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

convergence studies on iterative algorithms for image reconstruction we introduce a general iterative scheme for image reconstruction based on landweber s method in our configuration a sequential block iterative seqbi version can be readily formulated from a simultaneous block iterative simbi version and vice versa this provides a mechanism to derive new algorithms from known ones it is shown that some widely used iterative algorithms such as the algebraic reconstruction technique art simultaneous art sart cimmino s and the recently designed diagonal weighting and component averaging algorithms are special examples of the general scheme we prove convergence of the general scheme under conditions more general than assumed in earlier studies for its seqbi and simbi versions in the consistent and inconsistent cases respectively our results suggest automatic relaxation strategies for the seqbi and simbi versions and characterize the dependence of the limit image on the initial guess it is found that in all cases the limit is the sum of the minimum norm solution of a weighted least squares problem and an oblique projection of the initial image onto the null space of the system matrix

semi quantitative system identification abstract system identification takes a space of possible models and a stream of observational data of a physical system and attempts to identify the element of the model space that best describes the observed system in traditional approaches the model space is specified by a parameterized differential equation and identification selects numerical parameter values so that simulation of the model best matches the observations we present squid a method for system identification in which the space of potential models is defined by a semi quantitative differential equation sqde qualitative and monotonic function constraints as well as numerical intervals and functional envelopes bound the set of possible models the simulator sqsim predicts semi quantitative behavior descriptions from the sqde identification takes place by describing the observation stream in similar semi quantitative terms and intersecting the two descriptions to derive narrower bounds on the model space refinement is done by refuting impossible or implausible subsets of the model space squid therefore has strengths particularly robustness and expressive power for incomplete knowledge that complement the properties of traditional system identification methods we also present detailed examples evaluation and analysis of squid

restricted kernel canonical correlation analysis abstract kernel canonical correlation analysis kcca is a procedure for assessing the relationship between two sets of random variables when the classical method canonical correlation analysis cca fails because of the nonlinearity of the data the kcca method is mostly used in machine learning especially for information retrieval and text mining because the data is often represented with non negative numbers we propose to incorporate the non negativity restriction directly into the kcca method similar restrictions have been studied in relation to the classical cca and called restricted canonical correlation analysis rcca so that we call the proposed method restricted kernel canonical correlation analysis rkcca we also provide some possible approaches for solving the optimization problem to which our method translates the motivation for introducing rkcca is given in section 2

a general axiomatic system for image resolution quantification in this paper we generalize our previously published axiom system for quantification of image resolution and prove that any resolution measure consistent with the new axiom system must be a homogeneous symmetric function of order 1 2 of the eigenvalues of the covariance matrix of the psf we demonstrate that the previous axiom system is not consistent with the affine transformation axiom we propose a weak combination axiom to replace the previous strong combination axiom and use it to solve this conflict it is remarkable that the original finding in one dimension by wang and li can be easily rediscovered with aid of the weak combination axiom instead of using the previous strong combination axiom if the previous axiom system is modified with the weak combination axiom and augmented with the affine transformation axiom the resolution measure is shown to be proportional to the squared root of the geometric mean of the eigenvalues of the covariance matrix of the psf relevant discussions and possible extensions are also provided

kernel methods in machine learning we review machine learning methods employing positive definite kernels these methods formulate learning and estimation problems in a reproducing kernel hilbert space rkhs of functions defined on the data domain expanded in terms of a kernel working in linear spaces of function has the benefit of facilitating the construction and analysis of learning algorithms while at the same time allowing large classes of functions the latter include nonlinear functions as well as functions defined on nonvectorial data we cover a wide range of methods ranging from binary classifiers to sophisticated methods for estimation with structured data

canonical correlations of past inputs and future outputs for linear stochastic systems the dependence of future outputs on past inputs in a stochastic system is investigated by means of the canonical correlation analysis in particular a classification of minimal stochastic realizations of a given process with respect to the information transmitted from past inputs to future outputs is presented the results are then rephrased in terms of certain block hankel matrices and their relevance for the hankel norm approximation of stochastic systems is discussed

