on a system of klein gordon type equations with acoustic boundary conditions we prove the existence uniqueness and uniform stabilization of global solutions for a generalized system of klein gordon type equations with acoustic boundary conditions on a portion of the boundary and the dirichlet boundary condition on the rest

denoising of dynamic contrast enhanced mr images using dynamic nonlocal means this paper presents a new algorithm for denoising dynamic contrast enhanced dce mr images it is a novel variation on the nonlocal means nlm algorithm the algorithm called dynamic nonlocal means dnlm exploits the redundancy of information in the temporal sequence of images empirical evaluations of the performance of the dnlm algorithm relative to seven other denoising methods simple gaussian filtering the original nlm algorithm a trivial extension of nlm to include the temporal dimension bilateral filtering anisotropic diffusion filtering wavelet adaptive multiscale products threshold and traditional wavelet thresholding are presented the evaluations include quantitative evaluations using simulated data and real data 20 dce mri data sets from routine clinical breast mri examinations as well as qualitative evaluations using the same real data 24 observers 14 image signal processing specialists 10 clinical breast mri radiographers the results of the quantitative evaluation using the simulated data show that the dnlm algorithm consistently yields the smallest mse between the denoised image and its corresponding original noiseless version the results of the quantitative evaluation using the real data provide evidence at the 0 05 level of significance that the dnlm algorithm yields the smallest mse between the denoised image and its corresponding original noiseless version the results of the qualitative evaluation provide evidence at the 0 05 level of significance that the dnlm algorithm performs visually better than all of the other algorithms collectively the qualitative and quantitative results suggest that the dnlm algorithm more effectively attenuates noise in dce mr images than any of the other algorithms

on the wave equation with hyperbolic dynamical boundary conditions interior and boundary damping and supercritical sources abstract the aim of this paper is to study the problem u t t u p x u t f x u in 0 u 0 on 0 0 u t t u u q x u t g x u on 0 1 u 0 x u 0 x u t 0 x u 1 x in where is a bounded open subset of r n with c 1 boundary n 2 1 is relatively open on denotes the laplace beltrami operator on is the outward normal to and the terms p and q represent nonlinear damping terms while f and g are nonlinear perturbations in the paper we establish local and global existence uniqueness and hadamard well posedness results when source terms can be supercritical or super supercritical

gauge fields in a dsd and connections of its symmetry algebra the generalized connections of the de sitter algebra so d 1 and anti de sitter algebra so d 1 2 which are differential forms of arbitrary degree with values in any irreducible spin tensor representation of the anti de sitter algebra are studied it is shown that an arbitrary spin gauge field in anti de sitter space massless or partially massless can be described by a single connection a one to one correspondence between the connections of the anti de sitter algebra and the gauge fields is established the gauge symmetry is manifest and auxiliary fields are automatically included in the formalism

observer based boundary control of the sine gordon model energy abstract the problem of observer based boundary control of the sine gordon model energy is first posed a luenberger type observer for the sine gordon equation is analysed and explicit bounds on the system parameters ensuring the exponential decay of the estimation error are obtained with the use of this observer a speed gradient output feedback for sine gordon model energy control is proposed the achievement of the control goal is established under the assumption that system s energy does not vanish in finite time it is shown that the transient time in energy is close that the transient time in observation error i e the closed loop system has a reasonable performance it is also shown that the conditions on the observer gain sufficient for the state estimation error convergence are almost necessary in the sense that violation of these conditions makes the state estimation error transients too long

maximum likelihood estimation of rician distribution parameters the problem of parameter estimation from rician distributed data e g magnitude magnetic resonance images is addressed the properties of conventional estimation methods are discussed and compared to maximum likelihood ml estimation which is known to yield optimal results asymptotically in contrast to previously proposed methods ml estimation is demonstrated to be unbiased for high signal to noise ratio snr and to yield physical relevant results for low snr

scale space and edge detection using anisotropic diffusion a new definition of scale space is suggested and a class of algorithms used to realize a diffusion process is introduced the diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing rather than interregion smoothing it is shown that the no new maxima should be generated at coarse scales property of conventional scale space is preserved as the region boundaries in the approach remain sharp a high quality edge detector which successfully exploits global information is obtained experimental results are shown on a number of images parallel hardware implementations are made feasible because the algorithm involves elementary local operations replicated over the image

boundary stabilization for a coupled system abstract we investigate in this work the global existence of weak solutions for a nonlinear coupled system with mixed type boundary conditions more precisely dirichlet and feedback boundary conditions further we also prove the exponential decay of the energy associated with these solutions

