infinite dimensional primitive linearly compact lie superalgebras we classify open maximal subalgebras of all infinite dimensional linearly compact simple lie superalgebras this is applied to the classification of infinite dimensional lie superalgebras of vector fields acting transitively and primitively in a formal neighborhood of a point of a finite dimensional supermanifold

learning overcomplete representations in an overcomplete basis the number of basis vectors is greater than the dimensionality of the input and the representation of an input is not a unique combination of basis vectors overcomplete representations have been advocated because they have greater robustness in the presence of noise can be sparser and can have greater flexibility in matching structure in the data overcomplete codes have also been proposed as a model of some of the response properties of neurons in primary visual cortex previous work has focused on finding the best representation of a signal using a fixed overcomplete basis or dictionary we present an algorithm for learning an overcomplete basis by viewing it as probabilistic model of the observed data we show that overcomplete bases can yield a better approximation of the underlying statistical distribution of the data and can thus lead to greater coding efficiency this can be viewed as a generalization of the technique of independent component analysis and provides a method for bayesian reconstruction of signals in the presence of noise and for blind source separation when there are more sources than mixtures

a group based image inpainting using patch refinement in mrf framework this paper presents a markov random field mrf based image inpainting algorithm using patch selection from groups of similar patches and optimal patch assignment through joint patch refinement in patch selection a novel group formation strategy based on subspace clustering is introduced to search the candidate patches in relevant source region only this improves patch searching in terms of both quality and time we also propose an efficient patch refinement scheme using higher order singular value decomposition to capture underlying pattern among the candidate patches this eliminates random variation and unwanted artifacts as well finally a weight term is computed based on the refined patches and is incorporated in the objective function of the mrf model to improve the optimal patch assignment experimental results on a large number of natural images and comparison with well known existing methods demonstrate the efficacy and superiority of the proposed method

the capelli eigenvalue problem for lie superalgebras for a finite dimensional unital complex simple jordan superalgebra j the tits kantor koecher construction yields a 3 graded lie superalgebra mathfrak g flat cong mathfrak g flat 1 oplus mathfrak g flat 0 oplus mathfrak g flat 1 such that mathfrak g flat 1 cong j set v mathfrak g flat 1 and mathfrak g mathfrak g flat 0 in most cases the space mathscr p v of superpolynomials on v is a completely reducible and multiplicity free representation of mathfrak g and there exists a direct sum decomposition mathscr p v bigoplus lambda in omega v lambda where left v lambda right lambda in omega is a family of irreducible mathfrak g modules parametrized by a set of partitions omega in these cases one can define a natural basis left d lambda right lambda in omega of capelli operators for the algebra mathscr pd v mathfrak g of mathfrak g invariant superpolynomial differential operators on v in this paper we complete the solution to the capelli eigenvalue problem which asks for the determination of the scalar c mu lambda by which d mu acts on v lambda we associate a restricted root system varsigma to the symmetric pair mathfrak g mathfrak k that corresponds to j which is either a deformed root system of type mathsf a m n or a root system of type mathsf q n we prove a necessary and sufficient condition on the structure of varsigma for mathscr p v to be completely reducible and multiplicity free when varsigma satisfies the latter condition we obtain an explicit formula for the eigenvalue c mu lambda in terms of sergeev veselov s shifted super jack polynomials when varsigma is of type mathsf a m n and okounkov ivanov s factorial schur q polynomials when varsigma is of type mathsf q n along the way we prove that the natural map from the centre of the enveloping algebra of mathfrak g into mathscr pd v mathfrak g is surjective in all cases except when j cong f where f is the 10 dimensional exceptional jordan superalgebra

data imputation through the identification of local anomalies we introduce a comprehensive and statistical framework in a model free setting for a complete treatment of localized data corruptions due to severe noise sources e g an occluder in the case of a visual recording within this framework we propose 1 a novel algorithm to efficiently separate i e detect and localize possible corruptions from a given suspicious data instance and 2 a maximum a posteriori estimator to impute the corrupted data as a generalization to euclidean distance we also propose a novel distance measure which is based on the ranked deviations among the data attributes and empirically shown to be superior in separating the corruptions our algorithm first splits the suspicious instance into parts through a binary partitioning tree in the space of data attributes and iteratively tests those parts to detect local anomalies using the nominal statistics extracted from an uncorrupted clean reference data set once each part is labeled as anomalous versus normal the corresponding binary patterns over this tree that characterize corruptions are identified and the affected attributes are imputed under a certain conditional independency structure assumed for the binary patterns we analytically show that the false alarm rate of the introduced algorithm in detecting the corruptions is independent of the data and can be directly set without any parameter tuning the proposed framework is tested over several well known machine learning data sets with synthetically generated corruptions and experimentally shown to produce remarkable improvements in terms of classification purposes with strong corruption separation capabilities our experiments also indicate that the proposed algorithms outperform the typical approaches and are robust to varying training phase conditions

