a filtering approach to edge preserving map estimation of images the authors present a computationally efficient technique for maximum a posteriori map estimation of images in the presence of both blur and noise the image is divided into statistically independent regions each region is modelled with a wss gaussian prior classical wiener filter theory is used to generate a set of convex sets in the solution space with the solution to the map estimation problem lying at the intersection of these sets the proposed algorithm uses an underlying segmentation of the image and a means of determining the segmentation and refining it are described the algorithm is suitable for a range of image restoration problems as it provides a computationally efficient means to deal with the shortcomings of wiener filtering without sacrificing the computational simplicity of the filtering approach the algorithm is also of interest from a theoretical viewpoint as it provides a continuum of solutions between wiener filtering and inverse filtering depending upon the segmentation used we do not attempt to show here that the proposed method is the best general approach to the image reconstruction problem however related work referenced herein shows excellent performance in the specific problem of demosaicing

stability analysis of stochastic delay differential equations with levy noise abstract this paper is concerned with p th moment exponential stability problem for a class of stochastic delay differential equations driven by levy processes several new stability theorems are obtained by developing a method proof by contradiction moreover the results are applied to investigate the p th moment exponential stability of stochastic neural networks with levy noise in particular the time varying delay in our results is not required to be differentiable even not continuous the obtained results improve greatly some previous works given in the literature in particular our method can easily correct the incorrect proofs appeared in two recent papers finally two examples are provided to show the effectiveness of the theoretical results

bayesian reconstructions from emission tomography data using a modified em algorithm a novel method of reconstruction from single photon emission computerized tomography data is proposed this method builds on the expectation maximization em approach to maximum likelihood reconstruction from emission tomography data but aims instead at maximum posterior probability estimation which takes account of prior belief about smoothness in the isotope concentration a novel modification to the em algorithm yields a practical method the method is illustrated by an application to data from brain scans

solitary shock waves and other travelling waves in a general compressible hyperelastic rod in the literature it has been conjectured that solitary shock waves can arise in incompressible hyperelastic rods recently it has been shown that this conjecture is true one might guess that when compressibility is taken into account such a wave which is both a solitary wave and a shock wave can still arise one of the aims of this paper is to show the existence of this interesting type of wave in general compressible hyperelastic rods and provide an analytical description it is difficult to directly tackle the fully nonlinear rod equations here by using a non dimensionalization process and the reductive perturbation technique we derive a new type of nonlinear dispersive equation as the model equation we then focus on the travelling wave solutions of this new equation as a result we obtain a system of ordinary differential equations an important feature of this system is that there is a vertical singular line in the phase plane which leads to the appearance of shock waves by considering the equilibrium points and their relative positions to the singular line we are able to determine all qualitatively different phase planes those paths in phase planes which represent physically acceptable solutions are discussed one by one it turns out that there is a variety of travelling waves including solitary shock waves solitary waves periodic shock waves etc analytical expressions for all these waves are obtained a new phenomenon is also found a solitary wave can suddenly change into a periodic wave with finite period in dynamical systems this represents a homoclinic orbit suddenly changing into a closed orbit to the authors9 knowledge such a bifurcation has not been found in any other dynamical systems

image estimation using doubly stochastic gaussian random field models the two dimensional 2 d doubly stochastic gaussian dsg model was introduced by one of the authors to provide a complete model for spatial filters which adapt to the local structure in an image signal here we present the optimal estimator and 2 d fixed lag smoother for this dsg model extending earlier work of ackerson and fu as the optimal estimator has an exponentially growing state space we investigate suboptimal estimators using both a tree and a decision directed method experimental results are presented

hidden markov models and disease mapping we present new methodology to extend hidden markov models to the spatial domain and use this class of models to analyze spatial heterogeneity of count data on a rare phenomenon this situation occurs commonly in many domains of application particularly in disease mapping we assume that the counts follow a poisson model at the lowest level of the hierarchy and introduce a finite mixture model for the poisson rates at the next level the novelty lies in the model for allocation to the mixture components which follows a spatially correlated process the potts model and in treating the number of components of the spatial mixture as unknown inference is performed in a bayesian framework using reversible jump markov chain monte carlo the model introduced can be viewed as a bayesian semiparametric approach to specifying flexible spatial distribution in hierarchical models performance of the model and comparison with an alternative well known markov random field specification for the poisson rates are de

