a relationship subnormal polynomially hyponormal and semi weakly hyponormal weighted shifts abstract let x x a b c be a one step backward extension sequence of stampfli s subnormal completion where 0 x a b c and let w x be the associated weighted shift in this paper we prove that w x is subnormal if and only if w x is polynomially hyponormal which also is equivalent to that w x is completely semi weakly hyponormal

subnormality for arbitrary powers of 2 variable weighted shifts whose restrictions to a large invariant subspace are tensor products the lifting problem for commuting subnormals lpcs asks for necessary and sufficient conditions for a pair of subnormal operators onhilbert space to admit commuting normal extensions we study lpcs within the class of commuting 2 variable weighted shifts t t1 t2 with subnormal components t1 and t2 acting on the hilbert space 2 z 2 with canonical orthonormal basis fe k1 k2 gk1 k2 0 the core of a commuting 2 variable weighted shift t c t is the restriction of t to the invariant subspace generated by all vectors e k1 k2 with k1 k2 1 we say that c t is of tensor form if it is unitarily equivalent to

a rodriguez formula and integration measure for the quantum deformed legendre functions quantum deformed analogs of the legendre functions are constructed from shift operator representations of the quantum deformed orbital angular momentum operators a rodriguez formula is found as well as the measure used to orthonormalize the functions

approximation in the mean by polynomials for a positive measure al with compact support in the complex plane c and for 1 t co let pt i denote the closure in lt i of the polynomials in one complex variable the purpose of this paper is to describe pt a the main results are the following first there exists a borel partition ail of the support of al such that for i 1 the space pt t laai contains no nontrivial characteristic functions and

mixed bram halmos and agler embry conditions abstract the subnormality of a hilbert space operator may be characterized either by the bram halmos conditions positivity of certain operator matrices or the agler embry conditions positivity of certain operator differences we define and consider mixed conditions involving matrices of operator differences thus yielding conditions whose extremes are the bram halmos and agler embry conditions we study these conditions for weighted shifts showing that they reduce to matrices of differences of the moments of the shifts and examine these conditions under the perturbation of a single weight of a subnormal shift

global optimization of polynomials using gradient tentacles and sums of squares we consider the problem of computing the global infimum of a real polynomial f on mathbb r n every global minimizer of f lies on its gradient variety i e the algebraic subset of mathbb r n where the gradient of f vanishes if f attains a minimum on mathbb r n it is therefore equivalent to look for the greatest lower bound of f on its gradient variety nie demmel and sturmfels proved recently a theorem about the existence of sums of squares certificates for such lower bounds based on these certificates they find arbitrarily tight relaxations of the original problem that can be formulated as semidefinite programs and thus be solved efficiently we deal here with the more general case when f is bounded from below but does not necessarily attain a minimum in this case the method of nie demmel and sturmfels might yield completely wrong results in order to overcome this problem we replace the gradient variety by larger semialgebraic subsets of mathbb r n which we call gradient tentacles it now gets substantially harder to prove the existence of the necessary sums of squares certificates

probleme des moments sur un compact de rn et decomposition de polynomes a plusieurs variables on donne la solution du probleme des moments pour un compact d interieur non vide quelconque de r n on utilise cette resolution pour obtenir un resultat de decomposition des polynomes strictement positifs sur un compact d interieur non vide

a recursive soft decision approach to blind image deconvolution this paper presents a new approach to blind image deconvolution based on soft decision blur identification and hierarchical neural networks traditional blind algorithms require a hard decision on whether the blur satisfies a parametric form before their formulations as the blurring function is usually unknown a priori this precondition inhibits the incorporation of parametric blur knowledge domain into the restoration schemes the new technique addresses this difficulty by providing a continual soft decision blur adaptation with respect to the best fit parametric structure throughout deconvolution the approach integrates the knowledge of well known blur models without compromising its flexibility in restoring images degraded by nonstandard blurs an optimization scheme is developed where a new cost function is projected and minimized with respect to the image and blur domains a nested neural network called the hierarchical cluster model is employed to provide an adaptive perception based restoration its sparse synaptic connections are instrumental in reducing the computational cost of restoration conjugate gradient optimization is adopted to identify the blur due to its computational efficiency the approach is shown experimentally to be effective in restoring images degraded by different blurs

