direct 4 d pet list mode parametric reconstruction with a novel em algorithm the production of images of kinetic parameters is often the ultimate goal of positron emission tomography pet imaging the indirect method of pet parametric imaging also called the frame based method fm is performed by fitting the time activity curve tac for each voxel with an appropriate compartment model after image reconstruction the indirect method is simple and easily implemented however it usually leads to some loss of accuracy or precision due to the use of two separate steps this paper presents a direct 4 d method for producing 3 d images of kinetic parameters from list mode pet data in this application the tac for each voxel is described by a one tissue compartment model 1t extending previous em algorithms a new spatiotemporal complete data space was introduced to optimize the maximum likelihood function this leads to a straightforward closed form parametric image update equation this method was implemented by extending the current list mode platform molar to produce a parametric algorithm pmolar 1t using an ordered subset approach qualitative and quantitative evaluations were performed using 2 d x t and 4 d x y z t simulated list mode data based on brain receptor tracers and also with a human brain study comparisons with the indirect method showed that the proposed direct method can lead to accurate estimation of the parametric image values with reduced variance especially at low count levels in the 2 d test the direct method showed similar bias to the frame based method but with variance reduction of 23 60 in the 4 d test bias values of both methods were no more than 4 and the direct method had lower variability coefficient of variation reduction of 0 64 compared to the frame based method at the normal count level the direct method had a larger reduction in variability 27 81 and lower bias 1 5 for 4 d and 1 19 for fm at low count levels the results in the human brain study are similar with pmolar 1t showing lower noise than fm

the em algorithm an old folk song sung to a fast new tune celebrating the 20th anniversary of the presentation of the paper by dempster laird and rubin which popularized the em algorithm we investigate after a brief historical account strategies that aim to make the em algorithm converge faster while maintaining its simplicity and stability e g automatic monotone convergence in likelihood first we introduce the idea of a working parameter to facilitate the search for efficient data augmentation schemes and thus fast em implementations second summarizing various recent extensions of the em algorithm we formulate a general alternating expectation conditional maximization algorithm aecm that couples flexible data augmentation schemes with model reduction schemes to achieve efficient computations we illustrate these methods using multivariate t models with known or unknown degrees of freedom and poisson models for image reconstruction we show through both empirical and theoretical evidence the potential for a dramatic reduction in computational time with little increase in human effort we also discuss the intrinsic connection between em type algorithms and the gibbs sampler and the possibility of using the techniques presented here to speed up the latter the main conclusion of the paper is that with the help of statistical considerations it is possible to construct algorithms that are simple stable and fast

weight assignment for adaptive image restoration by neural networks this paper presents a scheme for adaptively training the weights in terms of varying the regularization parameter in a neural network for the restoration of digital images the flexibility of neural network based image restoration algorithms easily allow the variation of restoration parameters such as blur statistics and regularization value spatially and temporally within the image this paper focuses on spatial variation of the regularization parameter we first show that the previously proposed neural network method based on gradient descent can only find suboptimal solutions and then introduce a regional processing approach based on local statistics a method is presented to vary the regularization parameter spatially this method is applied to a number of images degraded by various levels of noise and the results are examined the method is also applied to an image degraded by spatially variant blur in all cases the proposed method provides visually satisfactory results in an efficient way

accelerated iterative reconstruction for positron emission tomography based on the em algorithm for maximum likelihood estimation the em method that was originally developed for maximum likelihood estimation in the context of mathematical statistics may be applied to a stochastic model of positron emission tomography pet the result is an iterative algorithm for image reconstruction that is finding increasing use in pet due to its attractive theoretical and practical properties its major disadvantage is the large amount of computation that is often required due to the algorithm s slow rate of convergence this paper presents an accelerated form of the em algorithm for pet in which the changes to the image as calculated by the standard algorithm are multiplied at each iteration by an overrelaxation parameter the accelerated algorithm retains two of the important practical properties of the standard algorithm namely the selfnormalization and nonnegativity of the reconstructed images experimental results are presented using measured data obtained from a hexagonal detector system for pet the likelihood function and the norm of the data residual were monitored during the iterative process according to both of these measures the images reconstructed at iterations 7 and 11 of the accelerated algorithm are similar to those at iterations 15 and 30 of the standard algorithm for two different sets of data important theoretical properties remain to be investigated namely the convergence of the accelerated algorithm and its performance as a maximum likelihood estimator

list mode likelihood em algorithm and image quality estimation demonstrated on 2 d pet using a theory of list mode maximum likelihood ml source reconstruction presented recently by barrett et al 1997 this paper formulates a corresponding expectation maximization em algorithm as well as a method for estimating noise properties at the ml estimate list mode ml is of interest in cases where the dimensionality of the measurement space impedes a binning of the measurement data it can be advantageous in cases where a better forward model can be obtained by including more measurement coordinates provided by a given detector different figures of merit for the detector performance can be computed from the fisher information matrix fim this paper uses the observed fim which requires a single data set thus avoiding costly ensemble statistics the proposed techniques are demonstrated for an idealized two dimensional 2 d positron emission tomography pet 2 d pet detector the authors compute from simulation data the improved image quality obtained by including the time of flight of the coincident quanta

tomographic reconstruction using an adaptive tetrahedral mesh defined by a point cloud medical images in nuclear medicine are commonly represented in three dimensions as a stack of two dimensional images that are reconstructed from tomographic projections although natural and straightforward this may not be an optimal visual representation for performing various diagnostic tasks a method for three dimensional 3 d tomographic reconstruction is developed using a point cloud image representation a point cloud is a set of points nodes in space where each node of the point cloud is characterized by its position and intensity the density of the nodes determines the local resolution allowing for the modeling of different parts of the image with different resolution the reconstructed volume which in general could be of any resolution size shape and topology is represented by a set of nonoverlapping tetrahedra defined by the nodes the intensity at any point within the volume is defined by linearly interpolating inside a tetrahedron from the values at the four nodes that define the tetrahedron this approach creates a continuous piecewise linear intensity over the reconstruction domain the reconstruction provides a distinct multiresolution representation which is designed to accurately and efficiently represent the 3 d image the method is applicable to the acquisition of any tomographic geometry such as parallel fan and cone beam and the reconstruction procedure can also model the physics of the image detection process an efficient method for evaluating the system projection matrix is presented the system matrix is used in an iterative algorithm to reconstruct both the intensity and location of the distribution of points in the point cloud examples of the reconstruction of projection data generated by computer simulations and projection data experimentally acquired using a jaszczak cardiac torso phantom are presented this work creates a framework for voxel less multiresolution representation of images in nuclear medicine

semiparametric estimation of censored selection models with a nonparametric selection mechanism abstract in this paper estimation of the coefficients in a single index selectivity bias model is considered under the assumption that the selection correction function depends on the conditional mean of some observable selection variable the estimation method follows a familiar two step strategy the first step uses a nonparametric regression estimator for the selection variable while the second step uses a weighted instrumental variables estimator for the coefficients in the equation of interest the paper gives conditions under which the proposed estimator is root n consistent and asymptotically normal the proposed method is applied to data on labor supply