orientability of fredholm families and topological degree for orientable nonlinear fredholm mappings abstract we construct a degree theory for oriented fredholm mappings of index zero between open subsets of banach spaces and between banach manifolds our approach is based on the orientation of fredholm mappings it does not use fredholm structures on the domain and target spaces we provide a computable formula for the change in degree through an admissible homotopy that is necessary for applications to global bifurcation the notion of orientation enables us to establish rather precise relationships between our degree and many other degree theories for particular classes of fredholm maps including the elworthy tromba degree which have appeared in the literature in a seemingly unrelated manner

global continuation in displacement problems of nonlinear elastostatics via the leray schauder degree we obtain global solution continua of forced displacement problems of nonlinear elastostatics via a leray schauder scheme we adopt strong ellipticity as a bsic constitutive hypothesis the usual leray schauder approach based in part upon the reduction of the boundary value problem to an operator equation for the zeros of a compact vector field apparently fails on the one hand strong ellipticity alone is not enough to insure invertibility rdquo of the principal quasilinear part of the differential operator more importantly the physical requirement of local injectivity of the deformation and the associated growth of the stored energy function dictate that ellipticity is not uniform we demonstrate how to overcome these difficulties finally with additional physically reasonable restrictions on the stored energy function we obtain unbounded branches of classical globally injective solutions

polynomial stability of exact solution and a numerical method for stochastic differential equations with time dependent delay abstract we consider a stochastic differential equations with time dependent delay in this paper we first obtain the existence uniqueness and polynomial stability of exact solution to this equation under suitable conditions then for the numerical method of the corresponding sdde we present a so called modified truncated euler maruyama mtem method and consider the almost sure and mean square polynomial stability of this numerical method by using the well known discrete semimartingale convergence theorem sufficient conditions are obtained for both bounded and unbounded delay to ensure the polynomial stability of the corresponding numerical approximation results suggest that the mtem method replicates the polynomial stability of given sdde under suitable conditions examples are presented to illustrate the conclusion

stability analysis for a class of stochastic delay nonlinear systems driven by g brownian motion abstract this paper is devoted to study the p th moment exponential stability problem for a class of stochastic delay nonlinear systems sdnss driven by g brownian motion the delays considered in this paper are time varying delays i t 0 1 i 3 and they are not required to be differentiable different from the traditional methods we use a new approach stochastic delay feedback controls we firstly compare the sdns with the corresponding stochastic nonlinear system sns instead of studying the stability of the sdns directly then we impose the condition on the sns to ensure the p th moment exponential stability of the sns furthermore we show that there is a positive constant such that the sdns is also p th moment exponentially stable provided in particular we give an implicit lower bound for which can be computed numerically

almost sure exponential stability of hybrid stochastic functional differential equations abstract this paper is concerned with the almost sure exponential stability of the n dimensional nonlinear hybrid stochastic functional differential equation sfde d x t f 1 x t t r t t d t g 2 x t t r t t d b t where x t x t u u 0 is a c 0 r n valued process b t is an m dimensional brownian motion while r t is a markov chain we show that if the corresponding hybrid stochastic differential equation sde d y t f y t r t t d t g y t r t t d b t is almost surely exponentially stable then there exists a positive number such that the sfde is also almost surely exponentially stable as long as we also describe a method to determine which can be computed numerically in practice

stabilisation of hybrid stochastic systems with levy noise by discrete time feedback control this paper is devoted to deal with the stabilisation problems of continuous time hybrid stochastic systems often described by stochastic differential equations with markovian switching with levy

