linograms in image reconstruction from projections the notion of a linogram is introduced it corresponds to the notion of a sinogram in the conventional representation of projection data in image reconstruction in the sinogram points which correspond to rays which go through a fixed point in the cross section to be reconstructed all fall on a sinusoidal curve in the linogram however these points fall on a straight line thus backprojection corresponds to integration along straight lines in the linogram a theorem is proved expressing the backprojection operator in terms of the radon transform and simple changes of variables consequences of this theorem are discussed a novel image reconstruction method based on the theorem is presented

maximum likelihood reconstruction for magnetic resonance fingerprinting this paper introduces a statistical estimation framework for magnetic resonance mr fingerprinting a recently proposed quantitative imaging paradigm within this framework we present a maximum likelihood ml formalism to estimate multiple mr tissue parameter maps directly from highly undersampled noisy bf k space data a novel algorithm based on variable splitting the alternating direction method of multipliers and the variable projection method is developed to solve the resulting optimization problem representative results from both simulations and in vivo experiments demonstrate that the proposed approach yields significantly improved accuracy in parameter estimation compared to the conventional mr fingerprinting reconstruction moreover the proposed framework provides new theoretical insights into the conventional approach we show analytically that the conventional approach is an approximation to the ml reconstruction more precisely it is exactly equivalent to the first iteration of the proposed algorithm for the ml reconstruction provided that a gridding reconstruction is used as an initialization

incremental backprojection algorithm modification of the searching flow scheme and utilization of the relationship among projection views a two dimensional 2 d search flow scheme is proposed for the incremental backprojection algorithm in this scheme the searching direction in a beam is determined only by the distance from the current pixel to the corresponding ray no pixels outside the beam are involved in the procedure in addition the geometrical relationships between the image grids and the projection rays in different views are fully exploited to further reduce the search operations it is found that backprojection of four views can be performed at the same time and the search operation is only required for one of them if the number of views is even thus backprojection is accomplished on a quartet by quartet of views basis as well as on beam by beam basis these approaches not only minimize the number of search operations but also possess a simple algorithm structure implementation results obtained with an ast 386 computer for the incremental backprojection algorithm using this search flow scheme and the relationship among projection views show that the processing time can be reduced by a factor of about 2

a fast sinc function gridding algorithm for fourier inversion in computer tomography the fourier inversion method for reconstruction of images in computerized tomography has not been widely used owing to the perceived difficulty of interpolating from polar or other measurement grids to the cartesian grid required for fast numerical fourier inversion although the fourier inversion method is recognized as being computationally faster than the back projection method for parallel ray projection data the artifacts resulting from inaccurate interpolation have generally limited application of the method this paper presents a computationally efficient gridding algorithm which can be used with direct fourier transformation to achieve arbitrarily small artifact levels the method has potential for application to other measurement geometries such as fan beam projections and diffraction tomography and nmr imaging

blocks with trivial intersection defect groups we show that each block whose defect groups intersect pairwise trivially either has cyclic or generalised quaternion defect groups or is morita equivalent to one of a given list of blocks of central extensions of automorphism groups of non abelian simple groups in particular we classify all blocks of automorphism groups of non abelian simple groups whose defect groups are non cyclic and intersect pairwise trivially a consequence is that donovans conjecture holds for blocks whose defect groups intersect pairwise trivially

broue s abelian defect group conjecture holds for the harada norton sporadic simple group hn abstract in representation theory of finite groups there is a well known and important conjecture due to m broue he conjectures that for any prime p if a p block a of a finite group g has an abelian defect group p then a and its brauer corresponding block b of the normaliser n g p of p in g are derived equivalent rickard equivalent this conjecture is called broue s abelian defect group conjecture we prove in this paper that broue s abelian defect group conjecture is true for a non principal 3 block a with an elementary abelian defect group p of order 9 of the harada norton simple group hn it then turns out that broue s abelian defect group conjecture holds for all primes p and for all p blocks of the harada norton simple group hn

