very large scale linear programming a case study in combining interior point and simplex methods experience with solving a 12 753 313 variable linear program is described this problem is the linear programming relaxation of a set partitioning problem arising from an airline crew scheduling application a scheme is described that requires successive solutions of small subproblems yielding a procedure that has little growth in solution time in terms of the number of variables experience using the simplex method as implemented in cplex an interior point method as implemented in obi and a hybrid interior point simplex approach is reported the resulting procedure illustrates the power of an interior point simplex combination for solving very large scale linear programs

a theoretical framework of regional cone beam tomography intuitively if only part of an object is to be reconstructed the information required to perform the reconstruction should be less than that required to perform global reconstruction global reconstruction is assumed by every published reconstruction formula with closed format the reduction of input information could lead to the simplification of data collection and the reduction of implementation cost the author has explored three basic issues of regional cone beam tomography 1 a completeness condition for regional reconstruction 2 an estimation formula and 3 a convergence condition the analysis of the first issue yields requirements for artifact free reconstruction and a convenient criterion for source curve design the closed format of the estimation formula developed permits efficient analysis the discussion of the third issue facilitates guidelines for selecting an appropriate interpolation technique for discrete input data

derivation and analysis of a filtered backprojection algorithm for cone beam projection data the authors address the problem of three dimensional image reconstruction from cone beam projections modifying a result due to a a kirillov soviet math dokl vol 2 p 268 9 1961 the authors derive an inversion formula for the case where the cone vertices form an unbounded curve for the special case in which the cone vertices form a circle an approximate reconstruction formula is developed and shown to be essentially equivalent to the practical cone beam algorithm of l a feldkamp et al 1984 for this approximate inverse the authors derive the resulting spatially varying point spread function examine the effect of bandlimiting due to sampling and compare the resulting image quality as a function of the radius of the circle formed by the cone vertices

regularization designs for uniform spatial resolution and noise properties in statistical image reconstruction for 3 d x ray ct statistical image reconstruction methods for x ray computed tomography ct provide improved spatial resolution and noise properties over conventional filtered back projection fbp reconstruction along with other potential advantages such as reduced patient dose and artifacts conventional regularized image reconstruction leads to spatially variant spatial resolution and noise characteristics because of interactions between the system models and the regularization previous regularization design methods aiming to solve such issues mostly rely on circulant approximations of the fisher information matrix that are very inaccurate for undersampled geometries like short scan cone beam ct this paper extends the regularization method proposed in to 3 d cone beam ct by introducing a hypothetical scanning geometry that helps address the sampling properties the proposed regularization designs were compared with the original method in with both phantom simulation and clinical reconstruction in 3 d axial x ray ct the proposed regularization methods yield improved spatial resolution or noise uniformity in statistical image reconstruction for short scan axial cone beam ct

basis and partition identification for quadratic programming and linear complementarity problems optimal solutions of interior point algorithms for linear and quadratic programming and linear complementarity problems provide maximally complementary solutions maximally complementary solutions can be characterized by optimal partitions on the other hand the solutions provided by simplex based pivot algorithms are given in terms of complementary bases a basis identification algorithm is an algorithm which generates a complementary basis starting from any complementary solution a partition identification algorithm is an algorithm which generates a maximally complementary solution and its corresponding partition starting from any complementary solution in linear programming such algorithms were respectively proposed by megiddo in 1991 and balinski and tucker in 1969 in this paper we will present identification algorithms for quadratic programming and linear complementarity problems with sufficient matrices the presented algorithms are based on the principal pivot transform and the orthogonality property of basis tableaus

direct least squares estimation of spatiotemporal distributions from dynamic spect projections using a spatial segmentation and temporal b splines artifacts can result when reconstructing a dynamic image sequence from inconsistent as well as insufficient and truncated cone beam single photon emission computed tomography spect projection data acquired by a slowly rotating gantry the artifacts can lead to biases in kinetic model parameters estimated from time activity curves generated by overlaying volumes of interest on the images however the biases in time activity curve estimates and subsequent kinetic parameter estimates can be reduced significantly by first modeling the spatial and temporal distribution of the radiopharmaceutical throughout the projected field of view and then estimating the time activity curves directly from the projections this approach is potentially useful for clinical spect studies involving slowly rotating gantries particularly those using a single detector system or body contouring orbits with a multidetector system the authors have implemented computationally efficient methods for fully four dimensional 4 d direct estimation of spatiotemporal distributions from dynamic spect projection data temporal b splines providing various orders of temporal continuity as well as various time samplings were used to model the time activity curves for segmented blood pool and tissue volumes in simulated cone beam and parallel beam cardiac data acquisitions least squares estimates of time activity curves were obtained quickly using a workstation given faithful spatial modeling accurate curve estimates were obtained using cubic quadratic or linear b splines and a relatively rapid time sampling during initial tracer uptake from these curves kinetic parameters were estimated accurately for noiseless data and with some bias for noisy data a preliminary study of spatial segmentation errors showed that spatial model mismatch adversely affected quantitative accuracy but also resulted in structured errors projected model versus raw data that were easily detected in the authors simulations this suggests iterative refinement of the spatial model to reduce structured errors as an area of future research