tomographic reconstruction of three dimensional volumes using the distorted born iterative method although real imaging problems involve objects that have variations in three dimensions a majority of work examining inverse scattering methods for ultrasonic tomography considers 2 d imaging problems therefore the study of 3 d inverse scattering methods is necessary for future applications of ultrasonic tomography in this work 3 d reconstructions using different arrays of rectangular elements focused on elevation were studied when reconstructing spherical imaging targets by producing a series of 2 d image slices using the 2 d distorted born iterative method dbim the effects of focal number f speed of sound contrast deltac and scatterer size were considered for comparison the 3 d wave equation was also inverted using point like transducers to produce fully 3 d dbim image reconstructions in 2 d slicing blurring in the vertical direction was highly correlated with the transmit receive elevation point spread function of the transducers for low deltac the eventual appearance of overshoot artifacts in the vertical direction were observed with increasing deltac these diffraction related artifacts were less severe for smaller focal number values and larger spherical target sizes when using 3 d dbim the overshoot artifacts were not observed and spatial resolution was improved however results indicate that array configuration in 3 d reconstructions is important for good image reconstruction practical arrays were designed and assessed for image reconstruction using 3 d dbim

nonparametric estimation of a point spread function in multivariate problems the removal of blur from a signal in the presence of noise is readily accomplished if the blur can be described in precise mathematical terms however there is growing interest in problems where the extent of blur is known only approximately for example in terms of a blur function which depends on unknown parameters that must be computed from data more challenging still is the case where no parametric assumptions are made about the blur function there has been a limited amount of work in this setting but it invariably relies on iterative methods sometimes under assumptions that are mathematically convenient but physically unrealistic e g that the operator defined by the blur function has an integrable inverse in this paper we suggest a direct noniterative approach to nonparametric blind restoration of a signal our method is based on a new ridge based method for deconvolution and requires only mild restrictions on the blur function we show that the convergence rate of the method is close to optimal from some viewpoints and demonstrate its practical performance by applying it to real images

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

the jackknife estimate of variance tukey s jackknife estimate of variance for a statistic s x 1 x 2 cdots x n which is a symmetric function of i i d random variables x i is investigated using an anova like decomposition of s it is shown that the jackknife variance estimate tends always to be biased upwards a theorem to this effect being proved for the natural jackknife estimate of operatorname var s x 1 x 2 cdots x n 1 based on x 1 x 2 cdots x n

maximizing bilinear forms subject to linear constraints abstract we present methods for maximizing a bilinear form x t ay x y or its absolute value subject to linear constraints the constraints are either of the form c x d g y h or of the form c x e r d g y e r h where r d and r h represent the column spaces of matrices d and h we also show how to compute the angle between two subspaces of r m subject to these types of linear constraints and how to compute linearly constrained canonical correlations and the corresponding canonical vectors

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

canonical analysis of two euclidean subspaces and its applications abstract we develop a canonical analysis both without constraints and under constraints for subspaces of euclidean space we also look into a canonical analysis of operators we then apply the definitions and some of the results to the field of probability and statistics

deblurring subject to nonnegativity constraints csiszar s i divergence is used as a discrepancy measure for deblurring subject to the constraint that all functions involved are nonnegative an iterative algorithm is proposed for minimizing this measure it is shown that every function in the sequence is nonnegative and the sequence converges monotonically to a global minimum other properties of the algorithm are shown including lower bounds on the improvement in the i divergence at each step of the algorithm and on the difference between the i difference at step k and at the limit point a method for regularizing the solution is proposed

use of canonical analysis in time series model identification summary the second order moment structure of time series models is used to derive a canonical analysis in time series modelling consistency properties of certain canonical correlations and the corresponding eigenvectors are shown based on these properties a canonical correlation approach for tentative order determination in building autoregressivemoving average models is proposed this approach can handle directly nonstationary as well as stationary processes and it also provides consistent estimates of the autoregressive parameters involved the asymptotic distribution of the identification statistic is discussed

blind deblurring of spiral ct images to discriminate fine anatomical features in the inner ear it has been desirable that spiral computed tomography ct may perform beyond their current resolution limits with the aid of digital image processing techniques in this paper we develop a blind deblurring approach to enhance image resolution retrospectively without complete knowledge of the underlying point spread function psf an oblique ct image can be approximated as the convolution of an isotropic gaussian psf and the actual cross section practically the parameter of the psf is often unavailable hence estimation of the parameter for the underlying psf is crucially important for blind image deblurring based on the iterative deblurring theory we formulate an edge to noise ratio enr to characterize the image quality change due to deblurring our blind deblurring algorithm estimates the parameter of the psf by maximizing the enr and deblurs images in the phantom studies the blind deblurring algorithm reduces image blurring by about 24 according to our blurring residual measure also the blind deblurring algorithm works well in patient studies after fully automatic blind deblurring the conspicuity of the submillimeter features of the cochlea is substantially improved