multiclass queueing systems polymatroidal structure and optimal scheduling control in many multiclass queueing systems certain performance measures of interest satisfy strong conservation laws that is the total performance over all job types is invariant under any nonidling service control rule and the total performance over any subset say a of job types is minimized or maximized by offering absolute priority to the types in a over all other types we develop a formal definition of strong conservation laws and show that as a necessary consequence of these strong conservation laws the state space of the performance vector is a base of a polymatroid from known results in polymatroidal theory the vertices of this polyhedron are easily identified and these vertices correspond to absolute priority rules a wide variety of multiclass queueing systems are shown to have this polymatroidal structure which greatly facilitates the study of the optimal scheduling control of such systems when the defining set function of the performance space belongs to the class of generalized symmet

zj controlled blocks of quasisimple groups for odd primes abstract we investigated the converses of glauberman s zj theorem and its block theoretic analogue proved by kessar linckelmann and robinson for a finite group g we proved that a block b of g with a defect group d is zj controlled that is n g z j d controls b fusion in g if and only if b is controlled provided that g is quasisimple and the characteristic p of the modular representation is odd this implies by a result of 5 that the converses of glauberman s zj theorem and its block theoretic analogue both hold in these cases as an application we obtain all q d p free quasisimple groups

decomposable markov decision processes a fluid optimization approach decomposable markov decision processes mdps are problems where the stochastic system can be decomposed into multiple individual components although such mdps arise naturally in many practical applications they are often difficult to solve exactly due to the enormous size of the state space of the complete system which grows exponentially with the number of components in this paper we propose an approximate solution approach to decomposable mdps that is based on re solving a fluid linear optimization formulation of the problem at each decision epoch this formulation tractably approximates the problem by modeling transition behavior at the level of the individual components rather than the complete system we prove that our fluid formulation provides a tighter bound on the optimal value function than three state of the art formulations the approximate linear optimization formulation the classical lagrangian relaxation formulation and a novel alternate lagrangian relaxation that is based on relax

perfect generalized characters inducing the alperin mckay conjecture it is well known that the perfect isometries predicted in broue s conjecture do not always exist when the defect groups are non abelian even when the blocks have equivalent brauer categories we consider perfect generalized characters which induce bijections between the sets of irreducible characters of height zero of a block and of its brauer correspondent in the normalizer of a defect group in this way the perfect isometries predicted in broue s conjecture for blocks with abelian defect groups are generalized whilst such generalized characters do not exist in general we show that they do exist when the defect groups are non abelian trivial intersection subgroups of order p 3 as well as for 2b 2 q for q a power of two and psu 3 q for all q further we show that these blocks satisfy a generalized version of an isotypy

controlled 2 blocks of quasisimple groups abstract controlled p blocks introduced by alperin and broue in 1979 were classified for quasisimple groups g for odd primes in 10 we classify the controlled 2 blocks of quasisimple groups g the results imply that every nilpotent 2 block of g has abelian defect groups this agrees with one of the main results proved in 15 we also give an explicit characterization of non controlled 2 blocks of all quasisimple groups this implies that the p 2 version of the block theoretic analogue of glauberman s zj theorem proved by kessar linckelmann and robinson in 27 holds for quasisimple groups g

some windows with very good sidelobe behavior some of the windows presented by harris 1 are not correct in terms of their reported peak sidelobes and optimal behavior we present corrected plots of harris windows and also derive additional windows with very good sidelobes and optimal behavior under several different constraints the temporal weightings are characterized as a sum of weighted cosines over a finite duration the plots enable the reader to select a window to suit his requirements in terms of bias due to nearby sidelobes and bias due to distant sidelobes

fourier based reconstruction for fully 3 d pet optimization of interpolation parameters fourier based approaches for three dimensional 3 d reconstruction are based on the relationship between the 3 d fourier transform ft of the volume and the two dimensional 2 d ft of a parallel ray projection of the volume the critical step in the fourier based methods is the estimation of the samples of the 3 d transform of the image from the samples of the 2 d transforms of the projections on the planes through the origin of fourier space and vice versa for forward projection reprojection the fourier based approaches have the potential for very fast reconstruction but their straightforward implementation might lead to unsatisfactory results if careful attention is not paid to interpolation and weighting functions in our previous work we have investigated optimal interpolation parameters for the fourier based forward and back projectors for iterative image reconstruction the optimized interpolation kernels were shown to provide excellent quality comparable to the ideal sinc interpolator this work presents an optimization of interpolation parameters of the 3 d direct fourier method with fourier reprojection 3d frp for fully 3 d positron emission tomography pet data with incomplete oblique projections the reprojection step is needed for the estimation from an initial image of the missing portions of the oblique data in the 3d frp implementation we use the gridding interpolation strategy combined with proper weighting approaches in the transform and image domains we have found that while the 3 d reprojection step requires similar optimal interpolation parameters as found in our previous studies on fourier based iterative approaches the optimal interpolation parameters for the main 3d frp reconstruction stage are quite different our experimental results confirm that for the optimal interpolation parameters a very good image accuracy can be achieved even without any extra spectral oversampling which is a common practice to decrease errors caused by interpolation in fourier reconstruction

