polygonal and polyhedral contour reconstruction in computed tomography this paper is about three dimensional 3 d reconstruction of a binary image from its x ray tomographic data we study the special case of a compact uniform polyhedron totally included in a uniform background and directly perform the polyhedral surface estimation we formulate this problem as a nonlinear inverse problem using the bayesian framework vertice estimation is done without using a voxel approximation of the 3 d image it is based on the construction and optimization of a regularized criterion that accounts for surface smoothness we investigate original deterministic local algorithms based on the exact computation of the line projections their update and their derivatives with respect to the vertice coordinates results are first derived in the two dimensional 2 d case which consists of reconstructing a 2 d object of deformable polygonal contour from its tomographic data then we investigate the 3 d extension that requires technical adaptations simulation results illustrate the performance of polygonal and polyhedral reconstruction algorithms in terms of quality and computation time

on the uniqueness of the inverse logarithmic potential problem uniqueness of the shape and density of plane gravitating bodies as determined from their exterior logaritmic potential has been studied uniqueness conditions have been derived for polygons and domains bounded by lemniscates filled with masses of constant or polynomial density the proofs are constructed on the basis of a study of the singular points of the exterior field using an apparatus that permits constructive solution of the inverse problem

mixed integer bilinear programming problems this paper addresses a class of problems called mixed integer bilinear programming problems these problems are identical to the well known bilinear programming problems with the exception that one set of variables is restricted to be binary valued and they arise in various production location allocation and distribution application contexts we first identify some special cases of this problem which are relatively more readily solvable even though their continuous relaxations are still nonconvex for the more general case we employ a linearization technique and design a composite lagrangian relaxation implicit enumeration cutting plane algorithm extensive computational experience is provided to test the efficacy of various algorithmic strategies and the effects of problem data on the computational effort of the proposed algorithm

a polyhedral study of the generalized vertex packing problem the traditional vertex packing problem defined on an undirected graph identifies the largest weighted independent set of nodes that is a set of nodes whose induced subgraph contains no edges in this paper we examine a generalized vertex packing problem gvp k in which k violations to the independent set restriction are permitted whereby k edges may exist within the subgraph induced by the chosen set of nodes a particular context in which such problems arise is in the national airspace planning model of sherali smith and trani 2000 where a set of flight plans need to be composed for various flights subject to conflict workload and equity considerations the gvp k structure arises in modeling the air traffic control sector workload restrictions which stipulate that for each sector and during each discretized time slot the number of aircraft conflicts that would need to be resolved should not exceed k for some k 1 we derive several classes of facetial valid inequalities for gvp k for certain specially structured subgraphs identifying polynomial sized convex hull representations for some of these cases related constraint generation routines are also developed and some computational results are provided to demonstrate the efficacy of utilizing the proposed valid inequalities in solving gvp k for different values of k

linearization strategies for a class of zero one mixed integer programming problems this paper is concerned with a new linearization strategy for a class of zero one mixed integer programming problems that contains quadratic cross product terms between continuous and binary variables and between the binary variables themselves this linearization scheme provides an equivalent mixed integer linear programming problem which yields a tighter continuous relaxation than that obtainable via the alternative linearization techniques available in the literature moreover the proposed technique provides a unifying framework in the sense that all the alternate methods lead to formulations that are accessible through appropriate surrogates of the constraints of the new linearized formulation extensions to various other types of mixed integer nonlinear programming problems are also discussed

roof duality complementation and persistency in quadratic 0 1 optimization the paper is concerned with the primal problem of maximizing a given quadratic pseudo boolean function four equivalent problems are discussed the primal the complementation the discrete rhys lp and the weighted stability problem of a sam graph each of them has a relaxation the roof dual the quadratic complementation the continuous rhys lp and the fractional weighted stability problem of a sam graph the main result is that the four gaps associated with the four relaxations are equal furthermore a solution to any of these problems leads at once to solutions of the other three equivalent ones the four relaxations can be solved in polynomial time by transforming them to a bipartite maximum flow problem the optimal solutions of the roof dual define best linear majorantsp x off having the following persistency property if theith coefficient inp is positive negative thenx i 1 0 in every optimum of the primal problem several characterizations are given for the case where these persistency results cannot be used to fix any variable of the primal on the other hand a class of gap free functions properly including the supermodular ones is exhibited