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

robust multidimensional matched subspace classifiers based on weighted least squares we propose and design two classes of robust subspace classifiers for classification of multidimensional signals our classifiers are based on robust m estimators and the least median of squares principle and we show that they may be unified as iterated reweighted oblique subspace classifiers the performance of the proposed classifiers are demonstrated by two examples noncoherent detection of space time frequency shift keying signals and shape classification of partially occluded two dimensional 2 d objects in both cases the proposed robust subspace classifiers outperform the conventional subspace classifiers

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

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

canonical analysis relative to a closed subspace first a maximum coefficient notion between two real closed hilbertian subspaces relative to a third one is given many examples illustrate the study when the third subspace is trivial or not then a relative canonical analysis between two closed subspaces relative to a third one is introduced it leads to relative or partial association measures and allows a notion of relative information between subspaces

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

state space formulae for the factorization of all pass matrix functions abstract we consider the factorization of an all pass matrix function e s using proper stable minimum phase factors stale space formulae for the stable minimum phase factors of e s are derived when they exist as well as state space formulae for the wiener hopf factors this is achieved using the state space characterization of all pass matrix functions given by glover 1984 in conjunction with the results of green and anderson 1987

estimation of the interpolation error variance and an index of linear determinism summary the autoregressive and window estimators of the inverse variance ri 0 say are adopted for estimating the interpolation error variance ri o and an index of linear determinism a of a stationary process x the index a is defined as 1 r o ri 0 where r o denotes the variance of x a measures the proportion of total variance explained by the interpolator when interpolating x say from xs s t some uses of a and ri o are discussed the asymptotic distributions of the estimators are derived the order of consistency of the autoregressive and window estimators of a is different when a 0 than when 0 a 1 the finite sample behaviour of the estimators is examined by means of a simulation study

principal component analysis with external information on both subjects and variables a method for structural analysis of multivariate data is proposed that combines features of regression analysis and principal component analysis in this method the original data are first decomposed into several components according to external information the components are then subjected to principal component analysis to explore structures within the components it is shown that this requires the generalized singular value decomposition of a matrix with certain metric matrices the numerical method based on the qr decomposition is described which simplifies the computation considerably the proposed method includes a number of interesting special cases whose relations to existing methods are discussed examples are given to demonstrate practical uses of the method

blind image restoration by anisotropic regularization this paper presents anisotropic regularization techniques to exploit the piecewise smoothness of the image and the point spread function psf in order to mitigate the severe lack of information encountered in blind restoration of shift invariantly and shift variantly blurred images the new techniques which are derived from anisotropic diffusion adapt both the degree and direction of regularization to the spatial activities and orientations of the image and the psf this matches the piecewise smoothness of the image and the psf which may be characterized by sharp transitions in magnitude and by the anisotropic nature of these transitions for shift variantly blurred images whose underlying psfs may differ from one pixel to another we parameterize the psf and then apply the anisotropic regularization techniques this is demonstrated for linear motion blur and out of focus blur alternating minimization is used to reduce the computational load and algorithmic complexity

a novel sure based criterion for parametric psf estimation we propose an unbiased estimate of a filtered version of the mean squared error the blur sure stein s unbiased risk estimate as a novel criterion for estimating an unknown point spread function psf from the degraded image only the psf is obtained by minimizing this new objective functional over a family of wiener processings based on this estimated blur kernel we then perform nonblind deconvolution using our recently developed algorithm the sure based framework is exemplified with a number of parametric psf involving a scaling factor that controls the blur size a typical example of such parametrization is the gaussian kernel the experimental results demonstrate that minimizing the blur sure yields highly accurate estimates of the psf parameters which also result in a restoration quality that is very similar to the one obtained with the exact psf when plugged into our recent multi wiener sure let deconvolution algorithm the highly competitive results obtained outline the great potential of developing more powerful blind deconvolution algorithms based on sure like estimates

asymptotic efficiency of the sample mean in markov chain monte carlo schemes in many cases a univariate time series derived from a time reversible stationary markov chain has the property that there is a distribution function on 1 1 0 1 such that for all non negative integers l its lth moment is the ith lag autocorrelation of the time series we discuss some consequences of this property effects of the asymptotic efficiency of the sample mean on the efficiency of subsampling a stationary markov chain are discussed the stationarity assumption is then relaxed we show that under certain regularity conditions the sample mean of a strongly asymptotically stationary process is asymptotically efficient in that it has the smallest mean square error asymptotically in a broad class of linear estimators