high dimensional camera shake removal with given depth map camera motion blur is drastically nonuniform for large depth range scenes and the nonuniformity caused by camera translation is depth dependent but not the case for camera rotations to restore the blurry images of large depth range scenes deteriorated by arbitrary camera motion we build an image blur model considering 6 degrees of freedom dof of camera motion with a given scene depth map to make this 6d depth aware model tractable we propose a novel parametrization strategy to reduce the number of variables and an effective method to estimate high dimensional camera motion as well the number of variables is reduced by temporal sampling motion function which describes the 6 dof camera motion by sampling the camera trajectory uniformly in time domain to effectively estimate the high dimensional camera motion parameters we construct the probabilistic motion density function pmdf to describe the probability distribution of camera poses during exposure and apply it as a unified constraint to guide the convergence of the iterative deblurring algorithm specifically pmdf is computed through a back projection from 2d local blur kernels to 6d camera motion parameter space and robust voting we conduct a series of experiments on both synthetic and real captured data and validate that our method achieves better performance than existing uniform methods and nonuniform methods on large depth range scenes

regularization of rif blind image deconvolution blind image restoration is the process of estimating both the true image and the blur from the degraded image using only partial information about degradation sources and the imaging system our main interest concerns optical image enhancement where the degradation often involves a convolution process we provide a method to incorporate truncated eigenvalue and total variation regularization into a nonlinear recursive inverse filter rif blind deconvolution scheme first proposed by kundar and by kundur and hatzinakos 1996 1998 tests are reported on simulated and optical imaging problems

a soft double regularization approach to parametric blind image deconvolution this paper proposes a blind image deconvolution scheme based on soft integration of parametric blur structures conventional blind image deconvolution methods encounter a difficult dilemma of either imposing stringent and inflexible preconditions on the problem formulation or experiencing poor restoration results due to lack of information this paper attempts to address this issue by assessing the relevance of parametric blur information and incorporating the knowledge into the parametric double regularization pdr scheme the pdr method assumes that the actual blur satisfies up to a certain degree of parametric structure as there are many well known parametric blurs in practical applications further it can be tailored flexibly to include other blur types if some prior parametric knowledge of the blur is available a manifold soft parametric modeling technique is proposed to generate the blur manifolds and estimate the fuzzy blur structure the pdr scheme involves the development of the meaningful cost function the estimation of blur support and structure and the optimization of the cost function experimental results show that it is effective in restoring degraded images under different environments

a solution to the cauchy dual subnormality problem for 2 isometries abstract the cauchy dual subnormality problem asks whether the cauchy dual operator t t t t 1 of a 2 isometry t is subnormal in the present paper we show that the problem has a negative solution the first counterexample depends heavily on a reconstruction theorem stating that if t is a 2 isometric weighted shift on a rooted directed tree with nonzero weights that satisfies the perturbed kernel condition then t is subnormal if and only if t satisfies the unperturbed kernel condition the second counterexample arises from a 2 isometric adjacency operator of a locally finite rooted directed tree again by thorough investigations of positive solutions of the cauchy dual subnormality problem in this context we prove that if t is a 2 isometry satisfying the kernel condition or a quasi brownian isometry then t is subnormal we construct a 2 isometric adjacency operator t of a rooted directed tree such that t does not satisfy the kernel condition t is not a quasi brownian isometry and t is subnormal

a new approach to constrained total least squares image restoration abstract recently there has been a growing interest and progress in using total least squares tls methods for solving blind deconvolution problems arising in image restoration here the true image is to be estimated using only partial information about the blurring operator or point spread function psf which is subject to error and noise in this paper we present a new iterative regularized and constrained tls image restoration algorithm neumann boundary conditions are used to reduce the boundary artifacts that normally occur in restoration processes preliminary numerical tests are reported on some simulated optical imaging problems in order to illustrate the effectiveness of the approach as well as the fast convergence of our iterative scheme

