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

fuzzy number valued fuzzy measure and fuzzy number valued fuzzy integral on the fuzzy set abstract in this paper some new concepts the fuzzy number valued fuzzy measure autocontinuity and null additivity of fuzzy number valued fuzzy measures on the fuzzy algebra and the fuzzy number valued fuzzy integral on the fuzzy set are introduced some properties of fuzzy number valued fuzzy integrals and some convergence theorems for sequences of fuzzy number valued fuzzy integrals on a fuzzy set are discussed

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

accelerating ordered subsets image reconstruction for x ray ct using spatially nonuniform optimization transfer statistical image reconstruction algorithms in x ray computed tomography ct provide improved image quality for reduced dose levels but require substantial computation time iterative algorithms that converge in few iterations and that are amenable to massive parallelization are favorable in multiprocessor implementations the separable quadratic surrogate sqs algorithm is desirable as it is simple and updates all voxels simultaneously however the standard sqs algorithm requires many iterations to converge this paper proposes an extension of the sqs algorithm that leads to spatially nonuniform updates the nonuniform nu sqs encourages larger step sizes for the voxels that are expected to change more between the current and the final image accelerating convergence while the derivation of nu sqs guarantees monotonic descent ordered subsets os algorithms can also accelerate sqs provided suitable subset balance conditions hold these conditions can fail in 3 d helical cone beam ct due to incomplete sampling outside the axial region of interest roi this paper proposes a modified os algorithm that is more stable outside the roi in helical ct we use ct scans to demonstrate that the proposed nu os sqs algorithm handles the helical geometry better than the conventional os methods and converges in less than half the time of ordinary os sqs

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

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

effect of overlapping projections on reconstruction image quality in multipinhole spect multipinhole single photon emission computed tomography spect imaging has several advantages over single pinhole spect imaging including an increased sensitivity and an improved sampling however the quest for a good design is challenging due to the large number of design parameters the effect of one of these the amount of overlap in the projection images on the reconstruction image quality is examined in this paper the evaluation of the quality is based on efficient approximations for the linearized local impulse response and the covariance in a voxel and on the bias of the reconstruction of the noiseless projection data two methods are proposed that remove the overlap in the projection image by blocking certain projection rays with the use of extra shielding between the pinhole plate and the detector also two measures to quantify the amount of overlap are suggested first the approximate method predicting the contrast to noise ratio cnr is validated using postsmoothed maximum likelihood expectation maximization mlem reconstructions with an imposed target resolution second designs with different amounts of overlap are evaluated to study the effect of multiplexing in addition the cnr of each pinhole design is also compared with that of the same design where overlap is removed third the results are interpreted with the overlap quantification measures fourth the two proposed overlap removal methods are compared from the results we can conclude that once the complete detector area has been used the extra sensitivity due to multiplexing is only able to compensate for the loss of information not to improve the cnr removing the overlap however improves the cnr the gain is most prominent in the central field of view though often at the cost of the cnr of some voxels at the edges since after overlap removal very little information is left for their reconstruction the reconstruction images provide insight in the multiplexing and truncation artifacts

on the comparison of semi analytical methods for the stability analysis of delay differential equations abstract this paper provides the first comparison of the semi discretization spectral element and legendre collocation methods each method is a technique for solving delay differential equations ddes as well as determining regions of stability in the dde parameter space we present the necessary concepts assumptions and equations required to implement each method to compare the relative performance between the methods the convergence rate and computational time for each method is compared in three numerical studies consisting of a ship stability example the delayed damped mathieu equation and a helicopter rotor control problem for each study we present one or more stability diagrams in the parameter space and one or more convergence plots the spectral element method is demonstrated to have the quickest convergence rate while the legendre collocation method requires the least computational time the semi discretization method on the other hand has both the slowest convergence rate and requires the most computational time

slowly oscillating periodic solutions for a delayed frustrated network of two neurons in this article we study a delayed frustrated network of two neurons we obtain a two dimensional closed disk bordered by a slowly oscillating periodic orbit and we give a complete description about the dynamics of the flow restricted to this closed disk

discriminative feature representation to improve projection data inconsistency for low dose ct imaging in low dose computed tomography ldct imaging the data inconsistency of measured noisy projections can significantly deteriorate reconstruction images to deal with this problem we propose here a new sinogram restoration approach the sinogram discriminative feature representation s dfr method different from other sinogram restoration methods the proposed method works through a 3 d representation based feature decomposition of the projected attenuation component and the noise component using a well designed composite dictionary containing atoms with discriminative features this method can be easily implemented with good robustness in parameter setting its comparison to other competing methods through experiments on simulated and real data demonstrated that the s dfr method offers a sound alternative in ldct