estimating latent processes on a network from indirect measurements in a communication network point to point traffic volumes over time are critical for designing protocols that route information efficiently and for maintaining security whether at the scale of an internet service provider or within a corporation while technically feasible the direct measurement of point to point traffic imposes a heavy burden on network performance and is typically not implemented instead indirect aggregate traffic volumes are routinely collected we consider the problem of estimating point to point traffic volumes from aggregate traffic volumes given information about the network routing protocol encoded in a matrix a this estimation task can be reformulated as finding the solutions to a sequence of ill posed linear inverse problems since the number of origin destination routes of interest is higher than the number of aggregate measurements available here we introduce a novel multilevel state space model ssm of aggregate traffic volumes with realistic features we imp

machine based methods in parameterized complexity theory we give machine characterizations of most parameterized complexity classes in particular of w p of the classes of the w hierarchy and of the a hierarchy for example we characterize w p as the class of all parameterized problems decidable by a nondeterministic fixed parameter tractable algorithm whose number of nondeterministic steps is bounded in terms of the parameter the machine characterizations suggest the introduction of a hierarchy wfunc between the w and the a hierarchy we study the basic properties of this hierarchy

informational content of special regressors in heteroskedastic binary response models we quantify the informational content of special regressors in heteroskedastic binary response models with median independent or conditionally symmetric errors based on lewbel 1998 a special regressor is additively separable in the latent payoff and conditionally independent from the error term we find that with median independent errors a special regressor does not increase the identifying power by a criterion in manski 1988 or lead to positive fisher information for the coefficients even though it does help recover the average structural function with conditionally symmetric errors a special regressor improves the identifying power and the information for coefficients is positive under mild conditions we propose two estimators for binary response models with conditionally symmetric errors and special regressors

symmetrically trimmed least squares estimation for tobit models this paper proposes alternatives to maximum likelihood estimation of the censored and truncated regression models known to economists as tobit models the proposed estimators are based upon symmetric censoring or truncation of the upper tail of the distribution of the dependent variable unlike methods based on the assumption of identically distributed gaussian errors the estimators are semiparametric in the sense that they are consistent and asymptotically normal for a wide class of symmetric error distributions with heteroskedasticity of unknown form the paper gives the regularity conditions and proofs of these large sample properties demonstrates how to construct consistent estimators of the asymptotic covariance matrices and presents the results of a simulation study for the censored case extensions and limitations of the approach are also considered

regularization in tomographic reconstruction using thresholding estimators in tomographic medical devices such as single photon emission computed tomography or positron emission tomography cameras image reconstruction is an unstable inverse problem due to the presence of additive noise a new family of regularization methods for reconstruction based on a thresholding procedure in wavelet and wavelet packet wp decompositions is studied this approach is based on the fact that the decompositions provide a near diagonalization of the inverse radon transform and of prior information in medical images a wp decomposition is adaptively chosen for the specific image to be restored corresponding algorithms have been developed for both two dimensional and full three dimensional reconstruction these procedures are fast noniterative and flexible numerical results suggest that they outperform filtered back projection and iterative procedures such as ordered subset expectation maximization

bias reduction for low statistics pet maximum likelihood reconstruction with a modified poisson distribution positron emission tomography data are typically reconstructed with maximum likelihood expectation maximization mlem however mlem suffers from positive bias due to the non negativity constraint this is particularly problematic for tracer kinetic modeling two reconstruction methods with bias reduction properties that do not use strict poisson optimization are presented and compared to each other to filtered backprojection fbp and to mlem the first method is an extension of negml where the poisson distribution is replaced by a gaussian distribution for low count data points the transition point between the gaussian and the poisson regime is a parameter of the model the second method is a simplification of abml abml has a lower and upper bound for the reconstructed image whereas aml has the upper bound set to infinity aml uses a negative lower bound to obtain bias reduction properties different choices of the lower bound are studied the parameter of both algorithms determines the effectiveness of the bias reduction and should be chosen large enough to ensure bias free images this means that both algorithms become more similar to least squares algorithms which turned out to be necessary to obtain bias free reconstructions this comes at the cost of increased variance nevertheless negml and aml have lower variance than fbp furthermore randoms handling has a large influence on the bias reconstruction with smoothed randoms results in lower bias compared to reconstruction with unsmoothed randoms or randoms precorrected data however negml and aml yield both bias free images for large values of their parameter

practical tradeoffs between noise quantitation and number of iterations for maximum likelihood based reconstructions emission computerised tomography images reconstructed using a maximum likelihood expectation maximization ml based method with different reconstruction kernels and 1 200 iterations are compared to images reconstructed using filtered backprojection fbp ml based reconstructions using a single pixel sp kernel with or without a sieve filter show no quantitative advantage over fbp except in the background where a reduction of noise is possible if the number of iterations is kept small

globally convergent image reconstruction for emission tomography using relaxed ordered subsets algorithms we present two types of globally convergent relaxed ordered subsets os algorithms for penalized likelihood image reconstruction in emission tomography modified block sequential regularized expectation maximization bsrem and relaxed os separable paraboloidal surrogates os sps the global convergence proof of the existing bsrem de pierro and yamagishi 2001 required a few a posteriori assumptions by modifying the scaling functions of bsrem we are able to prove the convergence of the modified bsrem under realistic assumptions our modification also makes stepsize selection more convenient in addition we introduce relaxation into the os sps algorithm erdogan and fessler 1999 that otherwise would converge to a limit cycle we prove the global convergence of diagonally scaled incremental gradient methods of which the relaxed os sps is a special case main results of the proofs are from nedic and bertsekas 2001 and correa and lemarechal 1993 simulation results showed that both new algorithms achieve global convergence yet retain the fast initial convergence speed of conventional unrelaxed ordered subsets algorithms

convergence of approximate and incremental subgradient methods for convex optimization we present a unified convergence framework for approximate subgradient methods that covers various stepsize rules including both diminishing and nonvanishing stepsizes convergence in objective values and convergence to a neighborhood of the optimal set we discuss ways of ensuring the boundedness of the iterates and give efficiency estimates our results are extended to incremental subgradient methods for minimizing a sum of convex functions which have recently been shown to be promising for various large scale problems including those arising from lagrangian relaxation

semiparametric and nonparametric estimation of sample selection models under symmetry this paper considers the semiparametric estimation of binary choice sample selection models under a joint symmetry assumption our approaches overcome various drawbacks associated with existing estimators in particular our method provides root n consistent estimators for both the intercept and slope parameters of the outcome equation in a heteroscedastic framework without the usual cross equation exclusion restriction or parametric specification for the error distribution and or the form of heteroscedasticity our two step estimators are shown to be consistent and asymptotically normal a monte carlo simulation study indicates the usefulness of our approaches

acceleration of maximum likelihood reconstruction using frequency amplification and attenuation compensation algorithms that calculate maximum likelihood ml and maximum a posteriori solutions using expectation maximization have been successfully applied to spect and pet these algorithms are appealing because of their solid theoretical basis and their guaranteed convergence a major drawback is the slow convergence which results in long processing times the authors present 2 new heuristic acceleration methods for maximum likelihood reconstruction of ect images the first method incorporates a frequency dependent amplification in the calculations to compensate for the low pass filtering of the backprojection operation in the second method an amplification factor is incorporated that suppresses the effect of attenuation on the updating factors both methods are compared to the 1 dimensional line search method proposed by lewitt all 3 methods accelerate the ml algorithm on the authors test images lewitt s method produced the strongest acceleration of the three individual methods however the combination of the frequency amplification with the line search method results in a new algorithm with still better performance under certain conditions an effective frequency amplification can be already achieved by skipping some of the calculations required for ml

