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

further developments on the robustness of clevenson zidek type means estimators abstract tsui 1984 showed that many clevenson zidek type poisson means estimators are better than the usual estimator under the normalized squared error loss 1 1 even when the underlying distributions are negative binomial this article shows that this dominance result is still true when the underlying distributions belong to a much larger class of distributions this class includes all mixtures of poisson distributions and hence the negative binomial result is a very special case

a progressive simultaneous iteration solution for dynamic element vibration analysis development and employment of dynamic elements can result in substantial gain in solution convergence for vibration analysis when compared with the usual finite element discretization efficient solution of the associated quadratic matrix eigenproblem is crucial in achieving a superior and relatively economical solution this paper first describes a novel eigensolution of the quadratic matrix equation by a progressive simultaneous iteration method free vibration analysis results of a rectangular prestressed membrane are next presented in detail that provides an assessment of relative solution convergence and computing expenses of the two idealization procedures

structural vibration analysis by a progressive simultaneous iteration method this paper provides details of a newly developed structural eigenproblem solution technique that effects simultaneous convergence of a set of desired roots and associated vectors in an accurate and efficient fashion the procedure is based on a progressive simultaneous iteration method that enables effective computation of either the first few or a specified number of intermediate roots and associated vectors without having to compute any other numerical results pertaining to some practical problems are also presented that testify to the superior convergence characteristics of the present procedure when compared with other existing ones

estimation of the mean of a multivariate normal distribution estimation of the means of independent normal random variables is considered using sum of squared errors as loss an unbiased estimate of risk is obtained for an arbitrary estimate and certain special classes of estimates are then discussed the results are applied to smoothing by use of moving averages and to trimmed analogs of the james stein estimate a suggestion is made for calculating approximate confidence sets for the mean vector centered at an arbitrary estimate

scale space and edge detection using anisotropic diffusion a new definition of scale space is suggested and a class of algorithms used to realize a diffusion process is introduced the diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing rather than interregion smoothing it is shown that the no new maxima should be generated at coarse scales property of conventional scale space is preserved as the region boundaries in the approach remain sharp a high quality edge detector which successfully exploits global information is obtained experimental results are shown on a number of images parallel hardware implementations are made feasible because the algorithm involves elementary local operations replicated over the image

an unbiased risk estimator for image denoising in the presence of mixed poisson gaussian noise the behavior and performance of denoising algorithms are governed by one or several parameters whose optimal settings depend on the content of the processed image and the characteristics of the noise and are generally designed to minimize the mean squared error mse between the denoised image returned by the algorithm and a virtual ground truth in this paper we introduce a new poisson gaussian unbiased risk estimator pg ure of the mse applicable to a mixed poisson gaussian noise model that unifies the widely used gaussian and poisson noise models in fluorescence bioimaging applications we propose a stochastic methodology to evaluate this estimator in the case when little is known about the internal machinery of the considered denoising algorithm and we analyze both theoretically and empirically the characteristics of the pg ure estimator finally we evaluate the pg ure driven parametrization for three standard denoising algorithms with and without variance stabilizing transforms and different characteristics of the poisson gaussian noise mixture

image denoising in mixed poisson gaussian noise we propose a general methodology pure let to design and optimize a wide class of transform domain thresholding algorithms for denoising images corrupted by mixed poisson gaussian noise we express the denoising process as a linear expansion of thresholds let that we optimize by relying on a purely data adaptive unbiased estimate of the mean squared error mse derived in a non bayesian framework pure poisson gaussian unbiased risk estimate we provide a practical approximation of this theoretical mse estimate for the tractable optimization of arbitrary transform domain thresholding we then propose a pointwise estimator for undecimated filterbank transforms which consists of subband adaptive thresholding functions with signal dependent thresholds that are globally optimized in the image domain we finally demonstrate the potential of the proposed approach through extensive comparisons with state of the art techniques that are specifically tailored to the estimation of poisson intensities we also present denoising results obtained on real images of low count fluorescence microscopy

