnegativity constraint on tau is not necessary i e tau can be extended to negative values first in some applications a negative tau leads to better accuracy second tau 1 corresponds to a simple solution that links svm and the classical kernel rule the solution for tau 1 can be obtained directly and then be used as a starting point of the solution path the proposed method efficiently traverses tau values through the solution path and then achieves good performance by a suitable tau in particular tau 0 corresponds to c svm meaning that the traversal algorithm can output a result at least as good as c svm with respect to validation error

statistical behavior and consistency of classification methods based on convex risk minimization we study how closely the optimal bayes error rate can be approximately reached using a classification algorithm that computes a classifier by minimizing a convex upper bound of the classification error function the measurement of closeness is characterized by the loss function used in the estimation we show that such a classification scheme can be generally regarded as a nonmaximum likelihood conditional in class probability estimate and we use this analysis to compare various convex loss functions that have appeared in the literature furthermore the theoretical insight allows us to design good loss functions with desirable properties another aspect of our analysis is to demonstrate the consistency of certain classification methods using convex risk minimization this study sheds light on the good performance of some recently proposed linear classification methods including boosting and support vector machines it also shows their limitations and suggests possible improvements

hierarchical segmentation based image coding using hybrid quad binary trees a novel segmentation based image approximation and coding technique is proposed a hybrid quad binary qb tree structure is utilized to efficiently model and code geometrical information within images compared to other tree based representation such as wedgelets the proposed qb tree based method is more efficient for a wide range of contour features such as junctions corners and ridges especially at low bit rates

convexity classification and risk bounds many of the classification algorithms developed in the machine learning literature including the support vector machine and boosting can be viewed as minimum contrast methods that minimize a convex surrogate of the 0 1 loss function the convexity makes these algorithms computationally efficient the use of a surrogate however has statistical consequences that must be balanced against the computational virtues of convexity to study these issues we provide a general quantitative relationship between the risk as assessed using the 0 1 loss and the risk as assessed using any nonnegative surrogate loss function we show that this relationship gives nontrivial upper bounds on excess risk under the weakest possible condition on the loss function that it satisfies a pointwise form of fisher consistency for classification the relationship is based on a simple variational transformation of the loss function that is easy to compute in many applications we also present a refined version of this result in the

l1 regularization path algorithm for generalized linear models summary we introduce a path following algorithm for l1 regularized generalized linear models the l1 regularization procedure is useful especially because it in effect selects variables according to the amount of penalization on the l1 norm of the coefficients in a manner that is less greedy than forward selection backward deletion the generalized linear model path algorithm efficiently computes solutions along the entire regularization path by using the predictor corrector method of convex optimization selecting the step length of the regularization parameter is critical in controlling the overall accuracy of the paths we suggest intuitive and flexible strategies for choosing appropriate values we demonstrate the implementation with several simulated and real data sets

arbitrary lagrangian eulerian formulation for fluid rigid body interaction a new formulation for two dimensional fluid rigid body interaction problems is developed in particular vortex induced oscillations of a rigid body in viscous incompressible flow are studied the incompressible navier stokes equations are used to describe the motion of the fluid while it is assumed that the rigid body is mounted on a system consisting of a spring and a dashpot an arbitrary lagrangian eulerian formulation ale is used in order to account for large boundary motion a general formulation for the coupled problem is obtained by uncoupling the translation motion of the body from its rotational motion and developing a specific algorithm to efficiently handle the nonlinear dependence of the rotations this general formulation can be easily applied to multi body problems two numerical examples involving either translations and rotations are presented as an illustration of the proposed methodologies for fluid rigid body interaction

