on global and local convergence of half quadratic algorithms this paper provides original results on the global and local convergence properties of half quadratic hq algorithms resulting from the geman and yang gy and geman and reynolds gr primal dual constructions first we show that the convergence domain of the gy algorithm can be extended with the benefit of an improved convergence rate second we provide a precise comparison of the convergence rates for both algorithms this analysis shows that the gr form does not benefit from a better convergence rate in general moreover the gy iterates often take advantage of a low cost implementation in this case the gy form is usually faster than the gr form from the cpu time viewpoint

modelling and estimation of multicomponent t_ 2 distributions estimation of multiple t2 components within single imaging voxels typically proceeds in one of two ways a nonparametric grid approximation to a continuous distribution is made and a regularized nonnegative least squares algorithm is employed to perform the parameter estimation or a parametric multicomponent model is assumed with a maximum likelihood estimator for the component estimation in this work we present a bayesian algorithm based on the principle of progressive correction for the latter choice of a discrete multicomponent model we demonstrate in application to simulated data and two experimental datasets that our bayesian approach provides robust and accurate estimates of both the t2 model parameters and nonideal flip angles the second contribution of the paper is to present a cramer rao analysis of t2 component width estimators to this end we introduce a parsimonious parametric and continuous model based on a mixture of inverse gamma distributions this analysis supports the notion that t2 spread is difficult if not infeasible to estimate from relaxometry data acquired with a typical clinical paradigm these results justify the use of the discrete distribution model

detection estimation of more uncorrelated gaussian sources than sensors in nonuniform linear antenna arrays part iii detection estimation nonidentifiability for pt ii see ibid vol 51 no 6 p 1492 507 2003 we investigate nonidentifiability conditions for the detection estimation problem with multiple uncorrelated plane waves incident upon a nonuniform sparse linear antenna array specifically we define conditions under which a given hermitian covariance matrix has a nonunique multiple decomposition into an admissible number of dyads weighted by the source powers and a white noise identity matrix our method is based on the proukakis manikas technique of generating ambiguity generator sets agss and allows ambiguous sets of sources associated with a given sparse antenna geometry to be determined

simulation of stopped diffusions in this work we study standard euler updates for simulating stopped diffusions as an immediate application we discuss the computation of first exit times of diffusions from a domain we focus on one dimensional situations and show how the ideas for the simulation of killed diffusions can be adapted to this problem in particular we give a fully implementable algorithm to compute the first exit time from an interval numerically the brownian motion case is treated in detail and extensions to general diffusions are given special emphasis is given to numerical experiments for every ansatz we include numerical experiments confirming the conjectured accuracy of our methods our algorithm is of order one in a weak sense comparisons with other algorithms are shown results that are superior to those obtained with other methods are presented when approximating a first hitting time distribution the results obtained with our algorithm are much better than those achieved with other methods

maximum likelihood estimation of rician distribution parameters the problem of parameter estimation from rician distributed data e g magnitude magnetic resonance images is addressed the properties of conventional estimation methods are discussed and compared to maximum likelihood ml estimation which is known to yield optimal results asymptotically in contrast to previously proposed methods ml estimation is demonstrated to be unbiased for high signal to noise ratio snr and to yield physical relevant results for low snr

on asymptotic normality of limiting density functions with bayesian implications walker 1969 presented a straightforward approach to asymptotic normality of posterior distributions based on independent and identically distributed i i d observations dawid 1970 extended this work by providing a weaker set of conditions to cover some distributions whose ranges depend on the parameters of interest more recently heyde and johnstone 1979 simplified walker s conditions for stochastic processes in this paper we introduce three basic normality conditions for limiting density functions in the bayesian context our approach is data determined and is nonprobabilistic in nature nevertheless the results thus obtained can be easily converted to probabilistic ones when compared with those given by other investigators it is shown that our conditions as a whole have a greater generality and flexibility than those previously assumed either by dawid or heyde and johnstone in particular for the i i d case the commonly assumed wald type uniform boundedness condition for tail behaviours is shown to be unnecessary for asymptotic normality section 3 3 the advantage of our approach is further exemplified by a simple proof of the asymptotic normality of distributions conjugate to the exponential family

