asymptotic behaviour of resolvents of abstract volterra equations abstract we give necessary and sufficient conditions for certain volterra integral and integrodifferential equations in some banach space to have a resolvent that belongs to some weighted l 1 space these conditions involve the invertibility of functions of the laplace transforms of the kernels

local existence and regularity of solutions for some partial functional integrodifferential equations with infinite delay in banach spaces abstract in this work we study the existence and regularity of solutions for some partial functional integrodifferential equations with infinite delay in banach spaces we suppose that the undelayed part admits a resolvent operator in the sense of grimmer r grimmer resolvent operators for integral equations in a banach space transactions of the american mathematical society 273 1982 333 349 the delayed part is assumed to be locally lipschitz firstly we show the existence of the mild solutions secondly we give sufficient conditions ensuring the existence of strict solutions

on linear volterra equations in banach spaces abstract in this paper we present the basic theory for a class of volterra differential integral equations of convolution type in banach spaces we show that existence of resolvent operator for such an equation is equivalent to its wellposedness and we obtain a hille yosida theorem unfortunately this result is not easy to apply and therefore it is important to have peturbation theorems available we present a result of this type which also contains an existence theorem and show by means of several examples that it cannot be improved

on global and local convergence of half quadratic algorithms this paper provides original results on the global and local convergence properties of half quadratic hq algorithms resulting from the geman and yang gy and geman and reynolds gr primal dual constructions first we show that the convergence domain of the gy algorithm can be extended with the benefit of an improved convergence rate second we provide a precise comparison of the convergence rates for both algorithms this analysis shows that the gr form does not benefit from a better convergence rate in general moreover the gy iterates often take advantage of a low cost implementation in this case the gy form is usually faster than the gr form from the cpu time viewpoint

calibration by correlation using metric embedding from nonmetric similarities this paper presents a new intrinsic calibration method that allows us to calibrate a generic single view point camera just by waving it around from the video sequence obtained while the camera undergoes random motion we compute the pairwise time correlation of the luminance signal for a subset of the pixels we show that if the camera undergoes a random uniform motion then the pairwise correlation of any pixels pair is a function of the distance between the pixel directions on the visual sphere this leads to formalizing calibration as a problem of metric embedding from nonmetric measurements we want to find the disposition of pixels on the visual sphere from similarities that are an unknown function of the distances this problem is a generalization of multidimensional scaling mds that has so far resisted a comprehensive observability analysis can we reconstruct a metrically accurate embedding and a solid generic solution how do we do so we show that the observability depends both on the local geometric properties curvature as well as on the global topological properties connectedness of the target manifold we show that in contrast to the euclidean case on the sphere we can recover the scale of the points distribution therefore obtaining a metrically accurate solution from nonmetric measurements we describe an algorithm that is robust across manifolds and can recover a metrically accurate solution when the metric information is observable we demonstrate the performance of the algorithm for several cameras pin hole fish eye omnidirectional and we obtain results comparable to calibration using classical methods additional synthetic benchmarks show that the algorithm performs as theoretically predicted for all corner cases of the observability analysis

convergence of an iterative method for total variation denoising in total variation denoising one attempts to remove noise from a signal or image by solving a nonlinear minimization problem involving a total variation criterion several approaches based on this idea have recently been shown to be very effective particularly for denoising functions with discontinuities this paper analyzes the convergence of an iterative method for solving such problems the iterative method involves a lagged diffusivity approach in which a sequence of linear diffusion problems are solved global convergence in a finite dimensional setting is established and local convergence properties including rates and their dependence on various parameters are examined

approximate controllability of semi linear neutral integro differential systems with finite delay abstract this paper considers the approximate controllability of semilinear neutral integrodifferential systems with finite delay in hilbert space since the considered equation admits nonlinear terms involving spatial derivatives the fraction power theory and norm are used to discuss the problem so that the established results can be applied to them the results are obtained by using the sadovskii fixed point theorem and the theory of analytic resolvent operator an example is presented to illustrate the applications of the obtained results