a gradient system approach for hankel structured low rank approximation abstract rank deficient hankel matrices are at the core of several applications however in practice the coefficients of these matrices are noisy due to e g measurements errors and computational errors so generically the involved matrices are full rank this motivates the problem of hankel structured low rank approximation structured low rank approximation problems in general do not have a global and efficient solution technique in this paper we propose a local optimization approach based on a two levels iteration experimental results show that the proposed algorithm usually achieves good accuracy and shows a higher robustness with respect to the initial approximation compared to alternative approaches

sampling moments and reconstructing signals of finite rate of innovation shannon meets strang fix consider the problem of sampling signals which are not bandlimited but still have a finite number of degrees of freedom per unit of time such as for example nonuniform splines or piecewise polynomials and call the number of degrees of freedom per unit of time the rate of innovation classical sampling theory does not enable a perfect reconstruction of such signals since they are not bandlimited recently it was shown that by using an adequate sampling kernel and a sampling rate greater or equal to the rate of innovation it is possible to reconstruct such signals uniquely these sampling schemes however use kernels with infinite support and this leads to complex and potentially unstable reconstruction algorithms in this paper we show that many signals with a finite rate of innovation can be sampled and perfectly reconstructed using physically realizable kernels of compact support and a local reconstruction algorithm the class of kernels that we can use is very rich and includes functions satisfying strang fix conditions exponential splines and functions with rational fourier transform this last class of kernels is quite general and includes for instance any linear electric circuit we thus show with an example how to estimate a signal of finite rate of innovation at the output of an rc circuit the case of noisy measurements is also analyzed and we present a novel algorithm that reduces the effect of noise by oversampling

prony pisarenko and the matrix pencil a unified presentation in the past the prony and pisarenko algorithms have been widely used in the pole zero identification of linear systems as well as in the problem of extracting harmonics embedded in noise these techniques have also been applied successfully to the direction of arrival doa problem it is shown that these algorithms are equivalent to a recently proposed doa estimation technique called the matrix pencil approach

software for weighted structured low rank approximation a software package is presented that computes locally optimal solutions to low rank approximation problems with the following features mosaic hankel structure constraint on the approximating matrix weighted 2 norm approximation criterion fixed elements in the approximating matrix missing elements in the data matrix and linear constraints on an approximating matrix s left kernel basis it implements a variable projection type algorithm and allows the user to choose standard local optimization methods for the solution of the parameter optimization problem for an mxn data matrix with n m the computational complexity of the cost function and derivative evaluation is o m 2n the package is suitable for applications with n m in statistical estimation and data modeling the main application areas of the package n m corresponds to modeling of large amount of data by a low complexity model performance results on benchmark system identification problems from the database daisy and approximate common divisor problems are presented

reconstructing polygons from moments with connections to array processing we establish a set of results showing that the vertices of any simply connected planar polygonal region can be reconstructed from a finite number of its complex moments these results find applications in a variety of apparently disparate areas such as computerized tomography and inverse potential theory where in the former it is of interest to estimate the shape of an object from a finite number of its projections whereas in the latter the objective is to extract the shape of a gravitating body from measurements of its exterior logarithmic potentials at a finite number of points we show that the problem of polygonal vertex reconstruction from moments can in fact be posed as an array processing problem and taking advantage of this relationship we derive and illustrate several new algorithms for the reconstruction of the vertices of simply connected polygons from moments

sampling piecewise sinusoidal signals with finite rate of innovation methods we consider the problem of sampling piecewise sinusoidal signals classical sampling theory does not enable perfect reconstruction of such signals since they are not band limited however they can be characterized by a finite number of parameters namely the frequency amplitude and phase of the sinusoids and the location of the discontinuities in this paper we show that under certain hypotheses on the sampling kernel it is possible to perfectly recover the parameters that define the piecewise sinusoidal signal from its sampled version in particular we show that at least theoretically it is possible to recover piecewise sine waves with arbitrarily high frequencies and arbitrarily close switching points extensions of the method are also presented such as the recovery of combinations of piecewise sine waves and polynomials finally we study the effect of noise and present a robust reconstruction algorithm that is stable down to snr levels of 7 db