cone beam reconstruction using the backprojection of locally filtered projections this paper describes a flexible new methodology for accurate cone beam reconstruction with source positions on a curve or set of curves the inversion formulas employed by this methodology are based on first backprojecting a simple derivative in the projection space and then applying a hilbert transform inversion in the image space the local nature of the projection space filtering distinguishes this approach from conventional filtered backprojection methods this characteristic together with a degree of flexibility in choosing the direction of the hilbert transform used for inversion offers two important features for the design of data acquisition geometries and reconstruction algorithms first the size of the detector necessary to acquire sufficient data for accurate reconstruction of a given region is often smaller than that required by previously documented approaches in other words more data truncation is allowed second redundant data can be incorporated for the purpose of noise reduction the validity of the inversion formulas along with the application of these two properties are illustrated with reconstructions from computer simulated data in particular in the helical cone beam geometry it is shown that 1 intermittent transaxial truncation has no effect on the reconstruction in a central region which means that wider patients can be accommodated on existing scanners and more importantly that radiation exposure can be reduced for region of interest imaging and 2 at maximum pitch the data outside the tam danielsson window can be used to reduce image noise and thereby improve dose utilization furthermore the degree of axial truncation tolerated by our approach for saddle trajectories is shown to be larger than that of previous methods

combining interior point and pivoting algorithms for linear programming we propose a new approach to combine linear programming lp interior point and simplex pivoting algorithms in any iteration of an interior point algorithm we construct a related lp problem which approximates the original problem with a known strictly complementary primal dual solution pair thus we can apply megiddo s megiddo n 1991 on finding primal and dual optimal bases orsa j comput 31 63 65 pivoting procedure to compute an optimal basis for the approximate problem in strongly polynomial time we show that if the approximate problem is constructed from an interior point iterate sufficiently close to the optimal face then any optimal basis of the approximate problem is an optimal basis for the original problem if the lp data are rational the total number of interior point iterations to create such a sufficient approximate problem is bounded by a polynomial in the data size we develop a modification of megiddo s procedure and discuss several implementation issues in solving the approximate problem we also report encouraging computational results for this combined approach

a factorization approach for cone beam reconstruction on a circular short scan in this paper we introduce a new algorithm for 3 d image reconstruction from cone beam cb projections acquired along a partial circular scan our algorithm is based on a novel exact factorization of the initial 3 d reconstruction problem into a set of independent 2 d inversion problems each of which corresponds to finding the object density on one single plane any such 2 d inversion problem is solved numerically using a projected steepest descent iteration scheme we present a numerical evaluation of our factorization algorithm using computer simulated cb data without and with noise of the forbild head phantom and of a disk phantom first we study quantitatively the impact of the reconstruction parameters on the algorithm performance next we present reconstruction results for visual assessment of the achievable image quality and provide for comparison results obtained with two other state of the art reconstruction algorithms for the circular short scan

green function of the inhomogeneous helmholtz equation with nonuniform refraction index using quaternion analysis in this paper we first show in the framework of quaternion analysis how the fundamental solutions of the dirac operators with vector potential can be obtained then we use the obtained results to present a derivation of the exact analytic green function for the helmholtz equation i e a x 2 g0 x x for the case a x is a monogenic analytic vector potential

quasi exact filtered backprojection algorithm for long object problem in helical cone beam tomography exact reconstruction from axially truncated cone beam projections acquired with a helical vertex path is a challenging problem for which solutions are currently under investigation by some researchers this paper deals with a difficult class of this problem called the long object problem its purpose is to reconstruct a central region of interest roi of a long object when the helical path extends only a little bit above and below the roi by extending the authors recent approach based on the triangular decomposition of the grangeat formula the authors derive quasi exact reconstruction algorithms whose overall structure is of filtered backprojection fbp style unlike the previous similar approaches to the long object problem the proposed fbp algorithms do not require additional two circular scans at the ends of the helical path furthermore the algorithms require a significantly smaller detector area and achieve improved image quality even for a large pitch compared with the approximate feldkamp algorithms one drawback of the proposed algorithms is the computational time which is much longer than for the feldkamp algorithms the authors show some simulation results to demonstrate the performances of the proposed algorithms