existence and regularity of solutions for some partial functional integrodifferential equations in banach spaces abstract in this work we study the existence and regularity of solutions for some partial functional integrodifferential equations in banach spaces we suppose that the undelayed part admits a resolvent operator in the sense given by grimmer in r grimmer resolvent operators for integral equations in a banach space transaction of american mathematical society 273 1982 333 349 the delayed part is assumed to be locally lipschitz firstly we show the existence of the mild solutions secondly we give sufficient conditions ensuring the existence of the strict solutions

asymptotically almost automorphic solutions for some integrodifferential equations with nonlocal initial conditions abstract of concern is a class of abstract semilinear integrodifferential equations with nonlocal initial conditions under some suitable hypotheses we establish some new theorems about the existence of asymptotically almost automorphic solutions to the integrodifferential equations moreover an example is given to illustrate our results

quantum groups verma modules and q oscillators general linear case the verma modules over the quantum groups for arbitrary values of l are analysed the explicit expressions for the action of the generators on the elements of the natural basis are obtained the corresponding representations of the quantum loop algebras are constructed via jimbo s homomorphism this allows us to find certain representations of the positive borel subalgebras of as degenerations of the shifted representations the latter are the representations used in the construction of the so called q operators in the theory of quantum integrable systems the interpretation of the corresponding simple quotient modules in terms of representations of the q deformed oscillator algebra is given

exponential stabilization of volterra integrodifferential equations in hilbert space we consider exponential stabilization of an abstract linear volterra integrodifferential equation in a hilbert space u e1au t e2 01k t s au s ds f t by a feedback control f t c0u t c1u t with bounded linear operators c0 and c1 of finite rank a is a positive semidefinite self adjoint unbounded operator k is nonnegative convex and decreasing with exponential decay k 0 being finite we introduce a concept of essential growth rate for resolvent operators similar to that for c0 semigroups and prove that the resolvent for the volterra equation has the same essential growth as the solution semigroup to u t e1au t e2k 0 e1u t f t stability can be checked by the location of poles and it is shown that exponential stabilization is possible with a decay rate of at most e2k 0 2e1 we apply our results to two problems concerning stabilization of motion of viscoelastic bodies

split bregman iteration algorithm for total bounded variation regularization based image deblurring many existing algorithms taking the seminorm in bv for regularization have achieved great success in image processing however this paper considers the total bounded variation regularization based approach to perform image deblurring based on this novel model we introduce an extended split bregman iteration to obtain the optimum solution quickly we also provide the rigorous convergence analysis of the iterative algorithm here compared with the results of the rof method numerical simulations illustrate the more excellent reconstruction performance of the proposed algorithm

on some fractional evolution equations abstract in this paper the solutions of some evolution equations with fractional orders in a banach space are considered conditions are given which ensure the existence of a resolvent operator for an evolution equation in a banach space

on almost automorphic type solutions of abstract integral equations a bohr neugebauer type property and some applications abstract in the present work we give some sufficient conditions to obtain a unique almost automorphic solution to abstract nonlinear integral equations which are simultaneously of advanced and delayed type and also a unique asymptotically almost automorphic mild solution to abstract integro differential equations with nonlocal initial conditions both situations are posed on banach spaces also we develop a bohr neugebauer type result for the abstract integral equations before that we introduce the notion of bounded functions develop the appropriate abstract theory and discuss the almost periodic situation as applications we study the existence of an asymptotically almost automorphic solution to integro differential equations modeling heat conduction in materials with memory and also the existence of the almost automorphic solution to semilinear parabolic evolution equations with finite delay

existence and exponential stability for impulsive neutral stochastic functional differential equations driven by fbm with noncompact semigroup via monch fixed point abstract in this paper we investigate the existence and exponential stability of mild solutions for a class of impulsive neutral stochastic functional differential equations driven by fbm with noncompact semigroup in hilbert spaces sufficient conditions for the existence of mild solutions are obtained using the hausdorff measure of noncompactness and the monch fixed point theorem further we establish a new impulsive integral inequality to prove the exponential stability of mild solutions in the mean square moment finally an example is presented to illustrate our obtained results