fuzzy fractional quadratic regulator problem under granular fuzzy fractional derivatives in this paper a class of uncertain linear dynamical systems called fuzzy fractional linear dynamical systems is investigated the aim is to find control inputs to keep the states of the fuzzy fractional dynamical systems near the zero in an optimal manner the optimality criterion is in a form of a granular fuzzy integral whose integrand is a quadratic function of the state variables and control inputs the fuzzy fractional dynamical system is described using fuzzy fractional differential equations ffdes in order to achieve the aim an effective approach for solving ffdes should be at disposal due to some restrictions imposed by the previous approaches dealing with ffdes a new approach is proposed the proposed approach is based on the granular derivative and the so called relative distance measure fuzzy interval arithmetic new definitions of fuzzy fractional derivatives and integral called left and right granular riemann liouville fuzzy fractional derivatives left and right granular caputo fuzzy fractional derivatives and the left and right granular fuzzy fractional integral are also presented in addition the concepts of granular fuzzy partial derivative and granular fuzzy chain rule are introduced by the approximations of the granular fuzzy fractional integral and the granular caputo fuzzy fractional derivative the approximation solution to the ffdes is obtained consequently based on the new concepts and theorems the solution to the fuzzy fractional quadratic regulator problem is given by a theorem this paper closes with an example of regulating the motion of boeing 747 in longitudinal direction with the presence of uncertainty in the initial conditions and the coefficients

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

inversion of the v line radon transform in a disc and its applications in imaging several novel imaging modalities proposed during the last couple of years are based on a mathematical model which uses the v line radon transform vrt this transform sometimes called broken ray radon transform integrates a function along v shaped piecewise linear trajectories composed of two intervals in the plane with a common endpoint image reconstruction problems in these modalities require inversion of the vrt while there are ample results about inversion of the regular radon transform integrating along straight lines very little is known for the case of the v line radon transform in this paper we derive an exact inversion formula for the vrt of functions supported in a disc of arbitrary radius the formula uses a two dimensional restriction of vrt data namely the incident ray is normal to the boundary of the disc and the breaking angle is fixed our method is based on the classical filtered back projection inversion formula of the radon transform and has similar features in terms of stability speed and accuracy

a spectral element approach for the stability of delay systems we describe a spectral element approach to study the stability and equilibria solutions of delay differential equations ddes in contrast to the prototypical temporal finite element analysis tfea the described spectral element approach admits spectral rates of convergence and allows exploiting hp convergence schemes the described approach also avoids the limitations of analytical integrations in tfea by using highly accurate numerical quadratures enabling the study of more complicated ddes the effectiveness of this new approach is compared with well established methods in the literature using various case studies specifically the stability results are compared with the conventional tfea and legendre collocation methods whereas the equilibria solutions are compared with the numerical simulations and the homotopy perturbation method hpm solutions our results reveal that the presented approach can have higher rates of convergence than both collocation methods and the hpm copyright 2011 john wiley sons ltd

the convergence for a sequence of fuzzy integrals of fuzzy number valued functions on the fuzzy set abstract in this paper a new concept of fuzzy number valued fuzzy integral of fuzzy number valued function with respect to fuzzy number valued fuzzy measure on the fuzzy set is introduced and some equivalent definitions of the above mentioned concept are given and its elementary properties are discussed and a series of the convergent theorems of fuzzy number valued fuzzy integrals on the fuzzy set are obtained

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

ill posed fuzzy initial boundary value problems based on generalized differentiability and regularization in this study based on a new generalized differentiability and parametric representation for fuzzy valued functions we discuss the existence of solutions for fuzzy partial differential equations fpdes and their ill posedness a regularization method is required to recover the numerical stability a stable approximation of the exact solution is obtained as an example of a cauchy problem for the fuzzy laplace equation

connecting orbits from synchronous periodic solutions to phase locked periodic solutions in a delay differential system we consider a system of delay differential equations modelling the excitatory interaction of two identical neurons assuming the delay is sufficiently large we show that the closure of the forward extension w5 of a 5 dimensional leading unstable manifold of the trivial solution contains a phase locked periodic orbit and a synchronized periodic orbit and we classify the dynamics of the semiflow restricted to w5 we also obtain the precise information about the floquet multipliers of the synchronized periodic orbit which enables us to establish the existence of heteroclinic orbits from the synchronized periodic orbit to the phase locked orbit

