adaptive bayesian wavelet shrinkage abstract when fitting wavelet based models shrinkage of the empirical wavelet coefficients is an effective tool for denoising the data this article outlines a bayesian approach to shrinkage obtained by placing priors on the wavelet coefficients the prior for each coefficient consists of a mixture of two normal distributions with different standard deviations the simple and intuitive form of prior allows us to propose automatic choices of prior parameters these parameters are chosen adaptively according to the resolution level of the coefficients typically shrinking high resolution frequency coefficients more heavily assuming a good estimate of the background noise level we obtain closed form expressions for the posterior means and variances of the unknown wavelet coefficients the latter may be used to assess uncertainty in the reconstruction several examples are used to illustrate the method and comparisons are made with other shrinkage methods

local solvability and loss of smoothness of the navier stokes maxwell equations with large initial data abstract the existence of a local in time unique solution and loss of smoothness of a full magneto hydro dynamics mhd system are considered for periodic initial data the result is proven using fujita kato s method in l 1 based for the fourier coefficients functional spaces enabling us to easily estimate nonlinear terms in the system as well as solutions to maxwell s equations a loss of smoothness result is shown for the velocity and magnetic field it comes from the damped wave operator which does not have any smoothing effect

fractal fractal dimensions of deterministic transport coefficients if a point particle moves chaotically through a periodic array of scatterers the associated transport coefficients are typically irregular functions under variation of control parameters for a piecewise linear two parameter map we analyse the structure of the associated irregular diffusion coefficient and current by numerically computing dimensions from box counting and from the autocorrelation function of these graphs we find that both dimensions are fractal for large parameter intervals and that both quantities are themselves fractal functions if computed locally on a uniform grid of small but finite subintervals we furthermore show that there is a simple functional relationship between the structure of fractal fractal dimensions and the difference quotient defined on these subintervals

the quasi stationary maxwell equations as singular limit of the complete equations the quasi linear case abstract the quasi stationary maxwell equations are considered as the time singular limit of the complete equations at the vanishing of the dielectric constant uniformly stable solutions of the complete equations are constructed and their convergence to a solution of the quasi stationary equations is proved and estimated

low mach number flows in time dependent domains we perform a multiple time scale single space scale analysis of a compressible fluid in a time dependent domain when the time variations of the boundary are small with respect to the acoustic velocity we introduce an average operator with respect to the fast time the averaged leading order variables satisfy modified incompressible equations which are coupled to linear acoustic equations with respect to the fast time we discuss possible initial boundary data for the asymptotic equations inherited from the initial boundary data for the compressible equations

zero dielectric constant limit of the full magnet hydro dynamics system abstract in this paper we study the zero dielectric constant limit to the full magnet hydro dynamics system or more precisely the maxwell navier stokes system for well prepared initial data the convergences of solutions of the full mhd system towards to the solutions of the classical 2d parabolic mhd system are justified rigorously by adapting the elaborate energy method as the dielectric constant tends to zero furthermore the corresponding convergence rates are also obtained

denoising and recognition using hidden markov models with observation distributions modeled by hidden markov trees hidden markov models have been found very useful for a wide range of applications in machine learning and pattern recognition the wavelet transform has emerged as a new tool for signal and image analysis learning models for wavelet coefficients have been mainly based on fixed length sequences but real applications often require to model variable length very long or real time sequences in this paper we propose a new learning architecture for sequences analyzed on short term basis but not assuming stationarity within each frame long term dependencies will be modeled with a hidden markov model which in each internal state will deal with the local dynamics in the wavelet domain using a hidden markov tree the training algorithms for all the parameters in the composite model are developed using the expectation maximization framework this novel learning architecture could be useful for a wide range of applications we detail two experiments with artificial and real data model based denoising and speech recognition denoising results indicate that the proposed model and learning algorithm are more effective than previous approaches based on isolated hidden markov trees in the case of the doppler benchmark sequence with 1024 samples and additive white noise the new method reduced the mean squared error from 1 0 to 0 0842 the proposed methods for feature extraction modeling and learning increased the phoneme recognition rates in 28 13 with better convergence than models based on gaussian mixtures