a moment based variational approach to tomographic reconstruction we describe a variational framework for the tomographic reconstruction of an image from the maximum likelihood ml estimates of its orthogonal moments we show how these estimated moments and their correlated error statistics can be computed directly and in a linear fashion from given noisy and possibly sparse projection data moreover thanks to the consistency properties of the radon transform this two step approach moment estimation followed by image reconstruction can be viewed as a statistically optimal procedure furthermore by focusing on the important role played by the moments of projection data we immediately see the close connection between tomographic reconstruction of nonnegative valued images and the problem of nonparametric estimation of probability densities given estimates of their moments taking advantage of this connection our proposed variational algorithm is based on the minimization of a cost functional composed of a term measuring the divergence between a given prior estimate of the image and the current estimate of the image and a second quadratic term based on the error incurred in the estimation of the moments of the underlying image from the noisy projection data we show that an iterative refinement of this algorithm leads to a practical algorithm for the solution of the highly complex equality constrained divergence minimization problem we show that this iterative refinement results in superior reconstructions of images from very noisy data as compared with the classical filtered back projection fbp algorithm

a lift and project cutting plane algorithm for mixed 0 1 programs we propose a cutting plane algorithm for mixed 0 1 programs based on a family of polyhedra which strengthen the usual lp relaxation we show how to generate a facet of a polyhedron in this family which is most violated by the current fractional point this cut is found through the solution of a linear program that has about twice the size of the usual lp relaxation a lifting step is used to reduce the size of the lp s needed to generate the cuts an additional strengthening step suggested by balas and jeroslow is then applied we report our computational experience with a preliminary version of the algorithm this approach is related to the work of balas on disjunctive programming the matrix cone relaxations of lovasz and schrijver and the hierarchy of relaxations of sherali and adams

estimating the parameters of exponentially damped sinusoids and pole zero modeling in noise we have presented techniques 1 6 based on linear prediction lp and singular value decomposition svd for accurate estimation of closely spaced frequencies of sinusoidal signals in noise in this note we extend these techniques to estimate the parameters of exponentially damped sinusoidal signals in noise the estimation procedure presented here makes use of backward prediction in addition to svd first the method is applied to data consisting of one and two exponentially damped sinusoids the choice of one and two signal components facilitates the comparison of estimation error in pole damping factors and pole frequencies to the appropriate cramer rao cr bounds and to traditional methods of linear prediction second our method is applied to an example due to steiglitz 8 in which the data consists of noisy values of the impulse response samples composed of many exponentially damped sinusoids of a linear system having both poles and zeros the poles of the system are accurately determined by our method and the zeros are obtained subsequently using shanks method

shape from moments an estimation theory perspective this paper discusses the problem of recovering a planar polygon from its measured complex moments these moments correspond to an indicator function defined over the polygon s support previous work on this problem gave necessary and sufficient conditions for such successful recovery process and focused mainly on the case of exact measurements being given in this paper we extend these results and treat the same problem in the case where a longer than necessary series of noise corrupted moments is given similar to methods found in array processing system identification and signal processing we discuss a set of possible estimation procedures that are based on the prony and the pencil methods relate them one to the other and compare them through simulations we then present an improvement over these methods based on the direct use of the maximum likelihood estimator exploiting the above methods as initialization finally we show how regularization and thus maximum a posteriori probability estimator could be applied to reflect prior knowledge about the recovered polygon

esprit a subspace rotation approach to estimation of parameters of cisoids in noise the application of a subspace invariance approach esprit to the estimation of parameters frequencies and powers of cisoids in noise is described esprit exploits an underlying rotational invariance of signal subspaces spanned by two temporally displaced data sets the new approach has several advantages including improved resolution over pisarenko s technique for harmonic retrieval

