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

mean and variance of implicitly defined biased estimators such as penalized maximum likelihood applications to tomography many estimators in signal processing problems are defined implicitly as the maximum of some objective function examples of implicitly defined estimators include maximum likelihood penalized likelihood maximum a posteriori and nonlinear least squares estimation for such estimators exact analytical expressions for the mean and variance are usually unavailable therefore investigators usually resort to numerical simulations to examine the properties of the mean and variance of such estimators this paper describes approximate expressions for the mean and variance of implicitly defined estimators of unconstrained continuous parameters we derive the approximations using the implicit function theorem the taylor expansion and the chain rule the expressions are defined solely in terms of the partial derivatives of whatever objective function one uses for estimation as illustrations we demonstrate that the approximations work well in two tomographic imaging applications with poisson statistics we also describe a plug in approximation that provides a remarkably accurate estimate of variability even from a single noisy poisson sinogram measurement the approximations should be useful in a wide range of estimation problems

nonlinear aggregation diffusion equations radial symmetry and long time asymptotics we analyze under which conditions equilibration between two competing effects repulsion modeled by nonlinear diffusion and attraction modeled by nonlocal interaction occurs this balance leads to continuous compactly supported radially decreasing equilibrium configurations for all masses all stationary states with suitable regularity are shown to be radially symmetric by means of continuous steiner symmetrization techniques calculus of variations tools allow us to show the existence of global minimizers among these equilibria finally in the particular case of newtonian interaction in two dimensions they lead to uniqueness of equilibria for any given mass up to translation and to the convergence of solutions of the associated nonlinear aggregation diffusion equations towards this unique equilibrium profile up to translations as t rightarrow infty

analysis of observer performance in known location tasks for tomographic image reconstruction we consider the task of detecting a statistically varying signal of known location on a statistically varying background in a reconstructed tomographic image we analyze the performance of linear observer models in this task we show that if one chooses a suitable reconstruction method a broad family of linear observers can exactly achieve the optimal detection performance attainable with any combination of a linear observer and linear reconstructor this conclusion encompasses several well known observer models from the literature including models with a frequency selective channel mechanism and certain types of internal noise interestingly the optimal reconstruction methods are unregularized and in some cases quite unconventional these results suggest that for the purposes of designing regularized reconstruction methods that optimize lesion detectability known location tasks are of limited use

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

large systems of interacting particles and the porous medium equation abstract we study the empirical processes of systems of interacting particles whose time evolution is given by coupled ordinary differential equations in particular as the population size tends to infinity we derive different versions of the porous medium equation as limit dynamics

penalized maximum likelihood image reconstruction using space alternating generalized em algorithms most expectation maximization em type algorithms for penalized maximum likelihood image reconstruction converge slowly particularly when one incorporates additive background effects such as scatter random coincidences dark current or cosmic radiation in addition regularizing smoothness penalties or priors introduce parameter coupling rendering intractable the m steps of most em type algorithms this paper presents space alternating generalized em sage algorithms for image reconstruction which update the parameters sequentially using a sequence of small hidden data spaces rather than simultaneously using one large complete data space the sequential update decouples the m step so the maximization can typically be performed analytically we introduce new hidden data spaces that are less informative than the conventional complete data space for poisson data and that yield significant improvements in convergence rate this acceleration is due to statistical considerations not numerical overrelaxation methods so monotonic increases in the objective function are guaranteed we provide a general global convergence proof for sage methods with nonnegativity constraints

resolution and noise properties of map reconstruction for fully 3 d pet derives approximate analytical expressions for the local impulse response and covariance of images reconstructed from fully three dimensional 3 d positron emission tomography pet data using maximum a posteriori map estimation these expressions explicitly account for the spatially variant detector response and sensitivity of a 3 d tomograph the resulting spatially variant impulse response and covariance are computed using 3 d fourier transforms a truncated gaussian distribution is used to account for the effect on the variance of the nonnegativity constraint used in map reconstruction using monte carlo simulations and phantom data from the micropet small animal scanner the authors show that the approximations provide reasonably accurate estimates of contrast recovery and covariance of map reconstruction for priors with quadratic energy functions they also describe how these analytical results can be used to achieve near uniform contrast recovery throughout the reconstructed volume

