oscillation caused by impulses the present paper is devoted to the investigation of the oscillation of a kind of very extensively studied second order nonlinear delay differential equations with impulses some interesting results are obtained which illustrate that impulses play a very important role in giving rise to the oscillations of equations

nonconvex sparse regularizer based speckle noise removal this paper focuses on the problem of speckle noise removal a new variational model is proposed for this task in the model a nonconvex regularizer rather than the classical convex total variation is used to preserve edges details of images the advantage of the nonconvex regularizer is pointed out in the sparse framework in order to solve the model a new fast iteration algorithm is designed in the algorithm to overcome the disadvantage of the nonconvexity of the model both the augmented lagrange multiplier method and the iteratively reweighted method are introduced to resolve the original nonconvex problem into several convex ones from the algorithm we can obtain restored images as well as edge indicator of the images comprehensive experiments are conducted to measure the performance of the algorithm in terms of visual evaluation and a variety of quantitative indices for the task of speckle noise removal

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

coupling image restoration and segmentation a generalized linear model bregman perspective we introduce a new class of data fitting energies that couple image segmentation with image restoration these functionals model the image intensity using the statistical framework of generalized linear models by duality we establish an information theoretic interpretation using bregman divergences we demonstrate how this formulation couples in a principled way image restoration tasks such as denoising deblurring deconvolution and inpainting with segmentation we present an alternating minimization algorithm to solve the resulting composite photometric geometric inverse problem we use fisher scoring to solve the photometric problem and to provide asymptotic uncertainty estimates we derive the shape gradient of our data fitting energy and investigate convex relaxation for the geometric problem we introduce a new alternating split bregman strategy to solve the resulting convex problem and present experiments and comparisons on both synthetic and real world images

primal and dual bregman methods with application to optical nanoscopy measurements in nanoscopic imaging suffer from blurring effects modeled with different point spread functions psf some apparatus even have psfs that are locally dependent on phase shifts additionally raw data are affected by poisson noise resulting from laser sampling and photon counts in fluorescence microscopy in these applications standard reconstruction methods em filtered backprojection deliver unsatisfactory and noisy results starting from a statistical modeling in terms of a map likelihood estimation we combine the iterative em algorithm with total variation tv regularization techniques to make an efficient use of a priori information typically tv based methods deliver reconstructed cartoon images suffering from contrast reduction we propose extensions to em tv based on bregman iterations and primal and dual inverse scale space methods in order to obtain improved imaging results by simultaneous contrast enhancement besides further generalizations of the primal and dual scale space methods in terms of general convex variational regularization methods we provide error estimates and convergence rates for exact and noisy data we illustrate the performance of our techniques on synthetic and experimental biological data

signal recovery with certain involved convex data fidelity constraints this paper proposes an optimization framework that can efficiently deal with convex data fidelity constraints onto which the metric projections are difficult to compute although such an involved data fidelity constraint is expected to play an important role in signal recovery under non gaussian noise contamination the said difficulty precludes existing algorithms from solving convex optimization problems with the constraint to resolve this dilemma we introduce a fixed point set characterization of involved data fidelity constraints based on a certain computable quasi nonexpansive mapping this characterization enables us to mobilize the hybrid steepest descent method to solve convex optimization problems with such a constraint the proposed framework can handle a variety of involved data fidelity constraints in a unified manner without geometric approximation to them in addition it requires no computationally expensive procedure such as operator inversion and inner loop as applications of the proposed framework we provide image restoration under several types of non gaussian noise contamination with illustrative examples

new oscillation criteria for forced second order half linear differential equations with damping abstract using variational principle and riccati technique new oscillation criteria for forced second order half linear differential equation with damped term are established which improve a recent paper by li and cheng w t li s s cheng an oscillation criterion for nonhomogenuous half linear differential equations appl math lett 15 2002 259 263 and generalized some of the results in the literature

