a lax pair for a lattice modified kdv equation reductions to q painleve equations and associated lax pairs we present a new nonautonomous lax pair for a lattice nonautomous modified korteweg devries equation and show that it can be consistently extended multidimensionally a property commonly referred to as being consistent around a cube this nonautonomous equation is reduced to a series ofq discrete painlev e equations and lax pairs for the reduced equations are found a 2 2 lax pair is given for a qpiii with multiple parameters and also for versions of qpii and qpv all for the first time pacs number 02 30 ik

three dimensional exact solution for the vibration of functionally graded rectangular plates abstract a three dimensional exact solution is presented for free and forced vibrations of simply supported functionally graded rectangular plates suitable displacement functions that identically satisfy boundary conditions are used to reduce equations governing steady state vibrations of a plate to a set of coupled ordinary differential equations which are then solved by employing the power series method the exact solution is valid for thick and thin plates and for arbitrary variation of material properties in the thickness direction results are presented for two constituent metal ceramic functionally graded rectangular plates that have a power law through the thickness variation of the volume fractions of the constituents the effective material properties at a point are estimated by either the mori tanaka or the self consistent schemes exact natural frequencies displacements and stresses are used to assess the accuracy of the classical plate theory the first order shear deformation theory and a third order shear deformation theory for functionally graded plates parametric studies are performed for varying ceramic volume fractions volume fraction profiles and length to thickness ratios results are also computed for a functionally graded plate that has a varying microstructure in the thickness direction using a combination of the mori tanaka and the self consistent methods forced vibrations of a plate with a sinusoidal spatial variation of the pressure applied on its top surface are scrutinized

discrete painleve equations coalescences limits and degeneracies abstract starting from the standard form of the five discrete painleve equations we show how one can obtain through appropriate limits a host of new equations which are also the discrete analogues of the continuous painleve equations a particularly interesting technique is the one based on the assumption that some simplification takes place in the autonomous form of the mapping following which the deautonomization leads to a new n dependence and introduces more new discrete painleve equations

on ell_1 data fitting and concave regularization for image recovery we propose a new family of cost functions for signal and image recovery they are composed of ell 1 data fitting terms combined with concave regularization we exhibit when and how to employ such cost functions our theoretical results show that the minimizers of these cost functions are such that each one of their entries is involved either in an exact data fitting component or in a null component of the regularization part this is a strong and particular property that can be useful for various image recovery problems the minimization of such cost functions presents a computational challenge we propose a fast minimization algorithm to solve this numerical problem the experimental results show the effectiveness of the proposed algorithm all illustrations and numerical experiments give a flavor of the possibilities offered by the minimizers of this new family of cost functions in solving specialized image processing tasks

common structure of techniques for choosing smoothing parameters in regression problems on tente de relier deux methodes de choix du parametre de lissage l une basee sur la mesure du risque et l autre sur le degre d ajustement de la regression aux donnees

active contours without edges we propose a new model for active contours to detect objects in a given image based on techniques of curve evolution mumford shah 1989 functional for segmentation and level sets our model can detect objects whose boundaries are not necessarily defined by the gradient we minimize an energy which can be seen as a particular case of the minimal partition problem in the level set formulation the problem becomes a mean curvature flow like evolving the active contour which will stop on the desired boundary however the stopping term does not depend on the gradient of the image as in the classical active contour models but is instead related to a particular segmentation of the image we give a numerical algorithm using finite differences finally we present various experimental results and in particular some examples for which the classical snakes methods based on the gradient are not applicable also the initial curve can be anywhere in the image and interior contours are automatically detected

threshold dynamics for the piecewise constant mumford shah functional we propose an efficient algorithm for minimizing the piecewise constant mumford shah functional of image segmentation it is based on the threshold dynamics of merriman bence and osher for evolving an interface by its mean curvature we show that a very fast minimization can be achieved by alternating the solution of a linear parabolic partial differential equation and simple thresholding

a systematic approach to reductions of type q abs equations we present a class of reductions of mobius type for the lattice equations known as q1 q2 and q3 from the abs list the deautonomized form of one particular reduction of q3 is shown to exist on the surface which belongs to the multiplicative type of rational surfaces in sakai s classification of painleve systems using the growth of degrees of iterates all other mappings that result from the class of reductions considered here are shown to be linearizable any possible linearizations are calculated explicitly by constructing a birational transformation defined by invariant curves in the blown up space of initial values for each reduction