resolving manifold ambiguities in direction of arrival estimation for nonuniform linear antenna arrays this paper addresses the problem of ambiguities in direction of arrival doa estimation for nonuniform sparse linear arrays usually doa estimation ambiguities are associated with linear dependence among the points on the antenna array manifold that is the steering vectors degenerate so that each may be expressed as a linear combination of the others most nonuniform array geometries including the so called minimum redundancy arrays admit such manifold ambiguities while the standard subspace algorithms such as music fail to provide unambiguous doa estimates under these conditions we demonstrate that this failure does not necessarily imply that consistent and asymptotically effective doa estimates do not exist we demonstrate that in most cases involving uncorrelated gaussian sources manifold ambiguity does not necessarily imply nonidentifiability most importantly we introduce algorithms designed to resolve manifold ambiguity we also show that for situations where the number of sources exceeds the number of array sensors a new class of locally nonidentifiable scenario exists

investigative study of planar array ambiguities based on hyperhelical parameterization in this paper a novel approach is proposed for the calculation of ambiguous generator sets of directions for planar arrays this approach is based on the concept of hyperhelical curves and their equivalent linear arrays which provide a vehicle for investigating planar array ambiguities by adopting and extending techniques proposed for linear arrays thus ambiguous generator sets of directions of constant azimuth and different elevation are initially calculated and the concept of ambiguous generator lines is introduced then by using cone angle parametrization ambiguities associated with directions of different azimuth and different elevation are investigated

sparse array design for azimuthal direction of arrival estimation we propose a novel approach to the design of array geometries for azimuthal direction of arrival doa estimation the proposed array design is related to that of minimum redundancy arrays but the array sensors are not required to lie on a uniform grid based on the proposed array geometry design we develop a subspace based doa estimation technique which allows to estimate the doas of more sources than sensors using only second order statistics of the received data this doa estimation technique is related to the covariance augmentation technique but in contrast to the latter technique it provides nonambiguous doa estimates for the full 360 azimuth field of view

combining probability distributions from dependent information sources inferences or decisions in the face of uncertainty should be based on all available information thus when probability distributions for an uncertain quantity are obtained from experts models or

bayesian and non bayesian approaches to statistical inference and decision making bayesian and non bayesian approaches to statistical inference and decision making are discussed and compared a pragmatic criterion success in practice as well as logical consistency are emphasized in comparing alternative approaches attention is given to learning models probability concepts prior information axiom systems and selected technical aspects of bayesian and non bayesian approaches

wavelet based rician noise removal for magnetic resonance imaging it is well known that magnetic resonance magnitude image data obey a rician distribution unlike additive gaussian noise rician noise is signal dependent and separating signal from noise is a difficult task rician noise is especially problematic in low signal to noise ratio snr regimes where it not only causes random fluctuations but also introduces a signal dependent bias to the data that reduces image contrast this paper studies wavelet domain filtering methods for rician noise removal we present a novel wavelet domain filter that adapts to variations in both the signal and the noise

a majorize minimize framework for rician and non central chi mr images the statistics of many mr magnitude images are described by the non central chi ncc family of probability distributions which includes the rician distribution as a special case these distributions have complicated negative log likelihoods that are nontrivial to optimize this paper describes a novel majorize minimize framework for ncc data that allows penalized maximum likelihood estimates to be obtained by solving a series of much simpler regularized least squares surrogate problems the proposed framework is general and can be useful in a range of applications we illustrate the potential advantages of the framework with real and simulated data in two contexts 1 mr image denoising and 2 diffusion profile estimation in high angular resolution diffusion mri the proposed approach is shown to yield improved results compared to methods that model the noise statistics inaccurately and faster computation relative to commonly used nonlinear optimization techniques

on unique localization of constrained signals sources conditions for unique localization of radiating sources by passive sensor arrays are presented unlike in previous analyses the case wherein the signals are constrained to certain loci in the complex plane is addressed two types of constraints are considered the first includes the case of constant amplitude signals and the second includes the case of complex exponential signals the conditions specify the maximum number of sources that can be uniquely localized by a general array satisfying some mild geometrical constraints in terms of the number of sensors and the rank of the correlation matrix of the sources this number exceeds substantially the corresponding number for the unconstrained signals case

on unique localization of multiple sources by passive sensor arrays necessary and sufficient conditions are derived for the unique localization of narrowband sources having the same known center frequency by passive sensor arrays the conditions specify the maximum number of sources that can be uniquely localized by a general array that satisfies some mild geometric constraints the conditions are expressed in terms of the number of sensors and the rank of the correlation matrix of the sources two different conditions are presented the first guarantees uniqueness for every batch of sampled data the second which is weaker guarantees uniqueness for almost every batch of sampled data with the exception of a set of batches of measure zero it is shown that a condition that is slightly weaker than the second one is also necessary