a variational model for polsar data speckle reduction based on the wishart distribution in this paper we propose a variational model for polarimetric synthetic aperture radar polsar data speckle reduction which is based on the complex wishart distribution of the covariance or coherency matrix and multichannel total variation tv regularization defined for complex valued matrices by assuming the tv regularization to be a prior and taking the statistical distribution of the covariance matrix in each resolution element into account the variational model for polsar covariance data speckle suppression named wistv c is derived from the maximum a posteriori estimate a similar variational model for polsar coherency data speckle reduction named wistv t is also obtained as far as we know this is the first variational model for the whole polsar covariance or coherency matrix data despeckling since the model is nonconvex a convex relaxation iterative algorithm is designed to solve the variational problem based on the variable splitting and alternating minimization techniques experimental results on both simulated and real polsar data demonstrate that the proposed approach notably removes speckles in the extended uniform areas and meanwhile better preserves the spatial resolution the details such as edges and point scatterers and the polarimetric scattering characteristics compared with other methods

idempotent completion of triangulated categories we show that the idempotent completion of a triangulated category has a natural structure of a triangulated category the idempotent completion of the bounded derived category of an exact category gives the derived category of the idempotent completion in particular the derived category of an idempotent complete exact category is idempotent complete

a convex relaxation method for computing exact global solutions for multiplicative noise removal we propose a convex relaxation technique for computing global solutions for the nonconvex multiplicative noise model the method is based on functional lifting by introducing an additional dimension we employ a primal dual based gradient type algorithm in numerical implementations to overcome the nondifferentiability of the total variation term numerical results show that our algorithm is highly efficient furthermore global solutions of the original model can be obtained with no dependence on the initial guess

hochschild cohomology of abelian categories and ringed spaces this paper continues the development of the deformation theory of abelian categories introduced in a previous paper by the authors we show first that the deformation theory of abelian categories is controlled by an obstruction theory in terms of a suitable notion of hochschild cohomology for abelian categories we then show that this hochschild cohomology coincides with the one defined by gerstenhaber schack and swan in the case of module categories over diagrams and schemes and also with the hochschild cohomology for exact categories introduced recently by keller in addition we show in complete generality that hochschild cohomology satisfies a mayer vietoris property and that for constantly ringed spaces it coincides with the cohomology of the structure sheaf

oscillation of a forced super linear second order differential equation with impulses some oscillation criteria are established for a forced super linear second order differential equation with impulses those results extend some well known results for the equation without impulses which are different from most existing ones in that they are based only on information on a sequence of subintervals of t 0 rather than on the whole half linear interval

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

speckle reduction via higher order total variation approach multiplicative noise also known as speckle reduction is a prerequisite for many image processing tasks in coherent imaging systems such as the synthetic aperture radar one approach extensively used in this area is based on total variation tv regularization which can recover significantly sharp edges of an image but suffers from the staircase like artifacts in order to overcome the undesirable deficiency we propose two novel models for removing multiplicative noise based on total generalized variation tgv penalty the tgv regularization has been mathematically proven to be able to eliminate the staircasing artifacts by being aware of higher order smoothness furthermore an efficient algorithm is developed for solving the tgv based optimization problems numerical experiments demonstrate that our proposed methods achieve state of the art results both visually and quantitatively in particular when the image has some higher order smoothness our methods outperform the tv based algorithms

triangulated categories without models we exhibit examples of triangulated categories which are neither the stable category of a frobenius category nor a full triangulated subcategory of the homotopy category of a stable model category even more drastically our examples do not admit any non trivial exact functors to or from these algebraic respectively topological triangulated categories

efficient multiplicative noise removal method using isotropic second order total variation to overcome and reduce the undesirable staircase effect commonly met in the total variation tv regularization based multiplicative noise removal methods a novel multiplicative noise removal model based on isotropic second order total variation isotv is proposed under the maximum a posteriori map framework under the spectral decomposition framework the isotv is first transformed into an equivalent formulation as a novel weighted l 1 l 2 mixed norm of the second order image derivatives then an efficient alternating iterative algorithm is designed to solve the proposed model finally we prove in detail the convergence of the proposed algorithm a set of experiments on both standard and medical images show that the proposed isotv method yields state of the art results both in terms of peak signal to noise ratio psnr and image perception quality specifically the proposed isotv method can better reduce the staircase effect and preserve image edges more sharpness with medical applications