on shear deformable beam theories the frequency and normal mode equations of the homogeneous orthotropic bickford beam abstract this paper provides a step forwards the construction and documentation of the frequency equations and the characteristic functions of a general three degrees of freedom theory that describes the plane motion of shear deformable elastic beams the governing equations of this shear deformable beam theory g3dofbt involve a general shape function of the transverse beam co ordinate parameter the a posteriori choice of which specifies the distribution of the transverse shear strain or stress along the beam thickness different choices of this shape function produce as particular cases the corresponding governing equations of different beam theories these include the differential equations of the euler bernoulli beam theory as well as the corresponding equations of the shear deformable theories due to timoshenko and bickford other examples can also be found by considering the shear deformable beam theories produced as one dimensional versions of relevant refined plate theories since corresponding developments of the timoshenko beam theory are already available in the literature the bickford theory is considered as the pilot beam theory in this study the frequency equations the characteristic functions and the orthogonality conditions of this theory which assumes a through thickness parabolic distribution of the transverse shear strain or stress are constructed analytically for all the classical sets of boundary conditions applied at the beam ends some preliminary numerical results are also presented and discussed for beams having both their ends simply supported or clamped

q difference equations of kdv type and chazy type second degree difference equations by imposing special compatible similarity constraints on a class of integrable partial q difference equations of kdv type we derive a hierarchy of second degree ordinary q difference equations the lowest non trivial member of this hierarchy is a second order second degree equation which can be considered as an analogue of equations in the class studied by chazy this second order second degree equation follows from a system in terms of two variables from which also follows an associated third order first degree equation we present the isomonodromic deformation problem for the two variable system and discuss the relation between the hierarchy of second degree ordinary q difference equations and other equations of painleve type

10e9 solution to the elliptic painleve equation a function formalism for sakai s elliptic painleve equation is presented this establishes the equivalence between the two formulations by sakai and by ohta ramani grammaticos we also give a simple geometric description of the elliptic painleve equation as a non autonomous deformation of the addition formula on elliptic curves by using these formulations we construct a particular solution of the elliptic painleve equation expressed in terms of the elliptic hypergeometric function 10e9

image restoration via the adaptive tvp regularization abstract to keep structures in the restoration problem is very important via coupling the local information of the image with the proposed model in this paper we propose a local self adaptive l p regularization model for p 0 2 based on the total variation scheme where the choice of p depends on the local structures described by the eigenvalues of the structure tensor since the proposed model as the classic l p problem unifies two classes of optimization problems such as the nonconvex and nonsmooth problem when p 0 1 and the convex and smooth problem when p 1 2 it is generally challenging to find a ready algorithmic framework to solve it here we propose a new and robust numerical method via coupling with the half quadratic scheme and the alternating direction method of multipliers admm the convergence of the proposed algorithm is established and the numerical experiments illustrate the possible advantages of the proposed model and numerical methods over some existing variational based models and methods

tropical representation of weyl groups associated with certain rational varieties abstract starting from certain rational varieties blown up from p 1 n we construct a tropical i e subtraction free birational representation of weyl groups as a group of pseudo isomorphisms of the varieties we develop an algebro geometric framework of functions as defining functions of exceptional divisors on the varieties in the case where the corresponding root system is of affine type our construction yields a class of higher order q difference painleve equations and its algebraic degree grows quadratically

parameter selection for total variation based image restoration using discrepancy principle there are two key issues in successfully solving the image restoration problem 1 estimation of the regularization parameter that balances data fidelity with the regularity of the solution and 2 development of efficient numerical techniques for computing the solution in this paper we derive a fast algorithm that simultaneously estimates the regularization parameter and restores the image the new approach is based on the total variation tv regularized strategy and morozov s discrepancy principle the tv norm is represented by the dual formulation that changes the minimization problem into a minimax problem a proximal point method is developed to compute the saddle point of the minimax problem by adjusting the regularization parameter adaptively in each iteration the solution is guaranteed to satisfy the discrepancy principle we will give the convergence proof of our algorithm and numerically show that it is better than some state of the art methods in terms of both speed and accuracy

completely convex formulation of the chan vese image segmentation model the active contours without edges model of chan and vese ieee transactions on image processing 10 2 266 277 2001 is a popular method for computing the segmentation of an image into two phases based on the piecewise constant mumford shah model the minimization problem is non convex even when the optimal region constants are known a priori in siam journal of applied mathematics 66 5 1632 1648 2006 chan esedo lu and nikolova provided a method to compute global minimizers by showing that solutions could be obtained from a convex relaxation in this paper we propose a convex relaxation approach to solve the case in which both the segmentation and the optimal constants are unknown for two phases and multiple phases in other words we propose a convex relaxation of the popular k means algorithm our approach is based on the vector valued relaxation technique developed by goldstein et al ucla cam report 09 77 2009 and brown et al ucla cam report 10 43 2010 the idea is to consider the optimal constants as functions subject to a constraint on their gradient although the proposed relaxation technique is not guaranteed to find exact global minimizers of the original problem our experiments show that our method computes tight approximations of the optimal solutions particularly we provide numerical examples in which our method finds better solutions than the method proposed by chan et al siam journal of applied mathematics 66 5 1632 1648 2006 whose quality of solutions depends on the choice of the initial condition