on resolving 2m 1 narrow band signals with an m sensor uniform linear array the problem of determining the maximum number of narrowband signals whose parameters can be estimated with a linear array of m equally spaced sensors is examined while this number previously has been taken to be m 1 when the signals are mutually uncorrelated it is shown how to estimate directions and amplitudes for as many as 2m 1 signals this over twofold increase is accomplished by retaining snapshot to snapshot phase information usually lost in algorithms based on spatial correlation matrices the approach uses length 2m real signal vectors rather than the usual m complex vectors it is shown that 2m of these real vectors are linearly independent with probability one and thus in the presence of additive white noise the parameters of 2m 1 signals can be estimated an algorithm for determining directions and amplitudes is presented because of the algorithm s computational complexity its application is limited to small m and low time bandwidth products

positive definite toeplitz completion in doa estimation for nonuniform linear antenna arrays ii partially augmentable arrays this paper considers the problem of direction of arrival doa estimation for multiple uncorrelated plane waves incident on so called fully augmentable sparse linear arrays in situations where a decision is made on the number of existing signal sources m prior to the estimation stage we investigate the conditions under which doa estimation accuracy is effective in the maximum likelihood sense in the case where m is less than the number of antenna sensors m a new approach called music maximum entropy equalization is proposed to improve doa estimation performance in the preasymptotic region of finite sample size n and signal to noise ratio a full sized positive definite p d toeplitz matrix is constructed from the m spl times m direct data covariance matrix and then alternating projections are applied to find a p d toeplitz matrix with m variate signal eigensubspace signal subspace truncations when m spl ges m cramer rao bound analysis suggests that the minimal useful sample size n is rather large even for arbitrarily strong signals it is demonstrated that the well known direct augmentation approach daa cannot approach the accuracy of the corresponding cramer rao bound even asymptotically as n spl rarr spl infin and therefore needs to be improved we present a new estimation method whereby signal subspace truncation of the daa augmented matrix is used for initialization and is followed by a local maximum likelihood optimization routine the accuracy of this method is demonstrated to be asymptotically optimal for the various superior scenarios m spl ges m presented

detection estimation of more uncorrelated gaussian sources than sensors in nonuniform linear antenna arrays ii partially augmentable arrays previous studies dealing with direction of arrival doa estimation for uncorrelated planes waves incident on nonuniform m sensor arrays assumed that the number of signal sources m was known or had already been estimated in the conventional case m m traditional detection techniques such as akaike s information criterion aic and minimum description length mdl that are based on the equality of several smallest eigenvalues in the covariance matrix may be applied although we demonstrate that these results can be misleading for nonuniform arrays in the superior case m spl ges m these standard techniques are not applicable we introduce a new approach to the detection problem for fully augmentable arrays whose set of intersensor differences is complete we show that the well known direct augmentation approach applied to the sample covariance matrix is not a solution by itself since the resulting toeplitz matrix is generally not positive definite for realistic sample volumes we propose a transformation of this augmented matrix into a positive definite toeplitz matrix t sub spl mu with the proper number of equal minimum eigenvalues that are appropriate for the candidate number of sources spl mu comparison of the results of these best fit transformations over the permissible range of candidates then allows us to select the most likely number of sources m spl circ using traditional criteria and yields uniquely defined doas simulation results demonstrate the high performance of this method since detection techniques for superior scenarios have not been previously described in the literature we compare our method with the standard aic and mdl techniques in a conventional case with similar cramer rao bound crb and find that it has a similar detection performance

convex half quadratic criteria and interacting auxiliary variables for image restoration this paper deals with convex half quadratic criteria and associated minimization algorithms for the purpose of image restoration it brings a number of original elements within a unified mathematical presentation based on convex duality firstly the geman and yang 1995 and geman and reynolds 1992 constructions are revisited with a view to establishing the convexity properties of the resulting half quadratic augmented criteria when the original nonquadratic criterion is already convex secondly a family of convex gibbsian energies that incorporate interacting auxiliary variables is revealed as a potentially fruitful extension of the geman and reynolds construction

regression to the mean for nonnormal populations summary regression to the mean is the term used to describe the effect by which individuals selected on the basis of an initial measurement which is particularly high or low compared with other members of the population have upon remeasurement values nearer to the population mean for the normal distribution simple expressions for estimates of the magnitude of this effect are available many biological variables however are not normally distributed estimates for regression to the mean for nonnormal data are given based on edgeworth series and saddlepoint approximations