baxter s relations and spectra of quantum integrable models generalized baxter s relations on the transfer matrices also known as bax ter s tq relations are constructed and proved for an arbitrary untwisted quantum affine algebra moreover we interpret them as relations in the grothendieck ring of the cate gory o introduced by jimbo and the second author in hj involving infinite dimensional representations constructed in hj which we call here prefundamental we define the transfer matrices associated to the prefundamental representations and prove that their eigenvalues on any finite dimensional representation are polynomials up to a universal factor these polynomials are the analogues of the celebrated baxter polynomials com bining these two results we express the spectra of the transfer matrices in the general quantum integrable systems associated to an arbitrary untwisted quantum affine algebra in terms of our generalized baxter polynomials this proves a conjecture of reshetikhin and the first author formulated in 1998 fr1 we also obtain generalized bethe ansatz equations for all untwisted quantum affine algebras

impulsive neutral stochastic functional integro differential equations with infinite delay driven by fbm in this paper we study a class of impulsive neutral stochastic functional integro differential equations with infinite delay driven by a standard cylindrical wiener process and an independent cylindrical fractional brownian motion fbm with hurst parameter h 1 2 1 in the hilbert space we prove the existence and uniqueness of the mild solution for this kind of equations with the coefficients satisfying some non lipschitz conditions which include the classical lipschitz conditions as special case an example is provided to illustrate the theory some well known results are generalized and extended

on state dependent delay partial neutral functional integro differential equations in this paper the existence of mild solutions for a class of abstract neutral integro differential equations with state dependent delay is studied

baxter s q operator for the w algebra wn the q oscillator representation for the borel subalgebra of the affine symmetry is presented by means of this q oscillator representation we give the free field realizations of baxter s q operator for the w algebra wn we give functional relations of the t q operators including the higher rank generalization of baxter s t q relation

integral equations as evolution equations abstract we study a class of time dependent linear integrodifferential equations ve with the evolution equation approach we determine the generators of a time dependent evolution equation de which is equivalent to the given integrodifferential equation under very general assumptions we prove the well posedness and continuity of ve from the stability of de the related question of convergence of a family of approximate solutions is examined as an application we include an example of hyperbolic integro partial differential equation to illustrate the theory

the equivalence of half quadratic minimization and the gradient linearization iteration a popular way to restore images comprising edges is to minimize a cost function combining a quadratic data fidelity term and an edge preserving possibly nonconvex regularization term mainly because of the latter term the calculation of the solution is slow and cumbersome half quadratic hq minimization multiplicative form was pioneered by geman and reynolds 1992 in order to alleviate the computational task in the context of image reconstruction with nonconvex regularization by promoting the idea of locally homogeneous image models with a continuous valued line process they reformulated the optimization problem in terms of an augmented cost function which is quadratic with respect to the image and separable with respect to the line process hence the name half quadratic since then a large amount of papers were dedicated to hq minimization and important results including edge preservation along with convex regularization and convergence have been obtained in this paper we show that hq minimization multiplicative form is equivalent to the most simple and basic method where the gradient of the cost function is linearized at each iteration step in fact both methods give exactly the same iterations furthermore connections of hq minimization with other methods such as the quasi newton method and the generalized weiszfeld s method are straightforward

radial multi focal tensors the 1d radial camera maps all points on a plane containing the principal axis onto the radial line which is the intersection of that plane and the image plane it is a sufficiently general model to express both central and non central cameras since the only assumption it makes is of known center of distortion in this paper we study the multi focal tensors arising out of 1d radial cameras there exist no two view constraints like the fundamental matrix for 1d radial cameras however the 3 view and 4 view cases are interesting for the 4 view case we have the radial quadrifocal tensor which has 15 d o f and 2 internal constraints for the 3 view case we have the radial trifocal tensor which has 7 d o f and no internal constraints under the assumption of a purely rotating central camera this can be used to do a non parametric estimation of the radial distortion of a 1d camera even in the case of a non rotating camera it can be used to do parametric estimation assuming a planar scene finally we examine the mixed trifocal tensor which models the case of two 1d radial cameras and one standard pin hole camera of the above radial multifocal tensors only the radial trifocal tensor is useful practically since it doesn t require any knowledge of the scene and is extremely robust we demonstrate results based on real images for this for the quadrifocal tensor too we present a way to do a metric reconstruction of the scene and to undistort the image given a sufficiently dense set of point correspondences we also show results on synthetic images however it must be noted that currently the quadrifocal and mixed trifocal tensors are useful only from a theoretical stand point