uniform stabilization of the damped cauchy ventcel problem with variable coefficients and dynamic boundary conditions in this paper the uniform stabilization of the cauchy ventcel problem with variable coefficients is considered and the uniform energy decay rate for the problem is established by riemannian geometry methods

global existence and uniform decay for wave equation with dissipative term and boundary damping in this paper we prove the existence uniqueness and uniform stability of strong and weak solutions of the nonlinear wave equation u t email protected b x u t f u 0 in bounded domains with nonlinear damped boundary conditions given by email protected email protected g u t 0 with restrictions on function f u g u t and b x we prove the existence by means of the glerkin method and obtain the asymptotic behavior by using of the multiplier technique from the idea of kmornik and zuazua see 7

technical communique exponential stabilization of an axially moving string by linear boundary feedback the system modeled by an axially moving string and a mass damper spring mds controller applied at the right hand side rhs boundary of the string is considered the feature of the controller is not restricted at all and is determined by the system implicitly the mathematical model of this system is composed of an ordinary differential equation ode describing the mds and a partial differential equation pde describing the string the c 0 semigroup theory provides an elegant state space representation for the analysis of the coupled system the exponential stability is verified through the total mechanical energy dissipation and the semigroup theory the lower bound of the feedback gain is obtained

deconvolution of a distribution function abstract we consider the estimation of a distribution function when observations from this distribution are contaminated by measurement error the unknown distribution is modeled as a mixture of a finite number of known distributions model parameters can be estimated and confidence intervals constructed using well known likelihood theory we show that it is also possible to apply this approach to estimation of a unimodal distribution an application is presented using data from a dietary survey simulation results are given to indicate the performance of the estimators and the confidence interval procedures

optimality of energy estimates for the wave equation with nonlinear boundary velocity feedbacks we consider the wave equation damped by a nonlinear boundary velocity feedback q ut first we consider the case where q has a linear growth at infinity we prove that the usual decay rate estimates proved by nakao differential integral equations 8 1995 pp 681 688 haraux and zuazua arch rational mech anal 100 1988 pp 191 206 conrad leblond and marmorat in proceedings of the fifth international federation of automatic control symposium on control of distributed parameter systems perpignan 1989 pp 101 116 zuazua siam j control optim 28 1990 pp 466 477 and komornik in control and estimation of distributed parameter systems nonlinear phenomena internat ser numer math 118 birkhauser basel 1994 pp 253 266 when q has a polynomial behavior at zero and by the second author esaim control optim calc var 4 1999 pp 419 444 in the general case are in fact optimal in one space dimension more generally we prove that the energy decays exactly like the solution of an explicit and simple ordinary differential equation next we study the problem when q is bounded at infinity we prove that strong solutions decay exponentially to zero and we exhibit a sequence of weak solutions for which the associated energy decays to zero at infinity as slowly as the iterated logarithms go to infinity at infinity

on the controllability of parabolic systems with a nonlinear term involving the state and the gradient we present some results concerning the controllability of a quasi linear parabolic equation with linear principal part in a bounded domain of mathbb r n with dirichlet boundary conditions we analyze the controllability problem with distributed controls supported on a small open subset and boundary controls supported on a small part of the boundary we prove that the system is null and approximately controllable at any time if the nonlinear term f y nabla y grows slower than y log 3 2 1 y nabla y nabla y log 1 2 1 y nabla y at infinity generally in this case in the absence of control blow up occurs the proofs use global carleman estimates parabolic regularity and the fixed point method

global existence and asymptotic behavior for a coupled hyperbolic system with localized damping abstract in this paper we investigate the global existence and energy decay rate for the solution of a coupled hyperbolic system the semi explicit energy decay rate is established by using piecewise multiplier techniques and weighted integral inequality we extend the energy decay result in alabau boussouira f alabau boussouira convexity and weighted integral inequalities for energy decay rates of nonlinear dissipative hyperbolic systems appl math optim 51 2005 61 105 for a single equation to the coupled hyperbolic system

prior learning and gibbs reaction diffusion this article addresses two important themes in early visual computation it presents a novel theory for learning the universal statistics of natural images and it proposes a general framework of designing reaction diffusion equations for image processing we studied the statistics of natural images including the scale invariant properties then generic prior models were learned to duplicate the observed statistics based on minimax entropy theory the resulting gibbs distributions have potentials of the form u i spl lambda s spl sigma sub spl alpha 1 sup k spl sigma sub x y spl lambda sup spl alpha f sup spl alpha i x y with s f sup 1 f sup 2 f sup k being a set of filters and spl lambda spl lambda sup 1 spl lambda sup 2 spl lambda sup k the potential functions the learned gibbs distributions confirm and improve the form of existing prior models such as line process but in contrast to all previous models inverted potentials were found to be necessary we find that the partial differential equations given by gradient descent on u i spl lambda s are essentially reaction diffusion equations where the usual energy terms produce anisotropic diffusion while the inverted energy terms produce reaction associated with pattern formation enhancing preferred image features we illustrate how these models can be used for texture pattern rendering denoising image enhancement and clutter removal by careful choice of both prior and data models of this type incorporating the appropriate features