analysis of a new variational model for multiplicative noise removal in this paper we consider a new variational model for multiplicative noise removal we prove the existence and uniqueness of the minimizer for the variational problem furthermore we derive the existence and uniqueness of weak solutions for the associated evolution equation finally some numerical experiments are shown to compare the proposed model with the model given by aubert and aujol

a nonlocal tv based variational method for polsar data speckle reduction in this paper we propose a nonlocal total variation nltv based variational model for polarimetric synthetic aperture radar polsar data speckle reduction this model named wisnltv is obtained based on the wishart fidelity term and the nltv regularization defined for the complex valued fourth order tensor data since the proposed model is non convex an equivalent bi convex model is obtained using the property of conjugate functions then an efficient iteration algorithm is developed to solve the equivalent bi convex model based on the alternating minimization and the forward backward operator splitting technique the proposed iteration algorithm is proved to be convergent under certain conditions theoretically and numerically experimental results on both synthetic and real polsar data demonstrate that the proposed method can effectively reduce speckle noise and meanwhile better preserve the details and the repetitive structures such as textures and edges and the polarimetric scattering characteristics compared with the other methods

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

an improved variational model for denoising magnetic resonance images abstract this paper presents an improved variational model for denoising mr images degraded by rician noise an additional data fidelity based on image gradient is introduced which can retain more details and edges in this model an automatic estimation of standard deviation of rician noise is designed to enhance the quality of denoised results the alternating direction method of multipliers admm is adopted to implement numerical schedule and gains the robust solution experimental results demonstrate that the proposed method is efficient and has better denoising capability than the state of the art models

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 doubly degenerate diffusion equation in multiplicative noise removal models abstract in this paper we consider the neumann problem of a doubly degenerate diffusion equation which is proposed to deal with multiplicative noise we prove the existence and the extremum principle of weak solutions for the problem

interval criteria for oscillation of second order linear ordinary differential equations abstract new oscillation criteria are established for the equation py qy 0 that are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of t 0 rather than on the whole half line our results are more natural according to the sturm separation theorem and sharper than some previous results and can be applied to extreme cases such as t 0 q t dt

interval oscillation criteria for second order forced impulsive differential equations with mixed nonlinearities abstract in this paper by arithmetic geometric mean inequality and riccati transformation interval oscillation criteria are established for second order forced impulsive differential equation with mixed nonlinearities of the form r t x t p 0 t x t i 1 n p i t i x t e t t k x k a k x k x k b k x k where t t 0 k n u u 1 u k is the impulse moments sequence with 0 t 0 0 1 2 k and lim k k p q p q are odds and the exponents satisfy 1 m m 1 n 0 some known results are generalized and improved examples are also given to illustrate the effectiveness and non emptiness of our results

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

the first obstructions to enhancing a triangulated category in this paper we relate triangulated category structures to the cohomology of small categories and define initial obstructions to the existence of an algebraic or topological enhancement we show that these obstructions do not vanish in an example of triangulated category without models we also obtain cohomological characterizations of pre triangulated dg a infinity and spectral categories

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

higher order regularization based image restoration with automatic regularization parameter selection abstract poisson and multiplicative rayleigh noises often appear in medical imaging such as x ray images positron emission tomography and ultrasound images in this study we propose novel variational models for removing poisson multiplicative rayleigh noise we make use of hybrid higher order total variation as the regularization terms of our proposed models to eliminate staircasing artifacts we also adopt the spatially adaptive parameter technique to adequately smooth homogenous regions while preserving the edges the spatially adaptive parameter selection is closely related to local constraints through a local expected value estimator we provide a convergence analysis including the existence and uniqueness of solution and the first order optimality conditions we apply the alternating direction method of multipliers for solving the proposed models numerical experiments demonstrate that our models exhibit a better performance than that of state of the art models in terms of edge preservation smoothness of the homogenous regions and various quality measures

cauchy noise removal by nonlinear diffusion equations abstract this paper focuses on the problem of image restoration under cauchy noise the variational method which constructs the data fidelity term involving the cauchy distribution by map estimator has been proven to be a successful approach in this paper a nonlinear diffusion equation is proposed to deal with it the main ingredients of the proposed equation are a gray level based diffusivity that estimates the amplitude of the noise and a classical gradient based diffusivity that controls the anisotropic diffusion according to the image s local structure the proposed equation has the nondivergence form and its properties including the existence uniqueness and stability of solutions are established by the notion of viscosity solution experimental results show the superiority of the proposed equation over variational methods in restoring small details of images