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

additive logistic regression a statistical view of boosting boosting is one of the most important recent developments in classification methodology boosting works by sequentially applying a classification algorithm to reweighted versions of the training data and then taking a weighted majority vote of the sequence of classifiers thus produced for many classification algorithms this simple strategy results in dramatic improvements in performance we show that this seemingly mysterious phenomenon can be understood in terms of well known statistical principles namely additive modeling and maximum likelihood for the two class problem boosting can be viewed as an approximation to additive modeling on the logistic scale using maximum bernoulli likelihood as a criterion we develop more direct approximations and show that they exhibit nearly identical results to boosting direct multiclass generalizations based on multinomial likelihood are derived that exhibit performance comparable to other recently proposed multiclass generalizations of boosting in most situations and far superior in some we suggest a minor modification to boosting that can reduce computation often by factors of 10 to 50 finally we apply these insights to produce an alternative formulation of boosting decision trees this approach based on best first truncated tree induction often leads to better performance and can provide interpretable descriptions of the aggregate decision rule it is also much faster computationally making it more suitable to large scale data mining applications

simple proof of convergence of the smo algorithm for different svm variants in this brief we give a new proof of the asymptotic convergence of the sequential minimum optimization smo algorithm for both the most violating pair and second order rules to select the pair of coefficients to be updated the proof is more self contained shorter and simpler than previous ones and has a different flavor partially building upon gilbert s original convergence proof of its algorithm to solve the minimum norm problem for convex hulls it is valid for both support vector classification svc and support vector regression which are formulated under a general problem that encompasses them moreover this general problem can be further extended to also cover other support vector machines svm related problems such as svc or one class svms while the convergence proof of the slight variant of smo needed for them remains basically unchanged

a robust minimax approach to classification when constructing a classifier the probability of correct classification of future data points should be maximized we consider a binary classification problem where the mean and covariance matrix of each class are assumed to be known no further assumptions are made with respect to the class conditional distributions misclassification probabilities are then controlled in a worst case setting that is under all possible choices of class conditional densities with given mean and covariance matrix we minimize the worst case maximum probability of misclassification of future data points for a linear decision boundary this desideratum is translated in a very direct way into a convex second order cone optimization problem with complexity similar to a support vector machine problem the minimax problem can be interpreted geometrically as minimizing the maximum of the mahalanobis distances to the two classes we address the issue of robustness with respect to estimation errors in the means and covariances of the classes via a simple modification of the input data we also show how to exploit mercer kernels in this setting to obtain nonlinear decision boundaries yielding a classifier which proves to be competitive with current methods including support vector machines an important feature of this method is that a worst case bound on the probability of misclassification of future data is always obtained explicitly

piecewise linear regularized solution paths we consider the generic regularized optimization problem argmin l y x j efron hastie johnstone and tibshirani ann statist 32 2004 407 499 have shown that for the lasso that is if l is squared error loss and j 1 is the l 1 norm of the optimal coefficient path is piecewise linear that is is piecewise constant we derive a general characterization of the properties of loss l penalty j pairs which give piecewise linear coefficient paths such pairs allow for efficient generation of the full regularized coefficient paths we investigate the nature of efficient path following algorithms which arise we use our results to suggest robust versions of the lasso for regression and classification and to develop new efficient algorithms for existing problems in the literature including mammen and van de geer s locally adaptive regression splines

distance weighted discrimination high dimension low sample size statistical analysis is becoming increasingly important in a wide range of applied contexts in such situations the popular support vector machine suffers from data piling at the margin which can diminish generalizability this leads naturally to the development of distance weighted discrimination which is based on second order cone programming a modern computationally intensive optimization method

aerodynamic and aeroelastic analysis of bundled cables by numerical simulation abstract a numerical model for the aerodynamic and aeroelastic analysis of bundled cables commonly used in energy transmission lines is presented in this work the bundles were idealized by a sectional model representing the section at the mid span between two supporting towers a slightly compressible viscous fluid was considered and the two dimensional flow was analyzed using a two step explicit method with an arbitrary eulerian lagrangean description a taylor series expansion was used in time and the classical galerkin technique with the finite element method were used for space discretization turbulence was modeled using large eddy simulation with the classical smagorinsky s sub grid scale model the set of cables forms a single body with elastic constrains working mechanically coupled being each cable linked to the others by spacers the fluid structure interaction was taken into account considering equilibrium and compatibility conditions at the fluid solid interfaces and the resulting dynamical equilibrium equation was solved using the newmark s method