global existence and uniform stabilization of a generalized dissipative klein gordon equation type with boundary damping in this paper we prove the existence uniqueness and uniform stability of strong and weak solutions of the nonlinear generalized klein gordon equation 1 1 1 see sec i in bounded domains with nonlinear damped boundary conditions given by 1 1 3 see sec i with some restrictions on function f u h u g ut and b x we prove the existence and uniqueness by means of nonlinear semigroup method and obtain the uniform stabilization by using the multiplier technique

noise removal using fourth order partial differential equation with applications to medical magnetic resonance images in space and time we introduce a new method for image smoothing based on a fourth order pde model the method is tested on a broad range of real medical magnetic resonance images both in space and time as well as on nonmedical synthesized test images our algorithm demonstrates good noise suppression without destruction of important anatomical or functional detail even at poor signal to noise ratio we have also compared our method with related pde models

conformal self dual fields conformal self dual fields in flat spacetime of even dimension greater than or equal to 4 are studied ordinary derivative formulation of such fields is developed gauge invariant lagrangian with conventional kinetic terms and corresponding gauge transformations are obtained gauge symmetries are realized by involving the stueckelberg fields the realization of global conformal symmetries is obtained the light cone gauge lagrangian is found also we demonstrate the use of the light cone gauge for counting the on shell degrees of freedom of the conformal self dual fields

wavelet based rician noise removal for magnetic resonance imaging it is well known that magnetic resonance magnitude image data obey a rician distribution unlike additive gaussian noise rician noise is signal dependent and separating signal from noise is a difficult task rician noise is especially problematic in low signal to noise ratio snr regimes where it not only causes random fluctuations but also introduces a signal dependent bias to the data that reduces image contrast this paper studies wavelet domain filtering methods for rician noise removal we present a novel wavelet domain filter that adapts to variations in both the signal and the noise

existence and boundary stabilization of solutions for the coupled semilinear system abstract we investigate the global existence of both strong and weak solutions for a semilinear coupled system with homogeneous feedback boundary conditions in bounded open domain in r n with n n we also prove the exponential decay of total energy associated with weak solutions

new stability and exact observability conditions for semilinear wave equations the problem of estimating the initial state of 1 d wave equations with globally lipschitz nonlinearities from boundary measurements on a finite interval was solved recently by using the sequence of forward and backward observers and deriving the upper bound for exact observability time in terms of linear matrix inequalities lmis fridman 2013 in the present paper we generalize this result to n d wave equations on a hypercube this extension includes new lmi based exponential stability conditions for n d wave equations as well as an upper bound on the minimum exact observability time in terms of lmis for 1 d wave equations with locally lipschitz nonlinearities we find an estimate on the region of initial conditions that are guaranteed to be uniquely recovered from the measurements the efficiency of the results is illustrated by numerical examples

uniform stabilization of the dynamic elastica by boundary feedback it is proved that the dynamic elastica which is a nonlinear model describing the large deflecting motion of an inextensible beam can be uniformly exponentially stabilized by boundary velocity feedback

a nonlocal maximum likelihood estimation method for rician noise reduction in mr images postacquisition denoising of magnetic resonance mr images is of importance for clinical diagnosis and computerized analysis such as tissue classification and segmentation it has been shown that the noise in mr magnitude images follows a rician distribution which is signal dependent when signal to noise ratio snr is low it is particularly difficult to remove the random fluctuations and bias introduced by rician noise the objective of this paper is to estimate the noise free signal from mr magnitude images we model images as random fields and assume that pixels which have similar neighborhoods come from the same distribution we propose a nonlocal maximum likelihood nlml estimation method for rician noise reduction our method yields an optimal estimation result that is more accurate in recovering the true signal from rician noise than nl means algorithm in the sense of snr contrast and method error we demonstrate that nlml performs better than the conventional local maximum likelihood lml estimation method in preserving and defining sharp tissue boundaries in terms of a well defined sharpness metric while also having superior performance in method error

