image denoising with edge preserving and segmentation based on mask nha in this paper we propose a zero mean white gaussian noise removal method using a high resolution frequency analysis it is difficult to separate an original image component from a noise component when using discrete fourier transform or discrete cosine transform for analysis because sidelobes occur in the results the 2d non harmonic analysis 2d nha is a high resolution frequency analysis technique that improves noise removal accuracy because of its sidelobe reduction feature however spectra generated by nha are distorted because of which the signal of the image is non stationary in this paper we analyze each region with a homogeneous texture in the noisy image non uniform regions that occur due to segmentation are analyzed by an extended 2d nha method called mask nha we conducted an experiment using a simulation image and found that mask nha denoising attains a higher peak signal to noise ratio psnr value than the state of the art methods if a suitable segmentation result can be obtained from the input image even though parameter optimization was incomplete this experimental result exhibits the upper limit on the value of psnr in our mask nha denoising method the performance of mask nha denoising is expected to approach the limit of psnr by improving the segmentation method

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

generalized pooling for robust object tracking feature pooling in a majority of sparse coding based tracking algorithms computes final feature vectors only by low order statistics or extreme responses of sparse codes the high order statistics and the correlations between responses to different dictionary items are neglected we present a more generalized feature pooling method for visual tracking by utilizing the probabilistic function to model the statistical distribution of sparse codes since immediate matching between two distributions usually requires high computational costs we introduce the fisher vector to derive a more compact and discriminative representation for sparse codes of the visual target we encode target patches by local coordinate coding utilize gaussian mixture model to compute fisher vectors and finally train semi supervised linear kernel classifiers for visual tracking in order to handle the drifting problem during the tracking process these classifiers are updated online with current tracking results the experimental results on two challenging tracking benchmarks demonstrate that the proposed approach achieves a better performance than the state of the art tracking algorithms

dirichlet series and the integrability of multilinear differential equations we explore the relationship between the integrability of nonsemilinear partial differential equations and formal dirichlet series solutions to this end we consider a variety of integrable and nonintegrable differential equations we also demonstrate that such series solutions are a natural extension to the nonlinear case of those obtained by basic solution techniques for linear ordinary differential equations

the non local delta problem and 2 1 dimensional soliton equations a method of constructing 2 1 dimensional non linear integrable equations and their solutions by means of the non local delta problem is developed a basic set of equations is obtained by using different normalisations of the non local delta problem and the lagrangian of the set is found other integrable equations which are degenerate cases of the basic set are also lagrangian

on the link between umbilic geodesics and soliton solutions of nonlinear pdes in this paper we describe a new class of soliton solutions called umbilic solitons for certain nonlinear integrable pdes these umbilic solitons have the property that as the space variable x tends to infinity the solution tends to a periodic wave and as x tends to minus infinity it tends to a phase shifted wave of the same shape the equations admitting solutions in this new class include the dym equation and equations in its hierarchy the methods used to find and analyse these solutions are those of algebraic and complex geometry we look for classes of solutions by constructing associated finite dimensional integrable hamiltonian systems on riemann surfaces in particular in this setting we use geodesics on n dimensional quadrics to find the spatial or x flow which together with the commuting t flow given by the equation itself defines new classes of solutions amongst these geodesics particularly interesting ones are the umbilic geodesics which then generate the class of umbilic soliton solutions this same setting also enables us to introduce another class of solutions of dym like equations which are related to elliptic and umbilic billiards

multidimensional hierarchies of 1 1 dimensional integrable partial differential equations nonsymmetric dressing in this paper the problem has been constructed for a class of multidimensional integrable partial differential equations pde which can be classified as the multidimensional hierarchies of the 1 1 dimensional systems of integrable pde we introduce the nonsymmetric dressing procedure for this purpose among the examples we consider the n 1 dimensional n 1 hierarchies of nonlinear schrodinger modified korteveg de vries and camassa holm equations

fast and robust object tracking via probability continuous outlier model this paper presents a novel visual tracking method based on linear representation first we present a novel probability continuous outlier model pcom to depict the continuous outliers within the linear representation model in the proposed model the element of the noisy observation sample can be either represented by a principle component analysis subspace with small guassian noise or treated as an arbitrary value with a uniform prior in which a simple markov random field model is adopted to exploit the spatial consistency information among outliers or inliners then we derive the objective function of the pcom method from the perspective of probability theory the objective function can be solved iteratively by using the outlier free least squares and standard max flow min cut steps finally for visual tracking we develop an effective observation likelihood function based on the proposed pcom method and background information and design a simple update scheme both qualitative and quantitative evaluations demonstrate that our tracker achieves considerable performance in terms of both accuracy and speed

sparse geometric image representations with bandelets this paper introduces a new class of bases called bandelet bases which decompose the image along multiscale vectors that are elongated in the direction of a geometric flow this geometric flow indicates directions in which the image gray levels have regular variations the image decomposition in a bandelet basis is implemented with a fast subband filtering algorithm bandelet bases lead to optimal approximation rates for geometrically regular images for image compression and noise removal applications the geometric flow is optimized with fast algorithms so that the resulting bandelet basis produces minimum distortion comparisons are made with wavelet image compression and noise removal algorithms

new tight frames of curvelets and optimal representations of objects with piecewise c2 singularities this paper introduces new tight frames of curvelets to address the problem of finding optimally sparse representations of objects with discontinuities along piecewise c 2 edges conceptually the curvelet transform is a multiscale pyramid with many directions and positions at each length scale and needle shaped elements at fine scales these elements have many useful geometric multiscale features that set them apart from classical multiscale representations such as wavelets for instance curvelets obey a parabolic scaling relation which says that at scale 2 j each element has an envelope that is aligned along a ridge of length 2 j 2 and width 2 j we prove that curvelets provide an essentially optimal representation of typical objects f that are c 2 except for discontinuities along piecewise c 2 curves such representations are nearly as sparse as if f were not singular and turn out to be far more sparse than the wavelet decomposition of the object for instance the n term partial reconstruction f c n obtained by selecting the n largest terms in the curvelet series obeys f f c n 2 l2 c n 2 log n 3 n this rate of convergence holds uniformly over a class of functions that are c 2 except for discontinuities along piecewise c 2 curves and is essentially optimal in comparison the squared error of n term wavelet approximations only converges as n 1 as n which is considerably worse than the optimal behavior