tomographic reconstruction from experimentally obtained cone beam projections direct reconstruction in three dimensions for two dimensional projection data has been achieved by cone beam reconstruction techniques in this paper explicit formulas for a cone beam convolution and back projection reconstruction algorithm are given in a form which can be easily coded for a computer the algorithm is justified by analyzing tomographic reconstructions of a uniformly attenuating sphere from simulated noisy projection data a particular feature of this algorithm is the use of a one dimensional rather than two dimensional convolution function greatly speeding up the reconstruction the technique is applicable however large the cone angle of data capture and correctly reduces to the pure fan beam reconstruction technique in the central section of the cone the method has been applied to data captured on a cone beam ct scanner designed for bone mineral densitometry

computation of unmeasured third generation vct views from measured views we compute unmeasured cone beam projections from projections measured by a third generation helical volumetric computed tomography system by solving a characteristic problem for an ultrahyperbolic differential equation john 1938 by working in the fourier domain we convert the second order pde into a family of first order ordinary differential equations a simple first order integration is used to solve the odes

a cone beam reconstruction algorithm using shift variant filtering and cone beam backprojection an exact inversion formula written in the form of shift variant filtered backprojection fbp is given for reconstruction from cone beam data taken from any orbit satisfying h k tuy s 1983 sufficiency conditions the method is based on a result of p grangeat 1987 involving the derivative of the three dimensional 3d radon transform but unlike grangeat s algorithm no 3d rebinning step is required data redundancy which occurs when several cone beam projections supply the same values in the radon domain is handled using an elegant weighting function and without discarding data the algorithm is expressed in a convenient cone beam detector reference frame and a specific example for the case of a dual orthogonal circular orbit is presented when the method is applied to a single circular orbit even though tuy s condition is not satisfied it is shown to be equivalent to the well known algorithm of l a feldkamp et al 1984

some remarks on g functors and the brauer morphism keywords finite group g functor restriction maps transfer maps mackey s formula frobenius reciprocity brauer morphism defect base nilpotent ideal burnside ring idempotent formula induction formula symmetric g functor character ring green ring reference ctg article 1988 003 record created on 2008 12 16 modified on 2017 05 12

cone beam local tomography methods systems and processes for providing efficient image reconstruction using local cone beam tomography which provide a reduced level of artifacts without suppressing the strength of the useful features and in a dynamic case provide reconstruction of objects that are undergoing a change during the scan an embodiment provides a method of reconstructing an image from cone beam data provided by at least one detector the method includes collecting cb projection data of an object storing the cb projection data in a memory and reconstructing the image from the local cb projection data in the reconstructing step a combination of derivatives of the cb projection data that will result in suppressing the artifacts are found the combination of derivatives includes collecting cone beam data that represents a collection of integrals that represent the object

elementary construction of the quiver of the mackey algebra for groups with cyclic normal p sylow subgroup through recent investigations of j thrvenaz and p j webb 4 8 the concept of mackey functors being originally introduced by j a green 3 and studied by a w m dress t yoshida h sasaki and others has regained considerable interest an important reason for this is i new interpretation of a conjecture of aiperin in terms of mackey functors in 8 using results of 7 given a commutative ring 4 by its definition it is immediate that the category of mackey functors over 4 for a finite group g is an abelian category even that it is the category of 4 representations of a quiver with relations 8 namely a mackey functor for g associates to each subgroup of g a module and moreover certain linear maps between these spaces satisfying certain relations involving g thus a mackey functor for g can be interpreted as a module over a path algebra of a quiver with relations the so called mackey algebra 6 9 the main difference to the usual representation theory of quivers and thus the main problem of interpreting mackey functors as such representations lies in the fact that the maps between these spaces do not lie in the radical of this path algebra and this path algebra is not basic in general so it is a natural problem to compute the quiver in the usual sense for the category of mackey functors for a group g in particular in the case where 4 is a field of characteristic p dividing the order of g the question of when there are up to isomorphism only finitely many indecomposable mackey functors for g led to recent investigations of thrvenaz and webb solving this problem in general and it also led to the investigations we present in this paper which presents in a special situation namely if g has a normal cyclic p sylow subgroup an explicit computation of the quiver of the now so called mackcy algebra by definition the mackey algebra is the basic algebra whose category of finitely generated

