partitions of elements in a monoid and its applications to systems theory abstract the feedback class of a locally brunovsky linear system is fully determined by the decomposition of state space as direct sum of system invariants 2 in this paper we attack the problem of enumerating all feedback classes of locally brunovsky systems over an n dimensional state space and translate to the combinatorial problem of enumerating all the partitions of integer n in some abelian semigroup the problem of computing the number n k of all the partitions of integer n into k different summands is pointed out

context aware sparse decomposition for image denoising and super resolution image prior models based on sparse and redundant representations are attracting more and more attention in the field of image restoration the conventional sparsity based methods enforce sparsity prior on small image patches independently unfortunately these works neglected the contextual information between sparse representations of neighboring image patches it limits the modeling capability of sparsity based image prior especially when the major structural information of the source image is lost in the following serious degradation process in this paper we utilize the contextual information of local patches denoted as context aware sparsity prior to enhance the performance of sparsity based restoration method in addition a unified framework based on the markov random fields model is proposed to tune the local prior into a global one to deal with arbitrary size images an iterative numerical solution is presented to solve the joint problem of model parameters estimation and sparse recovery finally the experimental results on image denoising and super resolution demonstrate the effectiveness and robustness of the proposed context aware method

feedback equivalence of constant linear systems abstract two constant linear systems are said to be feedback equivalent if one can be transformed into the other via an element of the feedback group which acts by state space feedback and by change of basis in the state and input spaces let c n m be the space of n dimensional completely reachable systems with m dimensional input pairs of matrices n n and n m the action of the feedback group partitions the space c n m into finitely many orbits equivalence classes and the closure of each orbit is a union of orbits if one views orbit closure as deformation then orbit closure may be considered in terms of perturbations or system failure in this paper we determine 1 a classification of the orbits and 2 the orbits contained in the closure of a given orbit both of these problems have been solved previously see 1 4 6 3 here we present simple proofs and point out a connection between this problem and the analogous problem for nilpotent matrices

on feedback invariants for linear dynamical systems abstract the goal of this paper is to prove that if r is a commutative ring containing a non zero finitely generated maximal ideal m containing its annihilator such that every unit of r m lifts to a unit of r then the category of reachable systems over r is wild in the sense of classical representation theory from this it follows that a canonical form for a reachable system over a pid is not likely to be found more specifically canonical forms are unlikely to be found for systems over z and k t when k is a field

enumeration of classes of linear systems via equations and via partitions in an ordered abelian monoid abstract we prove that the feedback classes of locally brunovsky linear systems are given by the decomposition of state space into direct summands hence the problem of enumerating feedback classes of systems is equivalent to the problem of enumerating all solutions of a linear equation over a commutative zerosumfree monoid if this monoid is also cancelative then the problem is solved by all the partitions

assignable polynomials to linear systems over von neumann regular rings abstract given a system a b over a commutative von neumann regular ring r it is proved that there exist a matrix f and a vector u such that the single input system a b f b u and the original system a b have the same module of reachable states and the same set of polynomials assignable by state feedback moreover there is a bijection between reachable states and assignable polynomials in the form of a certain isomorphism of r modules and the existence of this isomorphism for all systems actually characterizes von neumann regular rings finally the set of assignable polynomials to a single input system is completely described for arbitrary commutative rings which in the case of von neumann regular rings completes the study of assignable polynomials to multi input systems

sparsity preserving projections with applications to face recognition dimensionality reduction methods drs have commonly been used as a principled way to understand the high dimensional data such as face images in this paper we propose a new unsupervised dr method called sparsity preserving projections spp unlike many existing techniques such as local preserving projection lpp and neighborhood preserving embedding npe where local neighborhood information is preserved during the dr procedure spp aims to preserve the sparse reconstructive relationship of the data which is achieved by minimizing a l1 regularization related objective function the obtained projections are invariant to rotations rescalings and translations of the data and more importantly they contain natural discriminating information even if no class labels are provided moreover spp chooses its neighborhood automatically and hence can be more conveniently used in practice compared to lpp and npe the feasibility and effectiveness of the proposed method is verified on three popular face databases yale ar and extended yale b with promising results