geometry based demosaicking demosaicking is a particular case of interpolation problems where from a scalar image in which each pixel has either the red the green or the blue component we want to interpolate the full color image state of the art demosaicking algorithms perform interpolation along edges but these edges are estimated locally we propose a level set based geometric method to estimate image edges inspired by the image in painting literature this method has a time complexity of o s where s is the number of pixels in the image and compares favorably with the state of the art algorithms both visually and in most relevant image quality measures

differentiation of discrete multidimensional signals we describe the design of finite size linear phase separable kernels for differentiation of discrete multidimensional signals the problem is formulated as an optimization of the rotation invariance of the gradient operator which results in a simultaneous constraint on a set of one dimensional low pass prefilter and differentiator filters up to the desired order we also develop extensions of this formulation to both higher dimensions and higher order directional derivatives we develop a numerical procedure for optimizing the constraint and demonstrate its use in constructing a set of example filters the resulting filters are significantly more accurate than those commonly used in the image and multidimensional signal processing literature

multiple positive solutions for a coupled nonlinear hartree type equations with perturbations abstract in this paper we study the existence of multiple nontrivial solutions of coupled nonlinear hartree equations with perturbations this type of equations was used to describe the multi component bose einstein condensates and the basic quantum chemistry model of small number of electrons interacting with static nuclei by combining the nehari constraint and minimax methods we prove the existence of two nontrivial solutions of the equations

image denoising via sparse and redundant representations over learned dictionaries we address the image denoising problem where zero mean white and homogeneous gaussian additive noise is to be removed from a given image the approach taken is based on sparse and redundant representations over trained dictionaries using the k svd algorithm we obtain a dictionary that describes the image content effectively two training options are considered using the corrupted image itself or training on a corpus of high quality image database since the k svd is limited in handling small image patches we extend its deployment to arbitrary image sizes by defining a global image prior that forces sparsity over patches in every location in the image we show how such bayesian treatment leads to a simple and effective denoising algorithm this leads to a state of the art denoising performance equivalent and sometimes surpassing recently published leading alternative denoising methods

exact multiplicity of positive solutions for a class of semilinear problem ii we consider the positive solutions to the semilinear problem u f u 0 in b n u 0 on b n where bn is the unit ball in rn n 1 and is a positive parameter it is well known that if is a smooth function then any positive solution to the equation is radially symmetric and all solutions can be parameterized by their maximum values we develop a unified approach to obtain the exact multiplicity of the positive solutions for a wide class of nonlinear functions u and the precise shape of the global bifurcation diagrams are rigorously proved our technique combines the bifurcation analysis stability analysis and topological methods we show that the shape of the bifurcation curve depends on the shape of the graph of function u u as well as the growth rale of

an mdl framework for sparse coding and dictionary learning the power of sparse signal modeling with learned overcomplete dictionaries has been demonstrated in a variety of applications and fields from signal processing to statistical inference and machine learning however the statistical properties of these models such as underfitting or overfitting given sets of data are still not well characterized in the literature as a result the success of sparse modeling depends on hand tuning critical parameters for each data and application this work aims at addressing this by providing a practical and objective characterization of sparse models by means of the minimum description length mdl principle a well established information theoretic approach to model selection in statistical inference the resulting framework derives a family of efficient sparse coding and dictionary learning algorithms which by virtue of the mdl principle are completely parameter free furthermore such framework allows to incorporate additional prior information to existing models such as markovian dependencies or to define completely new problem formulations including in the matrix analysis area in a natural way these virtues will be demonstrated with parameter free algorithms for the classic image denoising and classification problems and for low rank matrix recovery in video applications however the framework is not limited to this imaging data and can be applied to a wide range of signal and data types and tasks

the nehari manifold for elliptic equation involving the square root of the laplacian abstract in this paper we introduce the nehari manifold for elliptic problems involving the square root of the laplacian we use it to establish the existence of solutions and multiple solutions for some nonlinear elliptic problem with sign changing weight we also establish some bifurcation results and non existence results

learning descriptive visual representation for image classification and annotation abstract this paper presents a novel semantic regularized matrix factorization method for learning descriptive visual bag of words bow representation although very influential in image classification the traditional visual bow representation has one distinct drawback that is for efficiency purposes this visual representation is often generated by directly clustering the low level visual feature vectors extracted from local keypoints or regions without considering the high level semantics of images in other words it still suffers from the semantic gap and may lead to significant performance degradation in more challenging tasks e g image classification over social collections with large intra class variations to learn descriptive visual bow representation for such image classification task we develop a semantic regularized matrix factorization method by adding laplacian regularization defined with the tags easy to access of social images into matrix factorization moreover given that image annotation only provides the tags of training images in advance while the tags of all social images are available we can readily apply the proposed method to image annotation by first running a round of image annotation to predict the tags maybe incorrect of test images and thus obtaining the tags of all images experimental results show the promising performance of the proposed method

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

multiple positive solutions for semilinear elliptic equations involving multi singular inverse square potentials and concave convex nonlinearities abstract in this paper we deal with the existence and multiplicity of positive solutions for the multi singular semilinear elliptic equations u i 1 k i x a i 2 u u 2 2 u u q 2 u x where r n n 3 is a smooth bounded domain such that the points a i i 1 2 k k 2 are different 0 i n 2 2 2 0 1 q 2 and 2 2 n n 2 the results depend crucially on the parameters q and i for i 1 2 k