equilibria of homogeneous functionals in the fair competition regime we consider macroscopic descriptions of particles where repulsion is modelled by non linear power law diffusion and attraction by a homogeneous singular non singular kernel leading to variants of the keller segel model of chemotaxis we analyse the regime in which both homogeneities scale the same with respect to dilations that we coin as fair competition in the singular kernel case we show that existence of global equilibria can only happen at a certain critical value and they are characterised as optimisers of a variant of hls inequalities we also study the existence of self similar solutions for the sub critical case or equivalently of optimisers of rescaled free energies these optimisers are shown to be compactly supported radially symmetric and non increasing stationary solutions of the non linear keller segel equation on the other hand we show that no radially symmetric non increasing stationary solutions exist in the non singular kernel case implying that there is no criticality however we show the existence of positive self similar solutions for all values of the parameter under the condition that diffusion is not too fast we finally illustrate some of the open problems in the non singular kernel case by numerical experiments

a law of large numbers for moderately interacting diffusion processes we consider two special models of interacting diffusion processes and derive in the limit as the number of different processes tends to infinity and the interaction is rescaled in a suitable moderate way a law of large numbers for the empirical processes as limit dynamics we obtain certain nonlinear diffusion equations

eventual c regularity and concavity for flows in one dimensional porous media we study the regularity and the asymptotic behavior of the solutions of the initial value problem for the porous medium equation u t eft u m ight xx inq r imes eft 0 nfty ight ueft x 0 ight u 0 eft x ight forx n r

penalized weighted least squares image reconstruction for positron emission tomography presents an image reconstruction method for positron emission tomography pet based on a penalized weighted least squares pwls objective for pet measurements that are precorrected for accidental coincidences the author argues statistically that a least squares objective function is as appropriate if not more so than the popular poisson likelihood objective the author proposes a simple data based method for determining the weights that accounts for attenuation and detector efficiency a nonnegative successive over relaxation sor algorithm converges rapidly to the global minimum of the pwls objective quantitative simulation results demonstrate that the bias variance tradeoff of the pwls sor method is comparable to the maximum likelihood expectation maximization ml em method but with fewer iterations and is improved relative to the conventional filtered backprojection fbp method qualitative results suggest that the streak artifacts common to the fbp method are nearly eliminated by the pwls sor method and indicate that the proposed method for weighting the measurements is a significant factor in the improvement over fbp

a theoretical study of the contrast recovery and variance of map reconstructions from pet data the authors examine the spatial resolution and variance properties of pet images reconstructed using maximum a posteriori map or penalized likelihood methods resolution is characterized by the contrast recovery coefficient crc of the local impulse response simplified approximate expressions are derived for the local impulse response crcs and variances for each voxel using these results the authors propose a practical scheme for selecting spatially variant smoothing parameters to optimize lesion detectability through maximization of the local crc to noise ratio in the reconstructed image

zoology of a non local cross diffusion model for two species we study a nonlocal two species cross interaction model with cross diffusion we propose a positivity preserving finite volume scheme based on the numerical method introduced in j a carrillo a chertock and y huang commun comput phys 17 2015 pp 233 258 and explore this new model numerically in terms of its long time behaviors using the so gained insights we compute analytical stationary states and travelling pulse solutions for a particular model in the case of attractive attractive attractive repulsive cross interactions we show that as the strength of the cross diffusivity decreases there is a transition from adjacent solutions to completely segregated densities and we compute the threshold analytically for attractive repulsive cross interactions other bifurcating stationary states with various coexistence components of the support are analyzed in the attractive attractive case we find a strong agreement between the numerically and the analytically computed steady states in thes