restricted canonical correlations given two random vectors y 1 and y 2 the first canonical correlation between them is defined as sup correlation y 1 y 2 e rp e rq however in many practical situations e g educational testing problems neural networks some natural restrictions on the coefficients and may arise which should be incorporated in this maximization procedure the maximum correlation subject to such constraints is referred to as the restricted canonical correlation this problem is treated here under the nonnegativity restriction on and the analysis is extended to more general form of inequality constraints and also when the restrictions are present only on some of the coefficients restricted versions of some other related measures are also discussed this includes principal component analysis and different modifications of canonical correlations anomalies with higher order correlation are also described some properties of restricted canonical correlation including its bounds are studied

a fuzziness measure for fuzzy numbers applications abstract extending the ideas of delgado et al 1995 to include the notion of fuzziness we obtain canonical representations of fuzzy numbers in particular we show that any fuzzy number can be represented by either a trapezoidal or a quasitrapezoidal number having the same basic attributes as the original fuzzy number

sound and complete qualitative simulation is impossible state of the art qualitative simulators for instance qsim are known to be sound no trajectory which is the solution of a concrete equation matching the input can be missing from the output a simulator which is seen to be incomplete that is which produces a spurious prediction for a particular input can usually be augmented with an additional filter which eliminates that particular class of spurious behaviors and the question of whether a simulator with purely qualitative input which never predicts spurious behaviors can ever be achieved by adding new filters in this way has remained unanswered until now we prove that such a sound and complete qualitative simulation algorithm does not exist

overcoming ho lder continuity in ill posed continuation problems many ill posed continuation problems in partial differential equations obey a logarithmic convexity inequality and can be stabilized in an appropriate banach space by imposing an a priori bound on

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

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

deconvolution when classifying noisy data involving transformations in the present study we consider the problem of classifying spatial data distorted by a linear transformation or convolution and contaminated by additive random noise in this setting we show that classifier performance can be improved if we carefully invert the data before the classifier is applied however the inverse transformation is not constructed so as to recover the original signal and in fact we show that taking the latter approach is generally inadvisable we introduce a fully data driven procedure based on cross validation and use several classifiers to illustrate numerical properties of our approach theoretical arguments are given in support of our claims our procedure is applied to data generated by light detection and ranging lidar technology where we improve on earlier approaches to classifying aerosols this article has supplementary materials online

parametric blur estimation for blind restoration of natural images linear motion and out of focus this paper presents a new method to estimate the parameters of two types of blurs linear uniform motion approximated by a line characterized by angle and length and out of focus modeled as a uniform disk characterized by its radius for blind restoration of natural images the method is based on the spectrum of the blurred images and is supported on a weak assumption which is valid for the most natural images the power spectrum is approximately isotropic and has a power law decay with the spatial frequency we introduce two modifications to the radon transform which allow the identification of the blur spectrum pattern of the two types of blurs above mentioned the blur parameters are identified by fitting an appropriate function that accounts separately for the natural image spectrum and the blur frequency response the accuracy of the proposed method is validated by simulations and the effectiveness of the proposed method is assessed by testing the algorithm on real natural blurred images and comparing it with state of the art blind deconvolution methods

direct blind deconvolution blind deconvolution seeks to deblur an image without knowing the cause of the blur iterative methods are commonly applied to that problem but the iterative process is slow uncertain and often ill behaved this paper considers a significant but limited class of blurs that can be expressed as convolutions of two dimensional symmetric levy stable probability density functions this class includes and generalizes gaussian and lorentzian distributions for such blurs methods are developed that can detect the point spread function from one dimensional fourier analysis of the blurred image a separate image deblurring technique uses this detected point spread function to deblur the image each of these two steps uses direct noniterative methods and requires interactive tuning of parameters as a result blind deblurring of 512 512 images can be accomplished in minutes of cpu time on current desktop workstations numerous blind experiments on synthetic data show that for a given blurred image several di

canonical correlations associated with symmetric reflexive generalized inverses of the dispersion matrix we consider the relations between two sets of canonical correlations one based on a possibly singular dispersion matrix v and the other on a symmetric reflexive generalized inverse of v special attention is paid to the number of unit canonical correlations in each set we establish series of results characterizing the situations where all canonical correlations in one or both sets are less than one it turns out that in all such situations the canonical correlations in the one set are uniformly comparable to those in the other set