characterization and optimization of achievable performance in general queueing systems this paper considers general single facility queueing systems with exponential service times dealing with a finite number j of distinct customer classes performance of the system as measured by the vector of steady state expected sojourn times of the customer classes the performance vector may be controlled by adopting an appropriate preemptive priority discipline we show that the performance space the set of performance vectors which are achievable under some preemptive work conserving rule is a polyhedron described by 2j 1 inequalities the special structure of this polyhedron nevertheless allows for efficient procedures to minimize any separable convex function of the performance vector linear objectives are shown to be minimized by absolute priority rules thus generalizing a well known result for m m 1 systems we also show that each point in the performance space may be achieved by a specific randomization of at most j 1 absolute priority rules

relaxations of weakly coupled stochastic dynamic programs we consider a broad class of stochastic dynamic programming problems that are amenable to relaxation via decomposition these problems comprise multiple subproblems that are independent of each other except for a collection of coupling constraints on the action space we fit an additively separable value function approximation using two techniques namely lagrangian relaxation and the linear programming lp approach to approximate dynamic programming we prove various results comparing the relaxations to each other and to the optimal problem value we also provide a column generation algorithm for solving the lp based relaxation to any desired optimality tolerance and we report on numerical experiments on bandit like problems our results provide insight into the complexity versus quality trade off when choosing which of these relaxations to implement

learning to optimize via posterior sampling this paper considers the use of a simple posterior sampling algorithm to balance between exploration and exploitation when learning to optimize actions such as in multiarmed bandit problems the algorithm also known as thompson sampling and as probability matching offers significant advantages over the popular upper confidence bound ucb approach and can be applied to problems with finite or infinite action spaces and complicated relationships among action rewards we make two theoretical contributions the first establishes a connection between posterior sampling and ucb algorithms this result lets us convert regret bounds developed for ucb algorithms into bayesian regret bounds for posterior sampling our second theoretical contribution is a bayesian regret bound for posterior sampling that applies broadly and can be specialized to many model classes this bound depends on a new notion we refer to as the eluder dimension which measures the degree of dependence among action rewards compared to ucb

on the optimality of the gridding reconstruction algorithm gridding reconstruction is a method to reconstruct data onto a cartesian grid from a set of nonuniformly sampled measurements this method is appreciated for being robust and computationally fast however it lacks solid analysis and design tools to quantify or minimize the reconstruction error least squares reconstruction lsr on the other hand is another method which is optimal in the sense that it minimizes the reconstruction error this method is computationally intensive and in many cases sensitive to measurement noise hence it is rarely used in practice despite their seemingly different approaches the gridding and lsr methods are shown to be closely related the similarity between these two methods is accentuated when they are properly expressed in a common matrix form it is shown that the gridding algorithm can be considered an approximation to the least squares method the optimal gridding parameters are defined as the ones which yield the minimum approximation error these parameters are calculated by minimizing the norm of an approximation error matrix this problem is studied and solved in the general form of approximation using linearly structured matrices this method not only supports more general forms of the gridding algorithm it can also be used to accelerate the reconstruction techniques from incomplete data the application of this method to a case of two dimensional 2 d spiral magnetic resonance imaging shows a reduction of more than 4 db in the average reconstruction error

image reconstruction from linograms implementation and evaluation the notion of a linogram corresponds to the notion of a sinogram in the conventional representation of projection data for image reconstruction in the sinogram points which correspond to rays through a fixed point in the cross section to be reconstructed all fall on a sinusoidal curve in the linogram however these points fall on a straight line the implementation of a novel image reconstruction method using this property is discussed the implementation is of order n sup 2 log n where n is proportional to the number of pixels on a side of the reconstruction region it is demonstrated that the performance of the algorithm is superior to that of the filter backprojection method in computational speed on realistic size problems and is equivalent to filtered backprojection in accuracy of reconstruction