denoising natural images based on a modified sparse coding algorithm this paper proposes a novel image reconstruction method for natural images using a modified sparse coding sc algorithm proposed by us this sc algorithm exploited the maximum kurtosis as the maximizing sparse measure criterion at one time a fixed variance term of sparse coefficients is used to yield a fixed information capacity on the other hand in order to improve the convergence speed we use a determinative basis function which is obtained by a fast fixed point independent component analysis fastica algorithm as the initialization feature basis function of our sparse coding algorithm instead of using a random initialization matrix the experimental results show that by using our sc algorithm the feature basis vectors of natural images can be successfully extracted then exploiting these features the original images can be reconstructed easily furthermore compared with the standard ica method the experimental results show that our sc algorithm is indeed efficient and effective in performing image reconstruction task

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

cyclic accessibility of reachable states characterizes von neumann regular rings abstract the class of commutative von neumann regular rings is characterized by a generalization of the feedback cyclization property to non necessarily reachable systems for any system a b there exist a matrix k and a vector u such that a b and the single input system a bk bu have the same submodule of reachable states an explicit algorithm is presented to obtain k u for a given system a b

canonical forms for single input linear systems in this paper we obtain a canonical form for single input n dimensional linear systems over z and in general over a bezout domain we also give an algorithm to obtain that canonical form

the pointwise feedback relation for linear dynamical systems abstract let and be two m input n dimensional linear dynamical systems over a commutative ring r if is feedback equivalent to then is pointwise feedback equivalent to i e for all prime ideal p of r the systems p and p are feedback equivalent over the residue field k p where p is the natural extension of to k p this paper is devoted to the study of the pointwise feedback relation we characterize when two systems and are pointwise equivalent we show that r is an absolutely flat ring if and only if the feedback relation and the pointwise feedback relation are equivalent the particular case of rings of real valued continuous functions is specially treated

direct computation of cauchy principal value integrals in advanced boundary elements this paper presents a new method for the direct computation of strongly singular integrals existing in the cauchy principal value sense it can be usefully applied in the solution by the direct boundary element method of many different problems initially some considerations are provided in order to summarize the state of the art on this issue then the features of the proposed method are reported the procedure allows the direct calculation of cauchy principal value integrals with first order singularity and it is applicable even in advanced boundary element methods employing high order elements it requires only the use of standard gaussian quadrature formulae plus the computation of a logarithmic term some examples show the effectiveness and efficiency of the procedure

rosenbrock s theorem for systems over von neumann regular rings abstract if a b is a finite system over a commutative von neumann regular ring r the problem of searching for a matrix f such that the pencil s i a b f has some prescribed smith normal form is reduced to the case where r is a field a problem which for controllable systems is described by a well known theorem of rosenbrock on pole assignment 12 and was then generalized to noncontrollable pairs 14 it this paper von neumann regular rings are characterized as the class of commutative rings for which the solution of the above problem over the ring is equivalent to its solution in each residue field

the effective calculation of all assignable polynomials to a single input system over a bezout domain the set of all feedback assignable polynomials to a given single input system over a bezout domain is obtained the general case is reduced to the case of weakly reachable systems for these systems a canonical form for the algebraic equivalence is obtained algorithms and examples over a euclidean domain and in particular over the ring z of rational integers are also given the problem of deciding and feedback assignment of a given polynomial to a given non reachable n dimensional linear system is solved effectively up to a cost of o n4 arithmetic operations