maximum likelihood reconstruction for emission tomography previous models for emission tomography et do not distinguish the physics of et from that of transmission tomography we give a more accurate general mathematical model for et where an unknown emission density x y z generates and is to be reconstructed from the number of counts n d in each of d detector units d within the model we give an algorithm for determining an estimate of which maximizes the probability p n of observing the actual detector count data n over all possible densities let independent poisson variables n b with unknown means b b 1 b represent the number of unobserved emissions in each of b boxes pixels partitioning an object containing an emitter suppose each emission in box b is detected in detector unit d with probability p b d d 1 d with p b d a one step transition matrix assumed known we observe the total number n n d of emissions in each detector unit d and want to estimate the unknown b b 1 b for each the observed data n has probability or likelihood p n the em algorithm of mathematical statistics starts with an initial estimate 0 and gives the following simple iterative procedure for obtaining a new estimate new from an old estimate old to obtain k k 1 2 new b old b dd 1 n d p b d old b p b d b 1 b

inhomogeneous prior models for image reconstruction abstract over recent years the use of homogeneous gibbs prior models in image processing has become widely accepted there has been however much discussion over precisely which models are most appropriate for most applications the simplest gaussian model tends to oversmooth reconstructions so it has been rejected in favor of various edge preserving alternatives we claim that the problem is not with the gaussian family but rather with the assumption of homogeneity in this article we propose an inhomogeneous gaussian random field as a general prior model for many image processing applications the simplicity of the gaussian model allows rapid calculation and the flexibility of the spatially varying prior parameter allows varying degrees of spatial smoothing this approach is in the spirit of adaptive kernel density methods where only the choice of the variable window width is important the analysis of real single photon emission computed tomography data is used to illustrate the methods and simu

asymptotic bifurcation solutions for compressions of a clamped nonlinearly elastic rectangle transition region and barrelling to a corner like profile in the two experiments by beatty and his coauthors on the compressions of elastic rectangles bars it was found that there is a transition region of the aspect ratio which separates buckling from b

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

an iterative gibbsian technique for reconstruction of m ary images abstract the reconstruction of m ary images corrupted by independent noise is treated the original image is modeled by a markov random field mrf whose parameters are unknown likewise the probabilistic structure of the noise is unknown this paper presents an iterative procedure which performs the parameter estimation and image reconstruction tasks at the same time the procedure that we call gibbsian em algorithm is a generalization to the mrf context of a general algorithm known as the em algorithm used to approximate maximum likelihood estimates for incomplete data problems a number of experiments are presented in the case of gaussian noise and binary noise showing that the gibbsian em algorithm is useful and effective for image reconstruction and segmentation

bayesian estimation for homogeneous and inhomogeneous gaussian random fields this paper investigates bayesian estimation for gaussian markov random fields in particular a new class of compound model is proposed which describes the observed intensities using an inhomogeneous model and the degree of spatial variation described by a second random field the coupled markov random fields are used as prior distributions and combined with gaussian noise models to produce posterior distributions on which estimation is based all model parameters are estimated in a fully bayesian setting using the metropolis hasting algorithm the full posterior estimation procedures are illustrated and compared using various artificial examples for these examples the inhomogeneous model performs very favorably when compared to the homogeneous model allowing differential degrees of smoothing and varying local textures

bifurcation to a corner like formation in a slender nonlinearly elastic cylinder asymptotic solution and mechanism in this paper we study the corner like formation in a slender nonlinearly elastic cylinder due to compression mathematically this is a very challenging problem one needs to study the bifurcation of the nonlinear field equations complicated nonlinear partial differential equations and show that there is a bifurcation leading to a solution with a corner like profile we also aim to obtain the asymptotic expression for this post bifurcation solution as far as we know there is no available analytical method to obtain the post bifurcation solution of nonlinear partial differential equation s here we use a novel approach to tackle the present problem through a method of coupled series asymptotic expansions we manage to derive the normal form equation of the original nonlinear field equations which can be written as a singular ordinary differential equation ode system the vector field has a singularity at one point with welding end conditions the problem is reduced to study the boundary value problem of a singular ode system it seems that such a boundary value problem of a singular ode system was not formulated or studied before in the context of the present problem with the help of phase planes we manage to solve such a boundary value problem it turns out that there is a vertical singular line in phase planes which causes the bifurcation to a corner like solution the expression for this post bifurcation solution is also obtained from the analytical results obtained we reveal that the coupling effect of the material nonlinearity and geometrical size is the physical mechanism that causes the formation of a corner like profile