log determinant relaxation for approximate inference in discrete markov random fields graphical models are well suited to capture the complex and non gaussian statistical dependencies that arise in many real world signals a fundamental problem common to any signal processing application of a graphical model is that of computing approximate marginal probabilities over subsets of nodes this paper proposes a novel method applicable to discrete valued markov random fields mrfs on arbitrary graphs for approximately solving this marginalization problem the foundation of our method is a reformulation of the marginalization problem as the solution of a low dimensional convex optimization problem over the marginal polytope exactly solving this problem for general graphs is intractable for binary markov random fields we describe how to relax it by using a gaussian bound on the discrete entropy and a semidefinite outer bound on the marginal polytope this combination leads to a log determinant maximization problem that can be solved efficiently by interior point methods thereby providing approximations to the exact marginals we show how a slightly weakened log determinant relaxation can be solved even more efficiently by a dual reformulation when applied to denoising problems in a coupled mixture of gaussian model defined on a binary mrf with cycles we find that the performance of this log determinant relaxation is comparable or superior to the widely used sum product algorithm over a range of experimental conditions

fractal dimension of transport coefficients in a deterministic dynamical system in many low dimensional dynamical systems transport coefficients are very irregular and are perhaps even fractal functions of control parameters to analyse this phenomenon we study a dynamical system defined by a piecewise linear map and investigate the dependence of transport coefficients on the slope of the map we present analytical arguments supported by numerical calculations showing that both the minkowski bouligand and hausdorff fractal dimension of the graphs of these functions is 1 with a logarithmic correction and we find that the exponent controlling this correction is bounded from above by 1 or 2 depending on some detailed properties of the system using numerical techniques we show local self similarity of the graphs the local self similarity scaling transformations turn out to be dependent irregularly on the values of the system control parameters

irregular diffusion in the bouncing ball billiard abstract we call a system bouncing ball billiard if it consists of a particle that is subject to a constant vertical force and bounces inelastically on a one dimensional vibrating periodically corrugated floor here we choose circular scatterers that are very shallow hence this billiard is a deterministic diffusive version of the well known bouncing ball problem on a flat vibrating plate computer simulations show that the diffusion coefficient of this system is a highly irregular function of the vibration frequency exhibiting pronounced maxima whenever there are resonances between the vibration frequency and the average time of flight of a particle in addition there exist irregularities on finer scales that are due to higher order dynamical correlations pointing towards a fractal structure of this curve we analyze the diffusive dynamics by classifying the attracting sets and by working out a simple random walk approximation for diffusion which is systematically refined by using a green kubo formula

low mach number limit of viscous polytropic fluid flows abstract this paper studies the singular limit of the non isentropic navier stokes equations with zero thermal coefficient in a two dimensional bounded domain as the mach number goes to zero a uniform existence result is obtained in a time interval independent of the mach number provided that the initial data satisfy the bounded derivative conditions that is the time derivatives up to order two are bounded initially and navier s slip boundary condition is imposed

a review on some contributions to perturbation theory singular limits and well posedness abstract in the beginning of the 1990s we devoted a sequence of papers to perturbation theory singular limits and well posedness problems in particular the strong well posedness of the initial boundary value problem for the compressible euler equations was demonstrate for the first time our method also allowed singular limit results in the strong norm even under assumptions weaker than the current ones in the literature where the strong norm is not reached it is worth noting that until now the above method and results have not been substantially improved hence an introduction to it still looks timely actually in a forthcoming paper by returning to this method we improve in a very substantial way some important results recently appeared in the literature

directional multiscale modeling of images using the contourlet transform the contourlet transform is a new two dimensional extension of the wavelet transform using multiscale and directional filter banks the contourlet expansion is composed of basis images oriented at various directions in multiple scales with flexible aspect ratios given this rich set of basis images the contourlet transform effectively captures smooth contours that are the dominant feature in natural images we begin with a detailed study on the statistics of the contourlet coefficients of natural images using histograms to estimate the marginal and joint distributions and mutual information to measure the dependencies between coefficients this study reveals the highly non gaussian marginal statistics and strong interlocation interscale and interdirection dependencies of contourlet coefficients we also find that conditioned on the magnitudes of their generalized neighborhood coefficients contourlet coefficients can be approximately modeled as gaussian random variables based on these findings we model contourlet coefficients using a hidden markov tree hmt model with gaussian mixtures that can capture all interscale interdirection and interlocation dependencies we present experimental results using this model in image denoising and texture retrieval applications in denoising the contourlet hmt outperforms other wavelet methods in terms of visual quality especially around edges in texture retrieval it shows improvements in performance for various oriented textures