a reconstruction algorithm for photoacoustic imaging based on the nonuniform fft fourier reconstruction algorithms significantly outperform conventional backprojection algorithms in terms of computation time in photoacoustic imaging these methods require interpolation in the fourier space domain which creates artifacts in reconstructed images we propose a novel reconstruction algorithm that applies the one dimensional nonuniform fast fourier transform to photoacoustic imaging it is shown theoretically and numerically that our algorithm avoids artifacts while preserving the computational effectiveness of fourier reconstruction

on constraint sampling in the linear programming approach to approximate dynamic programming in the linear programming approach to approximate dynamic programming one tries to solve a certain linear program the alp that has a relatively small numberk of variables but an intractable numberm of constraints in this paper we study a scheme that samples and imposes a subset ofm

on centres of 3 blocks of the ree groups g22 q abstract let g g 2 2 q be the simple ree group with q 3 2 k 1 and k a positive integer we show that the centre of the principal block z k g e 0 where k is an algebraically closed field of characteristic 3 is not isomorphic to the centre of the brauer corresponding block z k n g p where n g p is the normaliser in g of a sylow 3 subgroup

dynamic bid prices in revenue management we formally derive the standard deterministic linear program lp for bid price control by making an affine functional approximation to the optimal dynamic programming value function this affine functional approximation gives rise to a new lp that yields tighter bounds than the standard lp whereas the standard lp computes static bid prices our lp computes a time trajectory of bid prices we show that there exist dynamic bid prices optimal for the lp that are individually monotone with respect to time we provide a column generation procedure for solving the lp within a desired optimality tolerance and present numerical results on computational and economic performance

o n sup 2 log sub 2 n filtered backprojection reconstruction algorithm for tomography we present a new fast reconstruction algorithm for parallel beam tomography the new algorithm is an accelerated version of the standard filtered backprojection fbp reconstruction and uses a hierarchical decomposition of the backprojection operation to reduce the computational cost from o n sup 3 to o n sup 2 log sub 2 n we discuss the choice of the various parameters that affect the behavior of the algorithm and present numerical studies that demonstrate the cost versus distortion tradeoff comparisons with fourier reconstruction algorithms and a multilevel inversion algorithm by brandt et al both of which also have o n sup 2 log sub 2 n cost suggest that the proposed hierarchical scheme has a superior cost versus distortion performance it offers rms reconstruction errors comparable to the fbp with considerable speedup for an example with a 512 spl times 512 pixel image and 1024 views the speedup achieved with a particular implementation is over 40 fold with reconstructions visually indistinguishable from the fbp

restless bandits linear programming relaxations and a primal dual index heuristic we develop a mathematical programming approach for the classicalpspace hard restless bandit problem in stochastic optimization we introduce a hierarchy ofn wheren is the number of bandits increasingly stronger linear programming relaxations the last of which is exact and corresponds to the exponential size formulation of the problem as a markov decision chain while the other relaxations provide bounds and are efficiently computed we also propose a priority index heuristic scheduling policy from the solution to the firstorder relaxation where the indices are defined in terms of optimal dual variables in this way we propose a policy and a suboptimality guarantee we report results of computational experiments that suggest that the proposed heuristic policy is nearly optimal moreover the second order relaxation is found to provide strong bounds on the optimal value

selection of a convolution function for fourier inversion using gridding computerised tomography application in the technique known as gridding the data samples are weighted for sampling density and convolved with a finite kernel then resampled on a grid preparatory to a fast fourier transform the authors compare the artifact introduced into the image for various convolving functions of different sizes including the kaiser bessel window and the zero order prolate spheroidal wave function pswf they also show a convolving function that improves upon the pswf in some circumstances

accelerating the nonuniform fast fourier transform the nonequispaced fourier transform arises in a variety of application areas from medical imaging to radio astronomy to the numerical solution of partial differential equations in a typical problem one is given an irregular sampling of n data in the frequency domain and one is interested in reconstructing the corresponding function in the physical domain when the sampling is uniform the fast fourier transform fft allows this calculation to be computed in o n log n operations rather than o n 2 operations unfortunately when the sampling is nonuniform the fft does not apply over the last few years a number of algorithms have been developed to overcome this limitation and are often referred to as nonuniform ffts nuffts these rely on a mixture of interpolation and the judicious use of the fft on an oversampled grid a dutt and v rokhlin siam j sci comput 14 1993 pp 1368 1383 in this paper we observe that one of the standard interpolation or gridding schemes based on gaussians can be accelerated by a significant factor without precomputation and storage of the interpolation weights this is of particular value in two and three dimensional settings saving either 10 d n in storage in d dimensions or a factor of about 5 10 in cputime independent of dimension