cubically hyponormal weighted shifts and their examples we obtain criteria for cubical hyponormality which provide a tool for finding examples being distinct the classes of 2 hyponormal cubically hyponormal and quadratically hyponormal operators

moment problems for multi sequences of operators abstract we give an explicit solution to the scalar moment problem on semi algebraic compact subsets of r n and apply this result to the study of some operator multi sequences

iterative image restoration using approximate inverse preconditioning removing a linear shift invariant blur from a signal or image can be accomplished by inverse or wiener filtering or by an iterative least squares deblurring procedure because of the ill posed characteristics of the deconvolution problem in the presence of noise filtering methods often yield poor results on the other hand iterative methods often suffer from slow convergence at high spatial frequencies this paper concerns solving deconvolution problems for atmospherically blurred images by the preconditioned conjugate gradient algorithm where a new approximate inverse preconditioner is used to increase the rate of convergence theoretical results are established to show that fast convergence can be expected and test results are reported for a ground based astronomical imaging problem

constrained iterations for blind deconvolution and convexity issues the need for image restoration arises in many applications of various scientific disciplines such as medicine and astronomy and in general whenever an unknown image must be recovered from blurred and noisy data m bertero p boccacci introduction to inverse problems in imaging institute of physics publishing philadelphia pa usa 1998 the algorithm studied in this work restores the image without the knowledge of the blur using a little priori information and a blind inverse filter iteration it represents a variation of the methods proposed in kundur and hatzinakos a novel blind deconvolution scheme for image restoration using recursive filtering ieee trans signal process 46 2 1998 375 390 and ng et al regularization of rif blind image deconvolution ieee trans image process 9 6 2000 1130 1134 the problem of interest here is an inverse one that cannot be solved by simple filtering since it is ill posed the imaging system is assumed to be linear and space invariant this allows a simplified relationship between unknown and observed images described by a point spread function modeling the distortion the blurring though makes the restoration ill conditioned regularization is therefore also needed obtained by adding constraints to the formulation the restoration is modeled as a constrained minimization particular attention is given here to the analysis of the objective function and on establishing whether or not it is a convex function whose minima can be located by classic optimization techniques and descent methods numerical examples are applied to simulated data and to real data derived from various applications comparison with the behavior of methods d kundur d hatzinakos a novel blind deconvolution scheme for image restoration using recursive filtering ieee trans signal process 46 2 1998 375 390 and m ng r j plemmons s qiao regularization of rif blind image deconvolution ieee trans image process 9 6 2000 1130 1134 show the effectiveness of our variant

space variant restoration of images degraded by camera motion blur we examine the problem of restoration from multiple images degraded by camera motion blur we consider scenes with significant depth variations resulting in space variant blur the proposed algorithm can be applied if the camera moves along an arbitrary curve parallel to the image plane without any rotations the knowledge of camera trajectory and camera parameters is not necessary at the input the user selects a region where depth variations are negligible the algorithm belongs to the group of variational methods that estimate simultaneously a sharp image and a depth map based on the minimization of a cost functional to initialize the minimization it uses an auxiliary window based depth estimation algorithm feasibility of the algorithm is demonstrated by three experiments with real images