dictionary pair learning on grassmann manifolds for image denoising image denoising is a fundamental problem in computer vision and image processing that holds considerable practical importance for real world applications the traditional patch based and sparse coding driven image denoising methods convert 2d image patches into 1d vectors for further processing thus these methods inevitably break down the inherent 2d geometric structure of natural images to overcome this limitation pertaining to the previous image denoising methods we propose a 2d image denoising model namely the dictionary pair learning dpl model and we design a corresponding algorithm called the dpl on the grassmann manifold dplg algorithm the dplg algorithm first learns an initial dictionary pair i e the left and right dictionaries by employing a subspace partition technique on the grassmann manifold wherein the refined dictionary pair is obtained through a sub dictionary pair merging the dplg obtains a sparse representation by encoding each image patch only with the selected sub dictionary pair the non zero elements of the sparse representation are further smoothed by the graph laplacian operator to remove the noise consequently the dplg algorithm not only preserves the inherent 2d geometric structure of natural images but also performs manifold smoothing in the 2d sparse coding space we demonstrate that the dplg algorithm also improves the structural similarity values of the perceptual visual quality for denoised images using the experimental evaluations on the benchmark images and berkeley segmentation data sets moreover the dplg also produces the competitive peak signal to noise ratio values from popular image denoising algorithms

image denoising using the higher order singular value decomposition in this paper we propose a very simple and elegant patch based machine learning technique for image denoising using the higher order singular value decomposition hosvd the technique simply groups together similar patches from a noisy image with similarity defined by a statistically motivated criterion into a 3d stack computes the hosvd coefficients of this stack manipulates these coefficients by hard thresholding and inverts the hosvd transform to produce the final filtered image our technique chooses all required parameters in a principled way relating them to the noise model we also discuss our motivation for adopting the hosvd as an appropriate transform for image denoising we experimentally demonstrate the excellent performance of the technique on grayscale as well as color images on color images our method produces state of the art results outperforming other color image denoising algorithms at moderately high noise levels a criterion for optimal patch size selection and noise variance estimation from the residual images after denoising is also presented

scale space and edge detection using anisotropic diffusion a new definition of scale space is suggested and a class of algorithms used to realize a diffusion process is introduced the diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing rather than interregion smoothing it is shown that the no new maxima should be generated at coarse scales property of conventional scale space is preserved as the region boundaries in the approach remain sharp a high quality edge detector which successfully exploits global information is obtained experimental results are shown on a number of images parallel hardware implementations are made feasible because the algorithm involves elementary local operations replicated over the image

a joint inter and intrascale statistical model for bayesian wavelet based image denoising this paper presents a new wavelet based image denoising method which extends a geometrical bayesian framework the new method combines three criteria for distinguishing supposedly useful coefficients from noise coefficient magnitudes their evolution across scales and spatial clustering of large coefficients near image edges these three criteria are combined in a bayesian framework the spatial clustering properties are expressed in a prior model the statistical properties concerning coefficient magnitudes and their evolution across scales are expressed in a joint conditional model the three main novelties with respect to related approaches are 1 the interscale ratios of wavelet coefficients are statistically characterized and different local criteria for distinguishing useful coefficients from noise are evaluated 2 a joint conditional model is introduced and 3 a novel anisotropic markov random field prior model is proposed the results demonstrate an improved denoising performance over related earlier techniques

image denoising by exploring external and internal correlations single image denoising suffers from limited data collection within a noisy image in this paper we propose a novel image denoising scheme which explores both internal and external correlations with the help of web images for each noisy patch we build internal and external data cubes by finding similar patches from the noisy and web images respectively we then propose reducing noise by a two stage strategy using different filtering approaches in the first stage since the noisy patch may lead to inaccurate patch selection we propose a graph based optimization method to improve patch matching accuracy in external denoising the internal denoising is frequency truncation on internal cubes by combining the internal and external denoising patches we obtain a preliminary denoising result in the second stage we propose reducing noise by filtering of external and internal cubes respectively on transform domain in this stage the preliminary denoising result not only enhances the patch matching accuracy but also provides reliable estimates of filtering parameters the final denoising image is obtained by fusing the external and internal filtering results experimental results show that our method constantly outperforms state of the art denoising schemes in both subjective and objective quality measurements e g it achieves 2 db gain compared with bm3d at a wide range of noise levels