nonlocal cauchy problem for analytic resolvent integrodifferential equations in banach spaces abstract in this paper we prove the existence of semi classical and mild solutions of nonlinear integrodifferential equations with nonlocal conditions in banach spaces the results are obtained by using the theory of analytic resolvents and schaefer s fixed point theorem

resolvent operators for integral equations in a banach space conditions are given which ensure the existence of a resolvent operator for an integrodifferential equation in a banach space the resolvent operator is similar to an evolution operator for nonautonomous differential equations in a banach space as in the finite dimensional case this operator is used to obtain a variation of parameters formula which can be used to obtain results concerning the asymptotic behaviour of solutions and weak solutions

on s asymptotically ω periodic functions and applications abstract let x be a banach space and r a bounded function u c 0 x is called s asymptotically periodic if lim t u t u t 0 in this paper we establish conditions under which an s asymptotically periodic function is asymptotically periodic and we discuss the existence of s asymptotically periodic and asymptotically periodic solutions for an abstract integral equation some applications to partial differential equations and partial integro differential equations are considered

existence and regularity for a class of integrodifferential equations of parabolic type the method we use rests on the inversion of the formal laplace transform of r and allows one to analyze the regularity of the solution u problem 1 1 has been studied by several authors using various methods see for instance l 18 211 the laplace transform approach presented here has been used in s 7 9 14 153 in our previous papers s 7 93 we have in fact analyzed a more general situation while here we take full 36 0022 247x 85 3 00

a semilinear parabolic volterra integrodifferential equation abstract we consider the semilinear volterra integrodifferential equation u t a t u t t 0 t a t s g s u s ds t u t t t 0 u t 0 u 0 we assume that for each t 0 the linear operator a t is the negative generator of an analytic semigroup in a banach space x the nonlinear operator g t is lipschitz continuous on the domain of a 0 into x and the forcing term t u satisfies a holder condition in both variables we prove existence of solutions in the banach space x and uniqueness of solutions when x is a hilbert space we also consider an example where a t a a t s a t s and show that the corresponding solutions u t x converge as t to a solution u x of a related semilinear elliptic boundary value problem

generic self calibration of central cameras from two rotational flows we address the self calibration of a smooth generic central camera from only two dense rotational flows produced by rotations of the camera about two unknown linearly independent axes passing through the camera centre we give a closed form theoretical solution to this problem and we prove that it can be solved exactly up to a linear orthogonal transformation ambiguity using the theoretical results we propose an algorithm for the self calibration of a generic central camera from two rotational flows in order to solve the self calibration problem using real images we also study the computation of dense optical flows from image sequences acquired by the rotation of a smooth generic central camera we propose a method for the computation of dense smooth generic flows from rotational camera motions using splines the proposed methods are validated using both simulated and real image sequences

deterministic edge preserving regularization in computed imaging many image processing problems are ill posed and must be regularized usually a roughness penalty is imposed on the solution the difficulty is to avoid the smoothing of edges which are very important attributes of the image in this paper we first give conditions for the design of such an edge preserving regularization under these conditions we show that it is possible to introduce an auxiliary variable whose role is twofold first it marks the discontinuities and ensures their preservation from smoothing second it makes the criterion half quadratic the optimization is then easier we propose a deterministic strategy based on alternate minimizations on the image and the auxiliary variable this leads to the definition of an original reconstruction algorithm called artur some theoretical properties of artur are discussed experimental results illustrate the behavior of the algorithm these results are shown in the field of 2d single photon emission tomography but this method can be applied in a large number of applications in image processing

oscillator versus prefundamental representations we find the l weights and the corresponding l weight vectors for the finite and infinite dimensional representations of the quantum loop algebras uq x1d530 x1d529 2 and uq x1d530 x1d529 3 obtained from the verma representations of the quantum groups uq x1d524 x1d529 2 and uq x1d524 x1d529 3 via the jimbo s homomorphism then we find the l weights and the l weight vectors for the q oscillator representations of the positive borel subalgebras of the same quantum loop algebras this allows in particular to relate the q oscillator and prefundamental representations

semilinear integrodifferential equations with nonlocal initial conditions abstract of concern is the cauchy problem for semilinear integrodifferential equations with nonlocal initial conditions under general and natural hypotheses we establish some new theorems about the existence and uniqueness of solutions for the cauchy problem as a consequence we unify and extend the corresponding theorems given previously for the cauchy problem for differential equations or integrodifferential equations with nonlocal initial conditions moreover we present two examples one of which comes from heat conduction in materials with memory to show that the existing results are not applicable to them in contrast with ours