polynomial computations for blind image deconvolution this paper considers the problem of blind image deconvolution bid when the blur arises from a spatially invariant point spread function psf h which implies that a blurred image g is formed by the convolution of h and the exact form f of g since the multiplication of two bivariate polynomials is performed by convolving their coefficient matrices the equivalence of the formation of a blurred image and the product of two bivariate polynomials implies that bid can be performed by considering f g and h to be bivariate polynomials on which polynomial operations are performed these operations allow the psf to be computed which is then deconvolved from the blurred image g thereby obtaining a deblurred image that is a good approximation of the exact image f computational results show that the deblurred image obtained using polynomial computations is better than the deblurred image obtained using other methods for blind image deconvolution

cusp catastrophe model for sudden changes in a person s behavior standard research methods that employ questionnaires surveys and statistics do not provide the complete information necessary to fully account for the factors behind a sudden behavioral change such as that of an employee abruptly resigning from his job for this reason the catastrophe theory and qualitative simulation are used since the strict and rigorous mathematical catastrophe model cannot adapt to vague incomplete and time varying data a qualitative quantitative hybrid cusp model is proposed in this study it integrates qualitative simulation qsim with fuzzy set theory to facilitate the computing process a case study is used to explain and validate the proposed method results indicate that this proposed method can be used to model the person s sudden behavioral change and to explore the trajectory and mechanism of the change

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

canonical analysis of contingency tables with linear constraints a generalized least squares approach is presented for incorporating linear constraints on the standardized row and column scores obtained from a canonical analysis of a contingency table the method is easy to implement and may simplify considerably the interpretation of a data matrix the approach is compared to a restricted maximum likelihood procedure

a general hankel norm approximation scheme for linear recursive filtering let x t and y t be stochastic processes which are weakly stationary and stationarily correlated we consider the problem of finding an approximate recursive low dimensional filter of x t based on the observation of the past of y t using hankel norm techniques several estimation problems have been investigated in the past using these techniques we present here a general framework which includes many of these approaches as special cases we also discuss some new applications the approximate filter so constructed allows for an a priori bound on the estimation error

why triangular membership functions abstract in this note we look at a certain theoretically sound motivation behind the common use of triangular and trapezoidal membership functions the studies are completed within a conceptual framework of fuzzy modelling whose structure comprises of input and output interfaces linked with a single transformation module aimed at processing linguistic information it is shown that under some additional mild assumptions these triangular fuzzy sets comply with a request for a uniformly excited codebook in the case of the input interfaces and a satisfaction of a zero error reconstruction criterion being formulated for the output interface

linear and nonlinear image deblurring a documented study nonlinear image deblurring procedures based on probabilistic considerations are widely believed to outperform conventional linear methods this paper is exclusively concerned with nonsmooth images such as those that occur in biomedical imaging where reconstruction of high frequency detail is of prime interest and where avoidance of a priori smoothness constraints is a major concern the theoretical basis behind each of the following nonlinear procedures is examined the lucy richardson method the maximum likelihood e m algorithm the poisson maximum a posteriori method and the nunez llacer version of the maximum entropy method a linear iterative method vancittert s iteration is also studied it is shown that each of the first three methods as well as vancittert s method lack a necessary ingredient for successful solution of the ill posed deblurring problem while in the maximum entropy method the enforced smoothness may have adverse consequences in medical imaging a direct linear method the slow evolution from the continuation boundary secb method designed specifically for nonsmooth images is also considered that method is stabilized by constraining the blurring operator as well as the solution and does not require smoothness constraints it is shown that useful error estimates can be obtained in the secb method while this is impossible in tikhonov s method without a priori bounds on derivatives of the unknown solution reconstruction experiments on low noise synthetic mri data show that thousands of iterations are necessary to achieve sufficient resolution in the iterative procedures however the secb method provides higher resolution at considerable savings in computer time at high noise levels the iterative algorithms are shown to diverge at these same noise levels the secb method produces reconstructions comparable in quality to those that would be obtained in the iterative methods were one able to terminate the divergent algorithm at that iteration which best approximates the true solution in the l1 norm