weighted averaging for denoising with overcomplete dictionaries we consider the scenario where additive independent and identically distributed i i d noise in an image is removed using an overcomplete set of linear transforms and thresholding rather than the standard approach where one obtains the denoised signal by ad hoc averaging of the denoised estimates provided by denoising with each of the transforms we formulate the optimal combination as a conditional linear estimation problem and solve it for optimal estimates our approach is independent of the utilized transforms and the thresholding scheme and as we illustrate using oracle based denoisers it extends established work by exploiting a separate degree of freedom that is in general not reachable using previous techniques our derivation of the optimal estimates specifically relies on the assumption that the utilized transforms provide sparse decompositions at the same time our work is robust as it does not require any assumptions about image statistics beyond sparsity unlike existing work which tries to devise ever more sophisticated transforms and thresholding algorithms to deal with the myriad types of image singularities our work uses basic tools to obtain very high performance on singularities by taking better advantage of the sparsity that surrounds them with well established transforms we obtain results that are competitive with state of the art methods

automatic design of high sensitivity color filter arrays with panchromatic pixels in most of existing digital cameras color images have to be reconstructed from raw images which only have one color sensed at each pixel as their imaging sensors are covered by color filter arrays cfas at each pixel a cfa usually allows only a portion of the light spectrum to pass through and thereby reduces the light sensitivity of pixels to address this issue previous works have explored adding panchromatic pixels into cfas however almost all existing methods assign panchromatic pixels empirically making the designed cfas prone to aliasing artifacts in this paper based on a mathematical model we propose a fully automatic approach to designing high sensitivity cfas using panchromatic pixels by the frequency structure representation of cfas we formulate high sensitivity cfa design as a continuous multi objective optimization problem where robustness to aliasing artifacts and percentage of panchromatic pixels are simultaneously maximized we analyze the characteristics of our new formulation according to the analysis we develop a new method to propose frequency structure candidates which can produce cfas that reach a desired percentage of panchromatic pixels then for each candidate we optimize parameters to obtain the final cfa which is an appropriately balanced solution to the multi objective optimization problem we formulate the two design procedures as constrained optimization problems and solve them using the alternating direction method extensive experiments confirm the advantage of the proposed method in both low light and normal light conditions

on the duality principle for linear dynamical systems over commutative rings abstract the main result in this paper characterizes those commutative rings r having the property that every linear dynamical system over r verifies the duality principle i e the system is observable reachable if and only if the dual system t is reachable observable this characterization is given in terms of the finitely generated faithful ideals of r and it generalizes a result due to ching and wyman for the noetherian case in case r satisfies the additional condition of being a reduced ring we prove that the duality principle holds in r if and only if the height of every finitely generated ideal of r is zero

feedback invariants for linear dynamical systems over a principal ideal domain abstract this paper studies the action of the feedback group f n m on m input n dimensional reachable linear dynamical systems over a principal ideal domain r for such a 2 dimensional system a complete set of invariants is given which characterizes the feedback class of in particular it is characterized in terms of these invariants when has the feedback cyclization property the particular cases r z and r r x are studied in some detail finally when n is arbitrary the feedback classification is given for the class of reachable systems f g such that g is a matrix with at least n 1 invariant factors equal to one

dual boundary element formulation for fracture mechanics analysis of shear deformable shells this paper presents a new boundary element formulation for fracture mechanics analysis of shear deformable shells hyper singular boundary integral equations for shear deformable shells are derived dual boundary element formulations are constructed by using traction integral equations on one side of the crack surface and displacement integral equations on the other side of the crack surface and all other boundaries five stress intensity factors two for membrane behaviour and three for shear and bending are computed several crack configurations are analysed to demonstrate the efficiency and accuracy of the proposed formulation

on the k theory of feedback actions on linear systems abstract a categorical approach to linear control systems is introduced feedback actions on linear control systems arise as symmetric monodical category s r stable feedback isomorphisms generalize dynamic enlargement of pairs of matrices subcategory of locally brunovsky linear systems b r is studied we prove that the stable feedback isomorphisms of locally brunovsky linear systems are characterized by the grothendieck group k 0 b r hence a link from linear dynamical systems to algebraic k theory is established