on the resolvent of linear nonautonomous partial functional differential equations abstract we give sufficient conditions for the existence of the resolvent operator for nonautonomous linear partial differential equations with delay where the highest order derivatives are undelayed furthermore we analyse the connection between the resolvent and the solution operator of the homogeneous equation

oscillator versus prefundamental representations ii arbitrary higher ranks we find the l weights and the l weight vectors for the highest l weight q oscillator representations of the positive borel subalgebra of the quantum loop algebra uq l sll 1 for arbitrary values of l having this we establish the explicit relationship between the q oscillator and prefundamental representations our consideration allows us to conclude that the prefundamental representations can be obtained by tensoring q oscillator representations

controllability of nonlinear neutral evolution integrodifferential systems sufficient conditions for controllability of nonlinear neutral evolution integrodifferential systems in a banach space are established the results are obtained by using the resolvent operators and the schaefer fixed point theorem an application to partial integrodifferential equation is given

stability and stabilizability of infinite dimensional systems in this paper we are concerned with stability problems for infinite dimensional systems first we review the theory for linear systems where the dynamics are governed by strongly continuous semigro

new methods of controlled total variation reduction for digital functions we consider the functional of total variation for functions of either one or two discrete variables we introduce a new principle for construction of evolution processes that gradually reduce the total variation of a function the method is derived from analysis of relaxation of the functional along the directions given by the haar wavelets an approach that does not require regularization of either the functional or its singular gradient we further present a rigorous analysis of the analytical properties of the resulting evolution schemes the purely discrete theory grows out of universal observations about the relation between the total variation and the haar functions an additional advantage of the method is that it can be directly implemented as an effective numerical procedure moreover it can be intertwined in a natural way with a nonlinear phase space filtering which further increases control of the deformation of a signal finally we report that the algorithms can be used as remarkable tools for signal processing and image enhancement

iterative algorithms based on decoupling of deblurring and denoising for image restoration in this paper we propose iterative algorithms for solving image restoration problems the iterative algorithms are based on decoupling of deblurring and denoising steps in the restoration process in the deblurring step an efficient deblurring method using fast transforms can be employed in the denoising step effective methods such as the wavelet shrinkage denoising method or the total variation denoising method can be used the main advantage of this proposal is that the resulting algorithms can be very efficient and can produce better restored images in visual quality and signal to noise ratio than those by the restoration methods using the combination of a data fitting term and a regularization term the convergence of the proposed algorithms is shown in the paper numerical examples are also given to demonstrate the effectiveness of these algorithms

integrable structure of conformal field theory ii q operator and ddv equation this paper is a direct continuation of 1 where we began the study of the integrable structures in conformal field theory we show here how to construct the operators bf q pm lambda which act in the highest weight virasoro module and commute for different values of the parameter these operators appear to be the cft analogs of the q matrix of baxter 2 in particular they satisfy baxter s famous t q equation we also show that under natural assumptions about analytic properties of the operators as the functions of the baxter s relation allows one to derive the nonlinear integral equations of destri de vega ddv 3 for the eigenvalues of the q operators we then use the ddv equation to obtain the asymptotic expansions of the q operators at large it is remarkable that unlike the expansions of the t operators of 1 the asymptotic series for q contains the dual nonlocal integrals of motion along with the local ones we also discuss an intriguing relation between the vacuum eigenvalues of the q operators and the stationary transport properties in the boundary sine gordon model on this basis we propose a number of new exact results about finite voltage charge transport through the point contact in the quantum hall system

robustness of linear systems abstract in this paper we consider linear systems which are stable and examine the robustness of this property the perturbations are assumed to have unbounded structure and we determine the smallest perturbation which destroys stability we begin with an abstract analysis of the problem but in later sections specialize to three types of systems those whose mild solutions are given in terms of 1 a strongly continuous semigroups 2 b resolvent operators integrodifferential systems 3 c evolution operators time varying systems for b a banach space l2 t0 t b denotes the space of all square integrable functions defined on t0 t with values in b for b1 b2 banach spaces t0 t denotes the space of strongly measurable functions f t0 t l b1 b2 with ess sup f b 1 t0 l b1 b2 denotes the space of strongly measurable functions f t0 l b1 b2 with f t 0 and k l1 t0