wedgelets nearly minimax estimation of edges we study a simple horizon model for the problem of recovering an image from noisy data in this model the image has an edge with fi holder regularity adopting the viewpoint of computational harmonic analysis we develop an overcomplete collection of atoms called wedgelets dyadically organized indicator functions with a variety of locations scales and orientations the wedgelet representation provides nearly optimal representations of objects in the horizon model as measured by minimax description length we show how to rapidly compute a wedgelet approximation to noisy data by flnding a special edgelet decorated recursive partition which minimizes a complexity penalized sum of squares this estimate using su cient sub pixel resolution achieves nearly the minimax mean squared error in the horizon model in fact the method is adaptive in the sense that it achieves nearly the minimax risk for any value of the unknown degree of regularity of the horizon 1 fi 2 wedgelet analysis and de noising may be used successfully outside the horizon model we study images modelled as indicators of star shaped sets with smooth bound aries and show that complexity penalized wedgelet partitioning achieves nearly the minimax risk in that setting also

the design and use of steerable filters the authors present an efficient architecture to synthesize filters of arbitrary orientations from linear combinations of basis filters allowing one to adaptively steer a filter to any orientation and to determine analytically the filter output as a function of orientation steerable filters may be designed in quadrature pairs to allow adaptive control over phase as well as orientation the authors show how to design and steer the filters and present examples of their use in the analysis of orientation and phase angularly adaptive filtering edge detection and shape from shading one can also build a self similar steerable pyramid representation the same concepts can be generalized to the design of 3 d steerable filters

extended compressed tracking via random projection based on msers and online ls svm learning the compressed tracking algorithm ct tracker is a well known visual tracking method that models a target object s appearance through sparse random projection however the tracking results are not stable and robust due to the randomness of random projection to solve this problem a more stable and robust approach is proposed for visual tracking based on maximally stable extremal regions msers sparse random projection and online least squares svm classifier ls svm learning to obtain a relatively stable appearance model the stable connected components of an object based on msers in image feature space are extracted with the fusion of msers and sparse random projection we model adaptive object appearance to adapt the variation of appearance additionally an online closed form ls svm is employed to quickly and robustly predict the target object location in a tracking by detection framework experimental results on benchmark sequences show the stability and robustness of the proposed algorithm compared with the existing ct based trackers and other state of the art trackers highlightsa more stable and robust approach is proposed for visual tracking relying on maximally stable extremal regions msers sparse random projection and online least squares svm classifier ls svm learning with the fusion of msers and sparse random projection the stable adaptive object appearance is modeled to adapt the variation of appearance an online closed form ls svm is employed to quickly and robustly predict the target object location

patch based near optimal image denoising in this paper we propose a denoising method motivated by our previous analysis of the performance bounds for image denoising insights from that study are used here to derive a high performance practical denoising algorithm we propose a patch based wiener filter that exploits patch redundancy for image denoising our framework uses both geometrically and photometrically similar patches to estimate the different filter parameters we describe how these parameters can be accurately estimated directly from the input noisy image our denoising approach designed for near optimal performance in the mean squared error sense has a sound statistical foundation that is analyzed in detail the performance of our approach is experimentally verified on a variety of images and noise levels the results presented here demonstrate that our proposed method is on par or exceeding the current state of the art both visually and quantitatively

bounding multiple gaussians uncertainty with application to object tracking this paper proves the uncertainty bound for the multiple gaussian functions termed multiple gaussians uncertainty mgu which significantly generalizes the uncertainty principle for the single gaussian function first as a theoretical contribution we prove that the momentum velocity and position for the sum of multiple gaussians wave function are theoretically bounded second as for a practical application we show that the bound can be well exploited for object tracking to detect anomalies of local movement in an online learning framework by integrating mgu with a given object tracker we demonstrate that uncertainty principle can provide remarkable robustness in tracking extensive experiments are done to show that the proposed mgu can significantly help base trackers overcome the object drifting and reach state of the art results

image denoising using scale mixtures of gaussians in the wavelet domain we describe a method for removing noise from digital images based on a statistical model of the coefficients of an overcomplete multiscale oriented basis neighborhoods of coefficients at adjacent positions and scales are modeled as the product of two independent random variables a gaussian vector and a hidden positive scalar multiplier the latter modulates the local variance of the coefficients in the neighborhood and is thus able to account for the empirically observed correlation between the coefficient amplitudes under this model the bayesian least squares estimate of each coefficient reduces to a weighted average of the local linear estimates over all possible values of the hidden multiplier variable we demonstrate through simulations with images contaminated by additive white gaussian noise that the performance of this method substantially surpasses that of previously published methods both visually and in terms of mean squared error

the curvelet transform for image denoising we describe approximate digital implementations of two new mathematical transforms namely the ridgelet transform and the curvelet transform our implementations offer exact reconstruction stability against perturbations ease of implementation and low computational complexity a central tool is fourier domain computation of an approximate digital radon transform we introduce a very simple interpolation in the fourier space which takes cartesian samples and yields samples on a rectopolar grid which is a pseudo polar sampling set based on a concentric squares geometry despite the crudeness of our interpolation the visual performance is surprisingly good our ridgelet transform applies to the radon transform a special overcomplete wavelet pyramid whose wavelets have compact support in the frequency domain our curvelet transform uses our ridgelet transform as a component step and implements curvelet subbands using a filter bank of a spl grave trous wavelet filters our philosophy throughout is that transforms should be overcomplete rather than critically sampled we apply these digital transforms to the denoising of some standard images embedded in white noise in the tests reported here simple thresholding of the curvelet coefficients is very competitive with state of the art techniques based on wavelets including thresholding of decimated or undecimated wavelet transforms and also including tree based bayesian posterior mean methods moreover the curvelet reconstructions exhibit higher perceptual quality than wavelet based reconstructions offering visually sharper images and in particular higher quality recovery of edges and of faint linear and curvilinear features existing theory for curvelet and ridgelet transforms suggests that these new approaches can outperform wavelet methods in certain image reconstruction problems the empirical results reported here are in encouraging agreement

optimal spatial adaptation for patch based image denoising a novel adaptive and patch based approach is proposed for image denoising and representation the method is based on a pointwise selection of small image patches of fixed size in the variable neighborhood of each pixel our contribution is to associate with each pixel the weighted sum of data points within an adaptive neighborhood in a manner that it balances the accuracy of approximation and the stochastic error at each spatial position this method is general and can be applied under the assumption that there exists repetitive patterns in a local neighborhood of a point by introducing spatial adaptivity we extend the work earlier described by buades et al which can be considered as an extension of bilateral filtering to image patches finally we propose a nearly parameter free algorithm for image denoising the method is applied to both artificially corrupted white gaussian noise and real images and the performance is very close to and in some cases even surpasses that of the already published denoising methods