a characterization of gcu rings with the fc2 property abstract we study linear systems f g with coefficients in a commutative ring r with the gcu property whenever f g is controllable there exists a vector u with gu unimodular our main result is a gcu ring is an fc2 ring i e every two dimensional controllable system over r is feedback cyclizable if and only if r satisfies the following property for any finitely generated ideal i and f invertible modulo i there exist a unit u and an element h with f uh2 mod i

pole shifting for linear systems over commutative rings abstract this paper deals with the pole shifting problem for non necessarily reachable linear systems the notion of ps ring is introduced in the same way as the notion of pole assignable ring is given for reachable systems we prove that a bcs ring is a ps ring and that over a prufer domain these properties are equivalent finally we study when the converse of the pole shifting theorem is verified

hypersingular boundary element formulation for reissner plates in this work the hypersingular boundary element formulation for plate bending analysis based on reissner theory is presented first order taylor expansion are used to deal with the strong singularity o 1 r whereas rigid body considerations together with the taylor expansion are used to compute the hypersingular kernels o l r2 the plate boundary is discretised into quadratic isoparametric discontinuous boundary elements to satisfy the continuity requirements for the boundary unknowns several examples are tested including thin and thick plates the results show a good agreement with both the analytical solutions and the corresponding results for the standard displacement boundary element formulation 1998 elsevier science ltd all rights reserved

a boundary element formulation for geometrically nonlinear analysis of shear deformable shells abstract a new boundary element method to solve geometrically nonlinear deflection problems of shear deformable shallow shells having quadratic mid surface is presented the displacement integral equations have been derived to obtain five integral equations in term of displacements two rotations one out of plane displacement and two in plane displacements the boundary is discretised into quadratic isoparametric elements and the domain is transferred to the boundary using the dual reciprocity technique a simple yet efficient load incremental technique is developed to solve the nonlinear problem several examples are presented and the results are in good agreement with the finite element method

partition of unity and drilling rotations in the boundary element method bem abstract this paper presents a novel approach to include drilling rotations in the classical two dimensional boundary element method the approach is based on a simple partition of unity strategy that gives rise to a fictitious rotational degree of freedom using the well known allman s triangle strategy a functional based on the rotational residual ties the average fictitious drilling rotation field to the true rotation field induced from the two dimensional elasticity problem and additionally provides the required extra equation for the enriched bem formulation the approach maintains the boundary only character of bem and the partition of unity enrichment makes it general totally kernel independent and efficient just certain areas of the boundary could be enriched the accuracy of the proposed method is assessed with well known benchmark problems e g cook s membrane

robust locally linear embedding in the past few years some nonlinear dimensionality reduction nldr or nonlinear manifold learning methods have aroused a great deal of interest in the machine learning community these methods are promising in that they can automatically discover the low dimensional nonlinear manifold in a high dimensional data space and then embed the data points into a low dimensional embedding space using tractable linear algebraic techniques that are easy to implement and are not prone to local minima despite their appealing properties these nldr methods are not robust against outliers in the data yet so far very little has been done to address the robustness problem in this paper we address this problem in the context of an nldr method called locally linear embedding lle based on robust estimation techniques we propose an approach to make lle more robust we refer to this approach as robust locally linear embedding rlle we also present several specific methods for realizing this general rlle approach experimental results on both synthetic and real world data show that rlle is very robust against outliers

drm multidomain mass conservative interpolation approach for the bem solution of the two dimensional navier stokes equations abstract the dual reciprocity method drm is a technique to transform the domain integrals that appear in the boundary element method into equivalent boundary integrals in this approach the nonlinear terms are usually approximated by an interpolation applied to the convective terms of the navier stokes equations in this paper we introduce a radial basis function interpolation scheme for the velocity field that satisfies the continuity equation mass conservative the proposed method performs better than the classical interpolation used in the drm approach to represent such a field the new scheme together with a subdomain variation of the dual reciprocity method allows better approximation of the nonlinear terms in the navier stokes equations