spatiotemporal reconstruction of list mode pet data we describe a method for computing a continuous time estimate of tracer density using list mode positron emission tomography data the rate function in each voxel is modeled as an inhomogeneous poisson process whose rate function can be represented using a cubic b spline basis the rate functions are estimated by maximizing the likelihood of the arrival times of detected photon pairs over the control vertices of the spline modified by quadratic spatial and temporal smoothness penalties and a penalty term to enforce nonnegativity randoms rate functions are estimated by assuming independence between the spatial and temporal randoms distributions similarly scatter rate functions are estimated by assuming spatiotemporal independence and that the temporal distribution of the scatter is proportional to the temporal distribution of the trues a quantitative evaluation was performed using simulated data and the method is also demonstrated in a human study using sup 11 c raclopride

a fast fully 4 d incremental gradient reconstruction algorithm for list mode pet data we describe a fast and globally convergent fully four dimensional incremental gradient 4dig algorithm to estimate the continuous time tracer density from list mode positron emission tomography pet data detection of 511 kev photon pairs produced by positron electron annihilation is modeled as an inhomogeneous poisson process whose rate function is parameterized using cubic b splines the rate functions are estimated by minimizing the cost function formed by the sum of the negative log likelihood of arrival times spatial and temporal roughness penalties and a negativity penalty we first derive a computable bound for the norm of the optimal temporal basis function coefficients based on this bound we then construct and prove convergence of an incremental gradient algorithm fully 4 d simulations demonstrate the substantially faster convergence behavior of the 4dig algorithm relative to preconditioned conjugate gradient four dimensional reconstructions of real data are also included to illustrate the performance of this method

regularization for uniform spatial resolution properties in penalized likelihood image reconstruction traditional space invariant regularization methods in tomographic image reconstruction using penalized likelihood estimators produce images with nonuniform spatial resolution properties the local point spread functions that quantify the smoothing properties of such estimators are space variant asymmetric and object dependent even for space invariant imaging systems the authors propose a new quadratic regularization scheme for tomographic imaging systems that yields increased spatial uniformity and is motivated by the least squares fitting of a parameterized local impulse response to a desired global response the authors have developed computationally efficient methods for pet systems with shift invariant geometric responses they demonstrate the increased spatial uniformity of this new method versus conventional quadratic regularization schemes in simulated pet thorax scans

a row action alternative to the em algorithm for maximizing likelihood in emission tomography the maximum likelihood ml approach to estimating the radioactive distribution in the body cross section has become very popular among researchers in emission computed tomography ect since it has been shown to provide very good images compared to those produced with the conventional filtered backprojection fbp algorithm the expectation maximization em algorithm is an often used iterative approach for maximizing the poisson likelihood in ect because of its attractive theoretical and practical properties its major disadvantage is that due to its slow rate of convergence a large amount of computation is often required to achieve an acceptable image here the authors present a row action maximum likelihood algorithm ramla as an alternative to the em algorithm for maximizing the poisson likelihood in ect the authors deduce the convergence properties of this algorithm and demonstrate by way of computer simulations that the early iterates of ramla increase the poisson likelihood in ect at an order of magnitude faster that the standard em algorithm specifically the authors show that from the point of view of measuring total radionuclide uptake in simulated brain phantoms iterations 1 2 3 and 4 of ramla perform at least as well as iterations 45 60 70 and 80 respectively of em moreover the authors show that iterations 1 2 3 and 4 of ramla achieve comparable likelihood values as iterations 45 60 70 and 80 respectively of em the authors also present a modified version of a recent fast ordered subsets em os em algorithm and show that ramla is a special case of this modified os em furthermore the authors show that their modification converges to a ml solution whereas the standard os em does not

nonparametric identification and estimation of sample selection models under symmetry abstract under a conditional mean restriction das et al 2003 considered nonparametric estimation of sample selection models however their method can only identify the outcome regression function up to a constant in this paper we strengthen the conditional mean restriction to a symmetry restriction under which selection biases due to selection on unobservables can be eliminated through proper matching of propensity scores consequently we are able to identify and obtain consistent estimators for the average treatment effects and the structural regression functions the results from a simulation study suggest that our estimators perform satisfactorily

parameterized circuit complexity and the w hierarchy abstract a parameterized problem l k belongs to w t if there exists k computed from k such that l k reduces to the weight k satisfiability problem for weft t circuits we relate the fundamental question of whether the w t hierarchy is proper to parameterized problems for constant depth circuits we define classes g t as the analogues of ac 0 depth t for parameterized problems and n t by weight k existential quantification on g t by analogy with np p we prove that for each t w t equals the closure under fixed parameter reductions of n t then we prove using sipser s results on the ac 0 depth t hierarchy that both the g t and the n t hierarchies are proper if this separation holds up under parameterized reductions then the w t hierarchy is proper we also investigate the hierarchy h t defined by alternating quantification over g t by trading weft for quantifiers we show that h t coincides with h 1 we also consider the complexity of unique solutions and show a randomized reduction from w t to unique w t

application of the em algorithm for the multitarget multisensor tracking problem an important problem in surveillance and reconnaissance systems is the tracking of multiple moving targets in cluttered noise environments using outputs from a number of sensors possessing wide variations in individual characteristics and accuracies a number of approaches have been proposed for this multitarget multisensor tracking problem ranging from reasonably simple though ad hoc schemes to fairly complex but theoretically optimum approaches in this paper we describe an iterative procedure for time recursive multitarget multisensor tracking based on use of the expectation maximization em algorithm more specifically we pose the multitarget multisensor tracking problem as an incomplete data problem with the observable sensor outputs representing the incomplete data whereas the target associated sensor outputs constitute the complete data target updates at each time use an em based approach that calculates the maximum a posteriori map estimate of the target states under the assumption of appropriate motion models based on the outputs of disparate sensors the approach uses a markov random field mrf model of the associations between observations and targets and allows for estimation of joint association probabilities without explicit enumeration the advantage of this em based approach is that it provides a computationally efficient means for approaching the performance offered by theoretically optimum approaches that use explicit enumeration of the joint association probabilities we provide selected results illustrating the performance complexity characteristics of this em based approach compared with competing schemes