pointwise shape adaptive dct for high quality denoising and deblocking of grayscale and color images the shape adaptive discrete cosine transform sa dct transform can be computed on a support of arbitrary shape but retains a computational complexity comparable to that of the usual separable block dct b dct despite the near optimal decorrelation and energy compaction properties application of the sa dct has been rather limited targeted nearly exclusively to video compression in this paper we present a novel approach to image filtering based on the sa dct we use the sa dct in conjunction with the anisotropic local polynomial approximation intersection of confidence intervals technique which defines the shape of the transform s support in a pointwise adaptive manner the thresholded or attenuated sa dct coefficients are used to reconstruct a local estimate of the signal within the adaptive shape support since supports corresponding to different points are in general overlapping the local estimates are averaged together using adaptive weights that depend on the region s statistics this approach can be used for various image processing tasks in this paper we consider in particular image denoising and image deblocking and deringing from block dct compression a special structural constraint in luminance chrominance space is also proposed to enable an accurate filtering of color images simulation experiments show a state of the art quality of the final estimate both in terms of objective criteria and visual appearance thanks to the adaptive support reconstructed edges are clean and no unpleasant ringing artifacts are introduced by the fitted transform

structure based low rank model with graph nuclear norm regularization for noise removal nonlocal image representation methods including group based sparse coding and block matching 3 d filtering have shown their great performance in application to low level tasks the nonlocal prior is extracted from each group consisting of patches with similar intensities grouping patches based on intensity similarity however gives rise to disturbance and inaccuracy in estimation of the true images to address this problem we propose a structure based low rank model with graph nuclear norm regularization we exploit the local manifold structure inside a patch and group the patches by the distance metric of manifold structure with the manifold structure information a graph nuclear norm regularization is established and incorporated into a low rank approximation model we then prove that the graph based regularization is equivalent to a weighted nuclear norm and the proposed model can be solved by a weighted singular value thresholding algorithm extensive experiments on additive white gaussian noise removal and mixed noise removal demonstrate that the proposed method achieves a better performance than several state of the art algorithms

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

improved error estimation of dynamic finite element methods for second order parabolic equations dynamic finite element schemes are analyzed for second order parabolic problems these schemes permit different finite element spaces at different time levels in order to efficiently capture time changing localized phenomena such as moving sharp fronts or layers the dynamical change of grids and interpolation polynomials is necessary and essential to many large scale transient problems standard characteristic and mixed finite element methods with dynamic function spaces are considered for linear and nonlinear problems in a unified framework with improved a priori error estimates and convergence results

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

adaptive image denoising by targeted databases we propose a data dependent denoising procedure to restore noisy images different from existing denoising algorithms which search for patches from either the noisy image or a generic database the new algorithm finds patches from a database that contains relevant patches we formulate the denoising problem as an optimal filter design problem and make two contributions first we determine the basis function of the denoising filter by solving a group sparsity minimization problem the optimization formulation generalizes existing denoising algorithms and offers systematic analysis of the performance improvement methods are proposed to enhance the patch search process second we determine the spectral coefficients of the denoising filter by considering a localized bayesian prior the localized prior leverages the similarity of the targeted database alleviates the intensive bayesian computation and links the new method to the classical linear minimum mean squared error estimation we demonstrate applications of the proposed method in a variety of scenarios including text images multiview images and face images experimental results show the superiority of the new algorithm over existing methods

two stage image denoising by principal component analysis with local pixel grouping this paper presents an efficient image denoising scheme by using principal component analysis pca with local pixel grouping lpg for a better preservation of image local structures a pixel and its nearest neighbors are modeled as a vector variable whose training samples are selected from the local window by using block matching based lpg such an lpg procedure guarantees that only the sample blocks with similar contents are used in the local statistics calculation for pca transform estimation so that the image local features can be well preserved after coefficient shrinkage in the pca domain to remove the noise the lpg pca denoising procedure is iterated one more time to further improve the denoising performance and the noise level is adaptively adjusted in the second stage experimental results on benchmark test images demonstrate that the lpg pca method achieves very competitive denoising performance especially in image fine structure preservation compared with state of the art denoising algorithms

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

a characteristic mixed method with dynamic finite element space for convection dominated diffusion problems abstract a method for numerically solving convection dominated diffusion problems using a combination of the method of characteristics with the mixed finite element method is presented and analyzed in this paper different numbers of elements and different basis functions are implemented at different time levels in order to accurately resolve time changing critical features this new method provides the ability to obtain approximations of the solution and its gradient simultaneously adopt large time steps and make grid refinements and basis function adjustments at any time necessary convergence analysis and error estimates are established furthermore comments are made on the efficiency and capability of the method for accurately solving transient problems with localized phenomena such as fronts shocks and boundary layers