theoretical study of lesion detectability of map reconstruction using computer observers the low signal to noise ratio snr in emission data has stimulated the development of statistical image reconstruction methods based on the maximum a posteriori map principle experimental examples have shown that statistical methods improve image quality compared to the conventional filtered backprojection fbp method however these results depend on isolated data sets here the authors study the lesion detectability of map reconstruction theoretically using computer observers these theoretical results can be applied to different object structures they show that for a quadratic smoothing prior the lesion detectability using the prewhitening observer is independent of the smoothing parameter and the neighborhood of the prior while the nonprewhitening observer exhibits an optimum smoothing point the authors also compare the results to those of fbp reconstruction the comparison shows that for ideal positron emission tomography pet systems where data are true line integrals of the tracer distribution the map reconstruction has a higher snr for lesion detection than fbp reconstruction due to the modeling of the poisson noise for realistic systems map reconstruction further benefits from accurately modeling the physical photon detection process in pet

from a discrete model of chemotaxis with volume filling to a generalized patlak keller segel model we present a discrete model of chemotaxis whereby cells responding to a chemoattractant are seen as individual agents whose movement is described through a set of rules that result in a biased rand

a hierarchy of polynomial time lattice basis reduction algorithms we present a hierarchy of polynomial time lattice basis reduction algorithms that stretch from lenstra lenstra lovasz reduction to korkine zolotareff reduction let l be the length of a shortest nonzero element of a lattice l we present an algorithm which for k n finds a nonzero lattice vector b so that b 2 6k2 nk l 2 this algorithm uses o n2 kk o k n2 log b arithmetic operations on o n log b bit integers this holds provided that the given basis vectors b1 bn zn are integral and have the length bound b this algorithm successively applies korkine zolotareff reduction to blocks of length k of the lattice basis we also improve kannan s algorithm for korkine zolotareff reduction

factoring polynomials with rational coefficients in this paper we present a polynomial time algorithm to solve the following problem given a non zero polynomial fe q x in one variable with rational coefficients find the decomposition of f into irreducible factors in q x it is well known that this is equivalent to factoring primitive polynomials fez x into irreducible factors in z x here we call f z x primitive if the greatest common divisor of its coefficients the content of f is 1 our algorithm performs well in practice cf 8 its running time measured in bit operations is o nl2 n9 log fd3

analysis of resolution and noise properties of nonquadratically regularized image reconstruction methods for pet we present accurate and efficient methods for estimating the spatial resolution and noise properties of nonquadratically regularized image reconstruction for positron emission tomography pet it is well known that quadratic regularization tends to over smooth sharp edges many types of edge preserving nonquadratic penalties have been proposed to overcome this problem however there has been little research on the quantitative analysis of nonquadratic regularization due to its nonlinearity in contrast quadratically regularized estimators are approximately linear and are well understood in terms of resolution and variance properties we derive new approximate expressions for the linearized local perturbation response llpr and variance using the taylor expansion with the remainder term although the expressions are implicit we can use them to accurately predict resolution and variance for nonquadratic regularization where the conventional expressions based on the first order taylor truncation fail they also motivate us to extend the use of a certainty based modified penalty to nonquadratic regularization cases in order to achieve spatially uniform perturbation responses analogous to uniform spatial resolution in quadratic regularization finally we develop computationally efficient methods for predicting resolution and variance of nonquadratically regularized reconstruction and present simulations that illustrate the validity of these methods

theoretical analysis of penalized maximum likelihood patlak parametric image reconstruction in dynamic pet for lesion detection detecting cancerous lesions is a major clinical application of emission tomography in a previous work we studied penalized maximum likelihood pml image reconstruction for lesion detection in static pet here we extend our theoretical analysis of static pet reconstruction to dynamic pet we study both the conventional indirect reconstruction and direct reconstruction for patlak parametric image estimation in indirect reconstruction patlak parametric images are generated by first reconstructing a sequence of dynamic pet images and then performing patlak analysis on the time activity curves tacs pixel by pixel in direct reconstruction patlak parametric images are estimated directly from raw sinogram data by incorporating the patlak model into the image reconstruction procedure pml reconstruction is used in both the indirect and direct reconstruction methods we use a channelized hotelling observer cho to assess lesion detectability in patlak parametric images simplified expressions for evaluating the lesion detectability have been derived and applied to the selection of the regularization parameter value to maximize detection performance the proposed method is validated using computer based monte carlo simulations good agreements between the theoretical predictions and the monte carlo results are observed both theoretical predictions and monte carlo simulation results show the benefit of the indirect and direct methods under optimized regularization parameters in dynamic pet reconstruction for lesion detection when compared with the conventional static pet reconstruction