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

image regularization by nonnegatively constrained conjugate gradient abstract in the image reconstruction context the nonnegativity of the computed solution is often required conjugate gradient cg used as a reliable regularization tool may give solutions with negative entries particularly when large nearly zero plateaus are present the active constraints set detected by projection onto the nonnegative orthant turns out to be largely incomplete leading to poor effects on the accuracy of the reconstructed image in this paper an inner outer method based on cg is proposed to compute nonnegative reconstructed images with a strategy which enlarges subsequently the active constraints set this method appears to be especially suitable for the reconstruction of images having large nearly zero backgrounds the numerical experimentation validates the effectiveness of the proposed method when compared to other strategies for nonnegative reconstruction

pet image reconstruction using kernel method image reconstruction from low count positron emission tomography pet projection data is challenging because the inverse problem is ill posed prior information can be used to improve image quality inspired by the kernel methods in machine learning this paper proposes a kernel based method that models pet image intensity in each pixel as a function of a set of features obtained from prior information the kernel based image model is incorporated into the forward model of pet projection data and the coefficients can be readily estimated by the maximum likelihood ml or penalized likelihood image reconstruction a kernelized expectation maximization algorithm is presented to obtain the ml estimate computer simulations show that the proposed approach can achieve better bias versus variance trade off and higher contrast recovery for dynamic pet image reconstruction than the conventional maximum likelihood method with and without post reconstruction denoising compared with other regularization based methods the kernel method is easier to implement and provides better image quality for low count data application of the proposed kernel method to a 4 d dynamic pet patient dataset showed promising results

noise characterization of block iterative reconstruction algorithms i theory researchers have shown increasing interest in block iterative image reconstruction algorithms due to the computational and modeling advantages they provide although their convergence properties have been well documented little is known about how they behave in the presence of noise in this work the authors fully characterize the ensemble statistical properties of the rescaled block iterative expectation maximization rbi em reconstruction algorithm and the rescaled block iterative simultaneous multiplicative algebraic reconstruction technique rbi smart also included in the analysis are the special cases of rbi em maximum likelihood em ml em and ordered subset em os em and the special case of rbi smart smart a theoretical formulation strategy similar to that previously outlined for ml em is followed for the rbi methods the theoretical formulations in this paper rely on one approximation namely that the noise in the reconstructed image is small compared to the mean image in a second paper the approximation will be justified through monte carlo simulations covering a range of noise levels iteration points and subset orderings the ensemble statistical parameters could then be used to evaluate objective measures of image quality

new families of fourier eigenfunctions for steerable filtering a new diadic family of eigenfunctions of the 2 d fourier transform has been discovered specifically new wavelets are derived by steering the elongated hermite gauss filters with respect to rotations thus obtaining a natural generalization of the laguerre gauss harmonics interestingly these functions are also proportional to their 2 d fourier transform their analytical expression is provided in a compact and treatable form by means of a new ad hoc matrix notation in which the cases of even and odd orders of the hermite polynomials are unified moreover these functions can be efficiently implemented by means of a recursive formula that is derived in this paper the proposed filters are applied to the problem of gradient estimation to improve the theoretical canny tradeoff of position accuracy versus noise rejection that occurs in edge detection experimental results show considerable improvements in using the new wavelets over both isotropic gaussian derivatives and other elongated steerable filters more recently introduced finally being the proposed wavelets a set of fourier eigenfunctions they can be of interest in other fields of science such as optics and quantum mechanics

endogenous selection or treatment model estimation in a sample selection or treatment effects model common unobservables may affect both the outcome and the probability of selection in unknown ways this paper shows that the distribution function of potential outcomes conditional on covariates can be identified given an observed variable v that affects the treatment or selection probability in certain ways and is conditionally independent of the error terms in a model of potential outcomes selection model estimators based on this identification are provided which take the form of simple weighted averages gmm or two stage least squares these estimators permit endogenous and mismeasured regressors empirical applications are provided to estimation of a firm investment model and a schooling effects on wages model

inhomogeneous prior models for image reconstruction abstract over recent years the use of homogeneous gibbs prior models in image processing has become widely accepted there has been however much discussion over precisely which models are most appropriate for most applications the simplest gaussian model tends to oversmooth reconstructions so it has been rejected in favor of various edge preserving alternatives we claim that the problem is not with the gaussian family but rather with the assumption of homogeneity in this article we propose an inhomogeneous gaussian random field as a general prior model for many image processing applications the simplicity of the gaussian model allows rapid calculation and the flexibility of the spatially varying prior parameter allows varying degrees of spatial smoothing this approach is in the spirit of adaptive kernel density methods where only the choice of the variable window width is important the analysis of real single photon emission computed tomography data is used to illustrate the methods and simu

maximum likelihood reconstruction for emission tomography previous models for emission tomography et do not distinguish the physics of et from that of transmission tomography we give a more accurate general mathematical model for et where an unknown emission density x y z generates and is to be reconstructed from the number of counts n d in each of d detector units d within the model we give an algorithm for determining an estimate of which maximizes the probability p n of observing the actual detector count data n over all possible densities let independent poisson variables n b with unknown means b b 1 b represent the number of unobserved emissions in each of b boxes pixels partitioning an object containing an emitter suppose each emission in box b is detected in detector unit d with probability p b d d 1 d with p b d a one step transition matrix assumed known we observe the total number n n d of emissions in each detector unit d and want to estimate the unknown b b 1 b for each the observed data n has probability or likelihood p n the em algorithm of mathematical statistics starts with an initial estimate 0 and gives the following simple iterative procedure for obtaining a new estimate new from an old estimate old to obtain k k 1 2 new b old b dd 1 n d p b d old b p b d b 1 b

richardson lucy deblurring for scenes under a projective motion path this paper addresses how to model and correct image blur that arises when a camera undergoes ego motion while observing a distant scene in particular we discuss how the blurred image can be modeled as an integration of the clear scene under a sequence of planar projective transformations i e homographies that describe the camera s path this projective motion path blur model is more effective at modeling the spatially varying motion blur exhibited by ego motion than conventional methods based on space invariant blur kernels to correct the blurred image we describe how to modify the richardson lucy rl algorithm to incorporate this new blur model in addition we show that our projective motion rl algorithm can incorporate state of the art regularization priors to improve the deblurred results the projective motion path blur model along with the modified rl algorithm is detailed together with experimental results demonstrating its overall effectiveness statistical analysis on the algorithm s convergence properties and robustness to noise is also provided

incremental subgradient methods for nondifferentiable optimization we consider a class of subgradient methods for minimizing a convex function that consists of the sum of a large number of component functions this type of minimization arises in a dual context from lagrangian relaxation of the coupling constraints of large scale separable problems the idea is to perform the subgradient iteration incrementally by sequentially taking steps along the subgradients of the component functions with intermediate adjustment of the variables after processing each component function this incremental approach has been very successful in solving large differentiable least squares problems such as those arising in the training of neural networks and it has resulted in a much better practical rate of convergence than the steepest descent method in this paper we establish the convergence properties of a number of variants of incremental subgradient methods including some that are stochastic based on the analysis and computational experiments the methods appear very promising and effective for important classes of large problems a particularly interesting discovery is that by randomizing the order of selection of component functions for iteration the convergence rate is substantially improved

on use of the em algorithm for penalized likelihood estimation summary the em algorithm is a popular approach to maximum likelihood estimation but has not been much used for penalized likelihood or maximum a posteriori estimation this paper discusses properties of the em algorithm in such contexts concentrating on rates of conver gence and presents an alternative that is usually more practical and converges at least as quickly the em algorithm is a general approach to maximum likelihood estimation rather than a specific algorithm dempster et al 1977 discussed the method and derived basic properties demonstrating that a variety of procedures previously developed rather informally could be unified the common strand to problems where the approach is applicable is a notion of incomplete data this includes the conventional sense of missing data but is much broader than that the em algorithm demon strates its strength in situations where some hypothetical experiment yields data from which estimation is particularly convenient and economical the incomplete data actually at hand are regarded as observable functions of these complete data the resulting algorithms while usually slow to converge are often extremely simple and remain practical in large problems where no other approaches may be feasible dempster et al 1977 briefly refer to the use of the same approach to the problem of finding the posterior mode maximum a posteriori estimate in a bayesian estima