classification of hereditary matrices abstract a classical approach used to obtain basic facts in the theory of square matrices involves an analysis of the relationship between polynomials p in one variable and square matrices t such that p t 0 we consider matrices and operators which satisfy a different type of polynomial constraint let h be a complex hilbert space t be a bounded linear transformation of h t be the adjoint of t and c x y be the algebra of polynomials in x and y with complex coefficients for a polynomial p c x y in two variables with complex coefficients define p t m n 0 p m n t n t m where p m n is the coefficient of ynxm in the expansion of p in a power series about the point 0 0 t is called a root of p if and only if p t 0 note that if p c x y is a polynomial in the single variable x then the definition of p t given here agrees with the classical definition in this paper we study the relationships which p t 0 forces between p and t when t is an algebraic operator i e there exists n 1 and complex numbers a0 an 1 such that 0 a0 a1t an 1tn 1 tn the classification starts with the following observation suppose p c x y and an algebraic operator t l h satisfy p t 0 then certain subspaces of h which are invariant for t must be orthogonal or certain coefficients of p must vanish this leads to the notions of a graph attached to each p c x y and a graph attached to each square matrix t for diagonalizable t a necessary and sufficient graph theoretic condition for solving p t 0 is given for nondiagonalizable t this condition is necessary but not sufficient the use of these graphs does however reduce the problem to the problem of solving the equation p t 0 for t with exactly one or two eigenvalues for t with one eigenvalue we give a necessary and sufficient condition for solving p t 0 this leaves the case of solving p t 0 when t has exactly two eigenvalues this problem mixes algebra involving polynomials with matrix theory we show that it is equivalent to the purely algebraic problem of determining if equations of the form i j eci jxi r j s 0 have solutions of finite support with certain nonvanishing properties we call these equations bi hankel equations subordinate to a given subset e of the lattice of integer pairs i j 0 i m 1 0 j n 1 it turns out that there is an algorithm which uses grobner bases for determining if the type of solution we seek exists and for computing it

a new look to multichannel blind image deconvolution the aim of this paper is to propose a new look to mbid examine some known approaches and provide a new mc method for restoring blurred and noisy images first the direct image restoration problem is briefly revisited then a new method based on inverse filtering for perfect image restoration in the noiseless case is proposed the noisy case is addressed by introducing a regularization term into the objective function in order to avoid noise amplification second the filter identification problem is considered in the mc context a new robust solution to the degradation matrix filter is then derived and used in conjunction with a total variation approach to restore the original image simulation results and performance evaluations using recent image quality metrics are provided to assess the effectiveness of the proposed methods

unitary representations of the quantum algebra suq 2 on a real two dimensional sphere for q r or generic q s1 some time ago rideau and winternitz introduced a realization of the quantum algebra suq 2 on a real two dimensional sphere or a real plane and constructed a basis for its representations in terms of q special functions which can be expressed in terms of q vilenkin functions and are related to little q jacobi functions q spherical functions and q legendre polynomials in their study the values of q were implicitly restricted to q r in the present paper we extend their work to the case of generic values of q s1 i e q values different from a root of unity in addition we unitarize the representations for both types of q values q r and generic q s1 by determining some appropriate scalar products from the latter we deduce the orthonormality relations satisfied by the q vilenkin functions

representations of the quantum algebra suq 2 on a real two dimensional sphere representations of the quantum algebra suq 2 are constructed in terms of q special functions defined on real o 3 spheres and real planes they include q vilenkin functions related to little q jacobi functions q spherical functions and q legendre polynomials

k moment problem for recursive sequences of order application to the zeros of analytic functions in this paper we solve the k moment problem for a family of sequences defined by linear recursive relations of order indexed by z extension of some known properties are studied and others results are established moreover we paraphrase a fundamental application on the existence of zeros of an analytic function in terms of the support of the representing measure of the former sequences

bases for representations of quantum algebras we derive an explicit expression for the eigenfunctions and the corresponding eigenvalues of the operator q1 4j q q 1 4j q qj3 q 2 in an arbitrary irreducible representation of the algebra suq 2 the general form of the intertwining operator aj q which is a q extension of the classical su 2 operator aj j1aj ajj3 is also found the matrix elements of aj q are expressed in terms of the dual q kravchuk polynomials

harmonic functions of suq 2 for q ℝ and q s1 we show in this paper that a particular family of askey wilson polynomials can be interpreted directly in the light of q deformed suq 2 algebras this approach allows us to correct previous results concerning the q legendre functions investigated in granovskii and zhedanov 1993 j phys a math gen 26 4331 we also establish the orthonormalization and the special cases q 1 classical limit and q asymptote we conclude that these q legendre functions differ significantly from their classical counterparts only when q is in the vicinity of the unitary circle where the singular points of the absolute value of these q functions undergo a series of bifurcations