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

classification of linearly compact simple nambu poisson algebras we introduce the notion of a universal odd generalized poisson superalgebra associated with an associative algebra a by generalizing a construction made in the work of de sole and kac jpn j math 8 1 145 2013 by making use of this notion we give a complete classification of simple linearly compact generalized n nambu poisson algebras over an algebraically closed field of characteristic zero

group based image decomposition using 3 d cartoon and texture priors we propose a novel image decomposition method to decompose an image into its cartoon and texture components to exploit the nonlocal self similarity of cartoon plus texture images we construct groups by stacking together similar image patches into 3 d arrays and consider group as the basic unit of decomposition we decompose each group via a convex optimization model consisting of 3 d cartoon and texture priors these priors characterize the local properties of the cartoon and texture components and the nonlocal similarity within each component in a unified and natural manner we develop the alternating direction method of multipliers admm to efficiently solve the proposed model for further improvement we investigate an adaptive rule for the estimation of the regularization parameter the proposed method is also extended to tackle noisy images numerical experiments confirm that the performance of the proposed method is competitive with some of the state of the art schemes

fourth order partial differential equations for noise removal a class of fourth order partial differential equations pdes are proposed to optimize the trade off between noise removal and edge preservation the time evolution of these pdes seeks to minimize a cost functional which is an increasing function of the absolute value of the laplacian of the image intensity function since the laplacian of an image at a pixel is zero if the image is planar in its neighborhood these pdes attempt to remove noise and preserve edges by approximating an observed image with a piecewise planar image piecewise planar images look more natural than step images which anisotropic diffusion second order pdes uses to approximate an observed image so the proposed pdes are able to avoid the blocky effects widely seen in images processed by anisotropic diffusion while achieving the degree of noise removal and edge preservation comparable to anisotropic diffusion although both approaches seem to be comparable in removing speckles in the observed images speckles are more visible in images processed by the proposed pdes because piecewise planar images are less likely to mask speckles than step images and anisotropic diffusion tends to generate multiple false edges speckles can be easily removed by simple algorithms such as the one presented in this paper

solving inverse problems with piecewise linear estimators from gaussian mixture models to structured sparsity a general framework for solving image inverse problems with piecewise linear estimations is introduced in this paper the approach is based on gaussian mixture models which are estimated via a maximum a posteriori expectation maximization algorithm a dual mathematical interpretation of the proposed framework with a structured sparse estimation is described which shows that the resulting piecewise linear estimate stabilizes the estimation when compared with traditional sparse inverse problem techniques we demonstrate that in a number of image inverse problems including interpolation zooming and deblurring of narrow kernels the same simple and computationally efficient algorithm yields results in the same ballpark as that of the state of the art

the twist tensor nuclear norm for video completion in this paper we propose a new low rank tensor model based on the circulant algebra namely twist tensor nuclear norm t tnn the twist tensor denotes a three way tensor representation to laterally store 2 d data slices in order on one hand t tnn convexly relaxes the tensor multirank of the twist tensor in the fourier domain which allows an efficient computation using fast fourier transform on the other t tnn is equal to the nuclear norm of block circulant matricization of the twist tensor in the original domain which extends the traditional matrix nuclear norm in a block circulant way we test the t tnn model on a video completion application that aims to fill missing values and the experiment results validate its effectiveness especially when dealing with video recorded by a nonstationary panning camera the block circulant matricization of the twist tensor can be transformed into a circulant block representation with nuclear norm invariance this representation after transformation exploits the horizontal translation relationship between the frames in a video and endows the t tnn model with a more powerful ability to reconstruct panning videos than the existing state of the art low rank models

a new n 6 superconformal algebra in this paper we construct a newn 6 superconformal algebra which extends the virasoro algebra by theso 6 current algebra by 6 odd primary fields of conformal weight 3 2 and by 10 odd primary fields of conformal weight 1 2 the commutation relations of this algebra which we will refer to asck 6 are represented by short distance operator product expansions ope we constructck 6 as a subalgebra of theso 6 superconformal algebra k6 thus giving it a natural representation as first order differential operators on the circle withn 6 extended symmetry we show thatck 6 has no nontrivial central extensions

representations of simple noncommutative jordan superalgebras i abstract in this article we begin the study of representations of simple finite dimensional noncommutative jordan superalgebras in the case of degree 3 we show that any finite dimensional representation is completely reducible and depending on the superalgebra quasiassociative or jordan then we study representations of superalgebras d t and k 3 and prove the kronecker factorization theorem for superalgebras d t in the last section we use a new approach to study noncommutative jordan representations of simple jordan superalgebras

bivariate shrinkage functions for wavelet based denoising exploiting interscale dependency most simple nonlinear thresholding rules for wavelet based denoising assume that the wavelet coefficients are independent however wavelet coefficients of natural images have significant dependencies we only consider the dependencies between the coefficients and their parents in detail for this purpose new non gaussian bivariate distributions are proposed and corresponding nonlinear threshold functions shrinkage functions are derived from the models using bayesian estimation theory the new shrinkage functions do not assume the independence of wavelet coefficients we show three image denoising examples in order to show the performance of these new bivariate shrinkage rules in the second example a simple subband dependent data driven image denoising system is described and compared with effective data driven techniques in the literature namely visushrink sureshrink bayesshrink and hidden markov models in the third example the same idea is applied to the dual tree complex wavelet coefficients

classification of simple linearly compact kantor triple systems over the complex numbers abstract simple finite dimensional kantor triple systems over the complex numbers are classified in terms of satake diagrams we prove that every simple and linearly compact kantor triple system has finite dimension and give an explicit presentation of all the classical and exceptional systems