infinite solutions for a class of brezis nirenberg equations with an indefinite linear and nonlinear terms in sign let p q 0 1 in the present paper we study the existence of infinitely many nontrivial solutions for a class of brezis nirenberg equation du v x u a x u p 1u b x u q 1u inr n where n 3 a x and b x have a contrary sign and satisfy suitable conditions the proof is based on the variant fountain theorem established by zou

inverse sparse tracker with a locally weighted distance metric sparse representation has been recently extensively studied for visual tracking and generally facilitates more accurate tracking results than classic methods in this paper we propose a sparsity based tracking algorithm that is featured with two components 1 an inverse sparse representation formulation and 2 a locally weighted distance metric in the inverse sparse representation formulation the target template is reconstructed with particles which enables the tracker to compute the weights of all particles by solving only one ell 1 optimization problem and thereby provides a quite efficient model this is in direct contrast to most previous sparse trackers that entail solving one optimization problem for each particle however we notice that this formulation with normal euclidean distance metric is sensitive to partial noise like occlusion and illumination changes to this end we design a locally weighted distance metric to replace the euclidean one similar ideas of using local features appear in other works but only being supported by popular assumptions like local models could handle partial noise better than holistic models without any solid theoretical analysis in this paper we attempt to explicitly explain it from a mathematical view on that basis we further propose a method to assign local weights by exploiting the temporal and spatial continuity in the proposed method appearance changes caused by partial occlusion and shape deformation are carefully considered thereby facilitating accurate similarity measurement and model update the experimental validation is conducted from two aspects 1 self validation on key components and 2 comparison with other state of the art algorithms results over 15 challenging sequences show that the proposed tracking algorithm performs favorably against the existing sparsity based trackers and the other state of the art methods

multiple solutions for p kirchhoff equations in rn abstract in this paper we prove the existence of multiple ground state solutions for the nonhomogeneous p kirchhoff elliptic equation 0 1 m r n u p v x u p d x p u v x u p 2 u f x u g x in r n where v x c r n and v x as x the nonlinear function f x u is continuous and satisfies some conditions the solutions will be obtained by the mountain pass theorem ekeland s variational principle and krasnoselskii s genus theory in struwe 2000 1

the spectral problem and particular solutions to the 2 1 dimensional integrable generalization of the camassa holm equation abstract we represent the relation between spectral problems for 2 1 dimensional integrable generalization of the camassa holm ch and modified kadomtsev petviashvili mkp 2 equations through the hodograph type transformation which allows to establish the link between particular solutions to each of them we represent the algorithm for construction of the particular solutions to 2 1 dimensional generalization of ch based on the nonlocal problem as examples we present the traveling wave solutions and discuss briefly the rational solutions

exact multiplicity for semilinear elliptic dirichlet problems involving concave and convex nonlinearities let b be the unit ball in r n n 3 let 0 p q n 2 n 2 in 1994 ambrosetti et al found that the semilinear elliptic dirichlet problem admits at least two solutions for small 0 and no solution for large in this paper we prove that there is a critical number 0 such that this problem has exactly two solutions for 0 exactly one solution for and no solution for

on a class of physically important integrable equations abstract a methodology introduced by fuchssteiner and the author is used to derive a class of physically important integrable evolution equations among these equations are integrable generalizations of the korteweg devries kdv of the modified kdv of the nonlinear schrodinger nls and of the sine gordon equations the modeling of water waves as well as general asymptotic considerations are used to illustrate the occurrence of the generalized modified kdv and nls equations respectively

the nehari manifold for fractional p laplacian equation with logarithmic nonlinearity on whole space abstract we study a fractional p laplacian equation in the whole space with the sign changing logarithmic nonlinearity by using fibrering maps and nehari manifold we obtain the existence of at least two nontrivial solutions our result extends a recent result by tian 2017 the main difficulty is the lack of logarithmic sobolev inequality concerning to fractional p laplacian

multiplicity results for solutions of p biharmonic problems abstract in this paper we deal with the multiplicity existence of solutions for the following p biharmonic equation p 2 u u p 2 u u q 2 u in u u 0 on where is a bounded domain in r n p 2 u u p 2 u p q p n p n 2 p r is a parameter when p q p we prove that the above problem possesses infinitely many solutions while when q p a multiplicity existence result is obtained

framing pyramids burt and adelson 1983 introduced the laplacian pyramid lp as a multiresolution representation for images we study the lp using the frame theory and this reveals that the usual reconstruction is suboptimal we show that the lp with orthogonal filters is a tight frame and thus the optimal linear reconstruction using the dual frame operator has a simple structure that is symmetric with the forward transform in more general cases we propose an efficient filterbank fb for the reconstruction of the lp using projection that leads to a proved improvement over the usual method in the presence of noise setting up the lp as an oversampled fb we offer a complete parameterization of all synthesis fbs that provide perfect reconstruction for the lp finally we consider the situation where the lp scheme is iterated and derive the continuous domain frames associated with the lp

manifold regularized correlation object tracking in this paper we propose a manifold regularized correlation tracking method with augmented samples to make better use of the unlabeled data and the manifold structure of the sample space a manifold regularization based correlation filter is introduced which aims to assign similar labels to neighbor samples meanwhile the regression model is learned by exploiting the block circulant structure of matrices resulting from the augmented translated samples over multiple base samples cropped from both target and nontarget regions thus the final classifier in our method is trained with positive negative and unlabeled base samples which is a semisupervised learning framework a block optimization strategy is further introduced to learn a manifold regularization based correlation filter for efficient online tracking experiments on two public tracking data sets demonstrate the superior performance of our tracker compared with the state of the art tracking approaches