canonical correlation analysis with linear constraints abstract we develop canonical correlation analysis by imposing linear constraints upon parameters corresponding to two sets of variables the results of our method which we call canolc are shown in terms of projection operators both orthogonal and oblique further calc correspondence analysis with linear constraints turns out to be a special case of canolc

matrices with special reference to applications in psychometrics multidimensional scaling item response theory and factor analysis may be considered three major contributions of psychometricians to statistics matrix theory played an important role in early developments of these techniques unfortunately nonlinear models are currently very prevalent in these areas still one can identify several areas of psychometrics where matrix algebra plays a prominent role they include analysis of asymmetric square tables multiway data analysis reduced rank regression analysis and multiple set t set canonical correlation analysis among others in this article we review some of the important matrix results in these areas and suggest future studies

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

semi blind image restoration via mumford shah regularization image restoration and segmentation are both classical problems that are known to be difficult and have attracted major research efforts this paper shows that the two problems are tightly coupled and can be successfully solved together mutual support of image restoration and segmentation processes within a joint variational framework is theoretically motivated and validated by successful experimental results the proposed variational method integrates semi blind image deconvolution parametric blur kernel and mumford shah segmentation the functional is formulated using the spl gamma convergence approximation and is iteratively optimized via the alternate minimization method while the major novelty of this work is in the unified treatment of the semi blind restoration and segmentation problems the important special case of known blur is also considered and promising results are obtained

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

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

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

a regularization approach to joint blur identification and image restoration the primary difficulty with blind image restoration or joint blur identification and image restoration is insufficient information this calls for proper incorporation of a priori knowledge about the image and the point spread function psf a well known space adaptive regularization method for image restoration is extended to address this problem this new method effectively utilizes among others the piecewise smoothness of both the image and the psf it attempts to minimize a cost function consisting of a restoration error measure and two regularization terms one for the image and the other for the blur subject to other hard constraints a scale problem inherent to the cost function is identified which if not properly treated may hinder the minimization blind restoration process alternating minimization is proposed to solve this problem so that algorithmic efficiency as well as simplicity is significantly increased two implementations of alternating minimization based on steepest descent and conjugate gradient methods are presented good performance is observed with numerically and photographically blurred images even though no stringent assumptions about the structure of the underlying blur operator is made

some statistical methods for random process data from seismology and neurophysiology examples are presented of statistical techniques for the analysis of random process data and of their uses in the substantive fields of seismology and neurophysiology the problems addressed include frequency estimation for decaying cosinusoids signal estimation association measurement causal connection assessment estimation of speed and direction and structural modeling the techniques employed include complex demodulation nonlinear regression probit analysis deconvolution maximum likelihood singular value decomposition fourier analysis and averaging

relationships among several methods of linearly constrained correspondence analysis this paper shows essential equivalences among several methods of linearly constrained correspondence analysis they include fisher s method of additive scoring hayashi s second type of quantification method ter braak s canonical correspondence analysis nishisato s type of quantification method ter braak s canonical correspondence analysis nishisato s anova of categorical data correspondence analysis of manipulated contingency tables bockenholt and bockenholt s least squares canonical analysis with linear constraints and van der heijden and meijerink s zero average restrictions these methods fall into one of two classes of methods corresponding to two alternative ways of imposing linear constraints the reparametrization method and the null space method a connection between the two is established through khatri s lemma

more on restricted canonical correlations abstract the problem of the first canonical correlation between two random vectors subject to some natural constraints is treated in the paper the problem is usually referred to as restricted canonical correlation a new approach to solving the problem is given by translating it into a generalized eigenvalue problem with an n n real symmetric matrix a and a positive definite matrix b of the same size

a general framework for a class of non linear approximations with applications to image restoration abstract in this paper we establish sufficient conditions for the existence of optimal non linear approximations to a linear subspace generated by a given weakly closed non convex cone of a hilbert space most non linear problems have difficulties to implement good projection based algorithms due to the fact that the subsets where we would like to project the functions do not have the necessary geometric properties to use the classical existence results such as convexity for instance the theoretical results given here overcome some of these difficulties to see this we apply them to a fractional model for image deconvolution in particular we reformulate and prove the convergence of a computational algorithm proposed in a previous paper by some of the authors finally some examples are given