accelerated image reconstruction using ordered subsets of projection data the authors define ordered subset processing for standard algorithms such as expectation maximization em for image restoration from projections ordered subsets methods group projection data into an ordered sequence of subsets or blocks an iteration of ordered subsets em is defined as a single pass through all the subsets in each subset using the current estimate to initialize application of em with that data subset this approach is similar in concept to block kaczmarz methods introduced by eggermont et al 1981 for iterative reconstruction simultaneous iterative reconstruction sirt and multiplicative algebraic reconstruction mart techniques are well known special cases ordered subsets em os em provides a restoration imposing a natural positivity condition and with close links to the em algorithm os em is applicable in both single photon spect and positron emission tomography pet in simulation studies in spect the os em algorithm provides an order of magnitude acceleration over em with restoration quality maintained

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

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

the applicability of dip moveout azimuth moveout in the presence of caustics reflection seismic data continuation is the computation of data at source and receiver locations that differ from those in the original data using whatever data are available we develop a general theory of data continuation in the presence of caustics and illustrate it with three examples dip moveout dmo azimuth moveout amo and offset continuation this theory does not require knowledge of the reflector positions we construct the output data set from the input through the composition of three operators an imaging operator a modeling operator and a restriction operator this results in a single operator that maps directly from the input data to the desired output data we use the calculus of fourier integral operators to develop this theory in the presence of caustics for both dmo and amo we compute impulse responses in a constant velocity model and in a more complicated model in which caustics arise this analysis reveals errors that can be introduced by assuming for example a model with a constant vertical velocity gradient when the true model is laterally heterogeneous data continuation uses as input a subset common offset common angle of the available data which may introduce artifacts in the continued data one could suppress these artifacts by stacking over a neighborhood of input data using a small range of offsets or angles for example we test data continuation on synthetic data from a model known to generate imaging artifacts we show that stacking over input scattering angles suppresses artifacts in the continued data

evaluation of fisher information matrix based methods for fast assessment of image quality in pinhole spect the accurate determination of the local impulse response and the covariance in voxels from penalized maximum likelihood reconstructed images requires performing reconstructions from many noise realizations of the projection data as this is usually a very time consuming process efficient analytical approximations based on the fisher information matrix fim have been extensively used in pet and spect to estimate these quantities for 3d imaging however additional approximations need to be made to the fim in order to speed up the calculations the most common approach is to use the local shift invariant lsi approximation of the fim but this assumes specific conditions which are not always necessarily valid in this paper we take a single pinhole spect system and compare the accuracy of the lsi approximation against two other methods that have been more recently put forward the non uniform object space pixelation nuop and the subsampled fim these methods do not assume such restrictive conditions while still increasing the speed of the calculations considerably our results indicate that in pinhole spect the nuop and subsampled fim approaches could be more reliable than the lsi approximation especially when a high accuracy is required

data driven affine deformation estimation and correction in cone beam computed tomography in computed tomography ct motion and deformation during the acquisition lead to streak artefacts and blurring in the reconstructed images to remedy these artefacts we introduce an efficient algorithm to estimate and correct for global affine deformations directly on the cone beam projections the proposed technique is data driven and thus removes the need for markers and or a tracking system a relationship between affine transformations and the cone beam transform is proved and used to correct the projections the deformation parameters that describe deformation perpendicular to the projection direction are estimated for each projection by minimizing a plane based inconsistency criterion the criterion compares each projection of the main scan with all projections of a fast reference scan which is acquired prior or posterior to the main scan experiments with simulated and experimental data show that the proposed affine deformation estimation method is able to substantially reduce motion artefacts in cone beam ct images

theoretically exact filtered backprojection type inversion algorithm for spiral ct proposed is a theoretically exact formula for inversion of data obtained by a spiral computed tomography ct scan with a two dimensional detector array the detector array is supposed to be of limited extent in the axial direction the main property of the formula is that it can be implemented in a truly filtered backprojection fashion first one performs shift invariant filtering of a derivative of the cone beam projections and second the result is backprojected in order to form an image another property is that the formula solves the so called long object problem limitations of the algorithm are discussed results of numerical experiments are presented