missing intensity interpolation using a kernel pca based pocs algorithm and its applications a missing intensity interpolation method using a kernel principal component analysis pca based projection onto convex sets pocs algorithm and its applications are presented in this paper in order to interpolate missing intensities within a target image the proposed method reconstructs local textures containing the missing pixels by using the pocs algorithm in this reconstruction process a nonlinear eigenspace is constructed from each kind of texture and the optimal subspace for the target local texture is introduced into the constraint of the pocs algorithm in the proposed method the optimal subspace can be selected by monitoring errors converged in the reconstruction process this approach provides a solution to the problem in conventional methods of not being able to effectively perform adaptive reconstruction of the target textures due to missing intensities and successful interpolation of the missing intensities by the proposed method can be realized furthermore since our method can restore any images including arbitrary shaped missing areas its potential in two image reconstruction tasks image enlargement and missing area restoration is also shown in this paper

kernel based object tracking a new approach toward target representation and localization the central component in visual tracking of nonrigid objects is proposed the feature histogram based target representations are regularized by spatial masking with an isotropic kernel the masking induces spatially smooth similarity functions suitable for gradient based optimization hence the target localization problem can be formulated using the basin of attraction of the local maxima we employ a metric derived from the bhattacharyya coefficient as similarity measure and use the mean shift procedure to perform the optimization in the presented tracking examples the new method successfully coped with camera motion partial occlusions clutter and target scale variations integration with motion filters and data association techniques is also discussed we describe only a few of the potential applications exploitation of background information kalman tracking using motion models and face tracking

demosaicing by successive approximation in this paper we present a fast and high performance algorithm for color filter array cfa demosaicing cfa demosaicing is formulated as a problem of reconstructing correlated signals from their downsampled versions with an opposite phase the major contributions of this work include 1 a new iterative demosaicing algorithm in the color difference domain and 2 a spatially adaptive stopping criterion for suppressing color misregistration and zipper artifacts in the demosaiced images we have compared the proposed demosaicing algorithm with two current state of the art techniques reported in the literature ours outperforms both of them on demosaicing performance and computational cost

shift 2d rotation invariant sparse coding for multivariate signals classical dictionary learning algorithms dla allow unicomponent signals to be processed due to our interest in two dimensional 2d motion signals we wanted to mix the two components to provide rotation invariance so multicomponent frameworks are examined here in contrast to the well known multichannel framework a multivariate framework is first introduced as a tool to easily solve our problem and to preserve the data structure within this multivariate framework we then present sparse coding methods multivariate orthogonal matching pursuit m omp which provides sparse approximation for multivariate signals and multivariate dla m dla which empirically learns the characteristic patterns or features that are associated to a multivariate signals set and combines shift invariance and online learning once the multivariate dictionary is learned any signal of this considered set can be approximated sparsely this multivariate framework is introduced to simply present the 2d rotation invariant 2dri case by studying 2d motions that are acquired in bivariate real signals we want the decompositions to be independent of the orientation of the movement execution in the 2d space the methods are thus specified for the 2dri case to be robust to any rotation 2dri omp and 2dri dla shift and rotation invariant cases induce a compact learned dictionary and provide robust decomposition as validation our methods are applied to 2d handwritten data to extract the elementary features of this signals set and to provide rotation invariant decomposition

combined effects of concave and convex nonlinearities in some elliptic problems abstract this paper deals with a class of semilinear elliptic dirichlet boundary value problems where the combined effects of a sublinear and a superlinear term allow us to establish some existence and multiplicity results

n kirchhoff choquard equations with exponential nonlinearity abstract this article deals with the study of the following kirchhoff equation with exponential nonlinearity of choquard type see k c below we use the variational method in the light of moser trudinger inequality to show the existence of weak solutions to k c moreover analyzing the fibering maps and minimizing the energy functional over suitable subsets of the nehari manifold we prove existence and multiplicity of weak solutions to convex concave problem p m below

multiple positive solutions for a class of concave convex elliptic problems in rn involving sign changing weight in this paper we study the multiplicity of positive solutions for the following concave convex elliptic equation u u f x uq 1 g x up 1in rn u 0in rn u h1 rn where 1 q 2 p 2 2 2nn 2 if n 3 2 if n 1 2 and the parameters 0 we assume that f x f x f x is sign changing and g x a x b x where the functions f a and b satisfy suitable conditions

image completion by diffusion maps and spectral relaxation we present a framework for image inpainting that utilizes the diffusion framework approach to spectral dimensionality reduction we show that on formulating the inpainting problem in the embedding domain the domain to be inpainted is smoother in general particularly for the textured images thus the textured images can be inpainted through simple exemplar based and variational methods we discuss the properties of the induced smoothness and relate it to the underlying assumptions used in contemporary inpainting schemes as the diffusion embedding is nonlinear and noninvertible we propose a novel computational approach to approximate the inverse mapping from the inpainted embedding space to the image domain we formulate the mapping as a discrete optimization problem solved through spectral relaxation the effectiveness of the presented method is exemplified by inpainting real images where it is shown to compare favorably with contemporary state of the art schemes

image processing using smooth ordering of its patches we propose an image processing scheme based on reordering of its patches for a given corrupted image we extract all patches with overlaps refer to these as coordinates in high dimensional space and order them such that they are chained in the shortest possible path essentially solving the traveling salesman problem the obtained ordering applied to the corrupted image implies a permutation of the image pixels to what should be a regular signal this enables us to obtain good recovery of the clean image by applying relatively simple one dimensional smoothing operations such as filtering or interpolation to the reordered set of pixels we explore the use of the proposed approach to image denoising and inpainting and show promising results in both cases

sparse representation for color image restoration sparse representations of signals have drawn considerable interest in recent years the assumption that natural signals such as images admit a sparse decomposition over a redundant dictionary leads to efficient algorithms for handling such sources of data in particular the design of well adapted dictionaries for images has been a major challenge the k svd has been recently proposed for this task and shown to perform very well for various grayscale image processing tasks in this paper we address the problem of learning dictionaries for color images and extend the k svd based grayscale image denoising algorithm that appears in this work puts forward ways for handling nonhomogeneous noise and missing information paving the way to state of the art results in applications such as color image denoising demosaicing and inpainting as demonstrated in this paper