a new variational approach for restoring images with multiplicative noise this paper proposes a novel variational model for restoration of images corrupted with multiplicative noise it combines a fractional order total variational filter with a high order pde laplacian norm the combined approach is able to preserve edges while avoiding the blocky effect in smooth regions this strategy minimizes a certain energy subject to a fitting term derived from a maximum a posteriori map semi implicit gradient descent scheme is applied to efficiently finding the minimizer of the proposed functional to improve the numerical results we opt for an adaptive regularization parameter selection procedure for the proposed model by using the trial and error method the existence and uniqueness of a solution to the proposed variational model is established in this study parameter dependence is also discussed experimental results demonstrate the effectiveness of the proposed model in visual improvement as well as an increase in the peak signal to noise ratio comparing to corresponding pde methods

multiplicative noise removal via using nonconvex regularizers based on total variation and wavelet frame abstract total variation based regularization and wavelet frame based regularization are two different methods for image restoration moreover nonconvex regularization has advantages over convex regularization for preserving edges in images in this paper a variational model consisting of two nonconvex regularizers based respectively on total variation and wavelet frame is proposed for multiplicative noise removal the proposed model combines the advantages of the nonconvex regularization and the hybrid regularization so it can more effectively preserve edges and details in images than any single regularization can the alternating minimization method is proposed to solve the novel model although the corresponding minimization problem is nonconvex the convexity of all subproblems is guaranteed under some mild conditions therefore we study the convergence property of the algorithm numerical experiments have proved that the proposed model with the corresponding algorithm outperforms some state of the art models in terms of the peak signal to noise ratio and the relative error of the restored images

overlapping domain decomposition methods for total variation denoising alternating and parallel overlapping domain decomposition methods for the minimization of the total variation are presented their derivation is based on the predual formulation of the total variat

oscillation criteria for second order nonlinear differential equations with impulses abstract the present paper is devoted to the investigation of the oscillatory behavior of a kind of extensively studied second order nonlinear delay differential equations with impulses some interesting results are obtained which illustrate that impulses play a very important role in giving rise to the oscillations of equations

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

noise level estimation for natural images based on scale invariant kurtosis and piecewise stationarity noise level estimation is crucial in many image processing applications such as blind image denoising in this paper we propose a novel noise level estimation approach for natural images by jointly exploiting the piecewise stationarity and a regular property of the kurtosis in bandpass domains we design a k means based algorithm to adaptively partition an image into a series of non overlapping regions each of whose clean versions is assumed to be associated with a constant but unknown kurtosis throughout scales the noise level estimation is then cast into a problem to optimally fit this new kurtosis model in addition we develop a rectification scheme to further reduce the estimation bias through noise injection mechanism extensive experimental results show that our method can reliably estimate the noise level for a variety of noise types and outperforms some state of the art techniques especially for non gaussian noises

multiplicative noise and blur removal by framelet decomposition and l_ 1 based l curve method this paper proposes a framelet based convex optimization model for multiplicative noise and blur removal problem the main idea is to employ framelet expansion to represent the original image and use the variable decomposition to solve the problem because of the nature of multiplicative noise we decompose the observed data into the original image variable and the noise variable to obtain the resulting model the original image variable is represented by framelet and it is determined by using l 1 norm in the selection and shrinkage of framelet coefficients the noise variable is measured by using the mean and the variance of the underlying probability distribution this framelet setting can be applied to analysis synthesis and balanced approaches and the resulting optimization models are convex such that they can be solved very efficiently by the alternating direction of a multiplier method an another contribution of this paper is to propose to select the regularization parameter by using the l 1 based l curve method for these framelet based models numerical examples are presented to illustrate the effectiveness of these models and show that the performance of the proposed method is better than that by the existing methods