murthy s conjecture on 0 cycles we show that the levine weibel chow group of 0 cycles mathrm ch d a of a reduced affine algebra a of dimension d ge 2 over an algebraically closed field is torsion free among several applications it implies an affirmative solution to an old conjecture of murthy in classical k theory

cones of matrices and set functions and 0 1 optimization it has been recognized recently that to represent a polyhedron as the projection of a higher dimensional but simpler polyhedron is a powerful tool in polyhedral combinatorics a general method is developed to construct higher dimensional polyhedra or in some cases convex sets whose projection approximates the convex hull of 0 1 valued solutions of a system of linear inequalities an important feature of these approximations is that one can optimize any linear objective function over them in polynomial time in the special case of the vertex packing polytope a sequence of systems of inequalities is obtained such that the first system already includes clique odd hole odd antihole wheel and orthogonality constraints in particular for perfect and many other graphs this first system gives the vertex packing polytope for various classes of graphs including t perfect graphs it follows that the stable set polytope is the projection of a polytope with a polynomial number of facets an extension o

sets uniquely determined by projections on axes i continuous case this paper studies sets s in mathbb r which are uniquely reconstructible from their hyperplane integral projections p i x i s iint cdots int chi s x 1 cdots x i cdots x n dx 1 cdots dx i 1 dx i 1 cdots dx n onto the n coordinate axes of mathbb r it is shown that any additive set s bf x x 1 cdots x n sum nolimits i 1 n f i x i geqq 0 where each f i x i is a bounded measurable function is uniquely reconstructible in particular balls are uniquely reconstructible it is shown that in mathbb r 2 all uniquely reconstructible sets are additive for n geqq 3 kemperman has shown that there are uniquely reconstructible sets in mathbb r of bounded measure that are not additive it is also noted for n geqq 3 that neither of the properties of being additive and being a set of uniqueness is closed under monotone pointwise limits a necessary condition for s to be a set of uniqueness is that

reconstruction of polygonal shapes from sparse fourier samples in this paper we want to reconstruct polygonal shapes in the real plane from as few fourier samples as possible that is we want to recover an original polygonal domain d with n vertices by using sparse sampling values of the fourier transform of the characteristic function of the polygonal domain we consider only simply connected polygons i e polygons with non intersecting edges for this purpose we need to reconstruct the vertices of the polygon in the case of non convex polygons we also need to reconstruct the order of the vertices to determine the correct boundary line segments the method presented here is based on the prony method

on the shape from moments problem and recovering edges from noisy radon data we consider the problem of reconstructing a planar convex set from noisy observations of its moments an estimation method based on pointwise recovering of the support function of the set is developed we study intrinsic accuracy limitations in the shape from moments estimation problem by establishing a lower bound on the rate of convergence of the mean squared error it is shown that the proposed estimator is near optimal in the sense of the order an application to tomographic reconstruction is discussed and it is indicated how the proposed estimation method can be used for recovering edges from noisy radon data

fourier gauss fraunhofer porod and the shape from moments problem we show how the fourier transform of a shape in any number of dimensions can be simplified using gauss s law and evaluated explicitly for polygons in two dimensions polyhedra in three dimensions etc we also show how this combination of fourier and gauss can be related to numerous classical problems in physics and mathematics examples include fraunhofer diffraction patterns porod s law the shape from moments problem and davis s extension of the motzkin schoenberg formula to polygons in the complex plane

persistency model and its applications in choice modeling given a discrete maximization problem with a linear objective function where the coefficients are chosen randomly from a distribution we would like to evaluate the expected optimal value and the marginal distribution of the optimal solution we call this the persistency problem for a discrete optimization problem under uncertain objective and the marginal probability mass function of the optimal solution is named the persistence value in general this is a difficult problem to solve even if the distribution of the objective coefficient is well specified in this paper we solve a subclass of this problem when the distribution is assumed to belong to the class of distributions defined by given marginal distributions or given marginal moment conditions under this model we show that the persistency problem maximizing the expected objective value over the set of distributions can be solved via a concave maximization model the persistency model solved using this formulation can be used to obtain important qualitative insights to the behavior of stochastic discrete optimization problems we demonstrate how the approach can be used to obtain insights to problems in discrete choice modeling using a set of survey data from a transport choice modeling study we calibrate the random utility model with choice probabilities obtained from the persistency model numerical results suggest that our persistency model is capable of obtaining estimates that perform as well if not better than classical methods such as logit and cross nested logit models we can also use the persistency model to obtain choice probability estimates for more complex choice problems we illustrate this on a stochastic knapsack problem which is essentially a discrete choice problem under budget constraint