dade s invariant conjecture for steinberg s triality groups d43 2n in defining characteristic abstract in this paper we verify dade s invariant conjecture for steinberg s triality groups d 4 3 2 n in the defining characteristic i e in characteristic 2 together with the results in j an dade s conjecture for steinberg triality groups d 4 3 q in non defining characteristics math z 241 2002 445 469 and j an f himstedt s huang uno s invariant conjecture for steinberg s triality groups in defining characteristic in preparation this completes the proof of dade s conjecture for steinberg s triality groups furthermore we show that the isaacs malle navarro version of the mckay conjecture holds for d 4 3 2 n in the defining characteristic i e d 4 3 2 n is good for the prime 2 in the sense of isaacs malle and navarro

dade s inductive conjecture for the ree groups of type g2 in the defining characteristic abstract we verify the inductive form of dade s conjecture for the finite simple groups 2 g 2 3 2 m 1 where m is a positive integer for the prime p 3 together with work by j an 1994 indian j math 36 7 27 this completes the verification of the conjecture for this series of groups

uno s invariant conjecture for steinberg s triality groups in defining characteristic abstract we verify uno s invariant conjecture for steinberg s triality groups d 4 3 q q a power of an odd prime p in the defining characteristic p uno s invariant conjecture is a refinement of dade s invariant conjecture

controlled blocks of the finite quasisimple groups for odd primes abstract we classify controlled blocks introduced by alperin and broue in 1979 for all quasisimple groups g for odd primes the results imply that every nilpotent block of g has abelian defect groups which in turn is one of the main results proved in an and eaton 2011 6 we also give an explicit characterization of non controlled blocks of all quasisimple groups g for odd primes this implies the block theoretic analogue of glauberman s zj theorem for g proved by kessar linckelmann and robinson 2002 18

on finite groups of p local rank one and conjectures of dade and robinson abstract we use the classification of finite simple groups to demonstrate that conjecture 4 1 of g r robinson 1996 proc london math soc 3 72 312 330 and dade s projective conjecture hold for finite groups of p local rank one

fast multiple splitting algorithms for convex optimization we present in this paper two different classes of general multiple splitting algorithms for solving finite dimensional convex optimization problems under the assumption that the function being minimized can be written as the sum of k convex functions each of which has a lipschitz continuous gradient we prove that the number of iterations needed by the first class of algorithms to obtain an epsilon optimal solution is o k 1 l epsilon where l is an upper bound on all of the lipschitz constants the algorithms in the second class are accelerated versions of those in the first class where the complexity result is improved to o sqrt k 1 l epsilon while the computational effort required at each iteration is almost unchanged to the best of our knowledge the complexity results presented in this paper are the first ones of this type that have been given for splitting and alternating direction type methods moreover all algorithms proposed in this paper are parallelizable which makes the

on ti and ti defect blocks abstract we show that every trivial intersection block of a finite group as introduced by j l alperin and m broue 1979 ann of math 110 143 157 has trivial intersection ti defect groups but that the converse is not true in general we then present some conditions equivalent to b being a ti block generalizing the idea of a k generated p core to b subgroups in particular we give further weight to olsson s assertion that ti blocks are a better generalization of groups with ti sylow p subgroups than are ti defect blocks finally we describe the role of the generalized k generated p core in the control of fusion of subpairs

