improving filtered backprojection reconstruction by data dependent filtering filtered backprojection one of the most widely used reconstruction methods in tomography requires a large number of low noise projections to yield accurate reconstructions in many applications of tomography complete projection data of high quality cannot be obtained because of practical considerations algebraic methods tend to handle such problems better but are computationally more expensive in this paper we introduce a new method that improves the filtered backprojection method by using a custom data dependent filter that minimizes the projection error of the resulting reconstruction we show that the computational cost of the new method is significantly lower than that of algebraic methods experiments on both simulation and experimental data show that the method is able to produce more accurate reconstructions than filtered backprojection based on popular static filters when presented with data with a limited number of projections or statistical noise present furthermore the results show that the method produces reconstructions with similar accuracy to algebraic methods but is faster at producing them finally we show that the method can be extended to exploit certain forms of prior knowledge improving reconstruction accuracy in specific cases

computational analysis and improvement of sirt iterative x ray computed tomography ct algorithms have the potential for producing high quality images but are computationally very demanding especially when applied to high resolution problems focusing on simultaneous iterative reconstruction technique sirt we provide an eigenvalue based scheme for automatically determining a near optimal value of the relaxation parameter this accelerates the convergence rate of sirt to the point where only half the number of iterations normally required is needed we also modify the way sirt uses preconditioning to solve a weighted least squares problem the resulting algorithm which we call psirt is associated with a smaller memory footprint and calls for less data to be communicated in a distributed memory implementation experimental residual norm and timing results are provided based on cone beam micro ct mouse data including for an ordered subsets study

characterizations of symmetric polyconvexity symmetric quasiconvexity plays a key role for energy minimization in geometrically linear elasticity theory due to the complexity of this notion a common approach is to retreat to necessary and sufficient conditions that are easier to handle this article focuses on symmetric polyconvexity which is a sufficient condition we prove a new characterization of symmetric polyconvex functions in the two and three dimensional setting and use it to investigate relevant subclasses like symmetric polyaffine functions and symmetric polyconvex quadratic forms in particular we provide an example of a symmetric rank one convex quadratic form in 3d that is not symmetric polyconvex the construction takes the famous work by serre from 1983 on the classical situation without symmetry as inspiration beyond their theoretical interest these findings may turn out useful for computational relaxation and homogenization

some remarks on quasiconvexity and rank one convexity we explore some necessary conditions for quasiconvexity in an attempt to show that rank one convexity does not imply quasiconvexity when the target space for deformations is two dimensional an interesting construction is presented showing how rank one directions may fit with each other making the task harder than in higher dimensions

an improved algorithm for reprojecting rays through pixel images it is often desired to calculate line integrals through a field of reconstructed ct density pixels for the purpose of improving ct image quality two algorithms widely published and discussed in the past are known to either degrade spatial resolution or generate errors in the results due to the discontinuous square pixel modeling of the reconstructed image an algorithm is described based on linear interpolation between pixels which provides superior accuracy without unnecessary loss of resolution it was tested on simulated data for a head section and on a narrow gaussian density distribution the experimental results demonstrated improved performance the method is expected to prove useful for many types of post reconstruction processing including beam hardening missing data and noise supression algorithms

an investigation concerning optimal design of solid elastic plates abstract we consider the problem of maximizing the integral stiffness of solid elastic plates described by thin plate theory assuming the material volume and plate domain to be given we use the plate thickness function as the design variable and take both maximum and minimum allowable thickness values into account on the basis of a convenient tensorial formulation of the problem where the governing equations are derived by variational analysis and constitute necessary conditions for stationarity we develop an efficient and quite general numerical algorithm by means of which a number of stationary solutions for rectangular and axisymmetric annular plates with various boundary conditions are obtained these numerical results enable us to investigate the optimization problem itself in terms of its major parameters particularly the maximum and minimum values specified for the plate thickness for problems associated with large ratios between these constraint values plate designs with significant integral stiffeners are obtained we find however that these designs are only local optima and that a global optimal plate thickness function does generally neither exist within the class of smooth functions nor within the class of smooth functions with a finite number of discontinuities in order to determine a global optimal solution associated with given thickness constraint values it is therefore necessary to change the optimal design formulation with implications for a number of similar two dimensional optimization problems our results offer valuable indications of the lines along which such changes should be performed