on clique relaxation models in network analysis abstract increasing interest in studying community structures or clusters in complex networks arising in various applications has led to a large and diverse body of literature introducing numerous graph theoretic models relaxing certain characteristics of the classical clique concept this paper analyzes the elementary clique defining properties implicitly exploited in the available clique relaxation models and proposes a taxonomic framework that not only allows to classify the existing models in a systematic fashion but also yields new clique relaxations of potential practical interest some basic structural properties of several of the considered models are identified that may facilitate the choice of methods for solving the corresponding optimization problems in addition bounds describing the cohesiveness properties of different clique relaxation structures are established and practical implications of choosing one model over another are discussed

torsion and divisibility for reciprocity sheaves and 0 cycles with modulus the notion of modulus is a striking feature of rosenlicht serre s theory of generalized jacobian varieties of curves it was carried over to algebraic cycles on general varieties by bloch esnault park rulling krishna levine recently kerz saito introduced a notion of chow group of 0 cycles with modulus in connection with geometric class field theory with wild ramification for varieties over finite fields we study the non homotopy invariant part of the chow group of 0 cycles with modulus and show their torsion and divisibility properties modulus is being brought to sheaf theory by kahn saito yamazaki in their attempt to construct a generalization of voevodsky suslin friedlander s theory of homotopy invariant presheaves with transfers we prove parallel results about torsion and divisibility properties for them

duality via cycle complexes we show that bloch s complex of relative zero cycles can be used as a dualizing complex over perfect fields and number rings this leads to duality theorems for torsion sheaves on arbitrary separated schemes of finite type over algebraically closed fields finite fields local fields of mixed characteristic and rings of integers in number rings generalizing results which so far have only been known for smooth schemes or in low dimensions and unifying the p adic and l adic theory as an application we generalize rojtman s theorem to normal projective schemes

the boolean quadric polytope some characteristics facets and relatives we study unconstrained quadratic zero one programming problems havingn variables from a polyhedral point of view by considering the boolean quadric polytope qpn inn n 1 2 dimensions that results from the linearization of the quadratic form we show that qpn has a diameter of one descriptively identify three families of facets of qpn and show that qpn is symmetric in the sense that all facets of qpn can be obtained from those that contain the origin by way of a mapping the naive linear programming relaxation qpnlp of qpn is shown to possess the trubin property and its extreme points are shown to be 0 1 2 1 valued furthermore o n3 facet defining inequalities of qpn suffice to cut off all fractional vertices of qpnlp whereas the family of facets described by us has at least o 3n members the problem is also studied for sparse quadratic forms i e when several or many coefficients are zero and conditions are given for the previous results to carry over to this case polynomially solvable problem instances are discussed and it is shown that the known polynomiality result for the maximization of nonnegative quadratic forms can be obtained by simply rounding the solution to the linear programming relaxation in the case that the graph induced by the nonzero coefficients of the quadratic form is series parallel a complete linear description of the associated boolean quadric polytope is given the relationship of the boolean quadric polytope associated to sparse quadratic forms with the vertex packing polytope is discussed as well

persistency in quadratic 0 1 optimization this paper is concerned with persistency properties which allow the evaluation of some variables at all maximizing points of a quadratic pseudo boolean function hammer hansen and simeone 1984 have proposed to determine these variables using a procedure described by balinski for computing a strongly complementary pair of optimal primal and dual solutions for arbitrary linear programs we propose a linear time algorithm for determining these variables from a best roof off i e from a lowest upper linear bound off