color direction patch sparsity based image inpainting using multidirection features this paper proposes a color direction patch sparsity based image inpainting method to better maintain structure coherence texture clarity and neighborhood consistence of the inpainted region of an image the method uses super wavelet transform to estimate the multi direction features of a degraded image and combines with color information to construct the weighted color direction distance wcdd to measure the difference between two patches based on the wcdd the color direction structure sparsity is defined to obtain a more robust filling order and more suitable multiple candidate patches are searched then the target patches are sparsely represented by the multiple candidate patches under neighborhood consistency constraints in both the color and the multi direction spaces experimental results are presented to demonstrate the effectiveness of the proposed approach on tasks such as scratch removal text removal block removal and object removal the effects of super wavelet transforms and direction features are also investigated

existence of entire solutions for a class of variable exponent elliptic equations abstract the paper deals with the existence of entire solutions for a quasilinear equation e in r n depending on a real parameter which involves a general variable exponent elliptic operator a in divergence form and two main nonlinearities the competing nonlinear terms combine each other under some conditions we prove the existence of a critical value 0 with the property that e admits nontrivial nonnegative entire solutions if and only if furthermore under the further assumption that the potential a of a is uniform convex we give the existence of a second independent nontrivial nonnegative entire solution of e when our results extend the previous work of autuori and pucci 2013 6 from the case of constant exponents p q and r to the case of variable exponents more interesting we weaken the condition max 2 p q min r p to the simple request that 1 q r furthermore we extend the previous work of alama and tarantello 1996 2 from dirichlet laplacian problems in bounded domains of r n to the case of a general variable exponent differential equation in the entire r n and also remove the assumption q 2 hence the results of this paper are new even in the canonical case p 2

fast pixelwise adaptive visual tracking of non rigid objects in this paper we present a new algorithm for real time single object tracking in videos in unconstrained environments the algorithm comprises two different components that are trained in one shot at the first video frame a detector that makes use of the generalized hough transform with color and gradient descriptors and a probabilistic segmentation method based on global models for foreground and background color distributions both components work at pixel level and are used for tracking in a combined way adapting each other in a co training manner moreover we propose an adaptive shape model as well as a new probabilistic method for updating the scale of the tracker through effective model adaptation and segmentation the algorithm is able to track objects that undergo rigid and non rigid deformations and considerable shape and appearance variations the proposed tracking method has been thoroughly evaluated on challenging benchmarks and outperforms the state of the art tracking methods designed for the same task finally a very efficient implementation of the proposed models allows for extremely fast tracking

recovering edges in ill posed inverse problems optimality of curvelet frames we consider a model problem of recovering a function f x 1 x 2 from noisy radon data the function f to be recovered is assumed smooth apart from a discontinuity along a c 2 curve that is an edge we use the continuum white noise model with noise level varepsilon traditional linear methods for solving such inverse problems behave poorly in the presence of edges qualitatively the reconstructions are blurred near the edges quantitatively they give in our model mean squared errors mses that tend to zero with noise level varepsilon only as o varepsilon 1 2 as varepsilon to 0 a recent innovation nonlinear shrinkage in the wavelet domain visually improves edge sharpness and improves mse convergence to o varepsilon 2 3 however as we show here this rate is not optimal in fact essentially optimal performance is obtained by deploying the recently introduced tight frames of curvelets in this setting curvelets are smooth highly anisotropic elements ideally suited for detecting and synthesizing curved edges to deploy them in the radon setting we construct a curvelet based biorthogonal decomposition of the radon operator and build curvelet shrinkage estimators based on thresholding of the noisy curvelet coefficients in effect the estimator detects edges at certain locations and orientations in the radon domain and automatically synthesizes edges at corresponding locations and directions in the original domain we prove that the curvelet shrinkage can be tuned so that the estimator will attain within logarithmic factors the mse o varepsilon 4 5 as noise level varepsilon to 0 this rate of convergence holds uniformly over a class of functions which are c 2 except for discontinuities along c 2 curves and except for log terms is the minimax rate for that class our approach is an instance of a general strategy which should apply in other inverse problems we sketch a deconvolution example

robust discriminative tracking via landmark based label propagation the appearance of an object could be continuously changing during tracking thereby being not independent identically distributed a good discriminative tracker often needs a large number of training samples to fit the underlying data distribution which is impractical for visual tracking in this paper we present a new discriminative tracker via landmark based label propagation llp that is nonparametric and makes no specific assumption about the sample distribution with an undirected graph representation of samples the llp locally approximates the soft label of each sample by a linear combination of labels on its nearby landmarks it is able to effectively propagate a limited amount of initial labels to a large amount of unlabeled samples to this end we introduce a local landmarks approximation method to compute the cross similarity matrix between the whole data and landmarks moreover a soft label prediction function incorporating the graph laplacian regularizer is used to diffuse the known labels to all the unlabeled vertices in the graph which explicitly considers the local geometrical structure of all samples tracking is then carried out within a bayesian inference framework where the soft label prediction value is used to construct the observation model both qualitative and quantitative evaluations on the benchmark data set containing 51 challenging image sequences demonstrate that the proposed algorithm outperforms the state of the art methods

variational approach to semilinear elliptic equation with nonlinear boundary abstract we consider the existence of positive solutions for a certain class of semilinear elliptic equation with nonlinear boundary our approach is based on the variational methods

the nehari manifold for a semilinear elliptic equation with a sign changing weight function abstract the nehari manifold for the equation u x a x u x b x u x 1u x for x together with dirichlet boundary conditions is investigated exploiting the relationship between the nehari manifold and fibrering maps i e maps of the form t j tu where j is the euler functional associated with the equation we discuss how the nehari manifold changes as changes and show how existence and non existence results for positive solutions of the equation are linked to properties of the manifold