region of interest reconstruction from truncated data in circular cone beam ct the circular scanning trajectory is one of the most widely adopted data acquisition configurations in computed tomography ct the feldkamp davis kress fdk algorithm and its various modifications have been developed for reconstructing approximately three dimensional images from circular cone beam data when data contain transverse truncations however these algorithms may reconstruct images with significant truncation artifacts it is of practical significance to develop algorithms that can reconstruct region of interest roi images from truncated circular cone beam data that are free of truncation artifacts and that have an accuracy comparable to that obtained from nontruncated cone beam data in this work we have investigated and developed a backprojection filtration bpf based algorithm for roi image reconstruction from circular cone beam data containing transverse truncations furthermore we have developed a weighted bpf algorithm to exploit redundant information in data for improving image quality in an effort to validate and evaluate the proposed bpf algorithms for circular cone beam ct we have performed numerical studies by using both computer simulation data and experimental data acquired with a radiotherapy cone beam ct system quantitative results in these studies demonstrate that the proposed bpf algorithms for circular cone beam ct can reconstruct roi images free of truncation artifacts

cone beam reconstruction with sources on a curve an inversion procedure is developed for reconstructing a function of compact support in mathbb r 3 from its divergent beam x ray transform with sources on a curve the results apply to many curves not satisfying the conditions of tuy siam j appl math 43 1983 pp 546 552 for example planar circles of sufficiently large radius in some cases estimates in sobolev norms are established for the inversion operator

computation of the collapse state in limit analysis using the lp primal affine scaling algorithm abstract the object of this work is twofold the first goal is to demonstrate that for the duality problem of limit analysis with linearized yield condition the lp primal affine scaling algorithm shows properties which are significantly different from those of the simplex method and that as a consequence of this better results can be obtained the second goal is to compute the collapse state for a classical and hard problem in plane strain tension of a rectangular bar with symmetric thin cuts both the collapse multiplier and collapse fields are computed to a better accuracy and detail than previously

presolving in linear programming most modern linear programming solvers analyze the lp problem before submitting it to optimization some examples are the solvers whizard tomlin and welch 1983 ob1 lustig et al 1994 osl forrest and tomlin 1992 sciconic 1990 and cplex bixby 1994 the purpose of the presolve phase is to reduce the problem size and to discover whether the problem is unbounded or infeasible in this paper we present a comprehensive survey of presolve methods moreover we discuss the restoration procedure in detail i e the procedure that undoes the presolve computational results on the netlib problems gay 1985 are reported to illustrate the efficiency of the presolve methods

the dade group of mackey functors for p groups abstract we introduce endo permutation mackey functors and the mackey dade group of a p group and study their basic properties we exhibit relations between the mackey dade group of a finite p group p and the dade groups of the weyl groups of all subgroups of p as a result we show that the mackey dade group tensored with q over z is the kernel of the linearization map for mackey functors introduced by the author

duality in g algebras keywords finite group complete discrete valuation ring symmetric g algebra symmetric bilinear form projective ideal symmetric algebra rg lattice unimodular symmetric g algebra almost projective ideal almost split sequences block defect groups virtually irreducible lattices splitting trace lattices reference ctg article 1988 005doi 10 1007 bf01161746 record created on 2008 12 16 modified on 2017 05 12

maximum stopping value policies in finite markov population decision chains this paper considers infinite horizon finite state and action markov population decision chains mpdcs in which the goal is to find a stationary stopping policy with maximum stopping value that is with maximum value over all deterministic markov stopping policies a policy is stopping if the resulting expected population size in a period diminishes to zero as the period converges to infinity the paper shows that the following are equivalent a there is a stationary maximum stopping value policy b the maximum stopping value is finite c there is a stopping policy and an excessive point of the optimal return operator and d the maximum stopping value is the least excessive resp fixed point of the optimal return operator the paper shows how to use linear programming policy improvement and successive approximations to solve the problem the problem arises in stopping a markov chain as in optimally eradicating a pest or disease the problem is one of two key subproblems used repeatedly to f

mackey functors with chain conditions abstract letabe a green functor for a finite groupgand letmbe a lefta module mis callednoetherian artinian if the lattice of all submodules ofmsatisfies acc respectively dcc mis calledtotally noetherian totally artinian ifmxis noetherian respectively artinian for every finiteg setx in this paper it is shown that the totally noetherian totally artinian lefta modules behave in the same way as the classical noetherian artinian modules the left noetherian left artinian green functors are less well behaved but some properties from classical algebra still hold it is shown that cohen s theorem holds in this setting our main result shows that if a commutative green functorais artinian then the ringsa h jac a h are semisimple artinian for all subgroupshofg