constrained restoration and the recovery of discontinuities the linear image restoration problem is to recover an original brightness distribution x sup 0 given the blurred and noisy observations y kx sup 0 b where k and b represent the point spread function and measurement error respectively this problem is typical of ill conditioned inverse problems that frequently arise in low level computer vision a conventional method to stabilize the problem is to introduce a priori constraints on x sup 0 and design a cost functional h x over images x which is a weighted average of the prior constraints regularization term and posterior constraints data term the reconstruction is then the image x which minimizes h a prominent weakness in this approach especially with quadratic type stabilizers is the difficulty in recovering discontinuities the authors therefore examine prior smoothness constraints of a different form which permit the recovery of discontinuities without introducing auxiliary variables for marking the location of jumps and suspending the constraints in their vicinity in this sense discontinuities are addressed implicitly rather than explicitly

on the statistical analysis of dirty pictures may 7th 1986 professor a f m smith in the chair summary a continuous two dimensional region is partitioned into a fine rectangular array of sites or pixels each pixel having a particular colour belonging to a prescribed finite set the true colouring of the region is unknown but associated with each pixel there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model the aim is to reconstruct the true scene with the additional knowledge that pixels close together tend to have the same or similar colours in this paper it is assumed that the local characteristics of the true scene can be represented by a nondegenerate markov random field such information can be combined with the records by bayes theorem and the true scene can be estimated according to standard criteria however the computational burden is enormous and the reconstruction may reflect undesirable largescale properties of the random field thus a simple iterative method of reconstruction is proposed which does not depend on these large scale characteristics the method is illustrated by computer simulations in which the original scene is not directly related to the assumed random field some complications including parameter estimation are discussed potential applications are mentioned briefly

compound gauss markov random fields for image estimation algorithms for obtaining approximations to statistically optimal estimates for images modeled as compound gauss markov random fields are discussed the authors consider both the maximum a posteriori probability map estimate and the minimum mean squared error mmse estimate for image estimation and image restoration compound image models consist of several submodels having different characteristics along with an underlying structure model which govern transitions between these image submodels two different compound random field models are employed the doubly stochastic gaussian dsg random field and a compound gauss markov cgm random field the authors present map estimators for dsg and cgm random fields using simulated annealing a fast converging algorithm called deterministic relaxation which however converges to only a locally optimal map estimate is also presented as an alternative for reducing computational loading on sequential machines for comparison purposes the authors include results on the fixed lag smoothing mmse estimator for the dsg field and its suboptimal m algorithm approximation

simple parallel hierarchical and relaxation algorithms for segmenting noncausal markovian random fields the modeling and segmentation of images by mrf s markov random fields is treated these are two dimensional noncausal markovian stochastic processes two conceptually new algorithms are presented for segmenting textured images into regions in each of which the data are modeled as one of c mrf s the algorithms are designed to operate in real time when implemented on new parallel computer architectures that can be built with present technology a doubly stochastic representation is used in image modeling here a gaussian mrf is used to model textures in visible light and infrared images and an autobinary or autoternary etc mrf to model a priori information about the local geometry of textured image regions for image segmentation the true texture class regions are treated either as a priori completely unknown or as a realization of a binary or ternary etc mrf in the former case image segmentation is realized as true maximum likelihood estimation in the latter case it is realized as true maximum a posteriori likelihood segmentation in addition to providing a mathematically correct means for introducing geometric structure the autobinary or ternary etc mrf can be used in a generative mode to generate image geometries and artificial images and such simulations constitute a very powerful tool for studying the effects of these models and the appropriate choice of model parameters the first segmentation algorithm is hierarchical and uses a pyramid like structure in new ways that exploit the mutual dependencies among disjoint pieces of a textured region