parallel application of block iterative methods in medical imaging and radiation therapy some row action algorithms which exploit special objective function and constraints structure have proven advantageous for solving huge and sparse feasibility or optimization problems recently developed block iterative versions of such special purpose methods enable parallel computation when the underlying problem is appropriately decomposed this opens the door for parallel computation in image reconstruction problems of computerized tomography and in the inverse problem of radiation therapy treatment planning all in their fully discretized modelling approach since there is more than one way of deriving block iterative versions of any row action method the choice has to be made with reference to the underlying real world problem

fixed parameter tractability and completeness i basic results for many fixed parameter problems that are trivially soluable in polynomial time such as k dominating set essentially no better algorithm is presently known than the one which tries all possible solutions other problems such as k feedback vertex set exhibit fixed parameter tractability for each fixed k the problem is soluable in time bounded by a polynomial of degree c where c is a constant independent of k we establish the main results of a completeness program which addresses the apparent fixed parameter intractability of many parameterized problems in particular we define a hierarchy of classes of parameterized problems fpt subseteq w 1 subseteq w 2 subseteq cdots subseteq w sat subseteq w p and identify natural complete problems for w t for t geq 2 in other papers we have shown many problems complete for w 1 dominating set is shown to be complete for w 2 and thus is not fixed parameter tractable unless independent set clique irredundant set and many other natural problems in w 2 are also fixed parameter tractable we also give a compendium of currently known hardness results as an appendix

characterization of metal artifacts in x ray computed tomography metal streak artifacts in x ray computerized tomography ct are characterized here using the notion of the wavefront set from microlocal analysis the metal artifacts are caused mainly from the mismatch of the forward model of the filtered back projection the presence of metallic subjects in an imaging subject violates the model s assumption of the ct sinogram data being the radon transform of an image the increasing use of metallic implants has increased demand for the reduction of metal artifacts in the field of dental and medical radiography however it is a challenging issue due to the serious difficulties in analyzing the x ray data which depends nonlinearly on the distribution of the metallic subject in this paper we for the first time provide a mathematical analysis to characterize the structure of metal streaking artifacts the metal streaking artifacts are produced along the line tangent to boundaries of the metal region touching at least two different boundaries we also found a sufficient condition for the nonexistence of the metal streaking artifacts 2016 wiley periodicals inc

quality and precision of parametric images created from pet sinogram data by direct reconstruction proof of concept we have previously implemented the direct reconstruction of dense kinetic model parameter images parametric images from sinogram data and compared it to conventional image domain kinetic parameter estimation methods although it has been shown that the direct reconstruction algorithm estimates the kinetic model parameters with lower root mean squared error than the conventional image domain techniques some theoretical obstacles remain these obstacles include the difficulty of evaluating the accuracy and precision of the estimated parameters in image domain techniques the reconstructed time activity curve tac and the model predicted tac are compared and the goodness of fit is evaluated as a measure of the accuracy and precision of the estimated parameters this approach cannot be applied to the direct reconstruction technique as there are no reconstructed tacs in this paper we propose ways of evaluating the precision and goodness of fit of the kinetic model parameters estimated by the direct reconstruction algorithm specifically precision of the estimates requires the calculation of variance images for each parameter and goodness of fit is addressed by reconstructing the difference between the measured and the fitted sinograms we demonstrate that backprojecting the difference from sinogram space to image space creates error images that can be examined for goodness of fit and model selection purposes the presence of nonrandom structures in the error images may indicate an inadequacy of the kinetic model that has been incorporated into the direct reconstruction algorithm we introduce three types of goodness of fit images we propose and demonstrate a number of runs image as a means of quantifying the adequacy or deficiency of the model we further propose and demonstrate images of the f statistic and the change in the akaike information criterion as devices for identifying the statistical advantage of one model over another at each voxel as direct reconstruction to parametric images proliferates it will be essential for imagers to adopt methods such as those proposed herein to assess the accuracy and precision of their parametric images

a consistent nonparametric test of symmetry in linear regression models abstract this article proposes a consistent nonparametric test of the hypothesis that the disturbance in a linear regression model is distributed symmetrically around zero simulation results show that the test has good size and power properties for sample sizes as small as 50 we illustrate the use of the test in a cross country model of inflation and monetary growth

on the convergence of an em type algorithm for penalized likelihood estimation in emission tomography recently we proposed an extension of the expectation maximization em algorithm that was able to handle regularization terms in a natural way although very general convergence proofs were not valid for many possibly useful regularizations we present here a simple convergence result that is valid assuming only continuous differentiability of the penalty term and can be also extended to other methods for penalized likelihood estimation in tomography

spectrum estimation from quantum limited interferograms a quantitative model for interferogram data collected in a quantum limited hyperspectral imaging system is derived this model accounts for the geometry of the interferometer the poisson noise and the parameterization of the mean of the noise in terms of the autocorrelation function of the incident optical signal the crame spl acute r rao bound on the variance of unbiased spectrum estimates is derived and provides an explanation for what is often called the multiplex disadvantage in interferometer based methods three spectrum estimation algorithms are studied maximum likelihood via the expectation maximization em algorithm least squares ls and the fast fourier transform fft with data precorrection extensive simulation results reveal advantages and disadvantages with all three methods in different signal to noise ratio snr regimes

threshold dominating sets and an improved characterization of w 2 the threshold dominating set problem is that of determining for a graph g v e whether there is a subset v v of size k such that for each vertex v v there are at least r elements of the closed neighborhood n v that belong to v we consider the complexity of the problem parameterized by the pair k r it is trivial to observe that this is hard for w 2 it can also be easily shown to belong to a natural extension w 2 of w 2 defined in terms of circuit families of depth bounded by a function of the parameter we prove membership in w 2 and thus w 2 completeness using this as a starting point we prove that w 2 w 2

ml parameter estimation for markov random fields with applications to bayesian tomography markov random fields mrfs have been widely used to model images in bayesian frameworks for image reconstruction and restoration typically these mrf models have parameters that allow the prior model to be adjusted for best performance however optimal estimation of these parameters sometimes referred to as hyperparameters is difficult in practice for two reasons i direct parameter estimation for mrfs is known to be mathematically and numerically challenging ii parameters can not be directly estimated because the true image cross section is unavailable we propose a computationally efficient scheme to address both these difficulties for a general class of mrf models and we derive specific methods of parameter estimation for the mrf model known as generalized gaussian mrf ggmrf we derive methods of direct estimation of scale and shape parameters for a general continuously valued mrf for the ggmrf case we show that the ml estimate of the scale parameter spl sigma has a simple closed form solution and we present an efficient scheme for computing the ml estimate of the shape parameter p by an off line numerical computation of the dependence of the partition function on p we present a fast algorithm for computing ml parameter estimates when the true image is unavailable to do this we use the expectation maximization em algorithm we develop a fast simulation method to replace the e step and a method to improve the parameter estimates when the simulations are terminated prior to convergence experimental results indicate that our fast algorithms substantially reduce the computation and result in good scale estimates for real tomographic data sets