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

sar image regularization with fast approximate discrete minimization synthetic aperture radar sar images like other coherent imaging modalities suffer from speckle noise the presence of this noise makes the automatic interpretation of images a challenging task and noise reduction is often a prerequisite for successful use of classical image processing algorithms numerous approaches have been proposed to filter speckle noise markov random field mrf modelization provides a convenient way to express both data fidelity constraints and desirable properties of the filtered image in this context total variation minimization has been extensively used to constrain the oscillations in the regularized image while preserving its edges speckle noise follows heavy tailed distributions and the mrf formulation leads to a minimization problem involving nonconvex log likelihood terms such a minimization can be performed efficiently by computing minimum cuts on weighted graphs due to memory constraints exact minimization although theoretically possible is not achievable on large images required by remote sensing applications the computational burden of the state of the art algorithm for approximate minimization namely the alpha expansion is too heavy specially when considering joint regularization of several images we show that a satisfying solution can be reached in few iterations by performing a graph cut based combinatorial exploration of large trial moves this algorithm is applied to joint regularization of the amplitude and interferometric phase in urban area sar images

a new nonconvex approach for image restoration with gamma noise abstract in this paper a new total generalized variational tgv model for restoring images with multiplicative noise is proposed which contains a nonconvex fidelity term and a tgv term we use a difference of convex functions algorithm dca to deal with the proposed model for multiplicative noise removal there exist many models and algorithms most of which focus on convex approximation so that numerical algorithms with guaranteed convergence can be designed unlike these algorithms we use the dca algorithm to remove multiplicative noise by numerical experiments it is shown that the proposed approach leads to a better solution compared with the gradient projection algorithm for solving the classic multiplicative noise removal models we prove that the sequence generated by the dca algorithm converges to a stationary point which satisfies the first order optimality condition finally we demonstrate the performance of our whole scheme by numerical examples a comparison with other methods is provided as well numerical results demonstrate that the proposed algorithm significantly outperforms some previous methods for multiplicative gamma noise removal

rank minimization with applications to image noise removal abstract rank minimization problem has a wide range of applications in different areas however since this problem is np hard and non convex the frequently used method is to replace the matrix rank minimization with nuclear norm minimization nuclear norm is the convex envelope of the matrix rank and it is more computationally tractable matrix completion is a special case of rank minimization problem in this paper we consider directly using matrix rank as the regularization term instead of nuclear norm in the cost function for matrix completion problem the solution is analyzed and obtained by a hard thresholding operation on the singular values of the observed matrix then by exploiting patch based nonlocal self similarity scheme we apply the proposed rank minimization algorithm to remove white gaussian additive noise in images gamma multiplicative noise is also removed in logarithm domain the experimental results illustrate that the proposed algorithm can remove noises in images more efficiently than nuclear norm can do and the results are also competitive with those obtained by using the existing state of the art noise removal methods in the literature

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

adapting to unknown smoothness via wavelet shrinkage abstract we attempt to recover a function of unknown smoothness from noisy sampled data we introduce a procedure sureshrink that suppresses noise by thresholding the empirical wavelet coefficients the thresholding is adaptive a threshold level is assigned to each dyadic resolution level by the principle of minimizing the stein unbiased estimate of risk sure for threshold estimates the computational effort of the overall procedure is order n log n as a function of the sample size n sureshrink is smoothness adaptive if the unknown function contains jumps then the reconstruction essentially does also if the unknown function has a smooth piece then the reconstruction is essentially as smooth as the mother wavelet will allow the procedure is in a sense optimally smoothness adaptive it is near minimax simultaneously over a whole interval of the besov scale the size of this interval depends on the choice of mother wavelet we know from a previous paper by the authors that traditional smoot

oscillation criteria for a forced mixed type emden fowler equation with impulses some oscillation criteria for a forced mixed type emden fowler equation with impulses are given when the impulses are dropped our results extend those of sun and meng y g sun f w meng interval criteria for oscillation of second order differential equations with mixed nonlinearities appl math comput 15 2008 375 381 sun and wong y g sun j s w wong oscillation criteria for second order forced ordinary differential equations with mixed nonlinearities j math anal appl 334 2007 549 560 for second order forced ordinary differential equation with mixed nonlinearities nasr a h nasr sufficient conditions for the oscillation of forced superlinear second order differential equations with oscillatory potential proc am math soc 126 1998 123 125 yang q yang interval oscillation criteria for a forced second order nonlinear ordinary differential equations with oscillatory potential appl math comput 135 2003 49 64 for forced superlinear emden fowler equation kong q kong interval criteria for oscillation of second order linear differential equations j math anal appl 229 1999 483 492 for unforced second order linear differential equations and wong j s w wong oscillation criteria for a forced second order linear differential equation j math anal appl 231 1999 235 240 for forced second order linear differential equation