shiftable multiscale transforms one of the major drawbacks of orthogonal wavelet transforms is their lack of translation invariance the content of wavelet subbands is unstable under translations of the input signal wavelet transforms are also unstable with respect to dilations of the input signal and in two dimensions rotations of the input signal the authors formalize these problems by defining a type of translation invariance called shiftability in the spatial domain shiftability corresponds to a lack of aliasing thus the conditions under which the property holds are specified by the sampling theorem shiftability may also be applied in the context of other domains particularly orientation and scale jointly shiftable transforms that are simultaneously shiftable in more than one domain are explored two examples of jointly shiftable transforms are designed and implemented a 1 d transform that is jointly shiftable in position and scale and a 2 d transform that is jointly shiftable in position and orientation the usefulness of these image representations for scale space analysis stereo disparity measurement and image enhancement is demonstrated

infinitely many solutions for a class of sublinear schrodinger equations with indefinite potentials in this paper we are concerned with qualitative properties of entire solutions to a schrodinger equation with sublinear nonlinearity and sign changing potentials our analysis considers three distinct cases and we establish sufficient conditions for the existence of infinitely many solutions

the nehari manifold for a class of concave convex elliptic systems involving the p laplacian and nonlinear boundary condition abstract the existence and multiplicity of weak solutions is established for a class of concave convex elliptic systems of the form p u m x u p 2 u a x u 2 u x p v m x v p 2 v b x v 2 v x u p 2 u n u 2 u v v p 2 v n u v 2 v x here p denotes the p laplacian operator defined by p z div z p 2 z p 2 r n is a bounded domain with smooth boundary 1 1 2 p p p p n n p if n p p if n p n is the outer normal derivative r 2 0 0 the weight m x is a positive bounded function and a x b x c are functions which change sign in our technical approach is based on the nehari manifold which is similar to the fibering method of drabek and pohozaev 1997 29 together with the recent idea from brown and wu 2008 10

symplectic structures their backlund transformations and hereditary symmetries abstract it is shown that compatible symplectic structures lead in a natural way to hereditary symmetries we recall that a hereditary symmetry is an operator valued function which immediately yields a hierarchy of evolution equations each having infinitely many commuting symmetries all generated by this hereditary symmetry furthermore this hereditary symmetry usually describes completely the soliton structure and the conservation laws of these equations this result then provide us with a method for constructing hereditary symmetries and hence exactly solvable evolution equations in addition we show how symplectic structures transform under backlund transformations this leads to a method for generating a whole class of symplectic structures from a given one several examples and applications are given illustrating the above results also the connection of our results with those of gelfand and dikii and of magri is briefly pointed out

local superlinearity and sublinearity for indefinite semilinear elliptic problems in this paper the usual notions of superlinearity and sublinearity for semilinear problems like du f x u are given a local form and extended to indefinite nonlinearities here f x s is allowed to change sign or to vanish for s near zero as well as for s near infinity some of the well known results of ambrosetti bre zis cerami are partially extended to this context

occlusion aware fragment based tracking with spatial temporal consistency in this paper we present a robust tracking method by exploiting a fragment based appearance model with consideration of both temporal continuity and discontinuity information from the perspective of probability theory the proposed tracking algorithm can be viewed as a two stage optimization problem in the first stage by adopting the estimated occlusion state as a prior the optimal state of the tracked object can be obtained by solving an optimization problem where the objective function is designed based on the classification score occlusion prior and temporal continuity information in the second stage we propose a discriminative occlusion model which exploits both foreground and background information to detect the possible occlusion and also models the consistency of occlusion labels among different frames in addition a simple yet effective training strategy is introduced during the model training and updating process with which the effects of spatial temporal consistency are properly weighted the proposed tracker is evaluated by using the recent benchmark data set on which the results demonstrate that our tracker performs favorably against other state of the art tracking algorithms

the nehari manifold for a semilinear elliptic problem with the nonlinear boundary condition abstract using the nehari manifold and fibering maps we prove the existence theorem of the nonlinear boundary problem u u u p 2 u for x u n u q 2 u for x on a bounded domain r n we discuss how the nehari manifold changes as changes and show how the existence of solutions depends on the properties of the nehari manifold

multiple positive solutions for the critical kirchhoff type problems involving sign changing weight functions abstract this paper is concerned with the multiplicity of positive solutions for the critical kirchhoff type problems involving indefinite weight functions 0 1 m u 2 d x u q x u q 2 u k x u 2 2 u x u 0 x where is a smooth bounded domain in r n n 3 1 q 2 m s a b s with 0 a 0 and b 0 the weight functions q and k are continuous and changing sign using the nehari manifold fibering maps and ljusternik schnirelmann category we prove that at least two positive solutions for 0 1 exist provided that 1 and 2 4 furthermore by the mountain pass theorem and ekeland s variational principle it is shown that 0 1 possesses at least three positive solutions whenever 2 n 2 including the case that 1 and 2 4 our results generalize some recent results in the literature

image compression via joint statistical characterization in the wavelet domain we develop a probability model for natural images based on empirical observation of their statistics in the wavelet transform domain pairs of wavelet coefficients corresponding to basis functions at adjacent spatial locations orientations and scales are found to be non gaussian in both their marginal and joint statistical properties specifically their marginals are heavy tailed and although they are typically decorrelated their magnitudes are highly correlated we propose a markov model that explains these dependencies using a linear predictor for magnitude coupled with both multiplicative and additive uncertainties and show that it accounts for the statistics of a wide variety of images including photographic images graphical images and medical images in order to directly demonstrate the power of the model we construct an image coder called epwic embedded predictive wavelet image coder in which subband coefficients are encoded one bitplane at a time using a nonadaptive arithmetic encoder that utilizes conditional probabilities calculated from the model bitplanes are ordered using a greedy algorithm that considers the mse reduction per encoded bit the decoder uses the statistical model to predict coefficient values based on the bits it has received despite the simplicity of the model the rate distortion performance of the coder is roughly comparable to the best image coders in the literature