problems with different time scales for nonlinear partial differential equations consider a system of partial differential equations u t varepsilon 1 p 0 p 1 u here 0 varepsilon ll 1 is a small constant p 0 p 0 partial partial x is a differential operator with constant coefficients and p 1 p 1 x t u partial partial x is a quasilinear operator the coefficients of p 0 p 1 are of order o 1 it is shown how to prepare the initial data such that the solutions u x t and their derivatives can be bounded independently of varepsilon applications are discussed

minimum classification error learning for sequential data in the wavelet domain wavelet analysis has found widespread use in signal processing and many classification tasks nevertheless its use in dynamic pattern recognition have been much more restricted since most of wavelet models cannot handle variable length sequences properly recently composite hidden markov models which observe structured data in the wavelet domain were proposed to deal with this kind of sequences in these models hidden markov trees account for local dynamics in a multiresolution framework while standard hidden markov models capture longer correlations in time despite these models have shown promising results in simple applications only generative approaches have been used so far for parameter estimation the goal of this work is to take a step forward in the development of dynamic pattern recognizers using wavelet features by introducing a new discriminative training method for this markov models the learning strategy relies on the minimum classification error approach and provides re estimation formulas for fully non tied models numerical experiments on phoneme recognition show important improvement over the recognition rate achieved by the same models trained using maximum likelihood estimation

incompressible limits of the navier stokes equations for all time abstract we study the asymptotic behaviors of the regular solutions to the compressible navier stokes equations for well prepared initial data for all time as the mach number tends to zero by deriving a differential inequality with certain decay property the estimates obtained in this paper are uniform both in time and mach number

ekman layers of rotating fluids the case of general initial data in this paper we describe the weak solutions of the navier stokes equations with a large coriolis term as the rossby and the ekman numbers go to zero in a special domain with various boundary conditions this work extends the results in the case of well prepared initial data in 19 30 2000 john wiley sons inc

bivariate shrinkage functions for wavelet based denoising exploiting interscale dependency most simple nonlinear thresholding rules for wavelet based denoising assume that the wavelet coefficients are independent however wavelet coefficients of natural images have significant dependencies we only consider the dependencies between the coefficients and their parents in detail for this purpose new non gaussian bivariate distributions are proposed and corresponding nonlinear threshold functions shrinkage functions are derived from the models using bayesian estimation theory the new shrinkage functions do not assume the independence of wavelet coefficients we show three image denoising examples in order to show the performance of these new bivariate shrinkage rules in the second example a simple subband dependent data driven image denoising system is described and compared with effective data driven techniques in the literature namely visushrink sureshrink bayesshrink and hidden markov models in the third example the same idea is applied to the dual tree complex wavelet coefficients

a simple justification of the singular limit for equatorial shallow water dynamics the equatorial shallow water equations at low froude number form a symmetric hyperbolic system with large variable coefficient terms although such systems are not covered by the classical klainerman majda theory of singular limits the first two authors recently proved that solutions exist uniformly and converge to the solutions of the long wave equations as the height and froude number tend to 0 their proof exploits the special structure of the equations by expanding solutions in series of parabolic cylinder functions a simpler proof of a slight generalization is presented here in the spirit of the classical theory 2008 wiley periodicals inc

a fuzzy noise reduction method for color images a new fuzzy filter is presented for the reduction of additive noise for digital color images the filter consists of two subfilters the first subfilter computes fuzzy distances between the color components of the central pixel and its neighborhood these distances determine in what degree each component should be corrected all performed corrections preserve the color component distances the goal of the second subfilter is to correct the pixels where the color components differences are corrupted so much that they appear as outliers in comparison to their environment experimental results show the feasibility of the proposed approach we compare with other noise reduction methods by numerical measures and visual observations we also illustrate the performance of the proposed method as preprocessing step for edge detection

singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids many interesting problems in classical physics involve the limiting behavior of quasilinear hyperbolic systems as certain coefficients become infinite using classical methods the authors develop a general theory of such problems this theory is broad enough to study a wide variety of interesting singular limits in compressible fluid flow and magneto fluid dynamics including new constructive local existence theorems for the time singular limit equations in particular the authors give an entirely self contained classical proof of the convergence of solutions of the compressible fluid equations to their incompressible limits as the mach number becomes small the theory depends upon a balance between certain inherently nonlinear structural conditions on the matrix coefficients of the system together with appropriate initialization procedures similar results are developed also for the compressible and incompressible navier stokes equations with periodic initial data independent of the viscosity coefficients as they tend to zero