a kalman filtering approach to stochastic global and region of interest tomography we define two forms of stochastic tomography in global tomography the goal is to reconstruct an object from noisy observations of all of its projections in region of interest roi tomography the goal is to reconstruct a small portion of an object an roi from noisy observations of its projections densely sampled in and near the roi and sparsely sampled away from the roi we solve both problems by expanding the object and its projections in a circular harmonic fourier series in the angular variable so that the radon transform becomes abel transforms of integer orders applied to the harmonics the algorithm has three major components first we fit state space models to each order of abel transform and thus represent the radon transform operation as a parallel bank of systems each of which computes the appropriate abel transform of a circular harmonic a variable transformation here allows either the global or roi problem to be solved second the object harmonics are modeled as a brownian branch this is a two point boundary value system which is markovianized into a form suitable for the kalman filter finally a parallel bank of kalman smoothing filters independently estimates each circular harmonic from the noisy projection data numerical examples illustrate the proposed procedure

estimation of discrete distributions with a class of simplex constraints abstract simplex constraints such as monotonicity and convexity or concavity on the probabilities of a set of discrete distributions are useful for modeling and analyzing discrete data this article considers both maximum likelihood estimation and bayesian estimation of discrete distribution with a class of simplex constraints using the expectation maximization em algorithm and the data augmentation da algorithm the formulation and implementation of em and da for binomial poisson hierarchical poisson binomial multinomial and hierarchical multinomial distributions are considered in detail and illustrated with examples

how to compute the difference between tomographic images an algorithm for estimating the difference between two tomographic images is proposed if the two data vectors are obtained in nonoverlapping time intervals the algorithm takes advantage of statistical independence of the two vectors the results are significantly different from the traditional approach in which the two images are reconstructed separately and then subtracted

on the statistical analysis of dirty pictures may 7th 1986 professor a f m smith in the chair summary a continuous two dimensional region is partitioned into a fine rectangular array of sites or pixels each pixel having a particular colour belonging to a prescribed finite set the true colouring of the region is unknown but associated with each pixel there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model the aim is to reconstruct the true scene with the additional knowledge that pixels close together tend to have the same or similar colours in this paper it is assumed that the local characteristics of the true scene can be represented by a nondegenerate markov random field such information can be combined with the records by bayes theorem and the true scene can be estimated according to standard criteria however the computational burden is enormous and the reconstruction may reflect undesirable largescale properties of the random field thus a simple iterative method of reconstruction is proposed which does not depend on these large scale characteristics the method is illustrated by computer simulations in which the original scene is not directly related to the assumed random field some complications including parameter estimation are discussed potential applications are mentioned briefly

information theoretic image formation the emergent role of information theory in image formation is surveyed unlike the subject of information theoretic communication theory information theoretic imaging is far from a mature subject the possible role of information theory in problems of image formation is to provide a rigorous framework for defining the imaging problem for defining measures of optimality used to form estimates of images for addressing issues associated with the development of algorithms based on these optimality criteria and for quantifying the quality of the approximations the definition of the imaging problem consists of an appropriate model for the data and an appropriate model for the reproduction space which is the space within which image estimates take values each problem statement has an associated optimality criterion that measures the overall quality of an estimate the optimality criteria include maximizing the likelihood function and minimizing mean squared error for stochastic problems and minimizing squared error and discrimination for deterministic problems the development of algorithms is closely tied to the definition of the imaging problem and the associated optimality criterion algorithms with a strong information theoretic motivation are obtained by the method of expectation maximization related alternating minimization algorithms are discussed in quantifying the quality of approximations global and local measures are discussed global measures include the mean squared error and discrimination between an estimate and the truth and probability of error for recognition or hypothesis testing problems local measures include fisher information

distribution free estimation of the random coefficient dummy endogenous variable model this paper considers the estimation of the random coefficient dummy endogenous variable model under a symmetry and index condition for the error distribution we follow a two step approach the selection equation is estimated first in the second step an instrumental variables estimator is proposed for the ourcome equation through a pairwise comparison method our approach can be readily extended to the general switching regression model in constrast to the existing literature on sample selection models the exclusion restriction is not needed here for model identification furthermore the intercept term for the outcome equation can be estimated at the usual parametric rate

accelerating the emml algorithm and related iterative algorithms by rescaled block iterative methods analysis of convergence of the algebraic reconstruction technique art shows it to be predisposed to converge to a solution faster than simultaneous methods such as those of the cimmino landweber 1992 type the expectation maximization maximum likelihood method for the poisson model emml and the simultaneous multiplicative art smart which use all the data at each step although the choice of ordering of the data and of relaxation parameters are important as herman and meyer 1993 have shown they are not the full story the analogous multiplicative art mart which applies only to systems y px in which y 0 p spl ges 0 and a nonnegative solution is sought is also sequential or row action rather than simultaneous but does not generally exhibit the same accelerated convergence relative to its simultaneous version smart by dividing each equation by the maximum of the corresponding row of p we find that this rescaled mart rmart does converge faster when solutions exist significantly so in cases in which the row maxima are substantially less than one such cases arise frequently in tomography and when the columns of p have been normalized to have sum one between simultaneous methods which use all the data at each step and sequential or row action methods which use only a single data value at each step there are the block iterative or ordered subset methods in which a single block or subset of the data is processed at each step the ordered subset em osem of hudson et al see ieee trans med imag vol 13 p 601 9 1994 is significantly faster than the emml but often fails to converge the rescaled block iterative emml rbi emml is an accelerated block iterative version of emml that converges in the consistent case to a solution for any choice of subsets it reduces to osem when the restrictive subset balanced condition holds rescaled block iterative versions of smart and mart also exhibit accelerated convergence

theoretical study of penalized likelihood image reconstruction for region of interest quantification region of interest roi quantification is an important task in emission tomography e g positron emission tomography and single photon emission computed tomography it is essential for exploring clinical factors such as tumor activity growth rate and the efficacy of therapeutic interventions statistical image reconstruction methods based on the penalized maximum likelihood pml or maximum a posteriori principle have been developed for emission tomography to deal with the low signal to noise ratio of the emission data similar to the filter cut off frequency in the filtered backprojection method the regularization parameter in pml reconstruction controls the resolution and noise tradeoff and hence affects roi quantification in this paper we theoretically analyze the performance of roi quantification in pml reconstructions building on previous work we derive simplified theoretical expressions for the bias variance and ensemble mean squared error emse of the estimated total activity in an roi that is surrounded by a uniform background when the mean and covariance matrix of the activity inside the roi are known the theoretical expressions are readily computable and allow for fast evaluation of image quality for roi quantification with different regularization parameters the optimum regularization parameter can then be selected to minimize the emse computer simulations are conducted for small rois with variable uniform uptake the results show that the theoretical predictions match the monte carlo results reasonably well

numerical study of multigrid implementations of some iterative image reconstruction algorithms the numerical behavior of multigrid implementations of the landweber generalized landweber art and mlem iterative image reconstruction algorithms is investigated comparisons between these algorithms and with their single grid implementations are made on two small scale synthetic pet systems for phantom objects exhibiting different characteristics and on one full scale synthetic system for a shepp logan phantom the authors also show analytically the effects of noise and initial condition on the generalized landweber iteration and note how to choose the shaping operator to filter out noise in the data or to enhance features of interest in the reconstructed image original contributions include 1 numerical studies of the convergence rates of single grid and multigrid implementations of the landweber generalized landweber art and mlem iterations and 2 effects of noise and initial condition on the generalized landweber iteration with procedures for filtering out noise or enhancing image features