clique relaxations in social network analysis the maximum k plex problem this paper introduces and studies the maximum k plex problem which arises in social network analysis and has wider applicability in several important areas employing graph based data mining after establishing np completeness of the decision version of the problem on arbitrary graphs an integer programming formulation is presented followed by a polyhedral study to identify combinatorial valid inequalities and facets a branch and cut algorithm is implemented and tested on proposed benchmark instances an algorithmic approach is developed exploiting the graph theoretic properties of a k plex that is effective in solving the problem to optimality on very large sparse graphs such as the power law graphs frequently encountered in the applications of interest

tight bounds and 2 approximation algorithms for integer programs with two variables per inequality the problem of integer programming in bounded variables over constraints with no more than two variables in each constraint is np complete even when all variables are binary this paper deals with integer linear minimization problems inn variables subject tom linear constraints with at most two variables per inequality and with all variables bounded between 0 andu for such systems a 2 approximation algorithm is presented that runs in time o mnu2 log un2m so it is polynomial in the input size if the upper boundu is polynomially bounded the algorithm works by finding first a super optimal feasible solution that consists of integer multiples of 1 2 that solution gives a tight bound on the value of the minimum it furthermore has an identifiable subset of integer components that retain their value in an integer optimal solution of the problem these properties are a generalization of the properties of the vertex cover problem the algorithm described is in particular a 2 approximation algorithm for the problem of minimizing the total weight of true variables among all truth assignments to the 2 satisfiability problem

sampling schemes for multidimensional signals with finite rate of innovation in this paper we consider the problem of sampling signals that are nonband limited but have finite number of degrees of freedom per unit of time and call this number the rate of innovation streams of diracs and piecewise polynomials are the examples of such signals and thus are known as signals with finite rate of innovation fri we know that the classical band limited sine sampling theory does not enable perfect reconstruction of such signals from their samples since they are not band limited however the recent results on fri sampling suggest that it is possible to sample and perfectly reconstruct such nonband limited signals using a rich class of kernels in this paper we extend those results in higher dimensions using compactly supported kernels that reproduce polynomials satisfy strang fix conditions in fact the polynomial reproduction property of the kernel makes it possible to obtain the continuous moments of the signal from its samples using these moments and the annihilating filter method prony s method the innovative part of the signal and therefore the signal itself is perfectly reconstructed in particular we present local directional derivatives based and global complex moments based radon transform based sampling schemes for classes of fri signals such as sets of diracs bilevel and planar polygons quadrature domains e g circles ellipses and cardioids 2d polynomials with polygonal boundaries and n dimensional diracs and convex polytopes this work has been explored in a promising way in super resolution algorithms and distributed compression and might find its applications in photogrammetry computer graphics and machine vision

sampling curves with finite rate of innovation in this paper we extend the theory of sampling signals with finite rate of innovation fri to a specific class of two dimensional curves which are defined implicitly as the zeros of a mask function here the mask function has a parametric representation as a weighted summation of a finite number of complex exponentials and therefore has finite rate of innovation an associated edge image which is discontinuous on the predefined parametric curve is proved to satisfy a set of linear annihilation equations we show that it is possible to reconstruct the parameters of the curve i e to detect the exact edge positions in the continuous domain based on the annihilation equations robust reconstruction algorithms are also developed to cope with scenarios with model mismatch moreover the annihilation equations that characterize the curve are linear constraints that can be easily exploited in optimization problems for further image processing e g image up sampling we demonstrate one potential application of the annihilation algorithm with examples in edge preserving interpolation experimental results with both synthetic curves as well as edges of natural images clearly show the effectiveness of the annihilation constraint in preserving sharp edges and improving snrs

zero cycles and k theory on normal surfaces in this paper we prove a formula conjectured by bloch and srinivas s2 which describes the chow group of zero cycles of a normal quasi projective surface x over a field as an inverse limit of relative chow groups of a desingularisation x relative to multiples of the exceptional divisor we then give several applications of this result a relative version of the famous bloch conjecture on 0 cycles the triviality of the chow group of 0 cycles for any 2 dimensional normal graded q algebra analogue of the bloch beilinson conjecture and the analogue of the roitman theorem for torsion 0 cycles in characteristic p 0 for normal varieties including the case of p torsion