fast fully 3 d image reconstruction in pet using planograms we present a method of performing fast and accurate three dimensional 3 d backprojection using only fourier transform operations for line integral data acquired by planar detector arrays in positron emission tomography this approach is a 3 d extension of the two dimensional 2 d linogram technique of edholm by using a special choice of parameters to index a line of response lor for a pair of planar detectors rather than the conventional parameters used to index a lor for a circular tomograph all the lors passing through a point in the field of view fov lie on a 2 d plane in the four dimensional 4 d data space thus backprojection of all the lors passing through a point in the fov corresponds to integration of a 2 d plane through the 4 d planogram the key step is that the integration along a set of parallel 2 d planes through the planogram that is backprojection of a plane of points can be replaced by a 2 d section through the origin of the 4 d fourier transform of the data backprojection can be performed as a sequence of fourier transform operations for faster implementation in addition we derive the central section theorem for planogram format data and also derive a reconstruction filter for both backprojection filtering and filtered backprojection reconstruction algorithms with software based fourier transform calculations we provide preliminary comparisons of planogram backprojection to standard 3 d backprojection and demonstrate a reduction in computation time by a factor of approximately 15

a computational study of reconstruction algorithms for diffraction tomography interpolation versus filtered backpropagation from the standpoint of reporting a new contribution this paper shows that by using bilinear interpolation followed by direct two dimensional fourier inversion one can obtain reconstructions of quality which is comparable to that produced by the filtered backpropagation algorithm proposed recently by devaney for an n n image reconstructed from n diffracted projections the former approach requires approximately 4n fft s whereas the backpropagation technique requires approximately n2fft s we have also taken this opportunity to present the reader with a tutorial introduction to diffraction tomography an area that is becoming increasingly important not only in medical imaging but also in underwater and seismic mapping with microwaves and sound the main feature of the tutorial part is the statement of the fourier diffraction projection theorem which is an extension of the traditional fourier slice theorem to the case of image formation with diffracting illumination

the gridding method for image reconstruction by fourier transformation the authors explore a computational method for reconstructing an n dimensional signal f from a sampled version of its fourier transform f spl circ the method involves a window function w spl circ and proceeds in three steps first the convolution g spl circ w spl circ f spl circ is computed numerically on a cartesian grid using the available samples of f spl circ then g wf is computed via the inverse discrete fourier transform and finally f is obtained as g w due to the smoothing effect of the convolution evaluating w spl circ f spl circ is much less error prone than merely interpolating f spl circ the method was originally devised for image reconstruction in radio astronomy but is actually applicable to a broad range of reconstructive imaging methods including magnetic resonance imaging and computed tomography in particular it provides a fast and accurate alternative to the filtered backprojection the basic method has several variants with other applications such as the equidistant resampling of arbitrarily sampled signals or the fast computation of the radon hough transform

duality in infinite dimensional linear programming we consider the class of linear programs with infinitely many variables and constraints having the property that every constraint contains at most finitely many variables while every variable appears in at most finitely many constraints examples include production planning and equipment replacement over an infinite horizon we form the natural dual linear programming problem and prove strong duality under a transversality condition that dual prices are asymptotically zero that is we show under this transversality condition that optimal solutions are attained in both primal and dual problems and their optimal values are equal the transversality condition and hence strong duality is established for an infinite horizon production planning problem

a linear programming approach to nonstationary infinite horizon markov decision processes nonstationary infinite horizon markov decision processes mdps generalize the most well studied class of sequential decision models in operations research namely that of stationary mdps by relaxing the restrictive assumption that problem data do not change over time linear programming lp has been very successful in obtaining structural insights and devising solution methods for stationary mdps however an lp approach for nonstationary mdps is currently missing this is because the lp formulation of a nonstationary infinite horizon mdp includes countably infinite variables and constraints and research on such infinite dimensional lps has traditionally faced several hurdles for instance duality results may not hold an extreme point may not be a basic feasible solution and in the context of a simplex algorithm a pivot operation may require infinite data and computations and a sequence of improving extreme points need not converge in value to optimal in this paper we tackle these challenges a

resampling of data between arbitrary grids using convolution interpolation for certain medical applications resampling of data is required in magnetic resonance tomography mrt or computer tomography ct e g data may be sampled on nonrectilinear grids in the fourier domain for the image reconstruction a convolution interpolation algorithm often called gridding can be applied for resampling of the data onto a rectilinear grid resampling of data from a rectilinear onto a nonrectilinear grid are needed e g if projections of a given rectilinear data set are to be obtained in this paper the authors introduce the application of the convolution interpolation for resampling of data from one arbitrary grid onto another the basic algorithm can be split into two steps first the data are resampled from the arbitrary input grid onto a rectilinear grid and second the rectilinear data is resampled onto the arbitrary output grid furthermore the authors like to introduce a new technique to derive the sampling density function needed for the first step of their algorithm for fast sampling pattern independent determination of the sampling density function the voronoi diagram of the sample distribution is calculated the volume of the voronoi cell around each sample is used as a measure for the sampling density it is shown that the introduced resampling technique allows fast resampling of data between arbitrary grids furthermore it is shown that the suggested approach to derive the sampling density function is suitable even for arbitrary sampling patterns examples are given in which the proposed technique has been applied for the reconstruction of data acquired along spiral radial and arbitrary trajectories and for the fast calculation of projections of a given rectilinearly sampled image