a generalized matrix krylov subspace method for tv regularization abstract this paper presents efficient algorithms to solve both tv l1 and tv l2 models of images contaminated by blur and noise the unconstrained structure of the problems suggests that one can solve a constrained optimization problem by transforming the original unconstrained minimization problem to an equivalent constrained minimization one an augmented lagrangian method is developed to handle the constraints when the model is given with matrix variables and an alternating direction method adm is used to iteratively find solutions of the subproblems the solutions of some subproblems are belonging to subspaces generated by application of successive orthogonal projections onto a class of generalized matrix krylov subspaces of increasing dimension we give some theoretical results and report some numerical experiments to show the effectiveness of the proposed algorithms

classification of integrable equations on quad graphs the consistency approach a classification of discrete integrable systems on quad graphs i e on surface cell decompositions with quadrilateral faces is given the notion of integrability laid in the basis of the classification is the three dimensional consistency this property yields among other features the existence of the discrete zero curvature representation with a spectral parameter for all integrable systems of the obtained exhaustive list the so called three leg forms are found this establishes lagrangian and symplectic structures for these systems and the connection to discrete systems of the toda type on arbitrary graphs generalizations of these ideas to the three dimensional integrable systems and to the quantum context are also discussed

nonconvex nonsmooth optimization via convex nonconvex majorization minimization the class of majorization minimization algorithms is based on the principle of successively minimizing upper bounds of the objective function each upper bound or surrogate function is locally tight at the current estimate and each minimization step decreases the value of the objective function we present a majorization minimization approach based on a novel convex nonconvex upper bounding strategy for the solution of a certain class of nonconvex nonsmooth optimization problems we propose an efficient algorithm for minimizing the convex surrogate function based on the alternating direction method of multipliers a preliminary convergence analysis for the proposed approach is provided numerical experiments show the effectiveness of the proposed method for the solution of nonconvex nonsmooth minimization problems

a nonlinear primal dual method for total variation based image restoration we present a new method for solving total variation tv minimization problems in image restoration the main idea is to remove some of the singularity caused by the nondifferentiability of the quantity nabla u in the definition of the tv norm before we apply a linearization technique such as newton s method this is accomplished by introducing an additional variable for the flux quantity appearing in the gradient of the objective function which can be interpreted as the normal vector to the level sets of the image u our method can be viewed as a primal dual method as proposed by conn and overton a primal dual interior point method for minimizing a sum of euclidean norms preprint 1994 and andersen ph d thesis odense university denmark 1995 for the minimization of a sum of euclidean norms in addition to possessing local quadratic convergence experimental results show that the new method seems to be globally convergent

a study on the fourth q painleve equation a q difference analogue of the fourth painleve equation is proposed its symmetry structure and some particular solutions are investigated

efficient schemes for total variation minimization under constraints in image processing this paper presents new fast algorithms to minimize total variation and more generally l 1 norms under a general convex constraint such problems are standards of image processing the algorithms are based on a recent advance in convex optimization proposed by yurii nesterov depending on the regularity of the data fidelity term we solve either a primal problem or a dual problem first we show that standard first order schemes allow one to get solutions of precision epsilon in o frac 1 epsilon 2 iterations at worst we propose a scheme that allows one to obtain a solution of precision epsilon in o frac 1 epsilon iterations for a general convex constraint for a strongly convex constraint we solve a dual problem with a scheme that requires o frac 1 sqrt epsilon iterations to get a solution of precision epsilon finally we perform some numerical experiments which confirm the theoretical results on various problems of image processing