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

sparse representation in structured dictionaries with application to synthetic aperture radar sparse signal representations and approximations from overcomplete dictionaries have become an invaluable tool recently in this paper we develop a new heuristic graph structured sparse signal representation algorithm for overcomplete dictionaries that can be decomposed into subdictionaries and whose dictionary elements can be arranged in a hierarchy around this algorithm we construct a methodology for advanced image formation in wide angle synthetic aperture radar sar defining an approach for joint anisotropy characterization and image formation additionally we develop a coordinate descent method for jointly optimizing a parameterized dictionary and recovering a sparse representation using that dictionary the motivation is to characterize a phenomenon in wide angle sar that has not been given much attention before migratory scattering centers i e scatterers whose apparent spatial location depends on aspect angle finally we address the topic of recovering solutions that are sparse in more than one objective domain by introducing a suitable sparsifying cost function we encode geometric objectives into sar image formation through sparsity in two domains including the normal parameter space of the hough transform

a computational approach for predicting the hydroelasticity of flexible structures based on the pressure poisson equation this work is concerned with the modeling of the interaction of fluid flow with flexible solid structures the flow under consideration is governed by the navier stokes equations for incompressible viscous fluids and modeled with low order velocity pressure finite elements the motion of the fluid domain is accounted for by the arbitrary lagrangian eulerian formulation the structure is represented by means of an appropriate standard finite element formulation the spring smooth analogy is used to mesh control the time integrating algorithm is based on the predictor multi corrector algorithm an important aspect of the present work is the introduction of a new monolithic approach based on the fluid pressure poisson equation ppe to solve the hydroelasticity problem of an incompressible viscous fluid with an elastic body that is vibrating due to flow excitation the ppe is derived to be consistent with the coupled system equation for the fluid structure interaction fsi based on this approach an efficient monolithic method is adopted to simulate hydroelasticity between the flexible structure and the flow the fluid pressure is implicitly derived to satisfy the incompressibility constraint and the other unknown variables are explicitly derived the coefficient matrix of the ppe for the fsi becomes symmetric and positive definite to demonstrate the performance of the proposed approach two working examples a beam immersed in incompressible fluid and a guide vane of a francis turbine passage were used the results show the validity of the proposed approach copyright 2007 john wiley sons ltd

a weak coupling algorithm for seabed wave interaction analysis this paper proposes a weak coupling algorithm for the seabed wave interaction analysis this algorithm is based on the error integration over a time interval and space along fluid seabed interfaces with this weak coupling algorithm seabed wave interaction analysis can be easily carried out with a fluid solver in fluid domain and a meshless solver in seabed domain independently the fluid solver is based on a two step projection method for navier stokes equation the free surface of seawaters during wave propagation is traced through the volume of fluid vof the meshless solver is based on the biot s consolidation theory of saturated poroelasticity which considers the interaction of soil deformation and pore water pressure in seabed data exchange at the interface between fluid and porous medium domains is carried out through a point interpolation method interface condition is approximately satisfied in a variational sense through an iteration scheme between two solvers this algorithm does allow not only non matching mesh along the interface but also non matching time step in different subdomains numerical examples show that this weak coupling algorithm is able to capture the deformation of interface and improve the computation accuracy and efficiency 2004 elsevier b v all rights reserved

one bit compressed sensing with non gaussian measurements abstract in one bit compressed sensing previous results state that sparse signals may be robustly recovered when the measurements are taken using gaussian random vectors in contrast to standard compressed sensing these results are not extendable to natural non gaussian distributions without further assumptions as can be demonstrated by simple counter examples involving extremely sparse signals we show that approximately sparse signals that are not extremely sparse can be accurately reconstructed from single bit measurements sampled according to a sub gaussian distribution and the reconstruction comes as the solution to a convex program

second order cone programming approaches for handling missing and uncertain data we propose a novel second order cone programming formulation for designing robust classifiers which can handle uncertainty in observations similar formulations are also derived for designing regression functions which are robust to uncertainties in the regression setting the proposed formulations are independent of the underlying distribution requiring only the existence of second order moments these formulations are then specialized to the case of missing values in observations for both classification and regression problems experiments show that the proposed formulations outperform imputation