nonlinearly smoothed em density estimation with automated smoothing parameter selection for nonparametric deconvolution problems abstract we study a nonparametric deconvolution density estimation problem the estimator is obtained by an em algorithm for a smoothed maximum likelihood estimation problem which has a unique continuous solution we present an implementation of the procedure incorporating a data driven discrepancy principle for selecting the smoothing parameter simulations illustrate the good properties of the resulting estimator when the unknown distribution is smooth and has regularly varying thin tails comparisons with a fourier kernel deconvolution method are made for the case of normal noise we show that under mild smoothness conditions the estimator based on the data driven smoothing parameter is strongly consistent

pure let image deconvolution we propose a non iterative image deconvolution algorithm for data corrupted by poisson or mixed poisson gaussian noise many applications involve such a problem ranging from astronomical to biological imaging we parameterize the deconvolution process as a linear combination of elementary functions termed as linear expansion of thresholds this parameterization is then optimized by minimizing a robust estimate of the true mean squared error the poisson unbiased risk estimate each elementary function consists of a wiener filtering followed by a pointwise thresholding of undecimated haar wavelet coefficients in contrast to existing approaches the proposed algorithm merely amounts to solving a linear system of equations which has a fast and exact solution simulation experiments over different types of convolution kernels and various noise levels indicate that the proposed method outperforms the state of the art techniques in terms of both restoration quality and computational complexity finally we present some results on real confocal fluorescence microscopy images and demonstrate the potential applicability of the proposed method for improving the quality of these images

a data driven smooth test of symmetry in this paper we propose a data driven smooth test of symmetry we first transform the raw data via the probability integral transformation according to a symmetrized empirical distribution and show that under the null hypothesis of symmetry the transformed data has a limiting uniform distribution reducing testing for symmetry to testing for uniformity employing neyman s smooth test of uniformity we show that only odd ordered orthogonal moments of the transformed data are required in constructing the test statistic we present a standardized smooth test that is distribution free asymptotically and derive the asymptotic behavior of the test and establish its consistency extension to dependent data case is discussed we investigate the finite sample performance of the proposed tests on both homogeneous and mixed distributions with unobserved heterogeneity an empirical application on testing symmetry of wage adjustment process based on heterogeneous wage contracts with different durations is provided

a maximum a posteriori probability expectation maximization algorithm for image reconstruction in emission tomography the expectation maximization method for maximum likelihood image reconstruction in emission tomography based on the poisson distribution of the statistically independent components of the image and measurement vectors is extended to a maximum aposteriori image reconstruction using a multivariate gaussian a priori probability distribution of the image vector the approach is equivalent to a penalized maximum likelihood estimation with a special choice of the penalty function the expectation maximization method is applied to find the a posteriori probability maximizer a simple iterative formula is derived for a penalty function that is a weighted sum of the squared deviations of image vector components from their a priori mean values the method is demonstrated to be superior to pure likelihood maximization in that the penalty function prevents the occurrence of irregular high amplitude patterns in the image with a large number of iterations the so called checkerboard effect or noise artifact

positron emission tomography by markov chain monte carlo with auxiliary variables we propose a new algorithm for positron emission tomography pet image reconstruction the algorithm belongs to the family of markov chain monte carlo methods with auxiliary variables the idea is to iteratively generate hidden variables at one step and use them for image restoration at another step the well known model of vardi et al j amer statist assoc 80 1985 8 for pet is combined with the bayesian model of lasota and niemiro pattern recognition 36 2003 931 for the underlying images this latter model takes advantage of the fact that medical images often consist of relatively few grey levels of unknown intensity the algorithm of lasota and niemiro pattern recognition 36 2003 931 is used in the image restoration part of the pet algorithm essentially as a noise filtering and smoothing device it is now equipped with an additional data reconstruction step we include simulation results which suggest that the method is truly reliable we also describe a version of the basic algorithm in which a random simulation step is replaced by computation of expected value similarly as in the em algorithm

iterative shrinkage approach to restoration of optical imagery the problem of reconstruction of digital images from their degraded measurements is regarded as a problem of central importance in various fields of engineering and imaging sciences in such cases the degradation is typically caused by the resolution limitations of an imaging device in use and or by the destructive influence of measurement noise specifically when the noise obeys a poisson probability law standard approaches to the problem of image reconstruction are based upon using fixed point algorithms which follow the methodology first proposed by richardson and lucy the practice of using these methods however shows that their convergence properties tend to deteriorate at relatively high noise levels accordingly in the present paper a novel method for denoising and or deblurring of digital images corrupted by poisson noise is introduced the proposed method is derived under the assumption that the image of interest can be sparsely represented in the domain of a linear transform consequently a shrinkage based iterative procedure is proposed which guarantees the solution to converge to the global maximizer of an associated maximum a posteriori criterion it is shown in a series of computer simulated experiments that the proposed method outperforms a number of existing alternatives in terms of stability precision and computational efficiency

fully bayesian reconstructions from single photon emission computed tomography data abstract with suitably chosen priors bayesian models are useful in image reconstruction i consider reconstructions from single photon emission computerized tomography data using a gibbs pairwise difference prior a fully bayesian approach is presented where the prior parameters are considered drawn from hyperpriors the approach is problematical because the normalization constant in the prior is an intractable function of its parameters here the constant is estimated off line by reverse logistic regression markov chain monte carlo methods are used on simulated and real data to gain estimates of the posterior mean and pixelwise credibility bounds the resulting reconstructions are compared to those obtained by filtered back projection maximum likelihood em and the one step late solution to the fixed parameter posterior mode

parameterized computational complexity of dodgson and young elections abstract we show that the two np complete problems of dodgson score and young score have differing computational complexities when the winner is close to being a condorcet winner on the one hand we present an efficient fixed parameter algorithm for determining a condorcet winner in dodgson elections by a minimum number of switches in the votes on the other hand we prove that the corresponding problem for young elections where one has to delete votes instead of performing switches is w 2 complete in addition we study dodgson elections that allow ties between the candidates and give fixed parameter tractability as well as w 2 completeness results depending on the cost model for switching ties

direct parametric image reconstruction in reduced parameter space for rapid multi tracer pet imaging the separation of multiple pet tracers within an overlapping scan based on intrinsic differences of tracer pharmacokinetics is challenging due to limited signal to noise ratio snr of pet measurements and high complexity of fitting models in this study we developed a direct parametric image reconstruction dpir method for estimating kinetic parameters and recovering single tracer information from rapid multi tracer pet measurements this is achieved by integrating a multi tracer model in a reduced parameter space rps into dynamic image reconstruction this new rps model is reformulated from an existing multi tracer model and contains fewer parameters for kinetic fitting ordered subsets expectation maximization osem was employed to approximate log likelihood function with respect to kinetic parameters to incorporate the multi tracer model an iterative weighted nonlinear least square wnls method was employed the proposed multi tracer dpir mt dpir algorithm was evaluated on dual tracer pet simulations 18 rm f fdg and 11 rm c met as well as on preclinical pet measurements 18 rm f flt and 18 rm f fdg the performance of the proposed algorithm was compared to the indirect parameter estimation method with the original dual tracer model the respective contributions of the rps technique and the dpir method to the performance of the new algorithm were analyzed in detail for the preclinical evaluation the tracer separation results were compared with single 18 rm f fdg scans of the same subjects measured two days before the dual tracer scan the results of the simulation and preclinical studies demonstrate that the proposed mt dpir method can improve the separation of multiple tracers for pet image quantification and kinetic parameter estimations