existence of asymptotically almost automorphic solutions to some abstract partial neutral integro differential equations abstract the paper establishes the existence and uniqueness of asymptotically almost automorphic mild solution to an abstract partial neutral integro differential equation with unbounded delay an example is given to illustrate our results

existence of solutions for neutral integro differential equations with state dependent delay in this paper we study the existence and regularity of solutions for a neutral functional integro differential equation with state dependent delay in banach space the mild solutions are investigated by sadovskii fixed point theorem under compactness condition for the resolvent operator and the theory of fractional power and a norm are also used in the discussion since the nonlinear terms of the system involve spacial derivatives the strict solutions are obtained under holder continuity condition hence this work extends and develops the existed results on this topic in the end an example is provided to illustrate the application of the obtained results

existence and uniqueness of global mild solutions for a class of nonlinear fractional reaction diffusion equations with delay abstract in this paper we study the mild solutions of a class of nonlinear fractional reaction diffusion equations with delay and caputo s fractional derivatives by the measure of noncompactness the theory of resolvent operators the fixed point theorem and the banach contraction mapping principle we develop various theorems for the existence and uniqueness of the global mild solutions for the problem

vectorial total variation based regularization for variational image registration to use interdependence between the primary components of the deformation field for smooth and non smooth registration problems the channel by channel total variation or standard vectorial total variation svtv based regularization has been extended to a more flexible and efficient technique allowing high quality regularization procedures based on this method this paper proposes a fast nonlinear multigrid nmg method for solving the underlying euler lagrange system of two coupled second order nonlinear partial differential equations numerical experiments using both synthetic and realistic images not only confirm that the recommended vtv based regularization yields better registration qualities for a wide range of applications than those of the svtv based regularization but also that the proposed nmg method is fast accurate and reliable in delivering visually pleasing registration results

regularity of solutions of evolution integrodifferential equations with deviating argument abstract in this paper we prove the existence of mild and classical solutions of delay integrodifferential equation and delay integrodifferential evolution equations with nonlocal condition in banach spaces the regularity solutions of integrodifferential evolution equations interconnected with viscoelastic material is derived to guarantee the stabilization the results are established by using the resolvent operators and the fixed point principles finally an example is given to show the potential of the proposed techniques

a class of hyperbolic volterra integrodifferential equations on considere l existence des solutions pour l equation integrodifferentielle de volterra u t a t u t 0 t g t s u s ds f 0 t f 1 t u t t 0 u 0 u 0

minimizing the total variation under a general convex constraint for image restoration we present a general framework for image restoration despite its simplicity certain variational and certain wavelet approaches can be formulated within this framework this permits the construction of a natural model with only one parameter which has the advantages of both approaches we give a mathematical analysis of this model describe our algorithm and illustrate this by some experiments

analytic resolvent operators for integral equations in banach space on etudie l equation integrodifferentielle x t a 0 x t 0 t b t s x s ds f t t 0 x 0 x 0 ed a x et l equation integrale x t 0 t a t s x s ds f t dans un espace de banach x les operateurs a a 0 b t et a t sont des operateurs clos sur x a domaine dense

some well posed functional equations which generate semigroups consider the abstract linear functional equation fe dx t f t t 0 x t t t 0 in a banach space b a theorem is proven which contains the following result as a special case let y r b be a lp space or c0 space on r t8 with a suitable weight function and with values in b let d be a closed unbounded causal linear operator in y r b which commutes with translations suppose that d i has a continuous causal inverse for some complex and that d restricted to those functions in y r b which vanish on r 0 has a continuous causal inverse then fe generates a strongly continuous semigroup of translation type on a banach space which is essentially the cross product of the restriction of the domain of d to r and y r b examples with b cn on how the theory applies to a neutral functional differential equation a difference equation a volterra integrodifferential equation with nonintegrable kernel but integrable resolvent and a fractional order functional differential equation are given also an abstract neutral functional differential equation in a hilbert space is studied and applications to an abstract volterra integrodifferential equation in a banach space are indicated