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

approximation of nonnegative systems by finite impulse response convolutions we pose the deterministic nonparametric approximation problem for scalar nonnegative input output systems via finite impulse response convolutions based on repeated observations of input output signal pairs the problem is converted into a nonnegative matrix factorization with special structure for which we use csiszar s i divergence as the criterion of optimality conditions are given on the input output data that guarantee the existence and uniqueness of the minimum we propose an algorithm of the alternating minimization type for i divergence minimization and study its asymptotic behavior for the case of noisy observations we give the large sample properties of the statistical version of the minimization problem numerical experiments confirm the asymptotic results and exhibit the fast convergence of the proposed algorithm

attraction repulsion expectation maximization algorithm for image reconstruction and sensor field estimation in this paper we propose an attraction repulsion expectation maximization arem algorithm for image reconstruction and sensor field estimation we rely on a new method for density estimation to address the problems of image reconstruction from limited samples and sensor field estimation from randomly scattered sensors density estimation methods often suffer from undesirable phenomena such as over fitting and over smoothing specifically various density estimation techniques based on a gaussian mixture model gmm tend to cluster the gaussian functions together thus resulting in over fitting on the other hand other approaches repel the gaussian functions and yield over smooth density estimates we propose a method that seeks an equilibrium between over fitting and over smoothing in density estimation by incorporating attraction and repulsion forces among the gaussian functions and determining the optimal balance between the competing forces experimentally we model the attractive and repulsive forces by introducing the gibbs and inverse gibbs distributions respectively the maximization of the likelihood function augmented by the gibbs density mixture is solved under the expectation maximization em method computer simulation results are provided to demonstrate the effectiveness of the proposed arem algorithm in image reconstruction and sensor field estimation

image denoising via sparse and redundant representations over learned dictionaries we address the image denoising problem where zero mean white and homogeneous gaussian additive noise is to be removed from a given image the approach taken is based on sparse and redundant representations over trained dictionaries using the k svd algorithm we obtain a dictionary that describes the image content effectively two training options are considered using the corrupted image itself or training on a corpus of high quality image database since the k svd is limited in handling small image patches we extend its deployment to arbitrary image sizes by defining a global image prior that forces sparsity over patches in every location in the image we show how such bayesian treatment leads to a simple and effective denoising algorithm this leads to a state of the art denoising performance equivalent and sometimes surpassing recently published leading alternative denoising methods

practical poissonian gaussian noise modeling and fitting for single image raw data we present a simple and usable noise model for the raw data of digital imaging sensors this signal dependent noise model which gives the pointwise standard deviation of the noise as a function of the expectation of the pixel raw data output is composed of a poissonian part modeling the photon sensing and gaussian part for the remaining stationary disturbances in the output data we further explicitly take into account the clipping of the data over and under exposure faithfully reproducing the nonlinear response of the sensor we propose an algorithm for the fully automatic estimation of the model parameters given a single noisy image experiments with synthetic images and with real raw data from various sensors prove the practical applicability of the method and the accuracy of the proposed model

relative definability of boolean functions via hypergraphs the aim of this work is to show how hypergraphs can be used as a systematic tool in the classification of continuous boolean functions according to their degree of parallelism intuitively f is less parallel than g if it can be defined by a sequential program using g as its only free variable it turns out that the poset induced by this preorder is as for the degrees of recursion a sup semilattice although hypergraphs have already been used in bucciarelli theoret comput sci to appear as a tool for studying degrees of parallelism no general result relating the former to the latter has been proved in that work we show that the sup semilattice of degrees has a categorical counterpart we define a category of hypergraphs such that every object represents a monotone boolean function finite coproducts in this category correspond to lubs of degrees unlike degrees of recursion where every set has a recursive upper bound monotone boolean functions may have no sequential upper bound however the ones which do have a sequential upper bound can be nicely characterised in terms of hypergraphs these subsequential functions play a major role in the proof of our main result namely that f is less parallel than g if there exists a morphism between their associated hypergraphs

a region based segmentation method for multichannel image data abstract segmentation has become a widely used tool in modern image analysis typical methods are highly nonlinear and often ad hoc and none so far have proved accessible to detailed statistical analysis even by asymptotic approximations can such methods be any good this article describes a segmentation procedure for multichannel image data and attempts to develop an understanding of its statistical performance characteristics in terms of nonparametric regression the procedure is based on a recursive merging algorithm defined via a nested sequence of discretizations of the image domain a cross validation rule with a near neighbor block replacement strategy is proposed for selecting the final segmentation model idealized numerical simulation experiments are used to evaluate the rate of convergence of the mean square error of estimation and also to study the efficiency of the cross validation technique interestingly the results show that the rate of convergence tends to decrease as the degree of smo

