restoration of images based on subspace optimization accelerating augmented lagrangian approach we propose a new fast algorithm for solving a tv based image restoration problem our approach is based on merging subspace optimization methods into an augmented lagrangian method the proposed algorithm can be seen as a variant of the alm augmented lagrangian method and the convergence properties are analyzed from a drs douglas rachford splitting viewpoint experiments on a set of image restoration benchmark problems show that the proposed algorithm is a strong contender for the current state of the art methods

supersymmetry and algebraic darboux transformations we describe a class of algebraically solvable susy models by considering the deformation of invariant polynomial flags by means of the darboux transformation the algebraic deformations corresponding to the addition of a bound state to a shape invariant potential are particularly interesting the polynomial flags in question are indexed by a deformation parameter m 1 2 and lead to new algebraically solvable models we illustrate these ideas by considering deformations of the hyperbolic p schl teller potential

quadratic integral games and causal synthesis the game problem for an input output system governed by a volterra integral equation with respect to a quadratic performance functional is an untouched open problem in this paper it is studied by a new approach called projection causality the main result is the causal synthesis which pro vides a causal feedback implementation of the optimal strategies in the saddle point sense the linear feedback operator is determined by the solution of a fredholm integral operator equation which is independent of data functions and control functions two application examples are included the first one is quadratic differential games of a linear system with arbitrary finite delays in the state variable and control variables the second is the standard linear quadratic differential games for which it is proved that the causal synthesis can be reduced to a known result where the feedback operator is determined by the solution of a differential riccati operator equation

estimation of the mean of a multivariate normal distribution estimation of the means of independent normal random variables is considered using sum of squared errors as loss an unbiased estimate of risk is obtained for an arbitrary estimate and certain special classes of estimates are then discussed the results are applied to smoothing by use of moving averages and to trimmed analogs of the james stein estimate a suggestion is made for calculating approximate confidence sets for the mean vector centered at an arbitrary estimate

tikhonov regularization and the l curve for large discrete ill posed problems discretization of linear inverse problems generally gives rise to very ill conditioned linear systems of algebraic equations typically the linear systems obtained have to be regularized to make the computation of a meaningful approximate solution possible tikhonov regularization is one of the most popular regularization methods a regularization parameter specifies the amount of regularization and in general an appropriate value of this parameter is not known a priori we review available iterative methods and present new ones for the determination of a suitable value of the regularization parameter by the l curve criterion and the solution of regularized systems of algebraic equations

backward doubly stochastic volterra integral equations and their applications abstract in this paper we introduce a new class of equations called backward doubly stochastic volterra integral equations bdsvies for short first the well posedness of bdsvies in the sense of introduced m solutions is established second a comparison theorem of bdsvies is proved as an application of the comparison theorem we derive the existence of solutions of bdsvies with continuous coefficients third a duality principle between linear forward doubly stochastic volterra integral equations fdsvies for short and bdsvies is obtained moreover by virtue of the duality principle a maximum principle of pontryagin type is established for an optimal control problem of fdsvies

spatially adapted total variation model to remove multiplicative noise multiplicative noise removal based on total variation tv regularization has been widely researched in image science in this paper inspired by the spatially adapted methods for denoising gaussian noise we develop a variational model which combines the tv regularizer with local constraints it is also related to a tv model with spatially adapted regularization parameters the automated selection of the regularization parameters is based on the local statistical characteristics of some random variable the corresponding subproblem can be efficiently solved by the augmented lagrangian method numerical examples demonstrate that the proposed algorithm is able to preserve small image details whereas the noise in the homogeneous regions is sufficiently removed as a consequence our method yields better denoised results than those of the current state of the art methods with respect to the signal to noise ratio values

backward stochastic volterra integral equations with additive perturbations the paper discusses a large class of stochastic volterra integral equations whose coefficients additively depend on small perturbations their solutions are compared in the l2 sense with the solutions of the appropriate unperturbed equations of the equal or simpler type more precisely we prove for an arbitrary 0 that there exists an interval t t 0 t on which the l2 difference between the solutions of the perturbed and unperturbed equations is less than

causal feedback optimal control for volterra integral equations the optimal control problem for volterra integral equations with respect to quadratic criteria is studied by a projection causality approach the work features a synthesis result where the optimal control is implemented via a linear causal feedback in which the feedback operator is determined by solving an independent fredholm integral operator equation