injectivity and self contact in nonlinear elasticity let be a bounded open connected subset of 3 with a sufficiently smooth boundary the additional condition det dx vol is imposed on the admissible deformations of a hyperelastic body whose reference configuration is we show that the associated minimization problem provides a mathematical model for matter to come into frictionless contact with itself but not interpenetrate we also extend j ball s theorems on existence to this case by establishing the existence of a minimizer of the energy in the space w1 p 3 p 3 that is injective almost everywhere

fully bayesian reconstructions from single photon emission computed tomography data abstract with suitably chosen priors bayesian models are useful in image reconstruction i consider reconstructions from single photon emission computerized tomography data using a gibbs pairwise difference prior a fully bayesian approach is presented where the prior parameters are considered drawn from hyperpriors the approach is problematical because the normalization constant in the prior is an intractable function of its parameters here the constant is estimated off line by reverse logistic regression markov chain monte carlo methods are used on simulated and real data to gain estimates of the posterior mean and pixelwise credibility bounds the resulting reconstructions are compared to those obtained by filtered back projection maximum likelihood em and the one step late solution to the fixed parameter posterior mode

almost sure exponential stability of stochastic differential delay equations this paper is concerned with the almost sure exponential stability of the multi dimensional nonlinear stochastic differential delay equation sdde with variable delays of the form dx t f x t delta 1 t t dt g x t delta 2 t t db t where delta 1 delta 2 mathbb r to 0 tau stand for variable delays we show that if the corresponding nondelay stochastic differential equation sde dy t f y t t dt g y t t db t admits a lyapunov function which in particular implies the almost sure exponential stability of the sde then there exists a positive number tau such that the sdde is also almost sure exponentially stable as long as the delay is bounded by tau we provide an implicit lower bound for tau which can be computed numerically moreover our new theory enables us to design stochastic delay feedback controls in order to stabilize unstable differential equations

quasi sure exponential stability and stabilisation of stochastic delay differential equations under g expectation framework in this work we obtain the sufficient conditions to examine quasi sure exponential stability of stochastic delay differential equation under g expectation framework in short g sdde our argumen

bayesian methods applied to survey data from archeological magnetometry a model is presented for the interpretation of magnetometer data in terms of archeological features beneath the ground it describes the detector s response to the assemblage of buried features incorporating both a spread function and a statistical error process as well as appropriate prior beliefs about the nature of archeological features the problem is to estimate the magnetic susceptibility of the buried features at each horizontal location a monte carlo markov chain approach is used to estimate magnetic susceptibilities and all prior parameters this requires estimation of the normalization constant of the gibbs prior distribution the approach is illustrated with both simulated data and measurements from an archeological site in the latter case the reconstruction of the buried features corresponds well with the archeologist s observations during subsequent excavation

phase transitions in a slender cylinder composed of an incompressible elastic material i asymptotic model equation we present reasons both experimental and mathematical for why it is important to consider the radial deformation thus the lateral traction free boundary conditions as well for phase transitions in a slender elastic cylinder one of the main purposes of this paper is to derive an asymptotic model equation which takes into account the radial deformation and satisfies the traction free boundary conditions up to the right order this is achieved from the three dimensional field equations through a novel approach that combines a series expansion and an asymptotic expansion an alternative approach based on whitham s approach well used in fluids is also given then we present some interesting analytic solutions for an infinite cylinder including those that seem to describe the structure of a phase boundary the nucleation process and the merge of two phase boundaries in particular by considering the energy distribution based on the nucleation solution it is revealed that the nucleation process is one of energy localizations concentrations and separation