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

data consistency based translational motion artifact reduction in fan beam ct a basic assumption in the classic computed tomography ct theory is that an object remains stationary in an entire scan in biomedical ct micro ct this assumption is often violated to produce high resolution images such as for our recently proposed clinical micro ct cmct prototype it is desirable to develop a precise motion estimation and image reconstruction scheme in this paper we first extend the helgason ludwig consistency condition hlcc from parallel beam to fan beam geometry when an object is subject to a translation then we propose a novel method to estimate the motion parameters only from sinograms based on the hlcc to reconstruct the moving object we formulate two generalized fan beam reconstruction methods which are in filtered backprojection and backprojection filtering formats respectively furthermore we present numerical simulation results to show that our approach is accurate and robust

the core of a sequence of fuzzy numbers in this paper based on level sets we define the limit inferior and limit superior of a bounded sequence of fuzzy numbers and prove some properties we extend the concept of the core of a sequence of complex numbers first introduced by knopp in 1930 to a bounded sequence of fuzzy numbers and prove that the core of a sequence of fuzzy numbers is the interval n m where n and m are extreme limit points of the sequence

a series formula for inversion of the v line radon transform in a disc the paper presents an exact formula for a fourier series reconstruction of a function from its v line radon transform in a disc this transform often also called broken ray radon transform appears in mathematical models of several imaging modalities e g single scattering optical tomography and c ray emission tomography our inversion formula relaxes the support restriction on the image function required in the previously discovered inversion technique ambartsoumian 2012 8 and uses data from only half of the set of broken rays required before the general strategy of the current approach was outlined in ambartsoumian 2012 8

properties of b vex fuzzy mappings and applications to fuzzy optimization convexity plays a key role in operations research and fuzzy optimization theory the concept of b vex and logarithmic b vex for fuzzy mappings is introduced by relaxing the definition of convexity of a fuzzy mapping most of the basic properties of b vex fuzzy mapping are discussed and established for the nondifferentiable case necessary and sufficient conditions for b vex fuzzy mapping are presented several important results are given for nonlinear fuzzy optimization problems assuming that objective and constraint functions are b vex fuzzy mappings

lattice valued fuzzy measure and lattice valued fuzzy integral abstract in this paper 1 the concepts of lattice valued fuzzy measure with no valuation property and lower resp upper lattice valued fuzzy integral are proposed which give the unified discription to the fuzzy measures and fuzzy integrals studied by delgado and moral qiao ralescu adams sugeno wang and zhang 2 some asymptotic structural characteristics of lattice valued fuzzy measures are introduced and some relations between them are given 3 some concepts of convergences for lattice valued functions are defined and riesz theorem egoroff s theorems and lebesgue s theorem for lattice valued measurable function are proved 4 the monotone increasing resp decreasing convergence theorem and almost resp pseudo almost everywhere convergence theorrem for lower resp upper lattice valued fuzzy integral are shown under some weak conditions

the fuzzy neural network approximation lemma abstract it is well known that artificial neural networks are universal approximators but what about fuzzy neural networks only buckley and hayashi 1 presented a theoretical result for these networks they showed that there are fuzzy functions which cannot be approximated by a certain fuzzy neural network in this paper we answer the question for a special type of fuzzy neural networks especially with regard to the fuzzy arithmetic that is used it is simplified in order to minimize the computational expense as well as to simplify the theoretical examinations we prove that the class of fuzzy functions which is identical to the class of all continuous real functions extended by means of the extension principle can be approximated by certain fuzzy neural networks

elementary fuzzy calculus abstract in 2 dubois and prade introduced the notion of fuzzy numbers and defined the basic operations of addition subtraction multiplication and division a slightly modified definition of fuzzy numbers was presented in 4 and in that paper a metric was defined for this family of fuzzy sets another less restrictive definition of fuzzy numbers can be found in 1 in the present paper we consider fuzzy numbers from a somewhat different perspective basically we shall view fuzzy numbers in a topological vector space setting using the customary vector space operations together with the metric given in 4 we will define differentiation and integration of fuzzy valued functions in ways that parallel closely the corresponding definitions for real differentiation and integration

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

on fuzzy solutions for heat equation based on generalized hukuhara differentiability abstract in this paper a fuzzy heat equation with fuzzy initial values is considered the concept of generalized hukuhara differentiation is interpreted thoroughly in the univariate and multivariate cases and also several properties for generalized hukuhara differentiability are obtained on the topics such as switching point the univariate and multivariate fuzzy chain rules fuzzy mean value theorem among others the objective of this paper is to prove the uniqueness of a solution for a fuzzy heat equation and show that a fuzzy heat equation can be modeled as two systems of fuzzy differential equations by considering the type of differentiability of solutions finally some examples show the behavior of the solutions obtained