multiplicative noise removal using variable splitting and constrained optimization multiplicative noise also known as speckle noise models are central to the study of coherent imaging systems such as synthetic aperture radar and sonar and ultrasound and laser imaging these models introduce two additional layers of difficulties with respect to the standard gaussian additive noise scenario 1 the noise is multiplied by rather than added to the original image 2 the noise is not gaussian with rayleigh and gamma being commonly used densities these two features of multiplicative noise models preclude the direct application of most state of the art algorithms which are designed for solving unconstrained optimization problems where the objective has two terms a quadratic data term log likelihood reflecting the additive and gaussian nature of the noise plus a convex possibly nonsmooth regularizer e g a total variation or wavelet based regularizer prior in this paper we address these difficulties by 1 converting the multiplicative model into an additive one by taking logarithms as proposed by some other authors 2 using variable splitting to obtain an equivalent constrained problem and 3 dealing with this optimization problem using the augmented lagrangian framework a set of experiments shows that the proposed method which we name midal multiplicative image denoising by augmented lagrangian yields state of the art results both in terms of speed and denoising performance

computational acceleration for mr image reconstruction in partially parallel imaging in this paper we present a fast numerical algorithm for solving total variation and l1 tvl1 based image reconstruction with application in partially parallel magnetic resonance imaging our algorithm uses variable splitting method to reduce computational cost moreover the barzilai borwein step size selection method is adopted in our algorithm for much faster convergence experimental results on clinical partially parallel imaging data demonstrate that the proposed algorithm requires much fewer iterations and or less computational cost than recently developed operator splitting and bregman operator splitting methods which can deal with a general sensing matrix in reconstruction framework to get similar or even better quality of reconstructed images

mean field linear quadratic gaussian lqg games for stochastic integral systems in this technical note we formulate and investigate a class of mean field linear quadratic gaussian lqg games for stochastic integral systems unlike other literature on mean field games where the individual states follow the controlled stochastic differential equations sdes the individual states in our large population system are characterized by a class of stochastic volterra type integral equations we obtain the nash certainty equivalence nce equation and hence derive the set of associated decentralized strategies the epsilon nash equilibrium properties are also verified due to the intrinsic integral structure the techniques and estimates applied here are significantly different from those existing results in mean field lqg games for stochastic differential systems for example some fredholm equation in the mean field setup is introduced for the first time as for applications two types of stochastic delayed systems are formulated as the special cases of our stochastic integral system and relevant mean field lqg games are discussed

a variational approach to removing multiplicative noise this paper focuses on the problem of multiplicative noise removal we draw our inspiration from the modeling of speckle noise by using a map estimator we can derive a functional whose minimizer corresponds to the denoised image we want to recover although the functional is not convex we prove the existence of a minimizer and we show the capability of our model on some numerical examples we study the associated evolution problem for which we derive existence and uniqueness results for the solution we prove the convergence of an implicit scheme to compute the solution

a class of exactly solvable potentials related to the jacobi polynomials the author investigates a family of solvable potentials related to the jacobi polynomials this one dimensional potential family depends on three parameters and is restricted to the domain xo so it can be interpreted as the radial part of a central potential in three dimensions with l 0 closed expressions are obtained for the bound state energy spectrum and the wavefunctions the supersymmetric partner of this potential is also determined and it is found not to belong to the same potential family it is shown that this potential family is a special subclass of the general six parameter natanzon potential class and similarities with another subclass the ginocchio potentials are pointed out some aspects of supersymmetric quantum mechanics and shape invariance are also discussed in connection with the potential family under study

a new multiplicative denoising variational model based on m th root transformation in coherent imaging systems such as the synthetic aperture radar sar the observed images are contaminated by multiplicative noise due to the edge preserving feature of the total variation tv variational models with tv regularization have attracted much interest in removing multiplicative noise however the fidelity term of the variational model based on maximum a posteriori estimation is not convex and so it is usually difficult to find a global solution hence the logarithmic function is used to transform the nonconvex variational model to the convex one in this paper instead of using the log we exploit the th root function to relax the nonconvexity of the variational model an algorithm based on the augmented lagrangian function which has been applied to solve the log transformed convex variational model can be applied to solve our proposed model however this algorithm requires solving a subproblem which does not have a closed form solution at each iteration hence we propose to adapt the linearized proximal alternating minimization algorithm which does not require inner iterations for solving the subproblems in addition the proposed method is very simple and highly parallelizable thus it is efficient to remove multiplicative noise in huge sar images the proposed model for multiplicative noise removal shows overall better performance than the convex model based on the log transformation

adapted solution of a backward stochastic differential equation abstract let wt t 0 1 be a standard k dimensional weiner process defined on a probability space f p and let ft denote its natural filtration given a f1 measurable d dimensional random vector x we look for an adapted pair of processes x t y t t 0 1 with values in rd and rd k respectively which solves an equation of the form x t t 1 f s x s y s ds t 1 g s x s y s dw s x a linearized version of that equation appears in stochastic control theory as the equation satisfied by the adjoint process we also generalize our results to the following equation x t t 1 f s x s y s ds t 1 g s x s y s dw s x under rather restrictive assumptions on g