adapting to unknown smoothness via wavelet shrinkage abstract we attempt to recover a function of unknown smoothness from noisy sampled data we introduce a procedure sureshrink that suppresses noise by thresholding the empirical wavelet coefficients the thresholding is adaptive a threshold level is assigned to each dyadic resolution level by the principle of minimizing the stein unbiased estimate of risk sure for threshold estimates the computational effort of the overall procedure is order n log n as a function of the sample size n sureshrink is smoothness adaptive if the unknown function contains jumps then the reconstruction essentially does also if the unknown function has a smooth piece then the reconstruction is essentially as smooth as the mother wavelet will allow the procedure is in a sense optimally smoothness adaptive it is near minimax simultaneously over a whole interval of the besov scale the size of this interval depends on the choice of mother wavelet we know from a previous paper by the authors that traditional smoot

texture classification using refined histogram in this correspondence we propose a novel efficient and effective refined histogram rh for modeling the wavelet subband detail coefficients and present a new image signature based on the rh model for supervised texture classification our rh makes use of a step function with exponentially increasing intervals to model the histogram of detail coefficients and the concatenation of the rh model parameters for all wavelet subbands forms the so called rh signature to justify the usefulness of the rh signature we discuss and investigate some of its statistical properties these properties would clarify the sufficiency of the signature to characterize the wavelet subband information in addition we shall also present an efficient rh signature extraction algorithm based on the coefficient counting technique which helps to speed up the overall classification system performance we apply the rh signature to texture classification using the well known databases experimental results show that our proposed rh signature in conjunction with the use of symmetrized kullback leibler divergence gives a satisfactory classification performance compared with the current state of the art methods

the incompressible limit of the non isentropic euler equations we study the euler equations for slightly compressible fluids that is after rescaling the limits of the euler equations of fluid dynamics as the mach number tends to zero in this paper we consider the general non isentropic equations and general data we first prove the existence of classical solutions for a time independent of the small parameter then on the whole space d we prove that the solution converges to the solution of the incompressible euler equations

improved hidden markov models in the wavelet domain wavelet domain hidden markov models hmms in particular the hidden markov tree hmt model have been introduced and applied to signal and image processing e g signal denoising we develop a simple initialization scheme for the efficient hmt model training and then propose a new four state hmt model called hmt 2 we find that the new initialization scheme fits the hmt 2 model well experimental results show that the performance of signal denoising using the hmt 2 model is often improved over the two state hmt model developed by crouse et al see ibid vol 46 p 886 902 1998

wavelet based statistical signal processing using hidden markov models wavelet based statistical signal processing techniques such as denoising and detection typically model the wavelet coefficients as independent or jointly gaussian these models are unrealistic for many real world signals we develop a new framework for statistical signal processing based on wavelet domain hidden markov models hmms that concisely models the statistical dependencies and non gaussian statistics encountered in real world signals wavelet domain hmms are designed with the intrinsic properties of the wavelet transform in mind and provide powerful yet tractable probabilistic signal models efficient expectation maximization algorithms are developed for fitting the hmms to observational signal data the new framework is suitable for a wide range of applications including signal estimation detection classification prediction and even synthesis to demonstrate the utility of wavelet domain hmms we develop novel algorithms for signal denoising classification and detection

stability of isentropic navier stokes shocks in the high mach number limit by a combination of asymptotic ode estimates and numerical evans function calculations we establish stability of viscous shock solutions of the isentropic compressible navier stokes equations with law pressure i in the limit as mach number m goes to infinity for any 1 proved analytically and ii for m 2 500 gamma in 1 2 5 or m 13 000 gamma in 2 5 3 demonstrated numerically this builds on and completes earlier studies by matsumura nishihara and barker humpherys rudd zumbrun establishing stability for low and intermediate mach numbers respectively indicating unconditional stability independent of shock amplitude of viscous shock waves for law gas dynamics in the range gamma in 1 3 other values may be treated similarly but have not been checked numerically the main idea is to establish convergence of the evans function in the high mach number limit to that of a pressureless or infinitely compressible gas with additional upstream boundary condition determined by a boundary layer analysis recall that low mach number behavior is formally incompressible