an efficient tvl1 algorithm for deblurring multichannel images corrupted by impulsive noise we extend the alternating minimization algorithm recently proposed in y wang j yang w yin and y zhang siam j imag sci 1 2008 pp 248 272 j yang w yin y zhang and y wang siam j imag sci 2 2009 pp 569 592 to the case of recovering blurry multichannel color images corrupted by impulsive rather than gaussian noise the algorithm minimizes the sum of a multichannel extension of total variation and a data fidelity term measured in the ell 1 norm and is applicable to both salt and pepper and random valued impulsive noise we derive the algorithm by applying the well known quadratic penalty function technique and prove attractive convergence properties including finite convergence for some variables and q linear convergence rate under periodic boundary conditions the main computational requirements of the algorithm are fast fourier transforms and a low complexity gaussian elimination procedure numerical results on images with different blurs and impulsive noise are presented to demonstrate the efficiency of the algorithm in addition it is numerically compared to the least absolute deviation method h y fu m k ng m nikolova and j l barlow siam j sci comput 27 2006 pp 1881 1902 and the two phase method j f cai r chan and m nikolova aims j inverse problems and imaging 2 2008 pp 187 204 for recovering grayscale images we also present results of recovering multichannel images

reduction of lattice equations to the painleve equations piv and pv in this paper we construct a new relation between adler bobenko suris equations and painleve equations moreover using this connection we construct the difference differential lax representations of the fourth and fifth painleve equations

fractional tikhonov regularization with a nonlinear penalty term tikhonov regularization is one of the most popular methods for solving linear systems of equations or linear least squares problems with a severely ill conditioned matrix and an error contaminated data vector right hand side this regularization method replaces the given problem by a penalized least squares problem it is well known that tikhonov regularization in standard form may yield approximate solutions that are too smooth i e the computed approximate solution may lack many details that the desired solution of the associated but unavailable error free problem might possess fractional tikhonov regularization methods have been introduced to remedy this shortcoming however the computed solution determined by fractional tikhonov methods in standard form may display undesirable spurious oscillations this paper proposes that fractional tikhonov methods be equipped with a nonlinear penalty term such as a tv norm penalty term to reduce unwanted oscillations numerical examples illustrate the benefits of this approach

sparse signal estimation by maximally sparse convex optimization this paper addresses the problem of sparsity penalized least squares for applications in sparse signal processing e g sparse deconvolution this paper aims to induce sparsity more strongly than l1 norm regularization while avoiding non convex optimization for this purpose this paper describes the design and use of non convex penalty functions regularizers constrained so as to ensure the convexity of the total cost function f to be minimized the method is based on parametric penalty functions the parameters of which are constrained to ensure convexity of f it is shown that optimal parameters can be obtained by semidefinite programming sdp this maximally sparse convex msc approach yields maximally non convex sparsity inducing penalty functions constrained such that the total cost function f is convex it is demonstrated that iterative msc imsc can yield solutions substantially more sparse than the standard convex sparsity inducing approach i e l1 norm minimization

the tv p regularized mumford shah model for image labeling and segmentation the mumford shah model is an important tool for image labeling and segmentation which pursues a piecewise smooth approximation of the original image and the boundaries with the shortest length in contrast to previous efforts which use the total variation regularization to measure the total length of the boundaries we build up a novel piecewise smooth mumford shah model by utilizing a non convex ell p regularity term for p in 0 1 which can well preserve sharp edges and eliminate geometric staircasing effects we present optimization algorithms with convergence verification where all subproblems can be solved by either the closed form solution or fast fourier transform fft the method is compared to piecewise constant labeling algorithm and several state of the art piecewise smooth mumford shah models based on image decomposition approximations both labeling and segmentation results on synthetic and real images confirm the robustness and efficiency of the proposed method

a binary level set model and some applications to mumford shah image segmentation in this paper we propose a pde based level set method traditionally interfaces are represented by the zero level set of continuous level set functions instead we let the interfaces be represented by discontinuities of piecewise constant level set functions each level set function can at convergence only take two values i e it can only be 1 or 1 thus our method is related to phase field methods some of the properties of standard level set methods are preserved in the proposed method while others are not using this new method for interface problems we need to minimize a smooth convex functional under a quadratic constraint the level set functions are discontinuous at convergence but the minimization functional is smooth we show numerical results using the method for segmentation of digital images

applications of splitting algorithm to decomposition in convex programming and variational inequalities recently han and lou proposed a highly parallelizable decomposition algorithm for minimizing a strongly convex cost over the intersection of closed convex sets it is shown that their algorithm is in fact a special case of a splitting algorithm analyzed by gabay for finding a zero of the sum of two maximal monotone operators gabay s convergence analysis for the splitting algorithm is sharpened and new applications of this algorithm to variational inequalities convex programming and the solution of linear complementarily problems are proposed for convex programs with a certain separable structure a multiplier method that is closely related to the alternating direction method of multipliers of gabay mercier and of glowinski marrocco but which uses both ordinary and augmented lagrangians is obtained