energy decay for nondissipative distributed systems with boundary damping and source term abstract in this paper we consider energy decay for nondissipative distributed systems with boundary damping and source terms first we consider the wave equation u u h u u u second we consider the case h u u in both first and second cases we have the nonlinear boundary condition u 0 t k t s x u s d s a x g u 0 we study energy decay using the multiplier technique and equivalent energy

uniform stabilization of the wave equation by nonlinear boundary feedback the question of uniformly stabilizing the solution of the wave equation y delta y 0 in omega times 0 infty omega is a bounded domain of bf r n by means of a nonlinear feedback law of the following form is studied partial y partial v k x g y on gamma 0 times 0 infty y 0 on gamma 1 times 0 infty gamma 0 gamma 1 being a suitable partition of the boundary of omega and g a continuous nondecreasing function such that g 0 0 we choose k x in l infty k x geqq 0 such that k x vanishes linearly at the interface points x in bar gamma 0 cap bar gamma 1 then if g s behaves like s p 1 s as s to 0 with p 1 and linearly as s to infty it is proved that the energy of every solution decays like t 2 p 1 as t to infty in the case where p 1 the exponential decay rate is proved

existence and decay rate estimates for the wave equation with nonlinear boundary damping and source term the wave equation with a source term is considered utt u u uin 0 we prove the existence and uniform decay rates of the energy by assuming a nonlinear feedback ut acting on the boundary provided that has necessarily not a polynomial growth near the origin to obtain the existence of global solutions we make use of the potential well method combined with the faedo galerkin procedure and constructing a special basis furthermore we prove that the energy of the system decays uniformly to zero and we obtain an explicit decay rate estimate adapting the ideas of lasiecka and tataru differential integral equations 6 3 1993 507 and patrick martinez esain control optimisation calc var 4 1999 419 the resulting problem generalizes martinez results and complements the works of lasiecka and tataru 1993 and vitillaro glasgow math j 44 2002 375

on discontinuity adaptive smoothness priors in computer vision a variety of analytic and probabilistic models in connection with markov random fields mrfs have been proposed in the last decade for solving low level vision problems involving discontinuities this paper presents a systematic study of these models and defines a general discontinuity adaptive da mrf model by analyzing the euler equation associated with the energy minimization it shows that the fundamental difference between different models lies in the behavior of interaction between neighboring points which is determined by the a priori smoothness constraint encoded into the energy function an important necessary condition is derived for the interaction to be adaptive to discontinuities to avoid oversmoothing this forms the basis on which a class of adaptive interaction functions aifs is defined the da model is defined in terms of the euler equation constrained by this class of aifs its solution is c sup 1 continuous and allows arbitrarily large but bounded slopes in dealing with discontinuities because of the continuous nature it is stable to changes in parameters and data a good property for regularizing ill posed problems experimental results are shown

global carleman inequalities for parabolic systems and applications to controllability this paper has been conceived as an overview on the controllability properties of some relevant linear and nonlinear parabolic systems specifically we deal with the null controllability and the exact controllability to the trajectories we try to explain the role played by the observability inequalities in this context and the need of global carleman estimates we also recall the main ideas used to overcome the difficulties motivated by nonlinearities first we considered the classical heat equation with dirichlet conditions and distributed controls then we analyze recent extensions to other linear and semilinear parabolic systems and or boundary controls finally we review the controllability properties for the stokes and navier stokes equations that are known to date in this context we have paid special attention to obtaining the necessary carleman estimates some open questions are mentioned throughout the paper we hope that this unified presentation will be useful for those researchers interested in the field

a cure for noisy magnetic resonance images chi square unbiased risk estimation in this paper we derive an unbiased expression for the expected mean squared error associated with continuously differentiable estimators of the noncentrality parameter of a chi square random variable we then consider the task of denoising squared magnitude magnetic resonance mr image data which are well modeled as independent noncentral chi square random variables on two degrees of freedom we consider two broad classes of linearly parameterized shrinkage estimators that can be optimized using our risk estimate one in the general context of undecimated filterbank transforms and the other in the specific case of the unnormalized haar wavelet transform the resultant algorithms are computationally tractable and improve upon most state of the art methods for both simulated and actual mr image data

energy decay rate for a coupled hyperbolic system with nonlinear damping abstract in this paper we investigate the energy decay rate for the solution of a coupled hyperbolic system the explicit energy decay rate is established by using multiplier techniques and constructing a suitable energy functional

a uniform stability result for thermoelasticity of type iii with boundary distributed delay abstract in this paper we consider a thermoelastic system of type iii with boundary distributed delay under suitable assumption on the weight of the delay we prove using the energy method that the damping effect through heat conduction given by green and naghdi s theory is still strong enough to uniformly stabilize the system even in the presence of time delay

energy decay rates for von karman system with memory and boundary feedback abstract in this paper we study the von karman plate model with long range memory and boundary nonlinear feedback we establish an explicit and general decay rate result using some properties of the convex functions our result is obtained without imposing any restrictive growth assumption on the damping term and strongly weakening the usual assumptions on the relaxation function