an expanded theoretical treatment of iteration dependent majorize minimize algorithms the majorize minimize mm optimization technique has received considerable attention in signal and image processing applications as well as in statistics literature at each iteration of an mm algorithm one constructs a tangent majorant function that majorizes the given cost function and is equal to it at the current iterate the next iterate is obtained by minimizing this tangent majorant function resulting in a sequence of iterates that reduces the cost function monotonically a well known special case of mm methods are expectation maximization algorithms in this paper we expand on previous analyses of mm due to fessler and hero that allowed the tangent majorants to be constructed in iteration dependent ways also this paper overcomes an error in one of those earlier analyses there are three main aspects in which our analysis builds upon previous work first our treatment relaxes many assumptions related to the structure of the cost function feasible set and tangent majorants for example the cost function can be nonconvex and the feasible set for the problem can be any convex set second we propose convergence conditions based on upper curvature bounds that can be easier to verify than more standard continuity conditions furthermore these conditions allow for considerable design freedom in the iteration dependent behavior of the algorithm finally we give an original characterization of the local region of convergence of mm algorithms based on connected e g convex tangent majorants for such algorithms cost function minimizers will locally attract the iterates over larger neighborhoods than typically is guaranteed with other methods this expanded treatment widens the scope of the mm algorithm designs that can be considered for signal and image processing applications allows us to verify the convergent behavior of previously published algorithms and gives a fuller understanding overall of how these algorithms behave

a note on the levenberg marquardt parameter abstract in c ma l jiang some research on levenberg marquardt method for the nonlinear equations appl math comput 184 2007 1032 1040 the lm parameter at the kth iteration is chosen as k f k 2 1 j k t f k 2 where f is the residual function j is the jacobi of f and 0 1 is a constant in this note we point out that the lm parameter can be any combination of f k 2 and j k t f k 2 provided it is positive furthermore we give a more general choice of the lm parameter and show that the lm method still preserves the quadratic convergence under the local error condition which is weaker than nonsingularity

multiple level nested array an efficient geometry for 2q th order cumulant based array processing recently direction of arrival estimation doa algorithms based on arbitrary even order 2q cumulants of the received data have been proposed giving rise to new doa estimation algorithms namely the 2q music algorithm in particular it has been shown that the 2q music algorithm can identify o nq statistically independent non gaussian sources however in this paper it is demonstrated that the processing power of the 2qth order cumulant based methods can potentially be even larger it will be shown that the 2qth order cumulant matrix of the data is directly related to the concept of a 2qth order difference co array which can potentially have o n2q virtual sensors leading to identification of o n2q statistically independent non gaussian sources using 2q th order cumulants however the number of actually realizable virtual elements in the 2q th order difference co array depends on the geometry of the physical array in order to ensure that the co array indeed has the desired degrees of freedom a new generic class of linear one dimensional nonuniform arrays namely the 2qth order nested array is proposed whose 2q th order difference co array is proved to contain a uniform linear array with o n2q sensors in order to exploit these increased degrees of freedom of the co array a new algorithm for doa estimation is also developed which acts on the same 2q th order cumulant matrix as the earlier methods and can yet identify o n2q sources it is proved that the proposed method can identify the maximum number of sources among all methods that use 2q th order cumulants

fractional bayes factors for model comparison bayesian comparison of models is achieved simply by calculation of posterior probabilities of the models themselves however there are difficulties with this approach when prior information about the parameters of the various models is weak partial bayes factors offer a resoiution of the problem by setting aside part of the data as a training sampie the training sampie is used to obtain an initiai informative posterior distribution of the parameters in each model model comparison is then based on a bayes factor calculated from the remaining data properties of partial bayes factors are discussed particularly in the context of weak prior information and they are found to have advantages over other proposed methods of model comparison a new variant of the partial bayes factor the fractional bayes factor is advocated on grounds of consistency simplicity robustness and coherence

multi exponential transverse relaxation times estimation from magnetic resonance images under rician noise and spatial regularization relaxation signal inside each voxel of magnetic resonance images mri is commonly fitted by a multi exponential decay curve the estimation of a discrete multi component relaxation model parameters from magnitude mri data is a challenging nonlinear inverse problem since it should be conducted on the entire image voxels under non gaussian noise statistics this paper proposes an efficient algorithm allowing the joint estimation of relaxation time values and their amplitudes using different criteria taking into account a rician noise model combined with a spatial regularization accounting for low spatial variability of relaxation time constants and amplitudes between neighboring voxels the rician noise hypothesis is accounted for either by an adapted nonlinear least squares algorithm applied to a corrected least squares criterion or by a majorization minimization approach applied to the maximum likelihood criterion in order to solve the resulting large scale non negativity constrained optimization problem with a reduced numerical complexity and computing time an optimization algorithm based on a majorization approach ensuring separability of variables between voxels is proposed the minimization is carried out iteratively using an adapted levenberg marquardt algorithm that ensures convergence by imposing a sufficient decrease of the objective function and the non negativity of the parameters the importance of the regularization alongside the rician noise incorporation is shown both visually and numerically on a simulated phantom and on magnitude mri images acquired on fruit samples