improving upon standard estimators in discrete exponential families with applications to poisson and negative binomial cases assume that xi xp are independent random observations having discrete exponential densities p1 0 ti x rj 1 i 1 p respectively a general technique of improving upon the uniform minimum variance unbiased estimator umvue of o1 op is developed under possibly weighted squared error loss functions it is shown that improved estimators can be constructed by solving a difference inequality typical difference inequalities of a fairly general type are presented and solved when specialized to poisson and negative binomial cases broad classes of estimators are given that dominate the umvue these results unify many known results in this rapidly diverging field and some of them are new especially those related to negative binomial distributions improved estimators are also obtained for the problems in which some of the observations are from poisson families and some from negative binomial families for sum of squared errors loss estimators which dominate the umvue in the discrete exponential families are also given explicitly

em and beyond the basic theme of the em algorithm to repeatedly use complete data methods to solve incomplete data problems is also a theme of several more recent statistical techniques these techniques multiple imputation data augmentation stochastic relaxation and sampling importance resampling combine simulation techniques with complete data methods to attack problems that are difficult or impossible for em

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

alternatives to the discrete cosine transform for irreversible tomographic image compression full frame irreversible compression of medical images is currently being performed using the discrete cosine transform dct although the dct is the optimum fast transform for video compression applications the authors show here that it is outperformed by the discrete fourier transform dft and discrete hartley transform dht for images obtained using positron emission tomography pet and magnetic resonance imaging mri and possibly for certain types of digitized radiographs this difference occurs because pet and mri images are characterized by a roughly circular region d of non zero intensity bounded by a region r in which the image intensity is essentially zero clipping r to its minimum extent can reduce the number of low intensity pixels but the practical requirement that images be stored on a rectangular grid means that a significant region of zero intensity must remain an integral part of the image to be compressed with this constraint imposed the dct loses its advantage over the dft because neither transform introduces significant artificial discontinuities the dft and dht have the further important advantage of requiring less computation time than the dct

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

an algorithm for maximizing expected log investment return let the random stock market vector x geq 0 be drawn according to a known distribution function f x x in r m a log optimal portfolio b ast is any portfolio b achieving maximal expected log return w ast sup b e ln b t x where the supremum is over the simplex b geq 0 sum i 1 m b i 1 an algorithm is presented for finding b ast the algorithm consists of replacing the portfolio b by the expected portfolio b b i e b i x i b t x corresponding to the expected proportion of holdings in each stock after one market period the improvement in w b after each iteration is lower bounded by the kullback leibler information number d b b between the current and updated portfolios thus the algorithm monotonically improves the return w an upper bound on w ast is given in terms of the current portfolio and the gradient and the convergence of the algorithm is established

a subspace forward iteration method for solving the quadratic eigenproblem associated with the fde formulation this paper presents the development of an efficient and numerically stable algorithm for accurately computing the eigensolutions of the quadratic real symmetric eigenproblem arising in the finite dynamic element fde formulation closely related to the subspace forward iteration method the proposed scheme is well suited to extracting the lowest natural frequencies and associated mode shapes of large practical eigenproblems takes full advantage of the banded configuration of the stiffness inertia and dynamic correction matrices involved in the eigenproblem and ensures a monotonic convergence from above to the required eigenpairs a shifting technique for convergence acceleration and an eigenpair verification scheme are also presented numerical examples are shown demonstrating the excellent performance of the solution procedure

generalized sure for exponential families applications to regularization stein s unbiased risk estimate sure was proposed by stein for the independent identically distributed i i d gaussian model in order to derive estimates that dominate least squares ls recently the sure criterion has been employed in a variety of denoising problems for choosing regularization parameters that minimize an estimate of the mean squared error mse however its use has been limited to the i i d case which precludes many important applications in this paper we begin by deriving a sure counterpart for general not necessarily i i d distributions from the exponential family this enables extending the sure design technique to a much broader class of problems based on this generalization we suggest a new method for choosing regularization parameters in penalized ls estimators we then demonstrate its superior performance over the conventional generalized cross validation and discrepancy approaches in the context of image deblurring and deconvolution the sure technique can also be used to design estimates without predefining their structure however allowing for too many free parameters impairs the estimate s performance to address this inherent tradeoff we propose a regularized sure objective and demonstrate its use in the context of wavelet denoising