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

mean shift is a bound optimization we build on the current understanding of mean shift as an optimization procedure we demonstrate that in the case of piecewise constant kernels mean shift is equivalent to newton s method further we prove that for all kernels the mean shift procedure is a quadratic bound maximization

on exponential stability of a semilinear wave equation with variable coefficients under the nonlinear boundary feedback abstract the uniform stabilization of an originally regarded nondissipative system described by a semilinear wave equation with variable coefficients under the nonlinear boundary feedback is considered the existence of both weak and strong solutions to the system is proven by the galerkin method the exponential stability of the system is obtained by introducing an equivalent energy function and using the energy multiplier method on the riemannian manifold this equivalent energy function shows particularly that the system is essentially a dissipative system this result not only generalizes the result from constant coefficients to variable coefficients for these kinds of semilinear wave equations but also simplifies significantly the proof for constant coefficients case considered in a guesmia a new approach of stabilization of nondissipative distributed systems siam j control optim 42 2003 24 52 where the system is claimed to be nondissipative

rate of decay of solutions of the wave equation with arbitrary localized nonlinear damping abstract we study the rate of decay of solutions of the wave equation with localized nonlinear damping without any growth restriction and without any assumption on the dynamics providing regular initial data the asymptotic decay rates of the energy functional are obtained by solving nonlinear ode moreover we give explicit uniform decay rates of the energy more precisely we find that the energy decays uniformly at last as fast as 1 ln t 2 2 0 when the damping has a polynomial growth or sublinear and for an exponential damping at the origin the energy decays at last as fast as 1 ln ln t e 2 2 0

the nonlinear statistics of high contrast patches in natural images recently there has been a great deal of interest in modeling the non gaussian structures of natural images however despite the many advances in the direction of sparse coding and multi resolution analysis the full probability distribution of pixels values in a neighborhood has not yet been described in this study we explore the space of data points representing the values of 3 3 high contrast patches from optical and 3d range images we find that the distribution of data is extremely sparse with the majority of the data points concentrated in clusters and non linear low dimensional manifolds furthermore a detailed study of probability densities allows us to systematically distinguish between images of different modalities optical versus range which otherwise display similar marginal distributions our work indicates the importance of studying the full probability distribution of natural images not just marginals and the need to understand the intrinsic dimensionality and nature of the data we believe that object like structures in the world and the sensor properties of the probing device generate observations that are concentrated along predictable shapes in state space our study of natural image statistics accounts for local geometries such as edges in natural scenes but does not impose such strong assumptions on the data as independent components or sparse coding by linear change of bases

global existence for the wave equation with nonlinear boundary damping and source terms abstract the paper deals with local and global existence for the solutions of the wave equation in bounded domains with nonlinear boundary damping and source terms the typical problem studied is u tt u 0 in 0 u 0 on 0 0 u u t m 2 u t u p 2 u on 0 1 u 0 x u 0 x u t 0 x u 1 x on where r n n 1 is a regular and bounded domain 0 1 m 1 2 p r where r 2 n 1 n 2 when n 3 r when n 1 2 and the initial data are in the energy space we prove local existence of the solutions in the energy space when m r r 1 p or n 1 2 and global existence when p m or the initial data are inside the potential well associated to the stationary problem

approximate controllability of the semilinear heat equation this article is concerned with the study of approximate controllability for the semilinear heat equation in a bounded domain when the control acts on any open and nonempty subset of or on a part of the boundary in the case of both an internal and a boundary control the approximate controllability in l p for 1 p l in the case of the interior control we also prove approximate controllability in c 0 the proof combines a variational approach to the controllability problem for linear equations and a fixed point method we also prove that the control can be taken to be of quasi bang bang form

general decay rate estimates for viscoelastic dissipative systems abstract the linear viscoelastic equation is considered we prove uniform decay rates of the energy by assuming a nonlinear feedback acting on the boundary without imposing any restrictive growth assumption on the damping term and strongly weakening the usual assumptions on the relaxation function our estimate depends both on the behavior of the damping term near zero and on the behavior of the relaxation function at infinity the proofs are based on the multiplier method and on a general lemma about convergent and divergent series for obtaining the uniform decay rates