visual tracking via discriminative sparse similarity map in this paper we cast the tracking problem as finding the candidate that scores highest in the evaluation model based upon a matrix called discriminative sparse similarity map dss map this map demonstrates the relationship between all the candidates and the templates and it is constructed based on the solution to an innovative optimization formulation named multitask reverse sparse representation formulation which searches multiple subsets from the whole candidate set to simultaneously reconstruct multiple templates with minimum error a customized apg method is derived for getting the optimum solution in matrix form within several iterations this formulation allows the candidates to be evaluated accurately in parallel rather than one by one like most sparsity based trackers do and meanwhile considers the relationship between candidates therefore it is more superior in terms of cost performance ratio the discriminative information containing in this map comes from a large template set with multiple positive target templates and hundreds of negative templates a laplacian term is introduced to keep the coefficients similarity level in accordance with the candidates similarities thereby making our tracker more robust a pooling approach is proposed to extract the discriminative information in the dss map for easily yet effectively selecting good candidates from bad ones and finally get the optimum tracking results plenty experimental evaluations on challenging image sequences demonstrate that the proposed tracking algorithm performs favorably against the state of the art methods

existence and multiplicity results for some eigenvalue problems involving variable exponents abstract variational techniques are used to get some existence and multiplicity results for some eigenvalue problems involving variable exponents

extrinsic methods for coding and dictionary learning on grassmann manifolds sparsity based representations have recently led to notable results in various visual recognition tasks in a separate line of research riemannian manifolds have been shown useful for dealing with features and models that do not lie in euclidean spaces with the aim of building a bridge between the two realms we address the problem of sparse coding and dictionary learning in grassmann manifolds i e the space of linear subspaces to this end we propose to embed grassmann manifolds into the space of symmetric matrices by an isometric mapping this in turn enables us to extend two sparse coding schemes to grassmann manifolds furthermore we propose an algorithm for learning a grassmann dictionary atom by atom lastly to handle non linearity in data we extend the proposed grassmann sparse coding and dictionary learning algorithms through embedding into higher dimensional hilbert spaces experiments on several classification tasks gender recognition gesture classification scene analysis face recognition action recognition and dynamic texture classification show that the proposed approaches achieve considerable improvements in discrimination accuracy in comparison to state of the art methods such as kernelized affine hull method and graph embedding grassmann discriminant analysis

multiple solutions for the semilinear elliptic equations with the sign changing logarithmic nonlinearity abstract in this paper we study the semilinear elliptic equations with the sign changing logarithmic nonlinearity under some conditions we obtain at least two nontrivial solutions by nehari manifold and logarithmic sobolev inequality here the results are quite different from these in the polynomial case

existence and non existence results for quasilinear kirchhoff problems with the hardy sobolev exponent abstract in this paper we are concerned with the following quasilinear elliptic problems of kirchhoff type a b r n u p u p x p d x 1 p u u p 2 u x p u p 2 u x f x u q 2 u x where a 0 b 0 1 0 n p p p 0 p and q 1 p are constants and p u div u p 2 u with 1 p n p p n n p is the hardy sobolev exponent we establish the non existence and the existence of infinitely many nontrivial solutions when 0 for the above problem also for suitable weight function f x we prove the existence of two positive solutions by using nehari manifold and fibering map when 0 is sufficiently small

image super resolution via sparse representation this paper presents a new approach to single image superresolution based upon sparse signal representation research on image statistics suggests that image patches can be well represented as a sparse linear combination of elements from an appropriately chosen over complete dictionary inspired by this observation we seek a sparse representation for each patch of the low resolution input and then use the coefficients of this representation to generate the high resolution output theoretical results from compressed sensing suggest that under mild conditions the sparse representation can be correctly recovered from the downsampled signals by jointly training two dictionaries for the low and high resolution image patches we can enforce the similarity of sparse representations between the low resolution and high resolution image patch pair with respect to their own dictionaries therefore the sparse representation of a low resolution image patch can be applied with the high resolution image patch dictionary to generate a high resolution image patch the learned dictionary pair is a more compact representation of the patch pairs compared to previous approaches which simply sample a large amount of image patch pairs reducing the computational cost substantially the effectiveness of such a sparsity prior is demonstrated for both general image super resolution sr and the special case of face hallucination in both cases our algorithm generates high resolution images that are competitive or even superior in quality to images produced by other similar sr methods in addition the local sparse modeling of our approach is naturally robust to noise and therefore the proposed algorithm can handle sr with noisy inputs in a more unified framework

translation invariant contourlet transform and its application to image denoising most subsampled filter banks lack the feature of translation invariance which is an important characteristic in denoising applications in this paper we study and develop new methods to convert a general multichannel multidimensional filter bank to a corresponding translation invariant ti framework in particular we propose a generalized algorithme agrave trous which is an extension of the algorithme agrave trous introduced for 1 d wavelet transforms using the proposed algorithm as well as incorporating modified versions of directional filter banks we construct the ti contourlet transform tict to reduce the high redundancy and complexity of the tict we also introduce semi translation invariant contourlet transform stict then we employ an adapted bivariate shrinkage scheme to the stict to achieve an efficient image denoising approach our experimental results demonstrate the benefits and potential of the proposed denoising approach complexity analysis and efficient realization of the proposed ti schemes are also presented

integrable equations in 2 1 dimensions deformations of dispersionless limits we classify integrable third order equations in 2 1 dimensions which generalize the examples of kadomtsev petviashvili veselov novikov and harry dym equations our approach is based on the observation that dispersionless limits of integrable systems in 2 1 dimensions possess infinitely many multi phase solutions coming from the so called hydrodynamic reductions in this paper we adopt a novel perturbative approach to the classification problem based on the method of hydrodynamic reductions we first classify integrable quasilinear systems which may potentially occur as dispersionless limits of soliton equations in 2 1 dimensions to reconstruct dispersive deformations we require that all hydrodynamic reductions of the dispersionless limit be inherited by the corresponding dispersive counterpart this procedure leads to a complete list of integrable third order equations some of which are apparently new

on some indefinite and non powerlike elliptic equations abstract we consider a class of elliptic problems for the operator v acting on h 0 1 where is a bounded domain the main feature here is the indefinite behavior of both the operator and the nonlinearity based on the global geometry of the energy functional we prove the existence of two local minimizers and a mountain pass critical point for a concave convex type nonlinearity subcritical and critical growth are allowed on the nonlinearity