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

a linear spatial correlation model with applications to positron emission tomography abstract a simple spatial correlation model is presented for repeated measures data correlation between observations on the same subject is assumed to decay as a linear function of the squared distance separating the regions in three dimensional space where the observations are made this quadratic decay qd model has many attractive theoretical properties the covariance structure of the normalized data formed by subtracting the subject average is the same as that generated by random linear trends plus centered white noise which leads to a simple method for simulating the original data it also implies that the first three principal components of the normalized observations are the spatial coordinates of the regions thus principal components analysis can be used as an exploratory tool to verify the qd model provided the white noise component is small certain simple predictions can be made such as the fact that the variances of the normalized observations increase linearly with the squared dist

an invitation to quantum tomography we describe quantum tomography as an inverse statistical problem in which the quantum state of a light beam is the unknown parameter and the data are given by results of measurements performed on identical quantum systems the state can be represented as an infinite dimensional density matrix or equivalently as a density on the plane called the wigner function we present consistency results for pattern function projection estimators and for sieve maximum likelihood estimators for both the density matrix of the quantum state and its wigner function we illustrate the performance of the estimators on simulated data an em algorithm is proposed for practical implementation there remain many open problems e g rates of convergence adaptation and studying other estimators a main purpose of the paper is to bring these to the attention of the statistical community

a sure approach for digital signal image deconvolution problems in this paper we are interested in the classical problem of restoring data degraded by a convolution and the addition of a white gaussian noise the originality of the proposed approach is twofold first we formulate the restoration problem as a nonlinear estimation problem leading to the minimization of a criterion derived from stein s unbiased quadratic risk estimate secondly the deconvolution procedure is performed using any analysis and synthesis frames that can be overcomplete or not new theoretical results concerning the calculation of the variance of the stein s risk estimate are also provided in this work simulations carried out on natural images show the good performance of our method with respect to conventional wavelet based restoration methods

a study of least squares and maximum likelihood for image reconstruction in positron emission tomography positron emission tomography pet is a radiologic tool offering a unique capability for measuring tissue metabolism in vivo a number of biological and physical factors limit the resolution of pet so often the statistical aspects of image reconstruction have an appreciable effect on the quality of information obtained from a study to a first approximation reconstruction involves the solution of a linear inverse problem with a line integral radon type transform standard filtered back projection reconstruction is based on the method of least squares although computationally efficient the method does not enforce positivity constraints leading to undesirable negative artifacts in the results maximum likelihood based approaches to reconstruction do not suffer from this problem but their computational complexity has limited the ability to determine quantitatively the improvements in image quality in this paper asymptotic approximations and numerical simulations are used to examine the least squares and maximum likelihood methods in some detail the studies are carried out for idealized representations of conventional and time of flight tomographs the asymptotic analysis indicates that for a range of sobolev norms the rates of estimation of least squares and maximum likelihood reconstructions are of the same order this is borne out by numerical studies however in these studies maximum likelihood is found to be more efficient than least squares on a conventional distance angle tomograph the root mean square error is on the order of 10 20 smaller for maximum likelihood reconstructions the corresponding reduction in the root mean square error on a time of flight tomograph is in the 5 range similar results are found using more complex region of interest based measures of reconstruction accuracy in addition it is found that much of the effect of maximum likelihood can apparently be realized by postprocessing least squares solutions in an ad hoc manner to reduce negativity artifacts since the postprocessing scheme is computationally fast this suggests that in pet it may be possible to realize the benefits of maximum likelihood without the substantial computational overhead of the em algorithm

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

estimation of trends in the scram rate at nuclear power plants an important task of the u s nuclear regulatory commission is to examine annual operating data from the nation s population of nuclear power plants for trends over time we are interested here in trends in the scram rate at 66 commercial nuclear power plants based on annual observed scram data from 1984 1993 for an assumed poisson distribution on the number of unplanned scrams a gamma prior and an appropriate hyperprior a parametric empirical bayes peb approximation to a full hierarchical bayes formulation is used to estimate the scram rate for each plant for each year the peb estimated prior and posterior distributions are then subsequently smoothed over time using an exponentially weighted moving average the results indicate that such bidirectional shrinkage is quite useful for identifying reliability trends over time

filtered variate prior distributions for histogram smoothing abstract we develop prior distributions for histogram inference favoring smooth population frequencies that is probability vectors with small differences for neighboring categories we give a theory of prior random probability vectors representable as a linear transform or filter of a standard random probability vector or equivalently a random weighted average of nonrandom smooth probability vectors promising methods of prior assessment are given based on elicitation of a list of typically smooth probability vectors the empirical moments of which can then be matched by the mean vector and variance matrix of a constructed continuous type filtered variate prior distribution