a stable numerical method for inverting shape from moments we derive a stable technique based upon matrix pencils for the reconstruction of or approximation by polygonal shapes from moments we point out that this problem can be considered the dual of 2 d numerical quadrature over polygonal domains an analysis of the sensitivity of the problem is presented along with some numerical examples illustrating the relevant points finally an application to the problem of gravimetry is explored where the shape of a gravitationally anomalous region is to be recovered from measurements of its exterior gravitational field

matrix pencil method for estimating parameters of exponentially damped undamped sinusoids in noise a study of a matrix pencil method for estimating frequencies and damping factors of exponentially damped and or undamped sinusoids in noise is presented comparison of this method to a polynomial method svd prony method shows that the matrix pencil method and the polynomial method are two special cases of a matrix prediction approach and that the pencil method is more efficient in computation and less restrictive about signal probes it is found through perturbation analysis and simulation that for signals with unknown damping factors the pencil method is less sensitive to noise than the polynomial method an expression of the cramer rao bound for the exponential signals is presented

multidimensional integral inversion with applications in shape reconstruction in shape reconstruction the celebrated fourier slice theorem plays an essential role it allows one to reconstruct the shape of a quite general object from the knowledge of its radon transform s helgason the radon transform birkhauser boston boston 1980 in other words from the knowledge of projections of the object in case the object is a polygon g h golub p milanfar and j varah siam j sci comput 21 1999 pp 1222 1243 or when it defines a quadrature domain in the complex plane b gustafsson c he p milanfar and m putinar inverse problems 16 2000 pp 1053 1070 its shape can also be reconstructed from the knowledge of its moments essential tools in the solution of the latter inverse problem are quadrature rules and formal orthogonal polynomials in this paper we show how shape reconstruction from the knowledge of moments can also be realized in the case of general compact objects not only in two but also in higher dimensions to this end we use a less known homogeneous pade slice property again integral transforms in our case the multivariate stieltjes transform and univariate markov transform formal orthogonal polynomials in the form of pade denominators and multidimensional integration formulas or cubature rules play an essential role we emphasize that the new technique is applicable in all higher dimensions and illustrate it through the reconstruction of several two and three dimensional objects

persistency in 0 1 polynomial programming an optimal solution to the continuous relaxation of a mixed integer 0 1 linear programming problem is defined to be persistent if the set of 0 1 variables realizing binary values retains those same binary values in at least one integer optimum a mixed integer 0 1 linear program is said to possess the persistency property or equivalently to be persistent if every optimal solution to the continuous relaxation is a persistent solution we study the issue of persistency for a special family of mixed integer 0 1 linear programming problems which derive from the linearization strategy of sherali and adams 1990 in particular we first examine the hierarchy of linearizations which result from applying this strategy to the general class of unconstrained 0 1 polynomial programming problems and then consider a class of specially structured constrained problems our study of persistency differs from previous works in that we use the explicit algebraic representation of the convex hull of feasible binary solutions available at the highest level of this hierarchy as a tool for making inferences relative to optimal integer solutions from optimal continuous solutions each level of this hierarchy consists of a mixed integer 0 1 linear program and we provide for any given optimal solution to the continuous relaxation of any member of this hierarchy a set of sufficient conditions on the optimal dual multipliers for the solution to be persistent these sufficient conditions turn out to be satisfied at every optimal solution of the quadratic level and thus allow for the reformulation of any unconstrained 0 1 quadratic programming problem as a persistent mixed integer linear program in a suitably defined higher dimensional space we subsequently address the fa mily of constrained 0 1 polynomial programs and use a projection operation to prove that a special family of 0 1 linear programs possesses the persistency property included in this family is a generalization of the vertex packing problem that permits quadratic objective function coefficients unlike earlier published works on the vertex packing and related problems our proofs do not rely on balinski s 1965 extreme point characterization