dimensionality of local minimizers of the interaction energy in this work we consider local minimizers in the topology of transport distances of the interaction energy associated with a repulsive attractive potential we show how the dimensionality of the support of local minimizers is related to the repulsive strength of the potential at the origin

contractions in the 2 wasserstein length space and thermalization of granular media an algebraic decay rate is derived which bounds the time required for velocities to equilibrate in a spatially homogeneous flow through model representing the continuum limit of a gas of particles interacting through slightly inelastic collisions this rate is obtained by reformulating the dynamical problem as the gradient flow of a convex energy on an infinite dimensional manifold an abstract theory is developed for gradient flows in length spaces which shows how degenerate convexity or even non convexity if uniformly controlled will quantify contractivity limit expansivity of the flow

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

a unified approach to statistical tomography using coordinate descent optimization over the past years there has been considerable interest in statistically optimal reconstruction of cross sectional images from tomographic data in particular a variety of such algorithms have been proposed for maximum a posteriori map reconstruction from emission tomographic data while map estimation requires the solution of an optimization problem most existing reconstruction algorithms take an indirect approach based on the expectation maximization em algorithm we propose a new approach to statistically optimal image reconstruction based on direct optimization of the map criterion the key to this direct optimization approach is greedy pixel wise computations known as iterative coordinate decent icd we propose a novel method for computing the icd updates which we call icd newton raphson we show that icd newton raphson requires approximately the same amount of computation per iteration as em based approaches but the new method converges much more rapidly in our experiments typically five to ten iterations other advantages of the icd newton raphson method are that it is easily applied to map estimation of transmission tomograms and typical convex constraints such as positivity are easily incorporated

fast predictions of variance images for fan beam transmission tomography with quadratic regularization accurate predictions of image variances can be useful for reconstruction algorithm analysis and for the design of regularization methods computing the predicted variance at every pixel using matrix based approximations is impractical even most recently adopted methods that are based on local discrete fourier approximations are impractical since they would require a forward and backprojection and two fast fourier transform fft calculations for every pixel particularly for shift variant systems like fan beam tomography this paper describes new analytical approaches to predicting the approximate variance maps of 2 d images that are reconstructed by penalized likelihood estimation with quadratic regularization in fan beam geometries the simplest of the proposed analytical approaches requires computation equivalent to one backprojection and some summations so it is computationally practical even for the data sizes in x ray computed tomography ct simulation results show that it gives accurate predictions of the variance maps the parallel beam geometry is a simple special case of the fan beam analysis the analysis is also applicable to 2 d positron emission tomography pet

security of the most significant bits of the shamir message passing scheme boneh and venkatesan have recently proposed a polynomial time algorithm for recovering a hidden element of a finite field fp of p elements from rather short strings of the most significant bits of the remainder modulo p of t for several values of t selected uniformly at random from fp unfortunately the applications to the computational security of most significant bits of private keys of some finite field exponentiation based cryptosystems given by boneh and venkatesan are not quite correct for the diffie hellman cryptosystem the result of boneh and venkatesan has been corrected and generalized in our recent paper here a similar analysis is given for the shamir message passing scheme the results depend on some bounds of exponential sums

variability assessment in positron emission tomography and related generalized deconvolution models abstract the problem of variance assessment for positron emission tomography pet image reconstructions is considered in the context of generalized deconvolution a refinement of an approximate technique proposed by carson and colleagues is examined computational implications of representing the reconstruction kernel in terms of a weighted sum of gaussian densities are developed bias and variance characteristics of the resulting variance estimators are examined by numerical simulation for typical regions the error in estimated standard deviations is found to be on the order of 10 the use of smoothing to obtain more reliable pointwise variance estimators is described and some theoretical analysis of this technique is carried out for the pet application simulations suggest that the percent improvement in the root mean squared error accuracy of pointwise variance estimators obtained by smoothing can be on the order of 30 a practical application of the methodology to a pet study is presented