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

a characterization of von neumann rings in terms of linear systems abstract a new characterization of commutative von neumann regular rings is given in terms of linear control systems having locally a brunovsky canonical form the problem of enumerating reachable systems over certain von neumann regular ring is solved extending classical results over fields

translation invariant directional framelet transform combined with gabor filters for image denoising this paper is devoted to the study of a directional lifting transform for wavelet frames a nonsubsampled lifting structure is developed to maintain the translation invariance as it is an important property in image denoising then the directionality of the lifting based tight frame is explicitly discussed followed by a specific translation invariant directional framelet transform tidft the tidft has two framelets 1 2 with vanishing moments of order two and one respectively which are able to detect singularities in a given direction set it provides an efficient and sparse representation for images containing rich textures along with properties of fast implementation and perfect reconstruction in addition an adaptive block wise orientation estimation method based on gabor filters is presented instead of the conventional minimization of residuals furthermore the tidft is utilized to exploit the capability of image denoising incorporating the map estimator for multivariate exponential distribution consequently the tidft is able to eliminate the noise effectively while preserving the textures simultaneously experimental results show that the tidft outperforms some other frame based denoising methods such as contourlet and shearlet and is competitive to the state of the art denoising approaches

estimating quadrature errors for an efficient method for quasi singular boundary integral abstract the numerical resolution of the boundary integral equations applied to the differential equations of laplace helmholtz and maxwell requires the handling of quasi singular integrals with different order of singularity the numerical approximation of the integral equations of different kinds is made by boundary finite elements in this paper we present a complete survey for estimating quadrature errors for the numerical techniques proposed by huang and cruse q huang t a cruse some notes on singular integral techniques in boundary element analysis int j numer methods eng 36 15 1993 2643 2659 to calculate the quasi singular integrals to validate the accuracy and efficiency of these techniques and approve our study some numerical examples are presented and discussed

brunowsky local form of a holomorphic family of pairs of matrices abstract following arnold s techniques we obtain a local canonical form of a holomorphic family of pairs of matrices a b acted on by the state feedback group we obtain an explicit formula to compute the dimension of the base space of any miniversal deformation of a 0 b 0 we make some applications to local perturbations of a pair of matrices

local sparse structure denoising for low light level image sparse and redundant representations perform well in image denoising however sparsity based methods fail to denoise low light level lll images because of heavy and complex noise they consider sparsity on image patches independently and tend to lose the texture structures to suppress noises and maintain textures simultaneously it is necessary to embed noise invariant features into the sparse decomposition process we therefore used a local structure preserving sparse coding lspsc formulation to explore the local sparse structures both the sparsity and local structure in image it was found that with the introduction of spatial local structure constraint into the general sparse coding algorithm lspsc could improve the robustness of sparse representation for patches in serious noise we further used a kernel lspsc k lspsc formulation which extends lspsc into the kernel space to weaken the influence of linear structure constraint in nonlinear data based on the robust lspsc and k lspsc algorithms we constructed a local sparse structure denoising lssd model for lll images which was demonstrated to give high performance in the natural lll images denoising indicating that both the lspsc and k lspsc based lssd models have the stable property of noise inhibition and texture details preservation

error indicators for adaptive mesh refinement in the boundary element method a new approach in this paper a new approach to the development of a posteriori error indicators for the direct boundary element method bem is presented it takes advantage of a unique opportunity offered by the collocation bem that is the possibility of obtaining more than one numerical solution from a given boundary element mesh unlike other approaches the error indicator introduced in the present paper does not require any explicit evaluation of the residual of the approximate solution in order to test the capability of the proposed error indicators to actually control a selective mesh refinement process an h adaptive refinement strategy is also described together with the criteria for refinement and for the termination of the adaptive process full details on the whole numerical implementation for two dimensional problems are provided in particular there is described a direct method for the numerical evaluation of cauchy principal value integrals numerical examples show that pointwise convergence is always obtained in a few steps and the final meshes look nearly as if they were designed by an expert analyst

comments on pole assignability over rings abstract we observe that the proof by eising of the pole assignment theorem for linear systems over a principal ideal domain 4 actually remains valid for any elementary divisor ring for large classes of rings matrix characterizations of pole assignability are given