2d orthogonal locality preserving projection for image denoising sparse representations using transform domain techniques are widely used for better interpretation of the raw data orthogonal locality preserving projection olpp is a linear technique that tries to preserve local structure of data in the transform domain as well vectorized nature of olpp requires high dimensional data to be converted to vector format hence may lose spatial neighborhood information of raw data on the other hand processing 2d data directly not only preserves spatial information but also improves the computational efficiency considerably the 2d olpp is expected to learn the transformation from 2d data itself this paper derives mathematical foundation for 2d olpp the proposed technique is used for image denoising task recent state of the art approaches for image denoising work on two major hypotheses i e non local self similarity and sparse linear approximations of the data locality preserving nature of the proposed approach automatically takes care of self similarity present in the image while inferring sparse basis a global basis is adequate for the entire image the proposed approach outperforms several state of the art image denoising approaches for gray scale color and texture images

adaptive finite element methods for parabolic problems i a linear model problem this paper is the first part in a series of papers on adaptive finite element methods for parabolic problems in this paper an adaptive algorithm is presented and analyzed for choosing the space a

dynamic domain decomposition and grid modification for parabolic problems abstract a dynamic grid modification and domain decomposition method is given and analyzed for parabolic problems this method allows one to apply different domain decompositions and different grids and interpolation polynomials on the subdomains at different time levels when necessary the procedure relies on an implicit galerkin method in the subdomains and explicit flux calculation on the inter domain boundaries in addition a dynamic finite element scheme is proposed and analyzed which is applicable to general parabolic problems these methods are well suited to large scale time dependent problems involving localized phenomena such as sharp fronts or layers which also change with time convergence and stability analyses in the l 2 norm are given numerical experiments are provided to check the performance of the methods and make comparison with other methods

cluster based probability model and its application to image and texture processing we develop analyze and apply a specific form of mixture modeling for density estimation within the context of image and texture processing the technique captures much of the higher order nonlinear statistical relationships present among vector elements by combining aspects of kernel estimation and cluster analysis experimental results are presented in the following applications image restoration image and texture compression and texture classification

classification of linearly compact simple jordan and generalized poisson superalgebras abstract we classify all linearly compact simple jordan superalgebras over an algebraically closed field of characteristic zero as a corollary we deduce the classification of all linearly compact unital simple generalized poisson superalgebras

two families of mixed finite elements for second order elliptic problems two families of mixed finite elements one based on triangles and the other on rectangles are introduced as alternatives to the usual raviart thomas nedelec spaces error estimates inl 2 andh 5 are derived for these elements a hybrid version of the mixed method is also considered and some superconvergence phenomena are discussed

a family of higher order mixed finite element methods for plane elasticity the dirichler problem for the equations of plane elasticity is approximated by a mixed finite element method using a new family of composite finite elements having properties analogous to those possessed by the raviart thomas mixed finite elements for a scalar second order elliptic equation estimates of optimal order and minimal regularity are derived for the errors in the displacement vector and the stress tensor inl 2 and optimal order negative norm estimates are obtained inh s for a range ofs depending on the index of the finite element space an optimal order estimate inl for the displacement error is given also a quasioptimal estimate is derived in an appropriate space all estimates are valid uniformly with respect to the compressibility and apply in the incompressible case the formulation of the elements is presented in detail

nonparametric bayesian dictionary learning for analysis of noisy and incomplete images nonparametric bayesian methods are considered for recovery of imagery based upon compressive incomplete and or noisy measurements a truncated beta bernoulli process is employed to infer an appropriate dictionary for the data under test and also for image recovery in the context of compressive sensing significant improvements in image recovery are manifested using learned dictionaries relative to using standard orthonormal image expansions the compressive measurement projections are also optimized for the learned dictionary additionally we consider simpler incomplete measurements defined by measuring a subset of image pixels uniformly selected at random spatial interrelationships within imagery are exploited through use of the dirichlet and probit stick breaking processes several example results are presented with comparisons to other methods in the literature

image denoising via bandwise adaptive modeling and regularization exploiting nonlocal similarity this paper proposes a new image denoising algorithm based on adaptive signal modeling and regularization it improves the quality of images by regularizing each image patch using bandwise distribution modeling in transform domain instead of using a global model for all the patches in an image it employs content dependent adaptive models to address the non stationarity of image signals and also the diversity among different transform bands the distribution model is adaptively estimated for each patch individually it varies from one patch location to another and also varies for different bands in particular we consider the estimated distribution to have non zero expectation to estimate the expectation and variance parameters for every band of a particular patch we exploit the nonlocal correlation in image to collect a set of highly similar patches as the data samples to form the distribution irrelevant patches are excluded so that such adaptively learned model is more accurate than a global one the image is ultimately restored via bandwise adaptive soft thresholding based on a laplacian approximation of the distribution of similar patch group transform coefficients experimental results demonstrate that the proposed scheme outperforms several state of the art denoising methods in both the objective and the perceptual qualities