convex non convex image segmentation a convex non convex variational model is proposed for multiphase image segmentation we consider a specially designed non convex regularization term which adapts spatially to the image structures for a better control of the segmentation boundary and an easy handling of the intensity inhomogeneities the nonlinear optimization problem is efficiently solved by an alternating directions methods of multipliers procedure we provide a convergence analysis and perform numerical experiments on several images showing the effectiveness of this procedure

methods for choosing the regularization parameter and estimating the noise variance in image restoration and their relation the application of regularization to ill conditioned problems necessitates the choice of a regularization parameter which trades fidelity to the data with smoothness of the solution the value of the regularization parameter depends on the variance of the noise in the data the problem of choosing the regularization parameter and estimating the noise variance in image restoration is examined an error analysis based on an objective mean square error mse criterion is used to motivate regularization two approaches for choosing the regularization parameter and estimating the noise variance are proposed the proposed and existing methods are compared and their relationship to linear minimum mean square error filtering is examined experiments are presented that verify the theoretical results

a general theory for the accurate stress analysis of homogeneous and laminated composite beams abstract this paper has a twofold purpose initially it presents a general four degrees of freedom beam theory g4dofbt which takes into consideration the effects of both transverse shear and normal deformation on the basis of this new theory it then proposes a method suitable for the accurate stress analysis of either homogeneous or laminated composite beams subjected to arbitrary edge boundary conditions the new beam theory involves two general shape functions each of which is associated with one of the two unknown displacement components upon assigning simple particular forms to these shape functions most of the well known classical and variationally consistent refined beam models may be obtained as particular cases the new method for the accurate stress analysis of beam type structures is based on the specification of a new pair of shape functions these are obtained by introducing the stress distributions caused by the assumed g4dofbt displacement field into the appropriate equations of three dimensional elasticity which are subsequently solved for simply supported edges this is considered to provide an excellent choice of both shape functions as the method then yields the exact elasticity solution presented by pagano pagano n j 1969 exact solution for composite laminates in cylindrical bending j comp mat 3 398 411 for the cylindrical bending problem of simply supported infinite strips two particular examples are considered to show the potential of the present analysis these are dealing with stress analysis of homogeneous or laminated composite beams having one edge rigidly clamped and the other edge either guided or free of external tractions

a generalized krylov subspace method for ell_p ell_q minimization this paper presents a new efficient approach for the solution of the ell p ell q minimization problem based on the application of successive orthogonal projections onto generalized krylov subspaces of increasing dimension the subspaces are generated according to the iteratively reweighted least squares strategy for the approximation of ell p ell q norms by weighted ell 2 norms computed image restoration examples illustrate that it suffices to carry out only a few iterations to achieve high quality restorations the combination of a low iteration count and a modest storage requirement makes the proposed method attractive

two generalized higher order theories in free vibration studies of multilayered plates this paper presents an extension of two dimensional models for the analysis of freely vibrating laminated plates the extension concerns the enlargement of higher order theories recently introduced by different authors in several forms to encompass higher order terms over the cubic one usually taken into consideration higher order effects such as rotatory inertia and transverse shear stress are naturally included without any shear correction factors namely two different models are introduced by expanding on different functional bases displacements d2d and transverse shear stresses in conjunction with displacements m2d the expansion is considered to be consistent with the traction type boundary condition on the external surfaces of the plate the governing equations and associated boundary conditions are consistently obtained by the classical hamilton s variational principle and reissner s mixed variational theorem both models are equivalent single layer type and therefore differ according to the layer wise descriptions preserve the independence of the number of unknown variables on the number of layers however this feature is presented together with intrinsic physical violations for both models model d2d violates the interlaminar stress continuity requirement and model m2d violates in a weaker from the same requirement derivatives are not piecewise continuous besides neglecting the transverse normal stress the importance of completely fulfilling the mentioned continuity is then discussed once the relevant governing equations are tailored for the cylindrical bending condition the effectiveness of the models is indicated by making numerical comparisons with the exact three dimensional theory of the elasticity for several lamination schemes angle cross ply lay ups and characteristic geometric ratios for low and higher frequencies

analysis of discrete ill posed problems by means of the l curve when discrete ill posed problems are analyzed and solved by various numerical regularization techniques a very convenient way to display information about the regularized solution is to plot the norm or seminorm of the solution versus the norm of the residual vector in particular the graph associated with tikhonov regularization plays a central role the main purpose of this paper is to advocate the use of this graph in the numerical treatment of discrete ill posed problems the graph is characterized quantitatively and several important relations between regularized solutions and the graph are derived it is also demonstrated that several methods for choosing the regularization parameter are related to locating a characteristic l shaped corner of the graph