existence of non subnormal polynomially hyponormal operators in 1950 p r halmos motivated in part by the successful development of the theory of normal operators introduced the notions of subnormality and hyponormality for bounded hilbert space operators an operator t is subnormal if it is the restriction of a normal operator to an invariant subspace t is hyponormal if t t tt it is a simple matrix calculation to verify that subnormality implies hyponormality but the converse is false one reason is that subnormality is invariant under polynomial calculus indeed analytic functional calculus while hyponormality is not if one then defines t to be polynomially hyponormal when p t is hyponormal for every polynomial p e c z the following question arises naturally

solving moment problems by dimensional extension polynomial inequalities the second part of the paper uses the representation results of positive functionals on certain spaces of rational functions developed in the flrst part for decomposing a polynomial which is positive on such a semi algebraic set into a canonical sum of squares of rational functions times explicit multipliers let n 1 be a flxed integer due to the fact that for n 1 not every nonnegative polynomial in r n can be written as a sum of squares of polynomials see for instance 2 x6 3 the moment problems in n variables are more di cult than the classical one variable problems this very intriguing territory has been investigated by many authors see 2 7 12 and their references although characterizations for measures whose support lies in an arbitrary generally unbounded semi algebraic set do not seem to exist the present paper starts from an idea of the second author see 19 about solving moment problems by a change of basis via an embedding of r n into a submanifold of a higher dimensional euclidean space rougly speaking we prove that certain n 1 dimensional extensions of a moment sequence are naturally characterized by positivity conditions and moreover these extensions parametrize all possible solutions of the moment problem to be more speciflc let fi z r n x fi d x fi 2 z n

a regularization approach to joint blur identification and image restoration the primary difficulty with blind image restoration or joint blur identification and image restoration is insufficient information this calls for proper incorporation of a priori knowledge about the image and the point spread function psf a well known space adaptive regularization method for image restoration is extended to address this problem this new method effectively utilizes among others the piecewise smoothness of both the image and the psf it attempts to minimize a cost function consisting of a restoration error measure and two regularization terms one for the image and the other for the blur subject to other hard constraints a scale problem inherent to the cost function is identified which if not properly treated may hinder the minimization blind restoration process alternating minimization is proposed to solve this problem so that algorithmic efficiency as well as simplicity is significantly increased two implementations of alternating minimization based on steepest descent and conjugate gradient methods are presented good performance is observed with numerically and photographically blurred images even though no stringent assumptions about the structure of the underlying blur operator is made

a novel blind deconvolution scheme for image restoration using recursive filtering we present a novel blind deconvolution technique for the restoration of linearly degraded images without explicit knowledge of either the original image or the point spread function the technique applies to situations in which the scene consists of a finite support object against a uniformly black grey or white background this occurs in certain types of astronomical imaging medical imaging and one dimensional 1 d gamma ray spectra processing among others the only information required are the nonnegativity of the true image and the support size of the original object the restoration procedure involves recursive filtering of the blurred image to minimize a convex cost function we prove convexity of the cost function establish sufficient conditions to guarantee a unique solution and examine the performance of the technique in the presence of noise the new approach is experimentally shown to be more reliable and to have faster convergence than existing nonparametric finite support blind deconvolution methods for situations in which the exact object support is unknown we propose a novel support finding algorithm

solution of the truncated moment problem with variety y x 3 we show that positivity consistency and the variety condition which are sufficient to solve the truncated moment problem on planar curves of degree 2 are not sufficient for curves of higher degree using new partly algorithmic conditions based on positive moment matrix extensions we present a concrete solution to the truncated moment problem on the curve y x 3 we also use moment matrix extensions to solve in a less concrete sense truncated moment problems on curves of the form y g x and yg x 1 g x leading to degree bounded weighted sum of squares representations for polynomials which are strictly positive on such curves

quadratically hyponormal weighted shifts with recursive tail abstract we characterize positive quadratic hyponormality of the weighted shift w x associated to the weight sequence x 1 1 x u v w with stampfli recursive tail and produce an interval in x with non empty interior in the positive real line for quadratic hyponormality but not positive quadratic hyponormality for such a shift