alperin mckay implies brauer s problem 21 there are several outstanding open problems in modular representation w x theory including several on brauer s famous list b one such conjecture w x w x is the alperin mckay conjecture e g a1 f whenever b is a p block of a finite group g and b has defect group d then the number k b of 0 w x 5 irreducible characters x in b with g d x 1 is the same as the p corresponding number k b for the unique p block b of n d with 0 g g w x w x b s b another is r brauer s problem 21 see b f let b be a p block with defect group d and containing k b s k irreducible charac ters is d bounded in terms of k we prove here that a positive answer to brauer s question follows if the alperin mckay conjecture is correct by virtue of zelmanov s solution of w x w x the restricted burnside problem see z1 z2 and the positive solution w x of brauer s problem in the case of p solvable g by the first author k our main result is

direct fourier reconstruction in computer tomography direct fourier transform ft reconstruction of images in computerized tomography ct is not widely used because of the difficulty of precisely interpolating from polar to cartesian samples in this paper an exact interpolation scheme is proposed which in practice can be approached with arbitrary accuracy using well conditioned algorithms several features of the direct ft method are discussed a method that allows angular band limiting of the data before processing to avoid angular aliasing artifacts in the reconstructed image is discussed and experimentally verified the experimental results demonstrate the feasibility of direct ft reconstruction of ct data

fourier based forward and back projectors in iterative fan beam tomographic image reconstruction fourier based forward and back projection methods can reduce computation in iterative tomographic image reconstruction recently an optimized nonuniform fast fourier transform nufft approach was shown to yield accurate parallel beam projections in this paper we extend the nufft approach to describe an o n sup 2 log n projector backprojector pair for fan beam transmission tomography simulations and experiments with real ct data show that fan beam fourier based forward and back projection methods can reduce computation for iterative reconstruction while still providing accuracy comparable to their o n sup 3 space based counterparts

multiple overlapping k space junctions for investigating translating objects mojito it is a well known property in fourier transform magnetic resonance imaging mri that rigid body translational motion in image space results in linear phase accumulation in k space this work describes multiple overlapping k space junctions for investigating translating objects mojito a correction scheme based on phase differences at trajectory intersections caused by 2 d alterations in the position of an object during mr imaging the algorithm allows both detection and correction of motion artifacts caused by 2 d rigid body translational motion although similar in concept to navigator echoes mojito does not require a repeating path through k space uses k space data from a broader region of k space and uses the repeated data in image reconstruction this provides the potential for a highly efficient self navigating motion correction method here the concept and theoretical basis of mojito is demonstrated using the continuous sampling bowtie trajectory in simulation and mr experiments this particular trajectory is selected since it is well suited for such an algorithm due to numerous trajectory intersections specifically the validity of the technique in the presence of noise and off resonance effects is demonstrated through simulation

the linear programming approach to approximate dynamic programming the curse of dimensionality gives rise to prohibitive computational requirements that render infeasible the exact solution of large scale stochastic control problems we study an efficient method based on linear programming for approximating solutions to such problems the approach fits a linear combination of pre selected basis functions to the dynamic programming cost to go function we develop error bounds that offer performance guarantees and also guide the selection of both basis functions and state relevance weights that influence quality of the approximation experimental results in the domain of queueing network control provide empirical support for the methodology

on the direct fourier method for computer tomography considers the direct fourier methods dfm s for reconstructing an image from its given x ray projections the main purpose here is to use concepts from numerical analysis to estimate the errors in the methods the authors also suggest an alternative to the interpolations involved in the dfm s and estimate the number of terms involved realizing that one of the main reasons for the degradation of the quality of the reconstruction is the gibbs phenomenon the authors suggest a way to overcome this difficulty and give numerical evidence of its efficacy