a general stochastic maximum principle for optimal control problems the maximum principle for nonlinear stochastic optimal control problems in the general case is proved the control domain need not be convex and the diffusion coefficient can contain a control variable

fast linearized alternating direction minimization algorithm with adaptive parameter selection for multiplicative noise removal owing to the edge preserving ability and low computational cost of the total variation tv variational models with the tv regularizer have been widely investigated in the field of multiplicative noise removal the key points of the successful application of these models lie in the optimal selection of the regularization parameter which balances the data fidelity term with the tv regularizer the efficient algorithm to compute the solution in this paper we propose two fast algorithms based on the linearized technique which are able to estimate the regularization parameter and recover the image simultaneously in the iteration step of the proposed algorithms the regularization parameter is adjusted by a special discrepancy function defined for multiplicative noise the convergence properties of the proposed algorithms are proved under certain conditions and numerical experiments demonstrate that the proposed algorithms overall outperform some state of the art methods in the psnr values and computational time

linearized proximal alternating minimization algorithm for motion deblurring by nonlocal regularization abstract non blind motion deblurring problems are highly ill posed and so it is quite difficult to find the original sharp and clean image to handle ill posedness of the motion deblurring problem we use nonlocal total variation abbreviated as tv regularization approaches nonlocal tv can restore periodic textures and local geometric information better than local tv but since nonlocal tv requires weighted difference between pixels in the whole image it demands much more computational resources than local tv by using the linearization of the fidelity term and the proximal function our proposed algorithm does not require any inversion of blurring operator and nonlocal operator therefore the proposed algorithm is very efficient for motion deblurring problems we compare the numerical performance of our proposed algorithm with that of several state of the art algorithms for deblurring problems our numerical results show that the proposed method is faster and more robust than state of the art algorithms on motion deblurring problems

proximal linearized alternating direction method for multiplicative denoising multiplicative noise naturally appears in coherent imaging systems such as synthetic aperture radar due to the edge preserving feature of total variation tv variational models with tv regularization show good performance for multiplicative denoising recently proposed augmented lagrangian frameworks with the gauss seidel method are efficient for solving multiplicative denoising variational models with tv but recent algorithms based on the augmented lagrangian require inner iterations or an inverse involving the laplacian operator at each iteration in this paper we propose efficient algorithms for tv regularized convex variational models our proposed algorithms do not require any inner iteration or the inverse involving the laplacian operator by using a linearization scheme and a proximal function we establish global convergence under a lipschitz continuous assumption on the gradient of the fidelity term when a correction step is used numerical results show that our proposed algorithms overall

symmetrical martingale solutions of backward doubly stochastic volterra integral equations abstract this paper aims to study a new class of integral equations called backward doubly stochastic volterra integral equations bdsvies for short the notion of symmetrical martingale solutions sm solutions for short is introduced for bdsvies and the existence and uniqueness theorem for bdsvies in the sense of sm solutions is established

rte based parameter reconstruction with tv l1 regularization abstract optical tomography is an imaging modality that explores the distribution of optical parameters in tissues in this paper the regularization jointing both t v and l 1 norm is studied for absorption parameter identification based on radiative transport equation the t v l 1 framework is introduced containing l 2 data fidelity t v regularizer and l 1 regularizer we demonstrate the existence stability and convergence of the minima with respect to this t v l 1 regularization a novel algorithm for solving related optimization problem is proposed based on reweighted method and technique of split bregman simulations are performed to show that the proposed reweighted t v l 1 regularization is more capable of preserving geometric structure of inclusions quantifying values of absorption parameter and promoting fast convergence compared with t v or l 1 regularization and is potential for breast cancer imaging moreover it is robust to noise

primal dual algorithm based on gauss seidel scheme with application to multiplicative noise removal due to the strong edge preserving ability and low computational cost the total variation tv regularization has been developed as one promising approach to solve the multiplicative denoising problem in recent years many efficient algorithms have been proposed for computing the numerical solution of tv based convex variational models among these methods the linearized augmented lagrangian algorithm alm and the primal dual hybrid gradient pdhg algorithm are two of the most effective and most widely used techniques in this paper inspired by the connection of the alm and pdhg algorithms we develop an improved primal dual algorithm for multiplicative noise removal in the proposed algorithm an auxiliary variable which is updated by the gauss seidel scheme is introduced to accelerate the original primal dual framework the global convergence property of the proposed algorithm is also investigated numerical experiments on the multiplicative denoising show that the proposed algorithm outperforms the current state of the art methods