a new family of constrained principal component analysis cpca abstract several decompositions of the orthogonal projector p x x x x x are proposed with a prospect of their use in constrained principal component analysis cpca in cpca the main data matrix x is first decomposed into several additive components by the row side and or column side predictor variables g and h the decomposed components are then subjected to singular value decomposition svd to explore structures within the components unlike the previous proposal the current proposal ensures that the decomposed parts are columnwise orthogonal and stay inside the column space of x mathematical properties of the decompositions and their data analytic implications are investigated extensions to regularized pca are also envisaged considering analogous decompositions of ridge operators

common canonical variates in k independent groups abstract suppose that data are collected from k independent but closely related populations and that a canonical correlation analysis is to be performed within each group in such a situation it may turn out that the transformation to canonical variates is similar across all k groups the common canonical variates model studied in this article assumes that the transformation to canonical variates is actually identical across groups while the canonical correlations may vary we develop some algebra of the common canonical variates model discuss normal theory maximum likelihood estimation and likelihood ratio testing give illustrative examples

on oblique projectors abstract oblique projectors are useful in many contexts especially in the instrumental variable estimation in regression models in econometrics where the disturbance term tends to be correlated with predictor variables this paper addresses two important questions regarding oblique projectors 1 products of two oblique projectors and 2 decompositions of oblique projectors in 1 we investigate what determines the onto and the along spaces of an oblique projector defined as a product of two oblique projectors under a variety of conditions in 2 we examine various decompositions of oblique projectors when both predictor variables and instrumental variables consist of two distinct sets of variables these decompositions are analogous to those of orthogonal projectors

global and exploding solutions for nonlocal quadratic evolution problems nonlinear nonlocal parabolic equations modeling the evolution of density of mutually interacting particles are considered the inertial type nonlinearity is quadratic and nonlocal while the diffusive term also nonlocal is anomalous and fractal i e represented by a fractional power of the laplacian conditions for global in time existence versus finite time blow up are studied self similar solutions are constructed for certain homogeneous initial data

on two expressions of the mle for a special case of the extended growth curve models abstract an algebraic proof is given on the equivalence between two solutions of mles for a special case of the extended growth curve models called the banken model one solution given by verbyla and venables is an iterative solution in the general case but reduces to a non iterative one in the case of the banken model the other solution given by von rosen is a closed form solution specifically targeted at the banken model the proof has turned out to be quite challenging yet intriguing as it touches on many aspects of intricate matrix theory involving projection matrices

jump surface estimation edge detection and image restoration surface estimation is important in many applications when conventional smoothing procedures e g running averages local polynomial kernel smoothing procedures smoothing spline procedures are used for estimating jump surfaces from noisy data jumps are blurred at the same time when noise is removed in recent years new smoothing methodologies have been proposed in the statistical literature for detecting jumps in surfaces and for estimating jump surfaces with jumps preserved we provide a review of these methodologies because a monochrome image can be considered a jump surface of the image intensity function with jumps at the outlines of objects edge detection and image restoration problems in image processing are closely related to the jump surface estimation problem in statistics we also review major methodologies on edge detection and image restoration and discuss connections and differences among these methods and related methods in the statistical literature

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

a fuzzy envelope for hesitant fuzzy linguistic term set and its application to multicriteria decision making decision making is a process common to human beings the uncertainty and fuzziness of problems demand the use of the fuzzy linguistic approach to model qualitative aspects of problems related to decision the recent proposal of hesitant fuzzy linguistic term sets supports the elicitation of comparative linguistic expressions in hesitant situations when experts hesitate among different linguistic terms to provide their assessments the use of linguistic intervals whose results lose their initial fuzzy representation was introduced to facilitate the computing processes in which such expressions are used the aim of this paper is to present a new representation of the hesitant fuzzy linguistic term sets by means of a fuzzy envelope to carry out the computing with words processes this new fuzzy envelope can be directly applied to fuzzy multicriteria decision making models an illustrative example of its application to a supplier selection problem through the use of fuzzy topsis is presented

a dictionary learning approach for poisson image deblurring the restoration of images corrupted by blur and poisson noise is a key issue in medical and biological image processing while most existing methods are based on variational models generally derived from a maximum a posteriori map formulation recently sparse representations of images have shown to be efficient approaches for image recovery following this idea we propose in this paper a model containing three terms a patch based sparse representation prior over a learned dictionary the pixel based total variation regularization term and a data fidelity term capturing the statistics of poisson noise the resulting optimization problem can be solved by an alternating minimization technique combined with variable splitting extensive experimental results suggest that in terms of visual quality peak signal to noise ratio value and the method noise the proposed algorithm outperforms state of the art methods