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

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

a fuzzy solution of heat equation under generalized hukuhara differentiability by fuzzy fourier transform in this paper an analytical solution of a fuzzy heat equation under generalized hukuhara partial differentiability by fuzzy fourier transform is investigated a fuzzy fourier transform is introduced and the related theorems and properties are provided in detail some examples show the effectiveness and efficiency of the approach

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

stability bifurcation and multistability in a system of two coupled neurons with multiple time delays a system of delay differential equations representing a model for a pair of neurons with time delayed connections between the neurons and time delayed feedback from each neuron to itself is studied conditions for the linear stability of the trivial solution of this system are represented in a parameter space consisting of the sum of the time delays between the elements and the product of the strengths of the connections between the elements it is shown that the trivial fixed point may lose stability via a pitchfork bifurcation a hopf bifurcation or one of three types of codimension two bifurcations multistability near these latter bifurcations is predicted using center manifold analysis and confirmed using numerical simulations

synchronization phenomena for coupled delay line oscillators two coupled delay line oscillators are modeled by a system of delay differential equations and their oscillations are analyzed by reducing the delay equations to a system of ordinary differential equations on a finite dimensional center manifold in the corresponding infinite dimensional state space after averaging the finite dimensional system a bifurcation analysis reveals a complex structure of oscillatory behavior a complete bifurcation analysis is postponed in favor of a bifurcation analysis that is focused on applications to sensor design in particular the case of two adjacently mounted identically built surface acoustic wave saw delay line oscillators is examined a bifurcation analysis reveals the operation envelope for a dual saw sensor based on measurements of frequency differences the effective operating envelope of this design is limited due to synchronization caused by cross coupling on the other hand the operation envelope of a dual saw sensor can be enlarged by constructing a sensor based on phase differences in the synchronization regime

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

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

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

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

convergence of a sequence of fuzzy number valued fuzzy measurable functions on the fuzzy number valued fuzzy measure space abstract in this paper some new concepts convergences of a sequence of fuzzy number valued fuzzy measurable functions on the fuzzy set are introduced and the relations between these convergences are discussed on the fuzzy number valued fuzzy measure space riesz s theorem egoroff s theorem and lebesgue s theorem are proved

trkalian fields and radon transformation we write the spherical curl transformation for trkalian fields using differential forms then we consider radon transform of these fields the radon transform of a trkalian field satisfies a corresponding eigenvalue equation on a sphere in transform space the field can be reconstructed using knowledge of the radon transform on a canonical hemisphere we consider relation of the radon transformation with biot savart integral operator and discuss its transform introducing radon biot savart operator the radon transform of a trkalian field is an eigenvector of this operator we also present an ampere law type relation for these fields we apply these to lundquist solution we present a chandrasekhar kendall type solution of the corresponding equation in the transform space lastly we focus on the euclidean topologically massive abelian gauge theory the radon transform of an anti self dual field is related by antipodal map on this sphere to the transform of the self dual field obtained by inverting space c

characterization and source receiver continuation of seismic reflection data in reflection seismology one places sources and receivers on the earth s surface the source generates elastic waves in the subsurface that are reflected where the medium properties stiffness and density vary discontinuously in the field often there are obstructions to collect seismic data for all source receiver pairs desirable or needed for data processing and application of inverse scattering methods typically data are measured on the earth s surface we employ the term data continuation to describe the act of computing data that have not been collected in the field seismic data are commonly modeled by a scattering operator developed in a high frequency single scattering approximation we initially focus on the determination of the range of the forward scattering operator that models the singular part of the data in the mentioned approximation this encompasses the analysis of the properties of and the construction of a minimal elliptic projector that projects a space of distributions on the data acquisition manifold to the range of the mentioned scattering operator this projector can be directly used for the purpose of seismic data continuation and is derived from the global parametrix of a homogeneous pseudodifferential equation the solution of which coincides with the range of the scattering operator we illustrate the data continuation by a numerical example

formulation of fuzzy linear programming problems as four objective constrained optimization problems this paper concerns the solution of fuzzy linear programming flp problems which involve fuzzy numbers in coefficients of objective functions firstly a number of concepts of optimal solutions to flp problems are introduced and investigated then a number of theorems are developed so as to convert the flp to a multi objective optimization problem with four objective functions finally two illustrative examples are given to demonstrate the solution procedure it also shows that our method of solution includes an existing method as a special case