optimal approximations by piecewise smooth functions and associated variational problems abstract this reprint will introduce and study the most basic properties of three new variational problems which are suggested by applications to computer vision in computer vision a fundamental problem is to appropriately decompose the domain r of a function g x y of two variables this problem starts by describing the physical situation which produces images assume that a three dimensional world is observed by an eye or camera from some point p and that g1 rho represents the intensity of the light in this world approaching the point sub 1 from a direction rho if one has a lens at p focusing this light on a retina or a film in both cases a plane domain r in which we may introduce coordinates x y then let g x y be the strength of the light signal striking r at a point with coordinates x y g x y is essentially the same as sub 1 rho possibly after a simple transformation given by the geometry of the imaging syste the function g x y defined on the plane domain r will be called an image what sort of function is g the light reflected off the surfaces si of various solid objects o sub i visible from p will strike the domain r in various open subsets r sub i when one object o1 is partially in front of another object o2 as seen from p but some of object o2 appears as the background to the sides of o1 then the open sets r1 and r2 will have a common boundary the edge of object o1 in the image defined on r and one usually expects the image g x y to be discontinuous along this boundary jhd

using the l curve for determining optimal regularization parameters the l curve is a plot in ordinary or doubly logarithmic scale of the norm of tikhonov regularized solutions of an ill posed problem versus the norm of the residuals we show that the popular criterion of choosing the parameter corresponding to the point with maximal curvature of the l curve does not yield a convergent regularization strategy to solve the ill posed problem nevertheless the l curve can be used to compute the regularization parameters produced by morozov s discrepancy principle and by an order optimal variant of the discrepancy principle proposed by engl and gfrerer in an alternate way

square smoothing regularization matrices with accurate boundary conditions this paper is concerned with the solution of large scale linear discrete ill posed problems the determination of a meaningful approximate solution of these problems requires regularization we discuss regularization by the tikhonov method and by truncated iteration the choice of regularization matrix in tikhonov regularization may significantly affect the quality of the computed approximate solution the present paper describes the construction of square regularization matrices from finite difference equations with a focus on the boundary conditions the regularization matrices considered have a structure that makes them easy to apply in iterative methods including methods based on the arnoldi process numerical examples illustrate the properties and effectiveness of the regularization matrices described

group sparse signal denoising non convex regularization convex optimization convex optimization with sparsity promoting convex regularization is a standard approach for estimating sparse signals in noise in order to promote sparsity more strongly than convex regularization it is also standard practice to employ non convex optimization in this paper we take a third approach we utilize a non convex regularization term chosen such that the total cost function consisting of data consistency and regularization terms is convex therefore sparsity is more strongly promoted than in the standard convex formulation but without sacrificing the attractive aspects of convex optimization unique minimum robust algorithms etc we use this idea to improve the recently developed overlapping group shrinkage ogs algorithm for the denoising of group sparse signals the algorithm is applied to the problem of speech enhancement with favorable results in terms of both snr and perceptual quality

dynamic equations for a fully anisotropic elastic plate a hierarchy of dynamic plate equations is derived for a fully anisotropic elastic plate using power series expansions in the thickness coordinate for the displacement components recursion relations are obtained among the expansion functions adopting these in the boundary conditions on the plate surfaces and along the edges a set of dynamic equations with pertinent edge boundary conditions are derived on implicit form these can be truncated to any order and are believed to be asymptotically correct for the special case of an orthotropic plate explicit plate equations are presented and compared analytically and numerically to other approximate theories given in the literature these results show that the present theory capture the plate behavior accurately concerning dispersion curves eigenfrequencies as well as stress and displacement distributions

a three dimensional higher order elasticity based micromechanics model abstract the three dimensional 3d version of a new homogenization theory a two dimensional higher order elasticity based micromechanics model in print is presented the 3d theory utilizes a higher order elasticity based cell model ecm analysis for a periodic array of 3d unit cells the unit cell is discretized into eight subregions or subcells the displacement field within each subcell is approximated by a truncated eigenfunction expansion of up to fifth order the governing equations are developed by satisfying the pointwise governing equations of geometrically linear continuum mechanics exactly up through the given order of the subcell displacement fields the specified governing equations are valid for any type of constitutive model used to describe the behavior of the material in a subcell the specialization of the theory to lower orders and to two dimeinsions 2d and to the exact one dimensional 1d theory is discussed since the proposed 3d homogenization theory correctly reduces to both 2d and 1d the validation process applied to the 2d theory a two dimensional higher order elasticity based micromechanics model in print directly applies to the current formulation additional comparisons of the predicted responses obtained from the 3d ecm theory with existing published results are conducted the good agreement obtained shows that the current theory represents a viable 3d homogenization tool the improved agreement between the current theory results and published results as compared to the comparison of the moc results and the published results is due to the correct incorporation of the coupling effects between the local fields additional results showing the convergence behavior of the average fields as a function of the order of the analysis is presented these results show that the 1st order theory may not accurately predict the local averages but that consistent and converged behavior is obtained using the higher order ecm theories the proposed theory represents the necessary theoretical foundations for the development of exact homogenization solutions of generalized three dimensional microstructures