blind deconvolution using generalized cross validation approach to regularization parameter estimation in this paper we propose and present an algorithm for total variation tv based blind deconvolution both the unknown image and blur can be estimated within an alternating minimization framework with the generalized cross validation gcv method the regularization parameters associated with the unknown image and blur can be updated in alternating minimization steps experimental results confirm that the performance of the proposed algorithm is better than variational bayesian blind deconvolution algorithms with student s t priors or a total variation prior

convergence of the alternating minimization algorithm for blind deconvolution abstract blind deconvolution refers to the image processing task of restoring the original image from a blurred version without the knowledge of the blurring function one approach that has been proposed recently t chan c wong ieee trans image process 7 1998 370 375 y you m kaveh ieee trans image process 5 1996 416 428 is a joint minimization model in which an objective function is set up consisting of three terms the data fitting term and the regularization terms for the image and the blur this model implicitly defines a one parameter family of blurred images and point spread functions psfs from which the user can decide usually using additional information which is the best restored image to find a local minimum of the objective function we use an alternating minimization am procedure y you m kaveh ieee trans image process 5 1996 416 428 in which we fix either the blur or the image and minimize respect to the other variable each step of which is a standard non blind deconvolution problem while the model is not convex and thus allows multiple solutions we have found that the am procedure always converges globally but with the converged solution depending on the initial guess in this paper we give an analysis of the am procedure which explains the convergence behavior and the observed robustness of the method

disintegration of measure techniques for commuting multivariable weighted shifts we employ techniques from the theory of disintegration of measures to study the lifting problem for commuting n tuples of subnormal weighted shifts we obtain a new necessary condition for the existence of a lifting and generate new pathology associated with bringing together the berger measures associated to each individual weighted shift for subnormal 2 variable weighted shifts we then find the precise relation between the berger measure of the pair and the berger measures of the shifts associated to horizontal rows and vertical columns of weights

quartically hyponormal weighted shifts need not be 3 hyponormal we give the first example of a quartically hyponormal unilateral weighted shift which is not 3 hyponormal

k hyponormality of finite rank perturbations of unilateral weighted shifts in this paper we explore finite rank perturbations of unilateral weighted shifts w first we prove that the subnormality of w is never stable under nonzero finite rank perturbations unless the perturbation occurs at the zeroth weight second we establish that 2 hyponormality implies positive quadratic hyponormality in the sense that the maclaurin coefficients of d n s det p n w sw 2 w sw 2 p n are nonnegative for every n 0 where p n denotes the orthogonal projection onto the basis vectors e 0 e n finally for strictly increasing and w 2 hyponormal we show that for a small finite rank perturbation a of a the shift w remains quadratically hyponormal

the complex moment problem and subnormality a polar decomposition approach abstract it has been known that positive definiteness does not guarantee a bisequence to be a complex moment however it turns out that positive definite extendibility does theorems 1 and 22 and this is the main theme of this paper the main tool is generally understood polar decomposition to strengthen applicability of our approach we work out a criterion for positive definite extendibility in a fairly wide context theorems 9 and 29 all this enables us to prove characterizations of subnormality of unbounded operators having invariant domain theorems 37 and 39 and their further applications theorems 41 and 43 and a description of the complex moment problem on real algebraic curves theorems 52 and 56 the latter question is completed in the appendix in which we relate the complex moment problem to the two dimensional real one with emphasis on real algebraic sets

an analogue of the riesz haviland theorem for the truncated moment problem abstract let 2 n i i 2 n denote a d dimensional real multisequence let k denote a closed subset of r d and let p 2 n p r x 1 x d deg p 2 n corresponding to the riesz functional l l p 2 n r is defined by l a i x i a i i we say that l is k positive if whenever p p 2 n and p k 0 then l p 0 we prove that admits a k representing measure if and only if l admits a k positive linear extension l p 2 n 2 r this provides a generalization from the full moment problem to the truncated moment problem of the riesz haviland theorem we also show that a semialgebraic set solves the truncated moment problem in terms of natural degree bounded positivity conditions if and only if each polynomial strictly positive on that set admits a degree bounded weighted sum of squares representation