multiplicative noise removal via a learned dictionary multiplicative noise removal is a challenging image processing problem and most existing methods are based on the maximum a posteriori formulation and the logarithmic transformation of multiplicative denoising problems into additive denoising problems sparse representations of images have shown to be efficient approaches for image recovery following this idea in this paper we propose to learn a dictionary from the logarithmic transformed image and then to use it in a variational model built for noise removal extensive experimental results suggest that in terms of visual quality peak signal to noise ratio and mean absolute deviation error the proposed algorithm outperforms state of the art methods

forced oscillations for second order delay differential equations with impulses this paper is devoted to the study of the oscillations for forced second order delay differential equations with impulses the results gained here are based on the information of the forcing term on a sequence of subintervals of t 0 which develops some well known results for the equations without impulses and the equations without delay

on oscillation of a second order impulsive linear delay differential equation abstract for the delay differential equation x t k 1 m a k t x g k t 0 g k t t with impulsive conditions x j a j x j 0 x j b j x j 0 a connection between the following properties is established nonoscillation of the differential equation and the corresponding differential inequality positiveness of the fundamental function and the existence of a solution of a generalized riccati inequality explicit conditions for nonoscillation and oscillation and comparison theorems are presented

interval oscillation criteria for nonlinear impulsive delay differential equations with damping term in this paper a class of second order nonlinear impulsive delay differential equations with damping term is studied three factors impulse delay and damping that affect the interval qualitative properties of solutions of equations are taken into account together several interval oscillation criteria which generalize some known ones such as in huang and feng 2010 xing and zheng 2008 and liu and xu 2007 are established moreover examples are also given to illustrate the effectiveness and non emptiness of our results

minimax and minimax adaptive estimation in multiplicative regression locally bayesian approach this paper deals with the non parametric estimation in the regression with the multiplicative noise using the local polynomial fitting and the bayesian approach we construct the minimax on isotropic holder class estimator next applying lepski s method we propose an estimator which is optimally adaptive over the collection of isotropic holder classes to prove the optimality of the proposed procedure we establish in particular the exponential inequality for the deviation of locally bayesian estimator since the parameter estimated these theoretical results are illustrated by simulation study

interval oscillation criteria for second order quasi linear nonhomogeneous differential equations with damping by using two inequalities due to holder and hardy littlewood and polya as well as averaging functions several interval oscillation criteria are established for the second order quasi linear differential equation with forced term of the form r t y t a 1y t p t y t a 1y t q t y t b 1y t e t that are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of t 0 rather than on the whole half line where b a 0 our results make use of the oscillatory properties of the forcing term and extend a recent result which is obtained by means of a picone identity

uniqueness of enhancement for triangulated categories the paper contains general results on the uniqueness of a dg enhancement for trian gulated categories as a consequence we obtain such uniqueness for the unbounded categories of quasi coherent sheaves for the triangulated categories of perfect complexes and for the bounded de rived categories of coherent sheaves on quasi projective schemes if a scheme is projective then we also prove a strong uniqueness for the triangulated category of perfect complexes and for the bounded de rived categories of coherent sheaves these results directly imply that fully faithful functors from the bounded derived categories of coherent sheaves and the triangulated categories of perfect complexes on projective schemes can be represented by objects on the product

variational image segmentation model coupled with image restoration achievements image segmentation and image restoration are two important topics in image processing with a number of important applications in this paper we propose a new multiphase segmentation model by combining image restoration and image segmentation models utilizing aspects of image restoration the proposed segmentation model can effectively and robustly tackle images with a high level of noise or blurriness missing pixels or vector values in particular one of the most important segmentation models the piecewise constant mumford shah model can be extended easily in this way to segment gray and vector valued images corrupted for example by noise blur or information loss after coupling a new data fidelity term which borrowed from the field of image restoration it can be solved efficiently using the alternating minimization algorithm and we prove the convergence of this algorithm with three variables under mild conditions experiments on many synthetic and real world images demonstrate that our method gives better segmentation results in terms of quality and quantity in comparison to other state of the art segmentation models especially for blurry images and those with information loss highlightsprovide a new methodology and a new model for multiphase image segmentation extend the piecewise constant mumford shah model to handle blurry case easily has the ability to segment images with gaussian poisson and impulsive noises effective in segmenting vector valued image and image observed with information loss the convergence of the am algorithm with three variables adopted is proved