color image denoising via discriminatively learned iterative shrinkage in this paper we propose a novel model a discriminatively learned iterative shrinkage dlis model for color image denoising the dlis is a generalization of wavelet shrinkage by iteratively performing shrinkage over patch groups and whole image aggregation we discriminatively learn the shrinkage functions and basis from the training pairs of noisy noise free images which can adaptively handle different noise characteristics in luminance chrominance channels and the unknown structured noise in real captured color images furthermore to remove the splotchy real color noises we design a laplacian pyramid based denoising framework to progressively recover the clean image from the coarsest scale to the finest scale by the dlis model learned from the real color noises experiments show that our proposed approach can achieve the state of the art denoising results on both synthetic denoising benchmark and real captured color images

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

on the expressive power of first order boolean functions in pcf recent results of bucciarelli show that the semilattice of degrees of parallelism of first order boolean functions in pcf has both infinite chains and infinite antichains by considering a simple subclass of sieber s sequentiality relations we identify levels in the semilattice and derive inexpressibility results concerning functions on different levels this allows us to further explore the structure of the semilattice of degrees of parallelism we identify semilattices characterized by simple level properties and show the existence of new infinite hierarchies which are in a certain sense natural with respect to the levels copyright 2001 elsevier science b v

degrees of parallelism in the continuous type hierarchy a degree of parallelism is an equivalence class of scott continuous functions which are relatively definable by each other with respect to the language pcf a paradigmatic sequential language we introduce an infinite bi dimensional hierarchy of degrees this hierarchy is inspired by representing first order continuous functions as hypergraphs we assume some familiarity with the language pcf and with its continuous model keywordr sequentiality stability strong stability logical relations sequentiality relations

free and forced vibration analysis using the smoothed finite element method sfem abstract smoothed finite element method sfem was recently proposed by the authors to improve the accuracy and convergence rate of the existing standard four node isoparametric finite element method fem by 2 2 quadrature in the static analysis in this work it is further extended to the free and forced analysis of two dimensional 2d dynamic problems it is found that sfem achieves more accurate results and higher convergence rates as compared with the corresponding finite elements in solving dynamic problems without increasing the computational cost as only shape function itself is involved in computing the field gradients and no coordinate transformation is required the method is very easy to implement nonlinear elastic forced vibration problem is also examined by using smoothed deformation gradients on each cell

denoising for 3 d photon limited imaging data using nonseparable filterbanks in this paper we present a novel frame based denoising algorithm for photon limited 3d images we first construct a new 3d nonseparable filterbank by adding elements to an existing frame in a structurally stable way in contrast with the traditional 3d separable wavelet system the new filterbank is capable of using edge information in multiple directions we then propose a data adaptive hysteresis thresholding algorithm based on this new 3d nonseparable filterbank in addition we develop a new validation strategy for denoising of photon limited images containing sparse structures such as neurons the structure of interest is less than 5 of total volume the validation method based on tubular neighborhoods around the structure is used to determine the optimal threshold of the proposed denoising algorithm we compare our method with other state of the art methods and report very encouraging results on applications utilizing both synthetic and real data

adapting to unknown smoothness via wavelet shrinkage abstract we attempt to recover a function of unknown smoothness from noisy sampled data we introduce a procedure sureshrink that suppresses noise by thresholding the empirical wavelet coefficients the thresholding is adaptive a threshold level is assigned to each dyadic resolution level by the principle of minimizing the stein unbiased estimate of risk sure for threshold estimates the computational effort of the overall procedure is order n log n as a function of the sample size n sureshrink is smoothness adaptive if the unknown function contains jumps then the reconstruction essentially does also if the unknown function has a smooth piece then the reconstruction is essentially as smooth as the mother wavelet will allow the procedure is in a sense optimally smoothness adaptive it is near minimax simultaneously over a whole interval of the besov scale the size of this interval depends on the choice of mother wavelet we know from a previous paper by the authors that traditional smoot