an inversion formula for cone beam reconstruction an analytic inversion formula allowing the reconstruction of a three dimensional object from x ray cone beams is given the formula is valid for the case where the source of the beams describes a bounded curve satisfying a set of weak conditions

derivation and implementation of a cone beam reconstruction algorithm for nonplanar orbits b d smith ibid vol mi 4 p 15 25 1985 opt eng vol 29 p 524 34 1990 and p grangeat these de doctorat 1987 lecture notes in mathematics 1497 p 66 97 1991 derived a cone beam inversion formula that can be applied when a nonplanar orbit satisfying the completeness condition is used although grangeat s inversion formula is mathematically different from smith s one they have similar overall structures to each other the contribution of the present paper is two fold first based on the derivation of smith the authors point out that grangeat s inversion formula and smith s one can be conveniently described using a single formula the smith grangeat inversion formula that is in the form of space variant filtering followed by cone beam backprojection furthermore the resulting formula is reformulated for data acquisition systems with a planar detector to obtain a new reconstruction algorithm second the authors make two significant modifications to the new algorithm to reduce artifacts and numerical errors encountered in direct implementation of the new algorithm as for exactness of the new algorithm the following fact can be stated the algorithm based on grangeat s intermediate function is exact for any complete orbit whereas that based on smith s intermediate function should be considered as an approximate inverse excepting the special case where almost every plane in 3d space meets the orbit the validity of the new algorithm is demonstrated by simulation studies

direct reconstruction of cone beam data acquired with a vertex path containing a circle cone beam data acquired with a vertex path satisfying the data sufficiency condition of tuy can be reconstructed using exact filtered backprojection algorithms these algorithms are based on the application to each cone beam projection of a two dimensional 2 d filter that is nonstationary and therefore more complex than the one dimensional 1 d ramp filter used in the approximate algorithm of feldkamp davis and kress 1984 fdk we determine in this paper the general conditions under which the 2 d nonstationary filter reduces to a 2 d stationary filter and also give the explicit expression of the corresponding convolution kernel using this result and the redundancy of the cone beam data a composite algorithm is derived for the class of vertex paths that consist of one circle and some complementary subpath designed to guarantee data sufficiency in this algorithm the projections corresponding to vertex points along the circle are filtered using a 2 d stationary filter whereas the other projections are handled with a 2 d nonstationary filter the composite algorithm generalizes the method proposed by kudo and saito 1990 in which the circle data are processed with a 1 d ramp filter as in the fdk algorithm the advantage of the 2 d filter introduced in this paper is to guarantee that the filtered cone beam projections do not contain singularities in smooth regions of the object tests of the composite algorithm on simulated data are presented

single and multipinhole collimator design evaluation method for small animal spect high resolution functional imaging of small animals is often obtained by single pinhole spect with circular orbit acquisition multipinhole spect adds information due to its improved sampling and can improve the trade off between resolution and sensitivity to evaluate different pinhole collimator designs an efficient method is needed that quantifies the reconstruction image quality in this paper we propose a fast approximate method that examines the quality of individual voxels of a postsmoothed maximum likelihood expectation maximization mlem reconstruction by studying their linearized local impulse response llir and co variance for a predefined target resolution for validation the contrast to noise ratios cnrs in some voxels of a homogeneous sphere and of a realistic rat brain software phantom were calculated for many single and multipinhole designs a good agreement was observed between the cnrs obtained with the approximate method and those obtained with postsmoothed mlem reconstructions of simulated noisy projections this good agreement was quantified by a least squares fit through these results which yielded a line with slope 1 02 1 00 expected and a y intercept close to zero 0 expected 95 4 of the validation points lie within three standard deviations from that line using the approximate method the influence on the cnr of varying a parameter in realistic single and multipinhole designs was examined the investigated parameters were the aperture diameter the distance between the apertures and the axis of rotation the focal distance the acceptance angle the position of the apertures the focusing distance and the number of pinholes the results can generally be explained by the change in sensitivity the amount of postsmoothing and the amount of overlap in the projections the method was applied to multipinhole designs with apertures focusing at a single point but is also applicable to other designs