efficient calculation of resolution and covariance for penalized likelihood reconstruction in fully 3 d spect resolution and covariance predictors have been derived previously for penalized likelihood estimators these predictors can provide accurate approximations to the local resolution properties and covariance functions for tomographic systems given a good estimate of the mean measurements although these predictors may be evaluated iteratively circulant approximations are often made for practical computation times however when numerous evaluations are made repeatedly as in penalty design or calculation of variance images these predictors still require large amounts of computing time in stayman and fessler 2000 we discussed methods for precomputing a large portion of the predictor for shift invariant system geometries in this paper we generalize the efficient procedure discussed in stayman and fessler 2000 to shift variant single photon emission computed tomography spect systems this generalization relies on a new attenuation approximation and several observations on the symmetries in spect systems these new general procedures apply to both two dimensional and fully three dimensional 3 d spect models that may be either precomputed and stored or written in procedural form we demonstrate the high accuracy of the predictions based on these methods using a simulated anthropomorphic phantom and fully 3 d spect system the evaluation of these predictors requires significantly less computation time than traditional prediction techniques once the system geometry specific precomputations have been made

radial fractional laplace operators and hessian inequalities abstract in this paper we deduce a formula for the fractional laplace operator s on radially symmetric functions useful for some applications we give a criterion of subharmonicity associated with s and apply it to a problem related to the hessian inequality of sobolev type r n k k 1 u k 1 d x c r n u f k u d x where f k is the k hessian operator on r n 1 k n 2 under some restrictions on a k convex function u in particular we show that the class of u for which the above inequality was established in ferrari et al 5 contains the extremal functions for the hessian sobolev inequality of x j wang 1994 15 this is proved using logarithmic convexity of the gaussian ratio of hypergeometric functions which might be of independent interest

regularity of the obstacle problem for a fractional power of the laplace operator given a function and s 0 1 we will study the solutions of the following obstacle problem u in r n s u 0i nr n s u x 0 for those x such that u x x lim x u x 0 we show that when is c 1 s or smoother the solution u is in the space c 1 for every s in the case where the contact set u is convex we prove the optimal regularity result u c 1 s when is only c 1 for a s we prove that our solution u is c 1 for every c 2006 wiley periodicals inc

spatial resolution properties of penalized likelihood image reconstruction space invariant tomographs this paper examines the spatial resolution properties of penalized likelihood image reconstruction methods by analyzing the local impulse response the analysis shows that standard regularization penalties induce space variant local impulse response functions even for space invariant tomographic systems paradoxically for emission image reconstruction the local resolution is generally poorest in high count regions we show that the linearized local impulse response induced by quadratic roughness penalties depends on the object only through its projections this analysis leads naturally to a modified regularization penalty that yields reconstructed images with nearly uniform resolution the modified penalty also provides a very practical method for choosing the regularization parameter to obtain a specified resolution in images reconstructed by penalized likelihood methods

iterative versus filtered backprojection reconstruction for statistical parametric mapping of pet activation measurements a comparative case study the significance of task induced cerebral blood flow responses assessed using statistical parametric mapping depends among other things on the signal to noise ratio snr of these responses generally positron emission tomography sinograms of h2o o 15 activation studies are reconstructed using filtered backprojection fbp alternatively the acquired data can be reconstructed using an iterative reconstruction procedure it has been demonstrated that the application of iterative reconstruction methods improves image snr as compared with fbp the aim of this study was to compare fbp with iterative reconstruction to assess the statistical power of h2o o 15 pet activation studies using statistical parametric mapping for this case study pet data originating from a bimanual motor task were reconstructed using both fbp and maximum likelihood expectation maximization ml em an iterative algorithm both resulting data sets were statistically analyzed using statistical parametric mapping it was found with this dataset that the statistical analysis of the iteratively reconstructed data confirm the a priori expected physiological response in addition increased z scores were obtained in the iteratively reconstructed data in particular for the expected task related response activation of the posterior border of the left angular gyrus the z score increased from 3 00 to 3 96 furthermore the number of statistically significant clusters doubled while their volume increased by more than 50 in conclusion iterative reconstruction has the potential to increase the statistical power in h2o o 15 pet activation studies as compared with fbp reconstruction c 2002 elsevier science