lax pairs of discrete painleve equations a2 a1 1 case in this paper we provide a comprehensive method for constructing lax pairs of discrete painleve equations by using a reduced hypercube structure in particular we consider the a 5 1 surface q painleve system which has the affine weyl group symmetry of type a 2 a 1 1 two new lax pairs are found

deblurring methods using antireflective boundary conditions in this paper we consider the numerical solution of self adjoint deblurring problems on bounded intervals for these problems it has recently been shown that appropriate modeling of the solution near the boundary of the interval may significantly improve the numerical reconstructions among the alternatives the so called antireflective boundary condition appears to be the best known choice here we develop an appropriate i e stable and efficient implementation of this model in two steps namely by i transforming the problem to homogeneous boundary values and ii using the fast sine transform to solve the transformed problem this approach allows us to incorporate regularization in a very straightforward way numerical reconstructions are superior qualitatively and quantitatively to those obtained with the reblurring method of donatelli and serra capizzano

cylindrical bending of angle ply laminates subjected to different sets of edge boundary conditions this paper extends the applicability of a new stress analysis method towards the accurate determination of the detailed stress distributions in angle ply laminated plates subjected to cylindrical bending as far as simply supported plates are concerned this problem has an exact elasticity solution here however a simpler two dimensional shear deformable plate model is employed which accompanied with an appropriate set of through thickness shape functions makes the new stress analysis method very accurate hence the existing exact elasticity solution is used only for a further verification of the reliability of the new method which is then used for a more detailed stress analysis study of certain monoclinic and angle ply laminated plates subjected to realistic edge boundary conditions it is also shown that the corresponding stress analysis of cross ply laminated plates subjected to cylindrical bending is a particular case of the present analysis

geometric reductions of abs equations on an n cube to discrete painleve systems in this paper we show how to relate n dimensional cubes on which abs equations hold to the symmetry groups of discrete painlev equations we here focus on the reduction from the four dimensional cube to the q discrete third painlev equation which is a dynamical system on a rational surface of type with the extended affine weyl group we provide general theorems to show that this reduction also extends to other discrete painlev equations at least of type a

unsupervised multiphase segmentation a phase balancing model variational models have been studied for image segmentation application since the mumford shah functional was introduced in the late 1980s in this paper we focus on multiphase segmentation with a new regularization term that yields an unsupervised segmentation model we propose a functional that automatically chooses a favorable number of phases as it segments the image the primary driving force of the segmentation is the intensity fitting term while a phase scale measure complements the regularization term we propose a fast yet simple brute force numerical algorithm and present experimental results showing the robustness and stability of the proposed model

lattice equations arising from discrete painleve systems i a2 a1 1 and a1 a1 1 cases we introduce the concept of lattice constructed from functions of painleve systems on which quad equations of abs adler bobenko suris type appear in particular we consider the a5 1 and a6 1 surface q painleve systems corresponding affine weyl group symmetries are of a2 a1 1 and a1 a1 1 types respectively

a proximal iteration for deconvolving poisson noisy images using sparse representations we propose an image deconvolution algorithm when the data is contaminated by poisson noise the image to restore is assumed to be sparsely represented in a dictionary of waveforms such as the wavelet or curvelet transforms our key contributions are as follows first we handle the poisson noise properly by using the anscombe variance stabilizing transform leading to a nonlinear degradation equation with additive gaussian noise second the deconvolution problem is formulated as the minimization of a convex functional with a data fidelity term reflecting the noise properties and a nonsmooth sparsity promoting penalty over the image representation coefficients e g lscr1 norm an additional term is also included in the functional to ensure positivity of the restored image third a fast iterative forward backward splitting algorithm is proposed to solve the minimization problem we derive existence and uniqueness conditions of the solution and establish convergence of the iterative algorithm finally a gcv based model selection procedure is proposed to objectively select the regularization parameter experimental results are carried out to show the striking benefits gained from taking into account the poisson statistics of the noise these results also suggest that using sparse domain regularization may be tractable in many deconvolution applications with poisson noise such as astronomy and microscopy