low rankness transfer for realistic denoising current state of the art denoising methods such as non local low rank approaches have shown to give impressive results they are however mainly tuned to work with uniform gaussian noise corruption and known variance which is far from the real noise scenario in fact noise level estimation is already a challenging problem and denoising methods are quite sensitive to this parameter moreover these methods are based on shrinkage models that are too simple to reflect reality which results in over smoothing of important structures such as small scale text and textures we propose in this paper a new approach for more realistic image restoration based on the concept of low rankness transfer given a training clean noisy image pair our method learns a mapping between the non local noisy singular values and the optimal values for denoising to be transfered to a new noisy input one single image is enough for training the model and can be adapted to the noisy input by taking a correlated image experiments conducted on synthetic and real camera noise show that the proposed method leads to an important improvement both visually and in terms of psnr ssim

on the tits kantor koecher construction of unital jordan bimodules abstract in this paper we explore relationship between representations of a jordan algebra j and the lie algebra g obtained from j by the tits kantor koecher construction more precisely we construct two adjoint functors l i e j mod 1 g mod 1 and j o r g mod 1 j mod 1 where j mod 1 is the category of unital j bimodules and g mod 1 is the category of g modules admitting a short grading using these functors we classify j such that the semisimple part is of clifford type and the category j mod 1 is tame

calculus structure on the lie conformal algebra complex and the variational complex we construct a calculus structure on the lie conformal algebra cochain complex by restricting to degree one chains we recover the structure of a g complex introduced in a de sole and v g kac

on the structure of vector quantizers vector quantization is intrinsically superior to predictive coding transform coding and other suboptimal and em ad hoc procedures since it achieves optimal rate distortion performance subject only to a constraint on memory or block length of the observable signal segment being encoded the key limitation of existing techniques is the very large randomly generated code books which must be stored and the computational complexity of the associated encoding procedures the quantization operation is decomposed into its rudimentary structural components this leads to a simple and elegant approach to derive analytical properties of optimal quantizers some useful properties of quantizers and algorithmic approaches are given which are relevant to the complexity of both storage and processing in the encoding operation highly disordered quantizers which have been designed using a clustering algorithm are considered finally lattice quantizers are examined which circumvent the need for a code book by using a highly structured code based on lattices the code vectors are algorithmically generated in a simple manner rather than stored in a code book and fast algorithms perform the encoding algorithm with negligible complexity

estimating the probability of the presence of a signal of interest in multiresolution single and multiband image denoising we develop three novel wavelet domain denoising methods for subband adaptive spatially adaptive and multivalued image denoising the core of our approach is the estimation of the probability that a given coefficient contains a significant noise free component which we call signal of interest in this respect we analyze cases where the probability of signal presence is 1 fixed per subband 2 conditioned on a local spatial context and 3 conditioned on information from multiple image bands all the probabilities are estimated assuming a generalized laplacian prior for noise free subband data and additive white gaussian noise the results demonstrate that the new subband adaptive shrinkage function outperforms bayesian thresholding approaches in terms of mean squared error the spatially adaptive version of the proposed method yields better results than the existing spatially adaptive ones of similar and higher complexity the performance on color and on multispectral images is superior with respect to recent multiband wavelet thresholding

a global sparse gradient based coupled system for image denoising abstract we consider a coupled system for image denoising which consists of an anisotropic diffusion equation and a global sparse gradient model gsg the global sparse gradient model is used to estimate the edge map from the noisy image accurately and robustly the anisotropic diffusion process is guided by the edge map furthermore we prove the existence and uniqueness of the solutions of the coupled system with dirichlet initial boundary value problem finally comparing with the edge indicators based on local methods experimental results demonstrate that our proposed method has the state of the art performance among the pde based anisotropic diffusion approaches both in objective measurement and visual evaluation

the finite element method for parabolic equations ii a posteriori error estimation and adaptive approach abstract we extend in this paper the analysis of a posteriori estimates of the space discretization error presented in a previous paper 3 for time independent space meshes in the context of the model problem studied there results are given relating the effectivity of the error estimator to properties of the solution space meshes and manner in which the meshes change a procedure based upon this theory is presented for the adaptive construction of time dependent meshes the results of some computational experiments show that this procedure is practically very effective and suggest that it can be used to control the space discretization error in more general problems author