on the derivation of reaction diffusion equations as limit dynamics of systems of moderately interacting stochastic processes we consider systems of moderately interacting particles which are divided into a finite number of different subpopulations and show that in the limit as the population size tends to infinity the empirical processes of the subpopulations converge to the solution of a system of reaction diffusion equations

chapman enskog derivation of the generalized smoluchowski equation abstract we use the chapman enskog method to derive the smoluchowski equation from the kramers equation in a high friction limit we consider two main extensions of this problem we take into account a uniform rotation of the background medium and we consider a generalized class of kramers equations associated with generalized free energy functionals we mention applications of these results to systems with long range interactions self gravitating systems 2d vortices bacterial populations etc in that case the smoluchowski equation is non local in the limit of short range interactions it reduces to a generalized form of the cahn hilliard equation these equations are associated with an effective generalized thermodynamical formalism

fast gradient based methods for bayesian reconstruction of transmission and emission pet images the authors describe conjugate gradient algorithms for reconstruction of transmission and emission pet images the reconstructions are based on a bayesian formulation where the data are modeled as a collection of independent poisson random variables and the image is modeled using a markov random field a conjugate gradient algorithm is used to compute a maximum a posteriori map estimate of the image by maximizing over the posterior density to ensure nonnegativity of the solution a penalty function is used to convert the problem to one of unconstrained optimization preconditioners are used to enhance convergence rates these methods generally achieve effective convergence in 15 25 iterations reconstructions are presented of an sup 18 fdg whole body scan from data collected using a siemens cti ecat931 whole body system these results indicate significant improvements in emission image quality using the bayesian approach in comparison to filtered backprojection particularly when reprojections of the map transmission image are used in place of the standard attenuation correction factors

quantifying the importance of the statistical assumption in statistical x ray ct image reconstruction statistical image reconstruction sir is a promising approach to reducing radiation dose in clinical computerized tomography ct scans clinical ct scanners use energy integrating detectors the ct signal follows a compound poisson distribution its probability density function pdf does not have an analytical form hence cannot be used in an sir method the goal of this work is to quantify the effects of using an approximate statistical assumption in sir methods for clinical ct applications we apply a pseudo ideal observer pio to simulated ct projection data of the fanbeam geometry at different dose levels the simulation models the polychromatic x ray tube spectrum the effects of the bowtie filter and the energy integrating detectors the pio uses a pseudo likelihood function plf to calculate the pseudo likelihood ratio which is the decision variable used by the pio in a binary detection task the plf is an approximation to the true lf of the underlying data the pio has inferior performance than the io unless the plf coincides with the lf this performance difference quantifies the closeness between the pseudo likelihood and the exact one using lesion detectability in a signal known exactly background known exactly binary detection task as a figure of merit our results show that at down to 0 1 of a reference tube current level i0 the pio that uses a poisson approximation or a matched variance gaussian approximation in either the transmission or the line integral domain achieves 99 the performance of the io the constant variance gaussian approximation has only 70 80 of the io performance at tube currents lower than 0 1 i0 the performance difference is more substantial we conclude that at current clinical dose levels it is important to account for the mean dependent variance in ct projection data in sir problem formulation the exact pdf of the ct signal is not as important

a fluctuation theorem for moderately interacting diffusion processes we study the asymptotic behaviour of the fluctuations of the empirical processes of the second example of moderately interacting diffusion processes of 3 and show that in the limit as the number of different processes tends to infinity these fluctuations behave gaussian

hidden number problem with hidden multipliers timed release crypto and noisy exponentiation we consider a generalisation of the hidden number problem recently introduced by boneh and venkatesan the initial problem can be stated as follows recover a number a fp such that for many known random t fp approximations to the values of at p are known here we study a version of the problem where the multipliers t are not known but rather certain approximations to them are given we present a probabilistic polynomial time solution when the error is small enough and we show that the problem cannot be solved if the error is sufficiently large we apply the result to the bit security of timed release crypto introduced by rivest shamir and wagner to noisy exponentiation black boxes and to the bit security of the inverse exponentiation we also show that it implies a certain bit security result for weil pairing on elliptic curves