towards generalized fri sampling with an application to source resolution in radioastronomy it is a classic problem to estimate continuous time sparse signals like point sources in a direction of arrival problem or pulses in a time of flight measurement the earliest occurrence is the estimation of sinusoids in time series using prony s method this is at the root of a substantial line of work on high resolution spectral estimation the estimation of continuous time sparse signals from discrete time samples is the goal of the sampling theory for finite rate of innovation fri signals both spectral estimation and fri sampling usually assume uniform sampling but not all measurements are obtained uniformly as exemplified by a concrete radioastronomy problem we set out to solve thus we develop the theory and algorithm to reconstruct sparse signals typically sum of sinusoids from nonuniform samples we achieve this by identifying a linear transformation that relates the unknown uniform samples of sinusoids to the given measurements these uniform samples are known to satisfy the annihilation equations a valid solution is then obtained by solving a constrained minimization such that the reconstructed signal is consistent with the given measurements and satisfies the annihilation constraint thanks to this new approach we unify a variety of fri based methods we demonstrate the versatility and robustness of the proposed approach with five fri reconstruction problems namely dirac reconstructions with irregular time or fourier domain samples fri curve reconstructions dirac reconstructions on the sphere and point source reconstructions in radioastronomy the proposed algorithm improves substantially over state of the art methods and is able to reconstruct point sources accurately from irregularly sampled fourier measurements under severe noise conditions

continuous cubic formulations for cluster detection problems in networks the celebrated motzkin straus formulation for the maximum clique problem provides a nontrivial characterization of the clique number of a graph in terms of the maximum value of a nonconvex quadratic function over a standard simplex it was originally developed as a way of proving turan s theorem in graph theory but was later used to develop competitive algorithms for the maximum clique problem based on continuous optimization clique relaxations such as s defective clique and s plex emerged as attractive more practical alternatives to cliques in network based cluster detection models arising in numerous applications this paper establishes continuous cubic formulations for the maximum s defective clique problem and the maximum s plex problem by generalizing the motzkin straus formulation to the corresponding clique relaxations the formulations are used to extend turan s theorem and other known lower bounds on the clique number to the considered clique relaxations results of preliminary numerical experiments with the conopt solver demonstrate that the proposed formulations can be used to quickly compute high quality solutions for the maximum s defective clique problem and the maximum s plex problem the proposed formulations can also be used to generate interesting test instances for global optimization solvers

exploiting special structures in constructing a hierarchy of relaxations for 0 1 mixed integer problems a new hierarchy of relaxations is presented that provides a unifying framework for constructing a spectrum of continuous relaxations spanning from the linear programming relaxation to the convex hull representation for linear mixed integer 0 1 problems this hierarchy is an extension of the reformulation linearization technique rlt of sherali and adams 1990 1994a and is particularly designed to exploit special structures specifically inherent special structures are exploited by identifying particular classes of multiplicative factors that are applied to the original problem to reformulate it as an equivalent polynomial programming problem and subsequently this resulting problem is linearized to produce a tighter relaxation in a higher dimensional space this general framework permits us to generate an explicit hierarchical sequence of tighter relaxations leading up to the convex hull representation a similar hierarchy can be constructed for polynomial mixed integer 0 1 problems additional ideas for further strengthening rlt based constraints by using conditional logical implications as well as relationships with sequential lifting are also explored several examples are presented to demonstrate how underlying special structures including generalized and variable upper bounding covering partitioning and packing constraints as well as sparsity can be exploited within this framework for some types of structures low level relaxations are exhibited to recover the convex hull of integer feasible solutions

correction to rotation and gray scale transform invariant texture classification using spiral resampling subband decomposition and hidden markov model this paper proposes a new texture classification algorithm that is invariant to rotation and gray scale transformation first we convert two dimensional 2 d texture images to one dimensional 1 d signals by spiral resampling then we use a quadrature mirror filter qmf bank to decompose sampled signals into subbands in each band we take high order autocorrelation functions as features features in different bands which form a vector sequence are then modeled as a hidden markov model bmm during classification the unknown texture is matched against all the models and the best match is taken as the classification result simulations showed that the highest correct classification rate for 16 kinds of texture was 95 14