a doubly degenerate diffusion model based on the gray level indicator for multiplicative noise removal multiplicative noise removal is a challenging task in image processing inspired by the impressive performance of nonlinear diffusion models in additive noise removal we address this problem in the view of nonlinear diffusion equation theories rather than the traditional variation methods we develop a nonlinear diffusion filter denoising framework which considers not only the information of the gradient of the image but also the information of gray levels of the image furthermore under this framework we propose a doubly degenerate diffusion model for multiplicative noise removal which is analyzed with respect to some of its properties and behavior in denoising process in numerical aspects we present an efficient scheme which uses a stabilization by fast explicit diffusion for the implementation of the multiplicative noise removal model finally the experimental results illustrate effectiveness and efficiency of the proposed model

restoration of poissonian images using alternating direction optimization much research has been devoted to the problem of restoring poissonian images namely for medical and astronomical applications however the restoration of these images using state of the art regularizers such as those based upon multiscale representations or total variation is still an active research area since the associated optimization problems are quite challenging in this paper we propose an approach to deconvolving poissonian images which is based upon an alternating direction optimization method the standard regularization or maximum a posteriori map restoration criterion which combines the poisson log likelihood with a nonsmooth convex regularizer log prior leads to hard optimization problems the log likelihood is nonquadratic and nonseparable the regularizer is nonsmooth and there is a nonnegativity constraint using standard convex analysis tools we present sufficient conditions for existence and uniqueness of solutions of these optimization problems for several types of regularizers total variation frame based analysis and frame based synthesis we attack these problems with an instance of the alternating direction method of multipliers admm which belongs to the family of augmented lagrangian algorithms we study sufficient conditions for convergence and show that these are satisfied either under total variation or frame based analysis and synthesis regularization the resulting algorithms are shown to outperform alternative state of the art methods both in terms of speed and restoration accuracy

realizability of modules over tate cohomology let k be a field and let g be a finite group there is a canonical element in the hochschild cohomology of the tate cohomology g hh 3 h1 h g k with the following property given a graded h g k module x the image of g in ext 3 1 h g k x x vanishes if and only if x is isomorphic to a direct summand of h g m for some kg module m the description of the realizability obstruction works in any triangulated category with direct sums we show that in the case of the derived category of a differential graded algebra a there is also a canonical element of hochschild cohomology hh 3 1 h a which is a predecessor for these obstructions

a convex total generalized variation regularized model for multiplicative noise and blur removal multiplicative noise and blur corruptions usually happen in coherent imaging systems such as the synthetic aperture radar total variation regularized multiplicative noise and blur removal models have been widely studied in the literature which can preserve sharp edges of the recovered images however the images recovered from the total variation based models usually suffer from staircase effects to overcome this deficiency we propose a total generalized variation regularized convex optimization model the resulting objective function involves the total generalized variation regularization term the map based data fitting term and a quadratic penalty term which is based on the statistical property of the noise indeed the map estimated data fitting term in the multiplicative noise and blur removal model is nonconvex under a mild condition the quadratic penalty term makes the objective function convex a primal dual algorithm is developed to solve the minimization problem numerical experiments show that the proposed method outperforms some state of the art methods

a hybrid optimization method for multiplicative noise and blur removal the main contribution of this paper is to propose a new hybrid optimization method for the multiplicative noise and blur removal problem a degraded image can often be recovered efficiently by minimizing an objective function which consists of a data fidelity term and a regularization term in the paper we apply the quadratic penalty function method combined with the alternating direction method to minimize the corresponding objective function numerical experiments are presented to demonstrate the effectiveness of the proposed method experimental results illustrate the state of the art performance of the proposed method to handle multiplicative noise and blur removal problem

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