optimal control of volterra equations with impulses we consider an optimal control problem for a system governed by a volterra integral equation with impulsive terms the impulses act on both the state and the control the control consists of switchings at discrete times the cost functional includes both an integrated cost rate continuous part and switching costs at the discrete impulse times discrete part we prove necessary optimality conditions of a form analogous to a discrete maximum principle for the particular case of a system governed by impulsive ordinary differential equations we obtain an impulsive maximum principle as a special case of the necessary optimality conditions for impulsive volterra equations

optimal processes governed by integral equations abstract we consider a control process governed by an integral equation with an integral constraint we derive optimality conditions using relaxed controls existence of optimal pairs is automatic furthermore for problems with linear and certain quadratic cost functions with linear integral equations and linear integral constraint the optimal controls are actually ordinary controls in the case of the linear problem considered if the control set is a convex polyhedron the control is piecewise continuous with values in the vertices of the polyhedron control processes governed by integral equations have been considered in the work of v r vinokurov siam 7 324 355 1969 however in op cit existence is not shown for the general problem and the method is rather complicated furthermore the work in op cit has some errors as pointed out in neustadt and warga s comments on vinokurov siam 8 572 1970

a unified treatment of exactly solvable and quasi exactly solvable quantum potentials by exploiting the hidden algebraic structure of the schrodinger hamiltonian namely the sl 2 we propose a unified approach of generating both exactly solvable and quasi exactly solvable potentials we obtain in this way two new classes of quasi exactly solvable systems one of which is of periodic type while the other hyperbolic

comprehensive analysis of conditionally exactly solvable models we study a quantum mechanical potential introduced previously as a conditionally exactly solvable ces model besides an analysis following its original introduction in terms of the point canonical transformation we also present an alternative supersymmetric construction of it we demonstrate that from the three roots of the implicit cubic equation defining the bound state energy eigenvalues there is always only one that leads to a meaningful physical state finally we demonstrate that the present ces interaction is in fact an exactly solvable natanzon class potential

well posedness and regularity of backward stochastic volterra integral equations backward stochastic volterra integral equations bsvies for short are studied notion of adapted m solution is introduced well posedness of bsvies is established and some regularity results are proved for the adapted m solutions via malliavin calculus a pontryagin type maximum principle is presented for optimal controls of stochastic volterra integral equations

volterra equations driven by semimartingales existence and uniqueness of solutions is established for stochastic volterra integral equations driven by right continuous semimartingales this resolves in the affirmative a conjecture of m berger and v mizel

backward stochastic differential equations and partial differential equations with quadratic growth we provide existence comparison and stability results for one dimensional backward stochastic differential equations bsdes when the coefficient or generator f t y z is continuous and has a quadratic growth in z and the terminal condition is bounded we also give in this framework the links between the solutions of bsdes set on a diffusion and viscosity or sobolev solutions of the corresponding semilinear partial differential equations

an extended class of orthogonal polynomials defined by a sturm liouville problem abstract we present two infinite sequences of polynomial eigenfunctions of a sturm liouville problem as opposed to the classical orthogonal polynomial systems these sequences start with a polynomial of degree one we denote these polynomials as x 1 jacobi and x 1 laguerre and we prove that they are orthogonal with respect to a positive definite inner product defined over the compact interval 1 1 or the half line 0 respectively and they are a basis of the corresponding l 2 hilbert spaces moreover we prove a converse statement similar to bochner s theorem for the classical orthogonal polynomial systems if a self adjoint second order operator has a complete set of polynomial eigenfunctions p i i 1 then it must be either the x 1 jacobi or the x 1 laguerre sturm liouville problem a rodrigues type formula can be derived for both of the x 1 polynomial sequences

alternating minimization algorithm for speckle reduction with a shifting technique speckles multiplicative noise in synthetic aperture radar sar make it difficult to interpret the observed image due to the edge preserving feature of total variation tv variational models with tv regularization have attracted much interest in reducing speckles algorithms based on the augmented lagrangian function have been proposed to efficiently solve speckle reduction variational models with tv regularization however these algorithms require inner iterations or inverses involving the laplacian operator at each iteration in this paper we adapt tseng s alternating minimization algorithm with a shifting technique to efficiently remove the speckle without any inner iterations or inverses involving the laplacian operator the proposed method is very simple and highly parallelizable therefore it is very efficient to despeckle huge size sar images numerical results show that our proposed method outperforms the state of the art algorithms for speckle reduction variational models with a tv regularizer in terms of central processing unit time

exceptional orthogonal polynomials exactly solvable potentials and supersymmetry we construct two new exactly solvable potentials giving rise to bound state solutions to the schrodinger equation which can be written in terms of the recently introduced laguerre or jacobi type x1 exceptional orthogonal polynomials these potentials extending either the radial oscillator or the scarf i potential by the addition of some rational terms turn out to be translationally shape invariant as their standard counterparts and isospectral to them