support vector machine classifier with pinball loss traditionally the hinge loss is used to construct support vector machine svm classifiers the hinge loss is related to the shortest distance between sets and the corresponding classifier is hence sensitive to noise and unstable for re sampling in contrast the pinball loss is related to the quantile distance and the result is less sensitive the pinball loss has been deeply studied and widely applied in regression but it has not been used for classification in this paper we propose a svm classifier with the pinball loss called pin svm and investigate its properties including noise insensitivity robustness and misclassification error besides insensitive zone is applied to the pin svm for a sparse model compared to the svm with the hinge loss the proposed pin svm has the same computational complexity and enjoys noise insensitivity and re sampling stability

multilayered image representation application to image compression the main contribution of this work is a new paradigm for image representation and image compression we describe a new multilayered representation technique for images an image is parsed into a superposition of coherent layers piecewise smooth regions layer textures layer etc the multilayered decomposition algorithm consists in a cascade of compressions applied successively to the image itself and to the residuals that resulted from the previous compressions during each iteration of the algorithm we code the residual part in a lossy way we only retain the most significant structures of the residual part which results in a sparse representation each layer is encoded independently with a different transform or basis at a different bitrate and the combination of the compressed layers can always be reconstructed in a meaningful way the strength of the multilayer approach comes from the fact that different sets of basis functions complement each others some of the basis functions will give reasonable account of the large trend of the data while others will catch the local transients or the oscillatory patterns this multilayered representation has a lot of beautiful applications in image understanding and image and video coding we have implemented the algorithm and we have studied its capabilities

variational denoising of partly textured images by spatially varying constraints denoising algorithms based on gradient dependent regularizers such as nonlinear diffusion processes and total variation denoising modify images towards piecewise constant functions although edge sharpness and location is well preserved important information encoded in image features like textures or certain details is often compromised in the process of denoising we propose a mechanism that better preserves fine scale features in such denoising processes a basic pyramidal structure texture decomposition of images is presented and analyzed a first level of this pyramid is used to isolate the noise and the relevant texture components in order to compute spatially varying constraints based on local variance measures a variational formulation with a spatially varying fidelity term controls the extent of denoising over image regions our results show visual improvement as well as an increase in the signal to noise ratio over scalar fidelity term processes this type of processing can be used for a variety of tasks in partial differential equation based image processing and computer vision and is stable and meaningful from a mathematical viewpoint

image compression with adaptive local cosines a comparative study the goal of this work is twofold first we demonstrate that an advantage can be gained by using local cosine bases over wavelets to encode images that contain periodic textures we designed a coder that outperforms one of the best wavelet coders on a large number of images the coder finds the optimal segmentation of the image in terms of local cosine bases the coefficients are encoded using a scalar quantizer optimized for laplacian distributions this new coder constitutes the first concrete contribution of the paper second we used our coder to perform an extensive comparison of several optimized bells in terms of rate distortion and visual quality for a large collection of images this study provides for the first time a rigorous evaluation in realistic conditions of these bells our experiments show that bells that are designed to reproduce exactly polynomials of degree 1 resulted in the worst performance in terms of the psnr however a visual inspection of the compressed images indicates that these bells often provide reconstructed images with very few visual artifacts even at low bit rates the bell with the most narrow fourier transform gave the best results in terms of the psnr on most images this bell tends however to create annoying visual artifacts in very smooth regions at low bit rate

streamline upwind petrov galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier stokes equations abstract a new finite element formulation for convection dominated flows is developed the basis of the formulation is the streamline upwind concept which provides an accurate multidimensional generalization of optimal one dimensional upwind schemes when implemented as a consistent petrov galerkin weighted residual method it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods the accuracy of the streamline upwind petrov galerkin formulation for the linear advection diffusion equation is demonstrated on several numerical examples the formulation is extended to the incompressible navier stokes equations an efficient implicit pressure explicit velocity transient algorithm is developed which accomodates several treatments of the incompressibility constraint and allows for multiple iterations within a time step the effectiveness of the algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a reynolds number of 100