acceleration of landweber type algorithms by suppression of projection on the maximum singular vector a procedure that speeds up convergence during the initial stage the first 100 forward and backward projections of landweber type algorithms for iterative image reconstruction for positron emission tomography pet which include the landweber generalized landweber and steepest descent algorithms is discussed the procedure first identifies the singular vector associated with the maximum singular value of the pet system matrix and then suppresses projection of the data on this singular vector after a single landweber iteration it is shown that typical pet system matrices have a significant gap between their two largest singular values hence this suppression allows larger gains in subsequent iterations speeding up convergence by roughly a factor of three

assessing quantification for the ems algorithm abstract a framework is developed for assessing the potential of the ems estimate maximize and smooth algorithm to correctly quantify the emission it aims to reconstruct maximal eigenvector localization bounds of perron frobenius theory are used to show that the ability of the ems algorithm to quantify differences in emission is fundamentally limited by the smoothing imposed and the properties of the underlying model matrix in the algorithm in particular it is established that for nonnegative irreducible smoothing the ems algorithm will always fail to correctly reconstruct zero emission intensity

nonparametric regression with nonparametrically generated covariates we analyze the statistical properties of nonparametric regression estimators using covariates which are not directly observable but have be estimated from data in a preliminary step these so called generated covariates appear in numerous applications including two stage nonparametric regression estimation of simultaneous equation models or censored regression models yet so far there seems to be no general theory for their impact on the final estimator s statistical properties our paper provides such results we derive a stochastic expansion that characterizes the influence of the generation step on the final estimator and use it to derive rates of consistency and asymptotic distributions accounting for the presence of generated covariates

an iv model of quantile treatment effects the ability of quantile regression models to characterize the heterogeneous impact of variables on different points of an outcome distribution makes them appealing in many economic applications however in observational studies the variables of interest e g education prices are often endogenous making conventional quantile regression inconsistent and hence inappropriate for recovering the causal effects of these variables on the quantiles of economic outcomes in order to address this problem we develop a model of quantile treatment effects qte in the presence of endogeneity and obtain conditions for identification of the qte without functional form assumptions the principal feature of the model is the imposition of conditions that restrict the evolution of ranks across treatment states this feature allows us to overcome the endogeneity problem and recover the true qte through the use of instrumental variables the proposed model can also be equivalently viewed as a structural simultaneous equation model with nonadditive errors where qte can be interpreted as the structural quantile effects sqe

nonparametric identification of a binary random factor in cross section data suppose v and u are two independent mean zero random variables where v has an asymmetric distribution with two mass points and u has a symmetric distribution we show that the distributions of v and u are nonparametrically identifled just from observing the sum v u and provide a rate root n estimator we apply these results to the world income distribution to measure the extent of convergence over time where the values v can take on correspond to country types i e wealthy versus poor countries we also extend our results to include covariates x showing that we can nonparametrically identify and estimate cross section regression models of the form y g x d u where d is an unobserved

a statistical model for positron emission tomography abstract positron emission tomography pet still in its research stages is a technique that promises to open new medical frontiers by enabling physicians to study the metabolic activity of the body in a pictorial manner much as in x ray transmission tomography and other modes of computerized tomography the quality of the reconstructed image in pet is very sensitive to the mathematical algorithm to be used for reconstruction in this article we tailor a mathematical model to the physics of positron emissions and we use the model to describe the basic image reconstruction problem of pet as a standard problem in statistical estimation from incomplete data we describe various estimation procedures such as the maximum likelihood ml method using the em algorithm the method of moments and the least squares method a computer simulation of a pet experiment is then used to demonstrate the ml and the least squares reconstructions the main purposes of this article are to report on what we believe is an

fixed parameter tractability and completeness ii on completeness for w 1 abstract for many fixed parameter problems that are trivially solvable in polynomial time such as k dominating set essentially no better algorithm is presently known than the one which tries all possible solutions other problems such as feedback vertex set exhibit fixed parameter tractability for each fixed k the problem is solvable in time bounded by a polynomial of degree c where c is a constant independent of k in a previous paper the w hierarchy of parameterized problems was defined and complete problems were identified for the classes w t for t 2 our main result shows that independent set is complete for w 1

a modified expectation maximization algorithm for penalized likelihood estimation in emission tomography the maximum likelihood ml expectation maximization em approach in emission tomography has been very popular in medical imaging for several years in spite of this no satisfactory convergent modifications have been proposed for the regularized approach here a modification of the em algorithm is presented the new method is a natural extension of the em for maximizing likelihood with concave priors convergence proofs are given

efficient estimation of binary choice models under symmetry abstract this paper proposes a semiparametric maximum likelihood estimator for both the intercept and slope parameters in a binary choice model under symmetry and index restrictions the estimator attains the semiparametric efficiency bound in cosslett 1987 under the symmetry and independence restrictions compared with the estimator of klein and spady 1993 which attains the semiparametric efficiency bound in chamberlain 1986 and cosslett 1987 under the independence restriction we show that there are possible efficiency gains in estimating the slope parameters by imposing the additional symmetry restriction a small monte carlo study is carried out to illustrate the usefulness of our estimator

parameterized complexity of candidate control in elections and related digraph problems there are different ways for an external agent to influence the outcome of an election we concentrate on control by adding or deleting candidates our main focus is to investigate the parameterized complexity of various control problems for different voting systems to this end we introduce natural digraph problems that may be of independent interest they help in determining the parameterized complexity of control for different voting systems including llull copeland and plurality voting devising several parameterized reductions we provide an overview of the parameterized complexity of the digraph and control problems with respect to natural parameters such as adding deleting only a bounded number of candidates or having only few voters

the parametrized complexity of some fundamental problems in coding theory the parametrized complexity of a number of fundamental problems in the theory of linear codes and integer lattices is explored concerning codes the main results are that maximum likelihood decoding and weight distrubution are hard for the parametrized complexity class w 1 the np completeness of these two problems was established by berlekamp mceliece and van tilborg in 1978 using by means of a reduction from three dimensional matching on the other hand our proof of hardness for w 1 is based on a parametric polynomial time transformation from perfect code in graphs an immediate consequence of our results is that bounded distance decoding is likely to be hard for binary linear codes concerning lattices we address the theta series problem of determining for an integer lattice l given by a set of generators and a positive integer k whether there is a vector x in l of euclidean norm k we prove here for the first time that theta series is np complete and show that it is also hard for w 1 furthermore we prove that the nearest vector problem for integer lattices is hard for w 1 these problems are the counterparts of weight distrubution and maximum likelihood decoding for lattices relations between all these problems and combinatorial problems in graphs are discussed

trimmed lad and least squares estimation of truncated and censored regression models with fixed effects this paper considers estimation of truncated and censored regression models with fixed effects up until now no estimator has been shown to be consistent as the cross section dimension increases with the time dimension fixed trimmed least absolute deviations and trimmed least squares estimators are proposed for the case where the panel is of length two and it is proven that they are consistent and asymptotically normal it is not necessary to maintain parametric assumptions on the error terms to obtain this result a small scale monte carlo study demonstrates that these estimators can perform well in small samples copyright 1992 by the econometric society