dynamic feedback over principal ideal domains and quotient rings let r be a principal ideal domain in this paper we prove that for a large class of linear systems dynamic feedback over r is equivalent to static feedback over a quotient ring of r in particular when r is the ring of integers z one has that the static feedback classification problem over finite rings is equivalent to the dynamic feedback classification problem over z restricted to a special type of system

feedback classification of linear systems over von neumann regular rings abstract it is proved that feedback classification of a linear system over a commutative von neumann regular ring r can be reduced to the classification of a finite family of systems each of which is properly split into a reachable and a non reachable part where the reachable part is in a brunovski type canonical form while the non reachable part can only be altered by similarity if a canonical form is known for similarity of matrices over r then it can be used to construct a canonical form for feedback equivalence an explicit algorithm is given to obtain the canonical form in a computable context together with an example over a finite ring

the dynamic feedback equivalence over principal ideal domains we show that over a principal ideal domain the dynamic feedback equivalence for not necessarily reachable linear systems is reduced to the feedback equivalence for one augmented systems we also obtain the dynamic feedback classification for two dimensional linear systems

brunovsky s canonical form for linear dynamical systems over commutative rings abstract this paper is devoted to studying the action of the feedback group on linear dynamical systems over a commutative ring r with unit we characterize the class of m input n dimensional reachable linear dynamical systems f g over r that are feedback equivalent to a system c fc gc with brunovsky s canonical form this characterization is obtained in terms of the minors of the matrices g i g fg f i 1 g for 1 i n

the continuation approach a general framework for the analysis and evaluation of singular and near singular integrals the continuation approach presented in this paper is a simple and unified framework for analyzing and computing a large class of singular and near singular integrals such as those that arise in the boundary element method the analysis formulates singular and near singular integrals consistently as instances of a single phenomenon with all types of algebraic singularities treated in a similar way for domains of arbitrary dimension singular integrals are viewed merely as continuations of nonsingular but perhaps near singular ones by placing the singularity of the integrand outside the integration domain and taking the limit as it approaches the domain the technique exploits the functional homogeneity shared by the green s functions of many physical problems for flat surfaces this allows the integral to be mapped to the contour of the integration domain curved surfaces are handled by projecting the integration domain to a tangent hyperplane where the singular components of the integral can be

on matrix inverses modulo a subspace given a pair of matrices a b rn n rn m with coefficients in a commutative ring we study the problem of finding a matrix f such that a bf becomes invertible we point out some relations between the problem of finding feedback inverses of a modulo b and the pole shifting problem for the pair a b in fact we give feedback invertibility results over a well known large class of rings related with the pole shifting the class of pa rings on the other hand we also give a pointwise global characterization the ring r of rational integers and the coordinate ring of the real unit circle r x y x2 y2 1 are studied in some detail finally the problem of derivative feedback standardization of generalized linear systems is reviewed as a particular case

a new h adaptive refinement scheme for the boundary element method using local reanalysis abstract this paper presents a new way of estimating the discretization error in the boundary element method bem based on the concept of local reanalysis lr the principle of lr is implemented for the particular case of two dimensional potential problems in an attempt to find a technique to calculate a cheaply computable predicted solution to use in the evaluation of the quality of the boundary element results the error estimators are defined from the difference between the bem and lr solutions which measures the sensitivity of the boundary element results to a local change in the mesh an h adaptive method using lr is developed and different numerical experiments are carried out to test its performance

on higher order linear systems reachability and feedback invariants we consider l order linear control systems with coefficients in a commutative ring r the notion of reachability is studied for such systems and it is related to the reachability of the associated linearized system lin we prove that reachability is a pointwise property just as in the case of first order systems the feedback equivalence of l order linear control systems over a commutative ring is also studied we introduce some feedback invariants that generalize the hermida perez sanchezgiralda invariant modules mi to conclude we apply results in order to give classification results in low dimension