anisotropic interpolation of sparse generalized image samples practical image acquisition systems are often modeled as a continuous domain prefilter followed by an ideal sampler where generalized samples are obtained after convolution with the impulse response of the device in this paper our goal is to interpolate images from a given subset of such samples we express our solution in the continuous domain considering consistent resampling as a data fidelity constraint to make the problem well posed and ensure edge preserving solutions we develop an efficient anisotropic regularization approach that is based on an improved version of the edge enhancing anisotropic diffusion equation following variational principles our reconstruction algorithm minimizes successive quadratic cost functionals to ensure fast convergence we solve the corresponding sequence of linear problems by using multigrid iterations that are specifically tailored to their sparse structure we conduct illustrative experiments and discuss the potential of our approach both in terms of algorithmic design and reconstruction quality in particular we present results that use as little as 2 of the image samples

on the convergence of the lagged diffusivity fixed point method in total variation image restoration in this paper we show that the lagged diffusivity fixed point algorithm introduced by vogel and oman in siam j sci comput 17 1996 pp 227 238 to solve the problem of total variation denoising proposed by rudin osher and fatemi in phys d 60 1992 pp 259 268 is a particular instance of a class of algorithms introduced by voss and eckhardt in computing 25 1980 pp 243 251 whose origins can be traced back to weiszfeld s original work for minimizing a sum of euclidean lengths tohoku math j 43 1937 pp 355 386 there have recently appeared several proofs for the convergence of this algorithm g aubert et al technical report 94 01 informatique signaux et systemes de sophia antipolis 1994 a chambolle and p l lions technical report 9509 ceremade 1995 and d c dobson and c r vogel siam j numer anal 34 1997 pp 1779 1791 here we present a proof of the global and linear convergence using the framework introduced in h voss and u eckhart computing 25 1980 pp 243 251 and give a bound for the convergence rate of the fixed point iteration that agrees with our experimental results these results are also valid for suitable generalizations of the fixed point algorithm

approximate controllability of nonlocal and impulsive neutral integro differential equations using the resolvent operator theory and an approximating technique abstract our purpose in this paper is to study the approximate controllability of nonlocal and impulsive neutral integro differential equations using the resolvent operator theory the approximating technique semigroup theory and the theory of fixed point we also derive a variation of constants formula for representing a solution of the given system by resolvent operators and then study the existence of a mild solution of the system we prove the main results by taking the impulsive functions to be continuous only and taking the nonlocal initial condition function to be lipschitz continuous in the first case and continuous only in the second case finally the main results are illustrated using examples

approximate controllability results for analytic resolvent integro differential inclusions in hilbert spaces abstractin this work we consider a nonlinear resolvent integro differential evolution inclusions in hilbert spaces this paper deals with the approximate controllability for nonlinear resolvent integro differential inclusions in hilbert spaces we use bohnenblust karlin s fixed point theorem to establish a set of sufficient conditions for the approximate controllability for nonlinear resolvent integro differential inclusions in hilbert spaces further we extend the result to study the approximate controllability concept with non local conditions an example is presented to demonstrate the obtained theory

multiscale tikhonov total variation image restoration using spatially varying edge coherence exponent edge preserving regularization using partial differential equation pde based methods although extensively studied and widely used for image restoration still have limitations in adapting to local structures we propose a spatially adaptive multiscale variable exponent based anisotropic variational pde method that overcomes current shortcomings such as over smoothing and staircasing artifacts while still retaining and enhancing edge structures across scale our innovative model automatically balances between tikhonov and total variation tv regularization effects using scene content information by incorporating a spatially varying edge coherence exponent map constructed using the eigenvalues of the filtered structure tensor the multiscale exponent model we develop leads to a novel restoration method that preserves edges better and provides selective denoising without generating artifacts for both additive and multiplicative noise models mathematical analysis of our proposed method in variable exponent space establishes the existence of a minimizer and its properties the discretization method we use satisfies the maximum minimum principle which guarantees that artificial edge regions are not created extensive experimental results using synthetic and natural images indicate that the proposed multiscale tikhonov tv mttv and dynamical mttv methods perform better than many contemporary denoising algorithms in terms of several metrics including signal to noise ratio improvement and structure preservation promising extensions to handle multiplicative noise models and multichannel imagery are also discussed