enpit filtered back projection algorithm for helical ct using an n pi acquisition in this paper we formulate a reconstruction algorithm for an n pi acquisition where n can be any positive odd integer the algorithm is a generalization of the method presented in bontus et al 2003 it is based on the results obtained by katsevich 2004 for the algorithm different sets of filter lines have to be defined we describe the variation of these lines along the detector in some detail before we discuss how the method gives all radon plane contributions the correct weighting the different sets of filter lines are all contained within the n pi window such that a practical realization is possible reconstruction results which we present in the final section show convincing image quality

defect theory for maximal ideals and simple functors keywords green functor source green correspondence maximal ideal finite group fixed point algebra defect theory for g algebras defect group restriction transfer conjugation defect pair functorial ideal simple g functors reference ctg article 1991 002doi 10 1016 0021 8693 91 90168 8 record created on 2008 12 16 modified on 2017 05 12

on the inverse of the directional derivative operator in sbb r n in this work the simplest partial differential equation in is studied and some of its properties derived it describes the infinitesimal translation of a function in a fixed direction specified by a unit vector n and driven by a source function we work out several forms of the corresponding green s function and show that the solutions may be viewed as integral transforms of known as divergent beam x ray transform in imaging science physically this connection is simply due to straight line propagation of radiation emitted by the spatial source distribution in particular we examine the special two dimensional case to point out the connection with the classical radon transform we then show how the radon transform inversion can be obtained in the context of a complex extension of this equation perspectives in higher dimensional space based on the present approach are given in the conclusion

on artifact free projection overlaps in multi pinhole tomographic imaging in multi pinhole spect overlapping the projections from different pinholes has been used to increase sensitivity however the prevailing view is that the overall quality of the reconstructed image is not improved by the overlaps in the projections it is often stated in literatures that overlaps introduce ambiguous information which can lead to nonuniqueness of solution for the inverse problem and thus artifacts are introduced in the reconstructed image on the other hand contrary to the prevailing view a recent study on slit slat collimators shows that artifacts can be removed with the help of an extra complete nonoverlapped projection data set in this paper two types of artifact free projection overlaps are defined in general and the criteria for designing artifact free multi pinhole systems with overlaps are proposed it is shown that once the criteria are satisfied the solution of the inverse problem is unique and thus no artifact is expected in the reconstructed image via extensive simulation study various artifact free overlapping multi pinhole systems are designed and validated it is shown that overlaps in the artifact free systems can improve contrast to noise ratio cnr with a proper design the cnr for an artifact free overlapping system can be significantly higher than that for the corresponding nonoverlapping system the improved image quality is also confirmed with noisy reconstructions

exact radon rebinning algorithm for the long object problem in helical cone beam ct this paper addresses the long object problem in helical cone beam computed tomography the authors present the phi method a new algorithm for the exact reconstruction of a region of interest roi of a long object from axially truncated data extending only slightly beyond the roi the phi method is an extension of the radon method published by kudo et al in phys in med and biol vol 43 p 2885 909 1998 the key novelty of the phi method is the introduction of a virtual object f sub spl phi x for each value of the azimuthal angle spl phi in the image space with each virtual object having the property of being equal to the true object f x in some roi spl omega sub m the authors show that for each spl phi one can calculate exact radon data corresponding to the two dimensional 2 d parallel beam projection of f sub spl phi x onto the meridian plane of angle spl phi given an angular range of length spl pi of such parallel beam projections the roi spl omega sub m can be exactly reconstructed because f x is identical to f sub spl phi x in spl omega sub m simulation results are given for both the radon method and the phi method indicating that 1 for the case of short objects the radon and phi methods produce comparable image quality 2 for the case of long objects the phi method delivers the same image quality as in the short object case while the radon method fails and 3 the image quality produced by the phi method is similar for a large range of pitch values

support theorems for radon transforms on real analytic line complexes in three space in this article we prove support theorems for radon transforms with arbitrary nonzero real analytic measures on line complexes three dimensional sets of lines in r 3 let f be a distribution of compact support on r 3 assume y is a real analytic admissible line complex and y 0 is an open connected subset of y with one line in y 0 disjoint from supp f under weak geometric assumptions if the radon transform of f is zero for all lines in y 0 then supp f intersects no line in y 0 these theorems are more general than previous results even for the classical transform we also prove a support theorem for the radon transform on a nonadmissible line complex our proofs use analytic microlocal analysis and information about the analytic wave front set of a distribution at the boundary of its support