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

quasi newton projection methods and the discrepancy principle in image restoration abstract in this work the problem of the restoration of images corrupted by space invariant blur and noise is considered this problem is ill posed and regularization is required the image restoration problem is formulated as a nonnegatively constrained minimization problem whose objective function depends on the statistical properties of the noise corrupting the observed image the cases of gaussian and poisson noise are both considered a newton like projection method with early stopping of the iterates is proposed as an iterative regularization method in order to determine a nonnegative approximation to the original image a suitable approximation of the hessian of the objective function is proposed for a fast solution of the newton system the results of the numerical experiments show the effectiveness of the method in computing a good solution in few iterations when compared with some methods recently proposed as best performing

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

monte carlo sure a black box optimization of regularization parameters for general denoising algorithms we consider the problem of optimizing the parameters of a given denoising algorithm for restoration of a signal corrupted by white gaussian noise to achieve this we propose to minimize stein s unbiased risk estimate sure which provides a means of assessing the true mean squared error mse purely from the measured data without need for any knowledge about the noise free signal specifically we present a novel monte carlo technique which enables the user to calculate sure for an arbitrary denoising algorithm characterized by some specific parameter setting our method is a black box approach which solely uses the response of the denoising operator to additional input noise and does not ask for any information about its functional form this therefore permits the use of sure for optimization of a wide variety of denoising algorithms we justify our claims by presenting experimental results for sure based optimization of a series of popular image denoising algorithms such as total variation denoising wavelet soft thresholding and wiener filtering smoothing splines in the process we also compare the performance of these methods we demonstrate numerically that sure computed using the new approach accurately predicts the true mse for all the considered algorithms we also show that sure uncovers the optimal values of the parameters in all cases

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

interior point methodology for 3 d pet reconstruction interior point methods have been successfully applied to a wide variety of linear and nonlinear programming applications this paper presents a class of algorithms based on path following interior point methodology for performing regularized maximum likelihood ml reconstructions on three dimensional 3 d emission tomography data the algorithms solve a sequence of subproblems that converge to the regularized maximum likelihood solution from the interior of the feasible region the nonnegative orthant the authors propose two methods a primal method which updates only the primal image variables and a primal dual method which simultaneously updates the primal variables and the lagrange multipliers a parallel implementation permits the interior point methods to scale to very large reconstruction problems termination is based on well defined convergence measures namely the karush kuhn tucker first order necessary conditions for optimality the authors demonstrate the rapid convergence of the path following interior point methods using both data from a small animal scanner and monte carlo simulated data the proposed methods can readily be applied to solve the regularized weighted least squares reconstruction problem

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

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

image denoising by sparse 3 d transform domain collaborative filtering we propose a novel image denoising strategy based on an enhanced sparse representation in transform domain the enhancement of the sparsity is achieved by grouping similar 2d image fragments e g blocks into 3d data arrays which we call groups collaborative altering is a special procedure developed to deal with these 3d groups we realize it using the three successive steps 3d transformation of a group shrinkage of the transform spectrum and inverse 3d transformation the result is a 3d estimate that consists of the jointly filtered grouped image blocks by attenuating the noise the collaborative filtering reveals even the finest details shared by grouped blocks and at the same time it preserves the essential unique features of each individual block the filtered blocks are then returned to their original positions because these blocks are overlapping for each pixel we obtain many different estimates which need to be combined aggregation is a particular averaging procedure which is exploited to take advantage of this redundancy a significant improvement is obtained by a specially developed collaborative wiener filtering an algorithm based on this novel denoising strategy and its efficient implementation are presented in full detail an extension to color image denoising is also developed the experimental results demonstrate that this computationally scalable algorithm achieves state of the art denoising performance in terms of both peak signal to noise ratio and subjective visual quality

wavelets ridgelets and curvelets for poisson noise removal in order to denoise poisson count data we introduce a variance stabilizing transform vst applied on a filtered discrete poisson process yielding a near gaussian process with asymptotic constant variance this new transform which can be deemed as an extension of the anscombe transform to filtered data is simple fast and efficient in very low count situations we combine this vst with the filter banks of wavelets ridgelets and curvelets leading to multiscale vsts ms vsts and nonlinear decomposition schemes by doing so the noise contaminated coefficients of these ms vst modified transforms are asymptotically normally distributed with known variances a classical hypothesis testing framework is adopted to detect the significant coefficients and a sparsity driven iterative scheme reconstructs properly the final estimate a range of examples show the power of this ms vst approach for recovering important structures of various morphologies in very low count images these results also demonstrate that the ms vst approach is competitive relative to many existing denoising methods