a context quantization approach to universal denoising we revisit the problem of denoising a discrete time continuous amplitude signal corrupted by a known memoryless channel by modifying our earlier approach to the problem we obtain a scheme that is much more tractable than the original one and at the same time retains the universal optimality properties the universality refers to the fact that the proposed denoiser asymptotically with increasing block length of the data achieves the performance of an optimum denoiser that has full knowledge of the distribution of a source generating the underlying clean sequence the only restriction being that the distribution is stationary the optimality in a sense we will make precise of the denoiser also holds in the case where the underlying clean sequence is unknown and deterministic and the only source of randomness is in the noise the schemes involve a simple preprocessing step of quantizing the noisy symbols to generate quantized contexts the quantized context value corresponding to each sequence component is then used to partition the unquantized symbols into subsequences a universal symbol by symbol denoiser for unquantized sequences is then separately employed on each of the subsequences we identify a rate at which the context length and quantization resolution should be increased so that the resulting scheme is universal the proposed family of schemes is computationally attractive with an upper bound on complexity which is independent of the context length and the quantization resolution initial experimentation seems to indicate that these schemes are not only superior from a computational viewpoint but also achieve better denoising in practice

theoretical and numerical local null controllability for a parabolic system with local and nonlocal nonlinearities this paper deals with the null controllability of an initial boundary value problem for a parabolic coupled system with nonlinear terms of local and nonlocal kinds the control is distributed in space and time and is exerted through one scalar function whose support can be arbitrarily small we first prove that if the initial data are sufficiently small and the linearized system at zero satisfies an appropriate coupling condition the equations can be driven exactly to zero we also present an iterative algorithm of the quasi newton kind for the computation of the control and we prove a convergence result the behavior of this algorithm is illustrated with some numerical experiments

notes on conformal invariance of gauge fields in lagrangian gauge systems the vector space of global reducibility parameters forms a module under the lie algebra of symmetries of the action since the classification of global reducibility parameters is generically easier than the classification of symmetries of the action this fact can be used to constrain the latter when knowing the former we apply this strategy and its generalization for the non lagrangian setting to the problem of conformal symmetry of various free higher spin gauge fields this scheme allows one to show that in terms of potentials massless higher spin gauge fields in minkowski space and partially massless pm fields in a ds space are not conformal for spin strictly greater than one while in terms of curvatures maximal depth pm fields in four dimensions are also not conformal unlike the closely related but less constrained maximal depth fradkin tseytlin fields

two applications of wavelet transforms in magnetic resonance imaging the authors describe two different applications of wavelet transforms in magnetic resonance imaging mri in each case the use of wavelets offers tangible benefits over the traditional fourier transform based imaging these stem from the simultaneous time and frequency localization properties of the wavelets the first application utilizes the localization properties of wavelets to acquire single t sub 2 weighted images in times which are short relative to current methods an interesting combinatorial scheduling problem arises from the multiscale structure inherent in the formulation of this procedure its solution is sketched and applied to the imaging process the second example is a technique for potentially instant imaging image acquisition is modeled as an inverse wavelet transform of the spin density in the region in question signal acquisition takes place in as few as one or two echoes after the excitation by rf pulses designed to excite a moving band of spins in a slice these sweeping rf pulses excite strips of spins which rephase at different times during acquisition they replace phase encoding gradients no fast pulsed gradients are required

uniform stability for thermoelastic systems with boundary time varying delay abstract in this paper we consider a thermoelastic system with boundary time varying delay using the energy method we show under suitable assumptions that the damping effect through heat conduction is still strong enough to uniformly stabilize the system even in the presence of boundary time varying delay our result improves earlier results existing in the literature

hashed nonlocal means for rapid image filtering denoising algorithms can alleviate the trade off between noise level and acquisition time that still exists for certain image types nonlocal means a recently proposed technique outperforms other methods in removing noise while retaining image structure albeit at prohibitive computational cost modifications have been proposed to reduce the cost but the method is still too slow for practical filtering of 3d images this paper proposes a hashed approach to explicitly represent two summed frequency hash functions of local descriptors patches utilizing all available image data unlike other approaches the hash spaces are discretized on a regular grid so primarily linear operations are used the large memory requirements are overcome by recursing the hash spaces additional speed gains are obtained by using a marginal linear interpolation method careful choice of the patch features results in high computational efficiency at similar accuracies the proposed approach can filter a 3d image in less than a minute versus 15 minutes to 3 hours for existing nonlocal means methods