integral estimates for null lagrangians sobolev spaces of differential forms are studied lp projections onto exact forms are introduced as a tool to obtain integral estimates for null lagrangians new results on compensated compactness are given and mean coercive variational integrals are found existence of minima of certain mean coercive functionals is established

twisted genus bounds for subvarieties of generic hypersurfaces we prove some lower bounds on certain twists of the canonical bundle of a subvariety of a generic hypersurface in projective space in particular we prove that the generic sextic threefold contains no rational or elliptic curves and no nondegenerate curves of genus 2

fibered threefolds and lang vojta s conjecture over function fields using the techniques introduced by corvaja and zannier in 2008 we solve the non split case of the geometric lang vojta conjecture for affine surfaces isomorphic to the complement of a conic and two lines in the projective plane in this situation we deal with sections of an affine threefold fibered over a curve whose boundary in the natural projective completion is a quartic bundle over the base whose fibers have three irreducible components we prove that the image of each section has bounded degree in terms of the euler characteristic of the base curve

quasiconvexity and relaxation of nonconvex problems in the calculus of variations keywords quasiconvexity relaxation reference caa article 1982 002doi 10 1016 0022 1236 82 90046 5view record in web of science record created on 2008 11 25 modified on 2017 05 12

w1 p quasiconvexity and variational problems for multiple integrals abstract variational problems for the multiple integral i u g u x dx where r m and u r n are studied a new condition on g called w1 p quasiconvexity is introduced which generalizes in a natural way the quasiconvexity condition of c b morrey it being shown in particular to be necessary for sequential weak lower semicontinuity of i in w 1 p r n and for the existence of minimizers for certain related integrals counterexamples are given concerning the weak continuity properties of jacobians in w 1 p r n p n m an existence theorem for nonlinear elastostatics is proved under optimal growth hypotheses

general existence theorems for hamilton jacobi equations in the scalar and vectorial cases keywords dirichlet problem hamilton jacobi equation existence of solutions reference caa article 1997 002doi 10 1007 bf02392708view record in web of science record created on 2008 11 25 modified on 2017 05 12

fast approximation of algebraic reconstruction methods for tomography most reconstruction algorithms for transmission tomography can be subdivided in two classes variants of filtered backprojection fbp and iterative algebraic methods fbp is very fast and yields accurate results when a large number of projections are available with high signal to noise ratio and a full angular range algebraic methods require much more computation time yet they are more flexible in dealing with limited data problems and noise in this paper we propose an algorithm that combines the best of these two approaches for a given linear algebraic method a filter is computed that can be used within the fbp algorithm the fbp reconstructions that result from using this filter strongly resemble the algebraic reconstructions and have many of their favorable properties while the required reconstruction time is similar to standard fbp based on a series of experiments for both simulation data and experimental data we demonstrate the merits of the proposed algorithm

an optimization algorithm applied to the morrey conjecture in nonlinear elasticity abstract for a long time it has been studied whether rank one convexity and quasiconvexity give rise to different families of constitutive relations in planar nonlinear elasticity stated in 1952 the morrey conjecture says that these families are different but no example has come forward to prove it now we attack this problem by deriving a specialized optimization algorithm based on two ingredients first a recently found necessary condition for the quasiconvexity of fourth degree polynomials that distinguishes between both classes in the three dimensional case and secondly upon a characterization of rank one convex fourth degree polynomials in terms of infinitely many constraints after extensive computational experiments with the algorithm we believe that in the planar case the necessary condition mentioned above is also necessary for the rank one convexity of fourth degree polynomials hence the question remains open