clustering based denoising with locally learned dictionaries in this paper we propose k lld a patch based locally adaptive denoising method based on clustering the given noisy image into regions of similar geometric structure in order to effectively perform such clustering we employ as features the local weight functions derived from our earlier work on steering kernel regression these weights are exceedingly informative and robust in conveying reliable local structural information about the image even in the presence of significant amounts of noise next we model each region or cluster which may not be spatially contiguous by ldquolearningrdquo a best basis describing the patches within that cluster using principal components analysis this learned basis or ldquodictionaryrdquo is then employed to optimally estimate the underlying pixel values using a kernel regression framework an iterated version of the proposed algorithm is also presented which leads to further performance enhancements we also introduce a novel mechanism for optimally choosing the local patch size for each cluster using stein s unbiased risk estimator sure we illustrate the overall algorithm s capabilities with several examples these indicate that the proposed method appears to be competitive with some of the most recently published state of the art denoising methods

structurable superalgebras of cartan type abstract we describe the simple lie superalgebras arising from the unital structurable superalgebras of characteristic 0 and construct four series of the unital simple structurable superalgebras of cartan type we give a classification of simple structurable superalgebras of cartan type over an algebraically closed field f of characteristic 0 together with the faulkner theorem on the classification of classical such superalgebras it gives a classification of the simple structurable superalgebras over f

a method for compact image representation using sparse matrix and tensor projections onto exemplar orthonormal bases we present a new method for compact representation of large image datasets our method is based on treating small patches from a 2 d image as matrices as opposed to the conventional vectorial representation and encoding these patches as sparse projections onto a set of exemplar orthonormal bases which are learned a priori from a training set the end result is a low error highly compact image patch representation that has significant theoretical merits and compares favorably with existing techniques including jpeg on experiments involving the compression of orl and yale face databases as well as a database of miscellaneous natural images in the context of learning multiple orthonormal bases we show the easy tunability of our method to efficiently represent patches of different complexities furthermore we show that our method is extensible in a theoretically sound manner to higher order matrices tensors we demonstrate applications of this theory to compression of well known color image datasets such as the gatech and cmu pie face databases and show performance competitive with jpeg lastly we also analyze the effect of image noise on the performance of our compression schemes

denoise diffusion weighted images using higher order singular value decomposition noise usually affects the reliability of quantitative analysis in diffusion weighted dw magnetic resonance imaging mri especially at high b values and or high spatial resolution higher order singular value decomposition hosvd has recently emerged as a simple effective and adaptive transform to exploit sparseness within multidimensional data in particular the patch based hosvd denoising has demonstrated superb performance when applied to t1 t2 and proton density weighted mri data in this study we aim to investigate the feasibility of denoising dw data using the hosvd transform with the low signal to noise ratio in typical dw data the patch based hosvd denoising suffers from stripe artifacts in homogeneous regions because of the hosvd bases learned from the noisy patches to address this problem we propose a novel denoising method it first introduces a global hosvd based denoising as a prefiltering stage to guide the subsequent patch based hosvd denoising stage the hosvd bases from the patch groups in prefiltered images are then used to transform the noisy patch groups in original dw data experiments were performed using simulated and in vivo dw data results show that the proposed method significantly reduces stripe artifacts compared with conventional patch based hosvd denoising methods and outperforms two state of the art denoising methods in terms of denoising quality and diffusion parameters estimation

image denoising by sparse 3 d transform domain collaborative filtering we propose a novel image denoising strategy based on an enhanced sparse representation in transform domain the enhancement of the sparsity is achieved by grouping similar 2d image fragments e g blocks into 3d data arrays which we call groups collaborative altering is a special procedure developed to deal with these 3d groups we realize it using the three successive steps 3d transformation of a group shrinkage of the transform spectrum and inverse 3d transformation the result is a 3d estimate that consists of the jointly filtered grouped image blocks by attenuating the noise the collaborative filtering reveals even the finest details shared by grouped blocks and at the same time it preserves the essential unique features of each individual block the filtered blocks are then returned to their original positions because these blocks are overlapping for each pixel we obtain many different estimates which need to be combined aggregation is a particular averaging procedure which is exploited to take advantage of this redundancy a significant improvement is obtained by a specially developed collaborative wiener filtering an algorithm based on this novel denoising strategy and its efficient implementation are presented in full detail an extension to color image denoising is also developed the experimental results demonstrate that this computationally scalable algorithm achieves state of the art denoising performance in terms of both peak signal to noise ratio and subjective visual quality

robust multilinear tensor rank estimation using higher order singular value decomposition and information criteria model selection in tensor decomposition is important for real applications if the rank of the original data tensor is unknown and the observed tensor is noisy in the tucker model the minimum description length mdl or bayesian information criteria have been applied to tensors via matrix unfolding but these methods are sensitive to noise when the tensors have a multilinear low rank structure given by the tucker model in this study we propose new methods for improving the mdl so it is more robust to noise the proposed methods are justified theoretically by analyzing the multilinear low rank structure of tensors extensive experiments including numerical simulations and a real application to image denoising are provided to illustrate the advantages of the proposed methods