deterministic diffusion in flower shaped billiards we propose a flower shaped billiard in order to study the irregular parameter dependence of chaotic normal diffusion our model is an open system consisting of periodically distributed obstacles in the shape of a flower and it is strongly chaotic for almost all parameter values we compute the parameter dependent diffusion coefficient of this model from computer simulations and analyze its functional form using different schemes all generalizing the simple random walk approximation of machta and zwanzig the improved methods we use are based either on heuristic higher order corrections to the simple random walk model on lattice gas simulation methods or they start from a suitable green kubo formula for diffusion we show that dynamical correlations or memory effects are of crucial importance in reproducing the precise parameter dependence of the diffusion coefficent

fast averaging for long and short wave scaled equatorial shallow water equations with coriolis parameter deviating from linearity the equatorial shallow water equations at low froude number form a symmetric hyperbolic system with large terms containing a variable coefficient the coriolis parameter f which depends on the latitude the limiting behavior of the solutions as the froude number tends to zero was investigated rigorously a few years ago using the common approximation that the variations of f with latitude are linear in that case the large terms have a peculiar structure due to special properties of the harmonic oscillator hamiltonian which can be exploited to prove strong uniform a priori estimates in adapted functional spaces it is shown here that these estimates still hold when f deviates from linearity even though the special properties on which the proofs were based have no obvious generalization as in the linear case existence uniqueness and convergence properties of the solutions corresponding to general unbalanced data are deduced from the estimates

embedding hmms based models in a euclidean space the topological hidden markov models current extensions of hidden markov models such as structural hierarchical coupled and others have the power to classify complex and highly organized patterns however one of their major limitations is the inability to cope with topology when applied to a visible observation vo sequence the traditional hmm based techniques have difficulty predicting the n dimensional shape formed by the symbols of the vo sequence to fulfill this need we propose a novel paradigm named topological hidden markov models thmms that classifies vo sequences by embedding the nodes of an hmm state transition graph in a euclidean space this is achieved by modeling the noise embedded in the shape generated by the vo sequence we cover the first and second level topological hmms we describe five basic problems that are assigned to a second level topological hidden markov model 1 sequence probability evaluation 2 statistical decoding 3 structural decoding 4 topological decoding and 5 learning to show the significance of this research we have applied the concept of thmms to i predict the ascii class assigned to a handwritten numeral and ii map protein primary structures to their 3d folds the results show that the second level thmms outperform the shmms and the multi class svm classifiers significantly

removal of correlated noise by modeling the signal of interest in the wavelet domain images captured with digital imaging devices often contain noise in literature many algorithms exist for the removal of white uncorrelated noise but they usually fail when applied to images with correlated noise in this paper we design a new denoising method for the removal of correlated noise by modeling the significance of the noise free wavelet coefficients in a local window using a new significance measure that defines the ldquosignal of interestrdquo and that is applicable to correlated noise we combine the intrascale model with a hidden markov tree model to capture the interscale dependencies between the wavelet coefficients we propose a denoising method based on the combined model and a less redundant wavelet transform we present results that show that the new method performs as well as the state of the art wavelet based methods while having a lower computational complexity

some mathematical questions related to the mhd equations some questions relating to the large time behavior of the solutions of mhd equations for a viscous incompressible resistive fluid are investigated the physical system is briefly described and the functional setting of the equations a flow in a bounded domain or in whole space with a space periodicity property in all directions the main existence and uniqueness results for weak and strong solutions of the mhd equations are recalled regularity properties and bounds on the solutions to the equations which are valid for all time are established and the concept of functional invariant sets is introduced which is contained in the space of smooth functions if the data are sufficiently regular the squeezing property of the trajectories are stated and it is shown that any functional invariant set for the mhd equations and in particular any attractor has a finite haussdorf dimension the flow is found to be totally determined for large dimensions by a finite number of parameters 26 references

low mach number limit of full navier stokes equations in a 3d bounded domain abstract this paper studies the low mach number limit of the full compressible navier stokes equations in a three dimensional bounded domain where the velocity field and the temperature satisfy the slip boundary conditions and the neumann boundary condition respectively the uniform estimates in the mach number for the strong solutions are derived in a short time interval provided that the initial density and temperature are close to the constant states and satisfy the bounded derivative conditions thus the solutions of the full compressible navier stokes equations converge to the one of the isentropic incompressible navier stokes equations as the mach number vanishes

wave operators and the incompressible limit of the compressible euler equation in an exterior domain in rn n 2 the solution of the compressible euler equation is shown to converge to that of the incompressible euler equation when the mach number tends to 0 the initial layer appears