a relaxation theorem and its application to the equilibrium of gases keywords relaxed problem lower convex envelope gas equilibrium van der waal s equation reference caa article 1981 001doi 10 1007 bf00280643view record in web of science record created on 2008 11 25 modified on 2017 05 12

existence of minimizers for non quasiconvex integrals keywords quasiconvexity existence of minimizers reference caa article 1995 002doi 10 1007 bf00380915 record created on 2008 11 25 modified on 2017 05 12

hyperbolicity of generic surfaces of high degree in projective 3 space the main goal of this work is to prove that a very generic surface of degree at least 21 in complex projective 3 dimensional space is hyperbolic in the sense of kobayashi this means that every entire holomorphic map f inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i x to the surface is constant in 1970 kobayashi conjectured more generally that a very generic hypersurface of sufficiently high degree in projective space is hyperbolic our technique follows the stream of ideas initiated by green and griffiths in 1979 which consists of considering jet differentials and their associated base loci however a key ingredient is the use of a different kind of jet bundle namely the semple jet bundles previously studied by the first named author the base locus calculation is achieved through a sequence of riemann roch formulas combined with a suitable generic vanishing theorem for order 2 jets our method covers the case of surfaces of general type with picard group inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i and 13 12 2 c 2 1 9 c 2 0 where 2 is the 2 jet threshold bounded below by 1 6 for surfaces in inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 03i 3 the final conclusion is obtained by using recent results of mcquillan on holomorphic foliations

on the complement of a generic curve in the projective plane let c be a very generic smooth curve of degree d in the complex projective plane in this paper we show that for any curve d in the projective plane that does not contain c the set c d contains at least d 2 distinct points moreover this bound is sharp when d 3 our motivation for the study of this problem comes from the problem of hyperbolicity of the complement of a plane curve as an application of our result we give another proof of the following fact if c is a very generic smooth curve of degree d 5 in the complex projective plane then the intersection of the complement of c in the projective plane with any plane curve d which does not contain c is hyperbolic

some examples of rank one convex functions in dimension two keywords sobolev space quasiconvexity rank one convexity reference caa article 1990 004 record created on 2008 11 25 modified on 2017 05 12

hyperbolicity of geometric orbifolds we study complex hyperbolicity in the setting of geometric orbifolds introduced by f campana generalizing classical methods to this context we obtain degeneracy statements for entire curves with ramification in situations where no second main theorem is known from value distribution theory

regularized formulation for optimal design of axisymmetric plates abstract this paper presents a regularized mathematical formulation necessary conditions of optimality and solutions of problems of optimal design of solid elastic axisymmetric plates of prescribed total material volume single purpose design criteria of minimum static compliance maximum stiffness and maximum frequency of free transverse vibrations are considered the regularization which alleviates some anomalies and difficulties encountered earlier in plate optimization problems is based on a new compound plate model with two simultaneous design variables namely variable thickness of a solid part of the plate and variable concentration of a dense system of thin integral stiffeners attached to the solid plate part a numerical optimality criterion based method of solution is developed for the problem and several optimal designs are presented the results are compared with results obtained from optimal design formulations applied heretofore and substantiate the superiority of the new regularized formulation

vector fields on the total space of hypersurfaces in the projective space and hyperbolicity the results we obtain in this article concern the hyperbolicity of very generic hypersurfaces in the 3 dimensional projective space we show that the kobayashi conjecture is true in this setting as long as the degree of the hypersurface is greater than 18

optimal design and relaxation of variational problems iii abstract this paper has attempted a synthesis of three subjects that have developed separately optimal design homogenization and relaxation in the calculus of variations the underlying theme is that of oscillations they occur with certain definite patterns in minimizing sequences for the variational problem the same patterns recur in nearly optimal designs and in the coefficients of the equation being homogenized each problem is resolved by determining the structure of those oscillations and above all their macroscopic averages it is those averages that solve the relaxed problem they also determine the optimal design and the solution of the homogenized equation we emphasize also the role of optimization the homogenized equations and composite materials of interest here come not from arbitrary mixtures but from those that are extremal since they correspond to minimizing sequences for the variational problem the effective properties of these composites attain the optimal bounds for given materials in fixed proportions