a statistical model for positron emission tomography abstract positron emission tomography pet still in its research stages is a technique that promises to open new medical frontiers by enabling physicians to study the metabolic activity of the body in a pictorial manner much as in x ray transmission tomography and other modes of computerized tomography the quality of the reconstructed image in pet is very sensitive to the mathematical algorithm to be used for reconstruction in this article we tailor a mathematical model to the physics of positron emissions and we use the model to describe the basic image reconstruction problem of pet as a standard problem in statistical estimation from incomplete data we describe various estimation procedures such as the maximum likelihood ml method using the em algorithm the method of moments and the least squares method a computer simulation of a pet experiment is then used to demonstrate the ml and the least squares reconstructions the main purposes of this article are to report on what we believe is an

a note on delay dependent stability of ito type stochastic time delay systems different from the existing delay dependent stability criteria which depend on the size of the delays in both the drift and diffusion parts of stochastic time delay systems stdss this paper shows that the delay dependent stability criterion depends only on the drift part and works for arbitrary large delays of the diffusion part of stdss by developing the stochastic version descriptor system approach simple stability criterion is further derived for aperiodic sampled data stochastic systems the theoretical results are illustrated by means of a numerical example

exact steady periodic water waves with vorticity we consider the classical water wave problem described by the euler equations with a free surface under the influence of gravity over a flat bottom we construct two dimensional inviscid periodic traveling waves with vorticity they are symmetric waves whose profiles are monotone between each crest and trough we use bifurcation and degree theory to construct a global connected set of such solutions c 2004 wiley periodicals inc

fully bayesian estimation of gibbs hyperparameters for emission computed tomography data in recent years many investigators have proposed gibbs prior models to regularize images reconstructed from emission computed tomography data unfortunately hyperparameters used to specify gibbs priors can greatly influence the degree of regularity imposed by such priors and as a result numerous procedures have been proposed to estimate hyperparameter values from observed image data many of these procedures attempt to maximize the joint posterior distribution on the image scene to implement these methods approximations to the joint posterior densities are required because the dependence of the gibbs partition function on the hyperparameter values is unknown here the authors use recent results in markov chain monte carlo mcmc sampling to estimate the relative values of gibbs partition functions and using these values sample from joint posterior distributions on image scenes this allows for a fully bayesian procedure which does not fix the hyperparameters at some estimated or specified value but enables uncertainty about these values to be propagated through to the estimated intensities the authors utilize realizations from the posterior distribution for determining credible regions for the intensity of the emission source the authors consider two different markov random field mrf models the power model and a line site model as applications they estimate the posterior distribution of source intensities from computer simulated data as well as data collected from a physical single photon emission computed tomography spect phantom

post bifurcation equilibria in the plane strain test of a hyperelastic rectangular block abstract of interest here is the bifurcated equilibrium solution of a homogeneous hyperelastic rectangular block under finite plane strain tension or compression a general asymptotic analysis of the bifurcated equilibrium path about the principal solution s lowest critical load is presented using lagrangian kinematics the analysis is valid for any compressible hyperelastic material with axes of orthotropy aligned with the block s axes of symmetry in the reference stress free configuration the general theory is subsequently applied to blocks of different constitutive laws results are presented in the form of bifurcated equilibrium branch s curvature at the critical load as function of the block s aspect ratio since the sign of this curvature determines the branch s stability for small aspect ratios there is agreement with existing structural models while for relatively higher aspect ratios some rather counter intuitive stability results appear which strongly depend on the constitutive law

parity and generalized multiplicity assuming that x and y are banach spaces and a a b 2 x y is a path of linear fredholm operators with invertible endpoints in f pl we defined a homotopy invariant of a a a i g z2 the parity of a on i the parity plays a fundamental role in bifurcation problems and in degree theory for nonlinear fredholm type mappings here we prove a that generically the parity is a mod 2 count of the number of transversal intersec tions of a i with the set of singular operators b that if a0 is an isolated singular point of a then the local parity a a x0 lim o a x0 a0 remains invariant under lyapunov schmidt reduction and c that a a a0 1 i where mg x0 is any one of the various concepts of generalized multiplicity which have been defined in the context of linearized bifurcation data