inversion formula for the non uniformly attenuated x ray transform for emission imaging in mathbb r 3 using quaternionic analysis in this paper we present a new derivation of the inverse of the non uniformly attenuated x ray transform in three dimensions based on quaternion analysis an explicit formula is obtained using a set of three dimensional x ray projection data the result without attenuation is recovered as a special case

the evaluation of data completeness and image quality in multiplexing multi pinhole spect multi pinhole collimators are often used in pre clinical spect systems because they have a better resolution sensitivity tradeoff than parallel hole collimators when imaging small objects most multi pinhole collimators are designed to allow no or only a limited amount of overlap between the different pinhole projections because the ambiguity introduced by multiplexing pinholes can result in artifacts the origin of these artifacts is still not fully understood but previous research has already shown that data incompleteness could be part of the explanation therefore we developed a method to investigate data completeness in multiplexing multi pinhole systems and showed that a certain activity distribution can be successfully reconstructed when the nonmultiplexed data is complete or when the overlap can be sufficiently de multiplexed we validated this method using computer simulated phantom data of different multiplexing systems we also studied contrast to noise and nonprewhitening matched filter signal to noise ratio npw snr to compare the image quality in a single pinhole system with multiplexing systems we found that our method can indeed be used to evaluate data completeness in multiplexing systems and found no artifacts in the systems that had complete data sensitivity increased significantly with multiplexing but we found only small nonsignificant differences in contrast to noise ratio however the npw snr did slightly improve in the multiplexing setups we conclude that more multiplexing does not necessarily result in more artifacts and that even a high amount of multiplexing can still result in artifact free images if the nonmultiplexed data is complete or when the overlap can be sufficiently de multiplexed

a quaternionic approach to x ray transform inversion in sbb r 3 a new derivation of the inverse of the x ray transform is presented based on quaternion analysis as pointed out by practitioners a direct inversion formula offers more efficient reconstruction algorithms than tomographic inversion it is shown that the new inverse formula is equivalent to the existing one the advantage of this approach is that it paves the way for a potential inversion of the x ray transform with a non uniform attenuation map in three dimensions which models single photon emission imaging in nuclear medicine

a cone beam reconstruction algorithm for circle plus arc data acquisition geometry in cone beam computerized tomography ct projections acquired with the focal spot constrained on a planar orbit cannot provide a complete set of data to reconstruct the object function exactly there are severe distortions in the reconstructed noncentral transverse planes when the cone angle is large in this work a new method is proposed which can obtain a complete set of data by acquiring cone beam projections along a circle plus arc orbit a reconstruction algorithm using this circle plus arc orbit is developed based on the radon transform and grangeat s formula this algorithm first transforms the cone beam projection data of an object to the first derivative of the three dimensional 3 d radon transform using grangeat s formula and then reconstructs the object using the inverse radon transform in order to reduce interpolation errors new rebinning equations have been derived accurately which allows one dimensional 1 d interpolation to be used in the rebinning process instead of 3 d interpolation a noise free defrise phantom and a poisson noise added shepp logan phantom were simulated and reconstructed for algorithm validation the results from the computer simulation indicate that the new cone beam data acquisition scheme can provide a complete set of projection data and the image reconstruction algorithm can achieve exact reconstruction potentially the algorithm can be applied in practice for both a standard ct gantry based volume tomographic imaging system and a c arm based cone beam tomographic imaging system with little mechanical modification required

mackey functors induction from restriction functors and coinduction from transfer functors abstract boltje s plus constructions extend two well known constructions on mackey functors the fixed point functor and the fixed quotient functor in this paper we show that the plus constructions are induction and coinduction functors of general module theory as an application we construct simple mackey functors from simple restriction functors and simple transfer functors we also give new proofs for the classification theorem for simple mackey functors and semisimplicity theorem of mackey functors

the mathbb r 3 exponential x ray transform inversion in quaternion analysis in this paper we present a new derivation of the inverse of the exponential x ray transform in the three dimensions based on quaternion analysis an explicit formula is obtained using a set of three dimensional x ray projection data the result without attenuation is recovered as a special case

polynomial time computation of strong and n present value optimal policies in markov decision chains this paper studies the problem of finding a stationary strong present value optimal and more generally an n present value optimal policy for an infinite horizon stationary finite state action substochastic markov decision chain a policy is strong present value optimal if it has maximum present value for all small positive interest rates a policy is n present value optimal if its present value falls below the maximum present value for all small positive by o n 1 the importance of stationary n present value optimal policies arises from the following known facts the set of such policies diminishes with n and for n s is precisely the set of stationary strong present value optimal policies for 0 n s stationary n present value optimal policies are nearly strong present value optimal and are of independent interest the best algorithms for finding stationary strong present value optimal policies find stationary n present value policies for n 1 s in that order this paper decomposes th