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

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

fuzzy limit theory of fuzzy complex numbers abstract we introduce three important concepts of fuzzy complex numbers fuzzy distance and fuzzy limit of fuzzy complex numbers and give some elementary properties of the fuzzy complex numbers and fuzzy distance and fuzzy limit of the fuzzy complex numbers we also discuss some important theorems of fuzzy complex numbers nested closed rectangles theorem cauchy s criterion for convergence accumulation principle etc

filtered backprojection inversion of the cone beam transform for a general class of curves we extend a cone beam transform inversion formula proposed earlier for helices by one of the authors to a general class of curves the inversion formula remains efficient because filtering is shift invariant and is performed along a one parametric family of lines the conditions that describe the class are very natural curves c are smooth without self intersections have positive curvature and torsion do not bend too much and do not admit lines which are tangent to c at one point and intersect c at another point the notions of pi lines and pi segments are generalized and their properties are studied the domain u is found where pi lines are guaranteed to be unique results of numerical experiments demonstrate very good image quality

note on smith s reconstruction algorithm for cone beam tomography an error is pointed out in the derivation of the reconstruction algorithm for cone beam tomography proposed by b d smith the implications of this error on the mathematical and practical validity of the algorithm are discussed

the structural characteristics of the fuzzy number valued fuzzy measure on the fuzzy σ algebra and their applications abstract in this paper some structural characteristics of the fuzzy number valued fuzzy measure on the fuzzy algebra are discussed on the fuzzy number valued fuzzy measure space the concepts of almost and pseudo almost are introduced and riesz s theorem lebesgue s theorem and egoroff s theorem for sequences of fuzzy measurable functions and some convergence theorems for sequences of fuzzy number valued fuzzy integrals on fuzzy sets are proved by some structural characteristics of the fuzzy number valued fuzzy measure

on fuzzy number valued fuzzy measures defined by fuzzy number valued fuzzy integrals ii abstract in this paper we discuss some properties of a fuzzy number valued fuzzy set function defined by a fuzzy number valued fuzzy integral on the fuzzy set and give sufficient conditions that it is a fuzzy number valued fuzzy measure

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

a method for multiple periodic factor prediction problems using complex fuzzy sets multiple periodic factor prediction mpfp problems exist widely in multisensor data fusion applications development of an effective prediction method should integrate information for multiple periodically changing factors because the uncertainty and periodicity coexist in the information used the prediction method should be able to handle them simultaneously in this study complex fuzzy sets are used to represent the information with uncertainty and periodicity a product sum aggregation operator psao is developed for a set of complex fuzzy sets which is used to integrate information with uncertainty and periodicity and a psao based prediction psaop method is then proposed to generate a solution of mpfp problems this study illustrates the details of the psaop method through two real applications in annual sunspot number prediction and bushfire danger rating prediction experiments indicate that the proposed psaop method effectively handles the uncertainty and periodicity in the information of multiple periodic factors simultaneously and can generate accurate predictions for mpfp problems

an efficient fourier method for 3 d radon inversion in exact cone beam ct reconstruction the radial derivative of the three dimensional 3 d radon transform of an object is an important intermediate result in many analytically exact cone beam reconstruction algorithms the authors briefly review grangeat s 1991 approach for calculating radon derivative data from cone beam projections and then present a new efficient method for 3 d radon inversion i e reconstruction of the image from the radial derivative of the 3 d radon transform called direct fourier inversion dfi the method is based directly on the 3 d fourier slice theorem from the 3 d radon derivative data which is assumed to be sampled on a spherical grid the 3 d fourier transform of the object is calculated by performing fast fourier transforms ffts along radial lines in the radon space then an interpolation is performed from the spherical to a cartesian grid using a 3 d gridding step in the frequency domain finally this 3 d fourier transform is transformed back to the spatial domain via 3 d inverse fft the algorithm is computationally efficient with complexity in the order of n sup 3 log n the authors have done reconstructions of simulated 3 d radon derivative data assuming sampling conditions and image quality requirements similar to those in medical computed tomography ct

fuzzy continuous function and its properties abstract in this paper we introduce the concepts of fuzzy distance of fuzzy numbers fuzzy limit of fuzzy numbers fuzzy function and fuzzy limit of a fuzzy function and fuzzy continuous function on the set of fuzzy numbers and give some of their elementary properties we also discuss some important theorems of fuzzy numbers and the fuzzy continuous function on the m closed interval

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