on the logarithmic kobayashi conjecture we study the hyperbolicity of the log variety pn x where x is a very general hypersurface of degree d 2n 1 which is the bound predicted by the kobayashi conjecture using a positivity result for the sheaf of twisted logarithmic vector fields which may be of independent interest we show that any log subvariety of pn x is of log general type give a new proof of the algebraic hyperbolicity of pn x and exclude the existence of maximal rank families of entire curves in the complement of the universal degree d hypersurface moreover we prove that as in the compact case the algebraic hyperbolicity of a log variety is a necessary condition for the metric one

an example of a quasiconvex function that is not polyconvex in two dimensions we study the different notions of convexity for the function f 2 2 2 det where e 2 2 introduced by dacorogna marcellini we show that f is convex polyconvex quasiconvex rank one convex if and only if 2 3 2 1 1 for some 0 2 3 respectively

null lagrangians weak continuity and variational problems of arbitrary order abstract we consider the problem of minimizing integral functionals of the form i u f x k u x dx where r p u r and k u denotes the set of all partial derivatives of u with orders k the method is based on a characterization of null lagrangians l ku depending only on derivatives of order k applications to elasticity and other theories of mechanics are given

quasiconvex functions with subquadratic growth we establish the existence of quasiconvex functions which are not convex and which have subquadratic grow that infinity

rank one convexity implies polyconvexity for isotropic objective and isochoric elastic energies in the two dimensional case we show that in the two dimensional case every objective isotropic and isochoric energy function which is rank one convex on gl 2 is already polyconvex on gl 2 thus we negatively answer morrey s conjecture in the subclass of isochoric nonlinear energies since polyconvexity implies quasiconvexity our methods are based on different representation formulae for objective and isotropic functions in general as well as for isochoric functions in particular we also state criteria for these convexity conditions in terms of the deviatoric part of the logarithmic strain tensor

subvarieties of general type on a general projective hypersurface we study subvarieties of a general projective degree d hypersurface x d subset mathbf p n our main theorem which improves previous results of l ein and c voisin implies in particular the following sharp corollary any subvariety of a general hypersurface x d subset mathbf p n for n geq 6 and d geq 2n 2 is of general type

cauchy dirichlet problem for first order nonlinear systems abstract let r nbe open u r mand thus the gradient matrixdu r m n we lete r m nbe compact and denote byrcoeandpcoethe rank one convex and polyconvex hull ofe respectively we show that ifrcoe pcoe and two other hypotheses named the segment property and the extreme points property and if c1 r m is such that d x e int pcoe x then there exists a dense set of u w1 r m such that formula we apply this existence theorem to some relevant examples studied in the literature as well as to problems with x u dependence

relaxation results for functions depending on polynomials changing sign on rank one matrices abstract in this paper we are interested in computing the different convex envelopes of functions depending on polynomials especially those having it is main part change sign on rank one matrices our main result applies to functions of the type w f p f w f p f f det f or w f p f g adj n f defined on the space of matrices where f r r and g r 3 r are three continuous functions and p p 0 p 1 p d is a polynomial such that p d has the property of changing sign on rank one matrices then the polyconvex quasi convex and rank one convex envelopes of w are equal

an intuitive discussion on the ideal ramp filter in computed tomography i in x ray computed tomography ct the ideal ramp filter is a generalized function defined by the inverse fourier transform similar to dirac s discussion on the delta function we present an intuitive discussion on the ideal ramp filter with this concise discussion one obtains a better understanding of the filter backprojection algorithm fbp and can easily construct new practical filters