categorifying induction formulae via divergent series abstract we show how to get explicit induction formulae for finite group representations and more generally for rational green functors by summing a divergent series over dwyer s subgroup and centralizer decomposition spaces this results in formulae with rational coefficients the former space yields a well known induction formula the latter yields a new one as essentially immediate corollaries of the existing literature we get similar formulae in group cohomology and stable splittings of classifying spaces

new properties of the v line radon transform and their imaging applications this paper reports on new aspects of the so called v line radon transforms rts complementing those reported in an earlier work these new properties are nicely uncovered and described with cartesian coordinates in particular we show that the v line rt belongs to the class of rts on curves in the plane which can be mapped onto the standard rt on straight lines and thereby are fully characterizable and invertible next we show that the effect of geometric inversion on the v line rt is to produce a new rt on a pair of supplementary circular arcs which provides a new access to image reconstruction in the so called norton s modality of compton scatter tomography a front runner in the race for alternatives to current emission imaging

fourier rebinning applied to multiplanar circular orbit cone beam spect the authors study the application of fourier rebinning methods to dual planar cone beam spect dual planar cone beam spect involves the use of a pair of dissimilar cone beam collimators on a dual camera spect system each collimator has its focus in a different axial plane while dual planar data is best reconstructed with fully three dimensional 3 d iterative methods these methods are slow and have prompted a search for faster reconstruction techniques fourier rebinning was developed to estimate equivalent parallel projections from 3 d pet data but it simply expresses a relationship between oblique projections taken in planes not perpendicular to the axis of rotation and direct projections taken in those that are the authors find that it is possible to put cone beam data in this context as well the rebinned data ran then be reconstructed using either filtered backprojection fbp or parallel iterative algorithms such as os em the authors compare the feldkamp algorithm and fully 3 d osem reconstruction with fourier rebinned reconstructions on realistically simulated tc 99m hmpao brain spect data they find that the fourier rebinned reconstructions exhibit much less image noise and lower variance in region of interest roi estimates than feldkamp also fourier rebinning followed by osem with nonuniform attenuation correction exhibits less bias in roi estimates than feldkamp with chang attenuation correction the fourier rebinned roi estimates exhibit bias and variance comparable to those from fully 3 d osem and require considerably less processing time however in areas off the axis of rotation the axial direction resolution of fore reconstructed images is poorer than that of images reconstructed with 3 d osem the authors conclude that fourier rebinning is a practical and potentially useful approach to reconstructing data from dual planar circular orbit cone beam systems

augmented likelihood image reconstruction the presence of high density objects remains an open problem in medical ct imaging data of projections passing through objects of high density such as metal implants are dominated by noise and are highly affected by beam hardening and scatter reconstructed images become less diagnostically conclusive because of pronounced artifacts that manifest as dark and bright streaks a new reconstruction algorithm is proposed with the aim to reduce these artifacts by incorporating information about shape and known attenuation coefficients of a metal implant image reconstruction is considered as a variational optimization problem the afore mentioned prior knowledge is introduced in terms of equality constraints an augmented lagrangian approach is adapted in order to minimize the associated log likelihood function for transmission ct during iterations temporally appearing artifacts are reduced with a bilateral filter and new projection values are calculated which are used later on for the reconstruction a detailed evaluation in cooperation with radiologists is performed on software and hardware phantoms as well as on clinically relevant patient data of subjects with various metal implants results show that the proposed reconstruction algorithm is able to outperform contemporary metal artifact reduction methods such as normalized metal artifact reduction

a filtered backprojection algorithm for triple source helical cone beam ct multisource cone beam computed tomography ct is an attractive approach of choice for superior temporal resolution which is critically important for cardiac imaging and contrast enhanced studies in this paper we present a filtered backprojection fbp algorithm for triple source helical cone beam ct the algorithm is both exact and efficient it utilizes data from three inter helix pi arcs associated with the inter helix pi lines and the minimum detection windows defined for the triple source configuration the proof of the formula is based on the geometric relations specific to triple source helical cone beam scanning simulation results demonstrate the validity of the reconstruction algorithm this algorithm is also extended to a multisource version for 2n 1 source helical cone beam ct with parallel computing the proposed fbp algorithms can be significantly faster than our previously published multisource backprojection filtration algorithms thus the fbp algorithms are promising in applications of triple source helical cone beam ct