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

the notion of composite reliability and its hierarchical bayes estimation abstract in this article we introduce the notion of composite reliability as a measure of the overall reliability of a collection of heterogeneous but similar items we then propose a hierarchical bayes model for estimating the composite reliability of systems whose lifelengths are expressed as binary random variables subsequently we develop an alternative approach for the simultaneous inference about many small but related binomial parameters we propose a two stage prior for addressing problems of this type and use the gibbs sampler algorithm for addressing problems involving small proportions our topic though suggested by an issue pertaining to the safety of nuclear power plants arises in other commonly occurring situations pertaining to consumerism public policy government regulation our development generalizes for situations involving lifelengths that need not be binary

bandwidth selection for indirect density estimation based on corrupted histogram data abstract motivated by a number of practical applications we consider a class of indirect nonparametric density estimation problems in which the observed data consist of a histogram of binned empirically corrected counts due to variability in the process of correction the histogram cannot be modeled in terms of simple scaled poisson statistics this departure necessitates the development of a new methodology for bandwidth selection a variant of the method of unbiased risk estimation is proposed the methodology is studied using numerical simulations and asymptotic analysis tools in the context of a class of idealized density deconvolution problems the methodology is adapted for application to the practical reconstruction problem of positron emission tomography pet realistic numerical simulations and physical phantom data are presented to validate the approach in this setting some illustrations with cerebral glucose utilization and myocardial blood flow studies from some actual patient data sets

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

building robust wavelet estimators for multicomponent images using stein s principle multichannel imaging systems provide several observations of the same scene which are often corrupted by noise in this paper we are interested in multispectral image denoising in the wavelet domain we adopt a multivariate statistical approach in order to exploit the correlations existing between the different spectral components our main contribution is the application of stein s principle to build a new estimator for arbitrary multichannel images embedded in additive gaussian noise simulation tests carried out on optical satellite images show that the proposed method outperforms conventional wavelet shrinkage techniques

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

smooth finite element methods convergence accuracy and properties a stabilized conforming nodal integration finite element method based on strain smoothing stabilization is presented the integration of the stiffness matrix is performed on the boundaries of the finite elements a rigorous variational framework based on the hu washizu assumed strain variational form is developed we prove that solutions yielded by the proposed method are in a space bounded by the standard finite element solution infinite number of subcells and a quasi equilibrium finite element solution a single subcell we show elsewhere the equivalence of the one subcell element with a quasi equilibrium finite element leading to a global a posteriori error estimate we apply the method to compressible and incompressible linear elasticity problems the method can always achieve higher accuracy and convergence rates than the standard finite element method especially in the presence of incompressibility singularities or distorted meshes for a slightly smaller computational cost it is shown numerically that the one cell smoothed four noded quadrilateral finite element has a convergence rate of 2 0 in the energy norm for problems with smooth solutions which is remarkable for problems with rough solutions this element always converges faster than the standard finite element and is free of volumetric locking without any modification of integration scheme copyright 2007 john wiley sons ltd

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

robustness of clevenson zidek type estimators abstract for estimating the means of several independent poisson distributions clevenson and zidek 1975 were the first to propose a class of estimators that are better than the usual one under the normalized squared error loss 1 1 this class of estimators was subsequently enlarged by others this article examines the sensitivity of the superiority of the clevenson zidek cz type means estimators over the usual one with respect to the exactness of the poisson distribution assumption it is shown that many of the cz type means estimators dominate the usual estimator even when the underlying distributions are negative binomial whether they are close to the poisson or not this broadens the scope of use of cz type estimators

bayesian image recovery for dendritic structures under low signal to noise conditions experimental research seeking to quantify neuronal structure constantly contends with restrictions on image resolution and variability in particular experimentalists often need to analyze images with very low signal to noise ratio snr in many experiments dye toxicity scales with the light intensity this leads experimentalists to reduce image snr in order to preserve the viability of the specimen in this paper we present a bayesian approach for estimating the neuronal shape given low snr observations this bayesian framework has two major advantages first the method effectively incorporates known facts about 1 the image formation process including blur and the poisson nature of image noise at low intensities and 2 dendritic shape including the fact that dendrites are simply connected geometric structures with smooth boundaries second we may employ standard markov chain monte carlo techniques for quantifying the posterior uncertainty in our estimate of the dendritic shape we describe an efficient computational implementation of these methods and demonstrate the algorithm s performance on simulated noisy two photon laser scanning microscopy images