a patch based low rank tensor approximation model for multiframe image denoising abstract compared with matrix tensor is a more natural representation for multiframe image such as hyperspectral image and mri image low rankness of tensor is essential to describe the intrinsic geometrical structure of these data patch based low rank models have shown their ability to exploit spatial redundancy of computer vision data especially for natural image denoising however most of the existed patch based matrix models are based on two dimensional low rankness which cannot fully reveal the correlation of every direction in high order multiframe images the existed patch based tensor models either need additional assumptions or need svd in every loop of iteration which is computationally expensive in this paper we propose a novel patch based model to recover a low rank tensor by simultaneously performing low rank matrix factorizations to the all mode matricizations of the underlying low rank tensor an augmented lagrangian alternating minimization algorithm is implemented to solve the model along with two adaptive rank adjusting strategies when the exact rank is unknown we apply the proposed algorithm to multiframe image denoising by exploiting the nonlocal self similarity experimental results show that our algorithm can better preserve the sharpness of important image structures and outperforms several state of the art denoising methods

mixed methods with dynamic finite element spaces for miscible displacement in porous media abstract miscible displacement in porous media is modeled by a nonlinear coupled system of two partial differential equations we approximate the pressure equation which is elliptic and the concentration equation which is parabolic but normally convection dominated by the mixed methods with dynamic finite element spaces i e different number of elements and different basis functions are adopted at different time levels and the approximate concentration is projected onto the next finite element space in weighted l 2 norm for starting a new time step this allows us to make local grid refinements or unrefinements and basis function improvements two fully discrete schemes are presented and analysed error estimates show that these methods have optimal convergent rate in some sense the efficiency and capability of the dynamic finite element method are commented for accurately solving time dependent problems with localized phenomena such as fronts shocks and boundary layers

second order finite element approximations and a posteriori error estimation for two dimensional parabolic systems we discuss an adaptive local refinement finite element method of lines for solving vector systems of parabolic partial differential equations on two dimensional rectangular regions the partial differential system is discretized in space using a galerkin approach with piecewise eight node serendipity functions an a posteriori estimate of the spatial discretization error of the finite element solution is obtained using piecewise fifth degree polynomials that vanish on the edges of the rectangular elements of a grid ordinary differential equations for the finite element solution and error estimate are integrated in time using software for stiff differential systems the error estimate is used to control a local spatial mesh refinement procedure in an attempt to keep a global measure of the error within prescribed limits examples appraising the accuracy of the solution and error estimate and the computational efficiency of the procedure relative to one using bilinear finite elements are presented

a parallel primal dual splitting method for image restoration we develop a parallel primal dual splitting method to solve large scale image restoration problems which involve the sum of several linear operator coupled nonsmooth but proximable terms with the proposed method the objective function is decomposed into pieces that can be processed individually no inverse operator is involved in our method and the highly parallel structure makes it preferable in distributed computation the convergence is proven and the convergence rate is analyzed besides its equivalence to the relaxed parallel linearized alternating direction method of multipliers pladmm is addressed applications to image restoration problems with compound l1 regularizer and comparisons with state of the art methods are detailed to show the superiority of the proposed method

grid modification for second order hyperbolic problems a family of galerkin finite element methods is presented to accurately and efficiently solve the wave equation that includes sharp propagating wave fronts the new methodology involves different finite element discretizations at different time levels thus at any time level relatively coarse grids can be applied in regions where the solution changes smoothly while finer grids can be employed near wave fronts the change of grid from time step to time step need not be continuous and the number of grid points at different time levels can be arbitrarily different the formulation is applicable to general second order hyperbolic equations stability results are proved and a priori error estimates are established for several boundary conditions our error estimates consist of three parts the time finite difference discretization error the spatial finite element discretization error and the error due to the projections of the approximated solution from old grids onto new grids

grid modification for the wave equation with attenuation the wave equation with attenuation due to a linear friction is approximated by a new mixed finite element method which allows one to use different grids and basis functions at different times when necessary this method enables one to track sharp moving wave fronts more efficiently and accurately error estimates with optimal convergent rates are established unconditional stability is also proved for this method

an algorithm for improving non local means operators via low rank approximation we present a method for improving a non local means nlm operator by computing its low rank approximation the low rank operator is constructed by applying a filter to the spectrum of the original nlm operator this results in an operator which is less sensitive to noise while preserving important properties of the original operator the method is efficiently implemented based on chebyshev polynomials and is demonstrated on the application of natural images denoising for this application we provide a comparison of our method with other denoising methods

representations of simple jordan superalgebras abstract this paper completes description of categories of representations of finite dimensional simple unital jordan superalgebras over algebraically closed field of characteristic zero

different domain decompositions at different times for capturing moving local phenomena abstract a conservative galerkin domain decomposition method for time dependent problems is given and analyzed this method allows one to apply different domain decompositions at different time levels when necessary in order to capture time changing local phenomena such as propagating fronts or moving layers error estimates in the energy and l 2 norms are established numerical results are presented