vibrations of elastic string with nonhomogeneous material abstract in this paper we analyze from the mathematical point of view a model for small vertical vibrations of an elastic string with fixed ends and the density of the material being not constant we employ techniques of functional analysis mainly a theorem of compactness for the analysis of the approximation of faedo galerkin method we obtain strong global solutions with restrictions on the initial data u 0 and u 1 uniqueness of solutions and a rate decay estimate for the energy

uniform decay of the solution to a wave equation with memory conditions on the boundary abstract a wave equation with variable coefficients in principal part and memory conditions on the boundary is considered the riemannian geometry method is applied to prove the exponential decay of the energy provided the relaxation function also decays exponentially

tensor gauge fields in arbitrary representations of gl d ℝ duality and poincare lemma using a mathematical framework which provides a generalization of the de rham complex well designed for p form gauge fields we have studied the gauge structure and duality properties of theories for free gauge fields transforming in arbitrary irreducible representations of gl d we have proven a generalization of the poincare lemma which enables us to solve the above mentioned problems in a systematic and unified way

on a nonlinear thermoelastic system with nonlocal coefficients abstract this paper deals with the global existence and uniqueness of solutions and uniform stabilization of the energy of an initial boundary value problem for a thermoelastic system with nonlinear terms of nonlocal kind the asymptotic stabilization of the energy of system 1 1 is obtained without any dissipation mechanism acting in the displacement variable u of the membrane equation

local convergence and speed estimates for semilinear wave systems damped by boundary friction abstract we study the local convergence to equilibria as time goes to infinity of trajectories of semilinear wave systems with friction damping on the boundary and subject to nonlinear potential energy estimates for the speed of convergence are obtained in terms of the behavior of the nonlinear feedback close to the origin as an example of application we show that the trajectories of a sine gordon system with nonlinear boundary damping approach equilibria at least polynomially

exponential energy decay in a linear thermoelastic rod abstract we examine the stability of solutions to a pair of coupled linear partial differential equations which describe the temperature distribution and displacement within a one dimensional thermoelastic rod for particular sets of natural boundary conditions the eigenfunctions are shown to form a riesz basis on the hilbert space of finite energy states for these cases asymptotic eigenvalue estimates show that the spectrum is to the left of some vertical line re contained in the open left half of the complex plane an energy decay estimate of the form e t me t e 0 is then obtained

tensor gauge fields in arbitrary representations of gl d mathbb r ii quadratic actions quadratic second order non local actions for tensor gauge fields transforming in arbitrary irreducible representations of the general linear group in d dimensional minkowski space are explicitly written in a compact form by making use of levi civita tensors the field equations derived from these actions ensure the propagation of the correct massless physical degrees of freedom and are shown to be equivalent to non lagrangian local field equations proposed previously moreover these actions allow a frame like reformulation a la macdowell mansouri without any trace constraint in the tangent indices

null controllability for a parabolic equation with nonlocal nonlinearities abstract in this paper we establish a local null controllability result for a nonlinear parabolic pde with nonlocal nonlinearities the result relies on the global null controllability of similar linear equations and a fixed point argument we also analyze other similar controllability problems and we present several open questions

sharp energy estimates for nonlinearly locally damped pdes via observability for the associated undamped system abstract we consider the problem of sharp energy decay rates for nonlinearly damped abstract infinite dimensional systems direct methods for nonlinear stabilization generally rely on multiplier techniques and thus are valid under restrictive geometric conditions compared to the optimal geometric optics condition of bardos et al 1992 10 we prove sharp simple and quasi optimal energy decay rates through an indirect method namely an observability estimate for the corresponding undamped system one of the main advantage of these results is that they allow to combine optimal geometric conditions as for instance that of bardos et al 1992 10 and the optimal weight convexity method of the first author alabau boussouira 2010 6 alabau boussouira 2005 2 to deduce very simple and quasi optimal energy decay rates for nonlinearly locally damped systems we also show that using arguments based on russell s principle russell 1978 24 one can deduce sharp energy decay rates from the exponential stabilization of the linearly damped system our results extend to nonlinearly damped systems those of haraux 1989 14 and ammari and tucsnak 2001 9 which concern linearly damped systems

nonparametric maximum likelihood estimation by the method of sieves maximum likelihood estimation often fails when the parameter takes values in an infinite dimensional space for example the maximum likelihood method cannot be applied to the completely nonparametric estimation of a density function from an operatorname iid sample the maximum of the likelihood is not attained by any density in this example as in many other examples the parameter space positive functions with area one is too big but the likelihood method can often be salvaged if we first maximize over a constrained subspace of the parameter space and then relax the constraint as the sample size grows this is grenander s method of sieves application of the method sometimes leads to new estimators for familiar problems or to a new motivation for an already well studied technique we will establish some general consistency results for the method and then we will focus on three applications