special function solutions of the discrete painleve equations in this paper we present a review of the special solutions of discrete difference and q discrete painleve equations in terms of discrete special functions these solutions exist whenever the parameters of the painleve equation satisfy a particular constraint the discrete special functions belong to the hypergeometric family although in some cases they seem to go beyond the known discrete and q discrete hypergeometric functions the equations studied in this paper are chosen on the basis of our recent classification of discrete painleve equation with the help of affine weyl groups

a proximal based decomposition method for convex minimization problems this paper presents a decomposition method for solving convex minimization problems at each iteration the algorithm computes two proximal steps in the dual variables and one proximal step in the primal variables we derive this algorithm from rockafellar s proximal method of multipliers which involves an augmented lagrangian with an additional quadratic proximal term the algorithm preserves the good features of the proximal method of multipliers with the additional advantage that it leads to a decoupling of the constraints and is thus suitable for parallel implementation we allow for computing approximately the proximal minimization steps and we prove that under mild assumptions on the problem s data the method is globally convergent and at a linear rate the method is compared with alternating direction type methods and applied to the particular case of minimizing a convex function over a finite intersection of closed convex sets

generalization of variationally consistent plate theories on the basis of a vectorial formulation abstract this paper deals with the vectorial formulation of variationally consistent sets of differential equations that with either transverse shear or transverse normal deformation effects taken into consideration govern the static and or dynamic behaviour of homogeneous or inhomogeneous elastic plates the present formulation is based on a general form of the displacement representation and yields the kinematic relations constitutive equations and equations of motion of a variationally consistent shear and normal deformable general plate theory the number of degrees of freedom as well as the performance of which can be controlled a posteriori it is shown to be equivalent with a variational approach and can further be considered as a generalization of several variationally consistent transverse shear and normal deformable plate theories in the sense that in particular cases it quotes their governing equations derived elsewhere variationally moreover just as happens with the application of a variational approach an a priori knowledge of the elastic law governing the material behaviour of the plate considered is not required under the general assumption that there exists a strain energy density function the present vectorial approach can be applied successfully

solving constrained total variation image restoration and reconstruction problems via alternating direction methods in this paper we study alternating direction methods for solving constrained total variation image restoration and reconstruction problems alternating direction methods can be implementable variants of the classical augmented lagrangian method for optimization problems with separable structures and linear constraints the proposed framework allows us to solve problems of image restoration impulse noise removal inpainting and image cartoon texture decomposition as the constrained model is employed we need only to input the noise level and the estimation of the regularization parameter is not required in these imaging problems experimental results for such imaging problems are presented to illustrate the effectiveness of the proposed method we show that the alternating direction method is very efficient for solving image restoration and reconstruction problems

an lp lq minimization method with cross validation for the restoration of impulse noise contaminated images abstract discrete ill posed problems arise in many areas of science and engineering their solutions if they exist are very sensitive to perturbations in the data regularization aims to reduce this sensitivity many regularization methods replace the original problem by a minimization problem with a fidelity term and a regularization term recently the use of a p norm to measure the fidelity term and a q norm to measure the regularization term has received considerable attention the relative importance of these terms is determined by a regularization parameter when the perturbation in the available data is made up of impulse noise and a sparse solution is desired it often is beneficial to let 0 p q 1 then the p and q norms are not norms the choice of a suitable regularization parameter is crucial for the quality of the computed solution it therefore is important to develop methods for determining this parameter automatically without user interaction however the latter has so far not received much attention when the data is contaminated by impulse noise this paper discusses two approaches based on cross validation for determining the regularization parameter in this situation computed examples that illustrate the performance of these approaches when applied to the restoration of impulse noise contaminated images are presented

rational surfaces associated with affine root systems and geometry of the painleve equations we present a geometric approach to the theory of painleve equations based on rational surfaces our starting point is a compact smooth rational surface x which has a unique anti canonical divisor d of canonical type we classify all such surfaces x to each x there corresponds a root subsystem of e 1 8 inside the picard lattice of x we realize the action of the corresponding affine weyl group as the cremona action on a family of these surfaces we show that the translation part of the affine weyl group gives rise to discrete painleve equations and that the above action constitutes their group of symmetries by backlund transformations the six painleve differential equations appear as degenerate cases of this construction in the latter context x is okamoto s space of initial conditions and d is the pole divisor of the symplectic form defining the hamiltonian structure