convergence of the wave equation damped on the interior to the one damped on the boundary abstract in this paper we study the convergence of the wave equation with variable internal damping term n x u t to the wave equation with boundary damping x x u t when n x converges to x x in the sense of distributions when the domain in which these equations are defined is an interval in r we show that under natural hypotheses the compact global attractor of the wave equation damped on the interior converges in x h 1 l 2 to the one of the wave equation damped on the boundary and that the dynamics on these attractors are equivalent we also prove in the higher dimensional case that the attractors are lower semicontinuous in x and upper semicontinuous in h 1 e h e

global existence asymptotic stability and uniform attractors for non autonomous thermoelastic systems with constant time delay in this paper we first consider a non autonomous thermoelastic system with a boundary delay and obtain the asymptotic behavior then using the contractive function method and multiplier techniques we establish the asymptotic behavior and the existence of a uniform attractor of the system with a boundary time delay the main advantage of this method is that we only need to verify compactness condition with the type of energy estimates same as those for establishing the absorbing set moreover we investigate an alternative result of solutions to semilinear thermoelastic systems by virtue of the semigroup method

a dictionary learning approach for poisson image deblurring the restoration of images corrupted by blur and poisson noise is a key issue in medical and biological image processing while most existing methods are based on variational models generally derived from a maximum a posteriori map formulation recently sparse representations of images have shown to be efficient approaches for image recovery following this idea we propose in this paper a model containing three terms a patch based sparse representation prior over a learned dictionary the pixel based total variation regularization term and a data fidelity term capturing the statistics of poisson noise the resulting optimization problem can be solved by an alternating minimization technique combined with variable splitting extensive experimental results suggest that in terms of visual quality peak signal to noise ratio value and the method noise the proposed algorithm outperforms state of the art methods

on damped kirchhoff equation with variable coefficients in this work we are concerned with the existence and uniqueness of strong global solutions and exponential decay of the total energy for an initial boundary value problem associated with the kirchhoff equation with variable coefficients on the action of a nonlinear internal damping

a new approach of stabilization of nondissipative distributed systems in this paper we propose a new approach to prove the nonlinear internal or boundary stabilization of certain nondissipative distributed systems the usual energy is not decreasing this approach leads to decay estimates known in the dissipative case when the integral inequalities method due to komornik exact controllability and stabilization the multiplier method masson paris john wiley chichester uk 1994 cannot be applied due to the lack of dissipativity first we study the stability of a semilinear wave equation with a nonlinear damping based on the equation u delta u h nabla u f u g u 0 we consider the general case with a function h satisfying a smallness condition and we obtain uniform decay of strong and weak solutions under weak growth assumptions on the feedback function and without any control of the sign of the derivative of the energy related with the above equation in the second part we consider the case h nabla u nabla phi cdot nabla u with phi in w 1 infty omega we prove some precise decay estimates exponential or polynomial of equivalent energy without any restriction on phi the same results will be proved in the case of boundary feedback finally we comment on some applications of our approach to certain nondissipative distributed systems some results of this paper were announced without proof in a guesmia c r acad sci paris ser i math 332 2001 pp 633 636

energy decay of a microbeam model with a locally distributed nonlinear feedback control abstract in this paper we address the problem of internal stabilization of the deflection of a microbeam which is modeled by a sixth order hyperbolic equation employing multiplier techniques and an integral inequality we prove that a locally distributed nonlinear feedback control forces the energy associated to the deflection to decay exponentially or polynomially to zero as a consequence of this the deflection goes to the rest position as the time goes to infinity

feature preserving mri denoising a nonparametric empirical bayes approach this paper presents a novel method for bayesian denoising of magnetic resonance mr images that bootstraps itself by inferring the prior i e the uncorrupted image statistics from the corrupted input data and the knowledge of the rician noise model the proposed method relies on principles from empirical bayes eb estimation it models the prior in a nonparametric markov random field mrf framework and estimates this prior by optimizing an information theoretic metric using the expectation maximization algorithm the generality and power of nonparametric modeling coupled with the eb approach for prior estimation avoids imposing ill fitting prior models for denoising the results demonstrate that unlike typical denoising methods the proposed method preserves most of the important features in brain mr images furthermore this paper presents a novel bayesian inference algorithm on mrfs namely iterated conditional entropy reduction icer this paper also extends the application of the proposed method for denoising diffusion weighted mr images validation results and quantitative comparisons with the state of the art in mr image denoising clearly depict the advantages of the proposed method