doa estimation for noninteger linear antenna arrays with more uncorrelated sources than sensors we investigate direction of arrival doa estimation involving nonuniform linear arrays where the sensor positions may be noninteger values expressed in half wavelength units with some number of uncorrelated gaussian sources that is greater than or equal to the number of sensors we introduce an approach whereby the noninteger co array is treated as the most appropriate virtual array when considering an augmented covariance matrix since such virtual arrays have an incomplete set of covariance lags we discuss various completion philosophies to fill in the missing elements of the associated partially specified hermitian covariance matrix this process is followed by the application of an algorithm that searches for a specific number of plane wavefronts yielding the minimum fitting error for the specified covariance lags in the neighborhood of the completion initialized doa estimates in this way we are able to resolve possible ambiguity and to achieve asymptotically optimal estimation accuracy numerical simulations of doa estimation demonstrate a close proximity to the cramer rao bound

modeling and estimation of ambiguities in linear arrays the problem of ambiguities inherent in the manifold of any linear array structure is investigated ambiguities which can be classified into trivial and nontrivial depending on the ease of their identification arise when an array cannot distinguish between two different sets of directional sources initially the new concept of an ambiguous generator set is introduced it represents generates an infinite number of ambiguous sets of directions then by uniformly nonuniformly partitioning the array manifold curve of a linear array different ambiguous generator sets ran be calculated and as a direct result a sufficient condition for the presence of ambiguities is obtained the theoretical aspects of the investigation are followed by the proposal of an innovative approach that calculates not only all such ambiguities existing in a linear array of arbitrary geometry but the rank of ambiguity in each case as well the main results presented in the paper are supported by a number of representative examples

temporal and spatial sampling influence on the estimates of superimposed narrowband signals when less can mean more this paper addresses the influence that the sampling locations have on the estimated frequencies of superimposed sinusoids this problem has application in harmonic time series analysis or direction finding phased array systems generalized mathematical bounds are developed in terms that are independent of the array locations and have an intuitively appealing physical interpretation they establish the influence of the sampling locations on the variance of the frequency estimate and the limit at which two sources can be resolved using signal subspace estimators for the resolution criteria an expression dominated by the fourth central moment of the sensor locations expresses the resolving ability of the sensing array irrespective of the array aperture or number of sensors increasing the fourth central moment increases an array s resolution ability the commonly accepted notion that resolution necessarily depends on the array aperture is misleading and indeed that fewer snapshots from a reduced aperture array can outperform a larger array of more elements for the estimator variance criteria it is found that the product of the number of sensors and the second central moment array variance characterizes the estimator variance lower bound the metrics developed demonstrate that the sampling topology is itself an important factor in determining the performance of the sampling system and not the covariance lags sampled or the aperture spanned simulations are used to describe the results

invariant bayesian inference in regression models that is robust against the jeffreys lindley s paradox we obtain the prior and posterior probability of a nested regression model as the hausdorff integral of the prior and posterior on the parameters of an encompassing linear regression model over a lower dimensional set that represents the nested model the hausdorff integral is invariant and therefore avoids the borel kolmogorov paradox basing priors and prior probabilities of nested regression models on the prior on the parameters of an encompassing linear regression model reduces the discrepancies between classical and bayesian inference like the jeffreys lindley s paradox we illustrate the analysis with examples of linear restrictions i e a linear regression model and non linear restrictions i e a cointegration and an autoregressive moving average model on the parameters of an encompassing linear regression model

performance study of conditional and unconditional direction of arrival estimation a numerical and analytical study of conditional and unconditional direction of arrival doa estimation is presented explicit expressions for the unconditional cramer rao bounds on the doa estimation accuracy and the covariance matrix of the conditional maximum likelihood method are given it is shown that many doa estimation methods have the same asymptotic statistical properties under conditional and unconditional models the situation of two narrowband plane signals impinging on a uniformly spaced linear array is discussed

some new tests of the power law process the power law process plp is often used to model failure data from repairable systems and its adequacy is tested with goodness of fit tests such as the cramer von mises test no single test however can be sensitive to all possible deviations from the plp exact tests that are powerful against some departures from the plp of particular interest to practitioners are derived heuristically the computation of their p values is described and their use is illustrated with examples one test is a modified version of the laplace test for trend another a modification of greenwood s test for clustering it is shown that these tests can be derived as score tests which ensures that they are powerful for large samples

bayesian estimation and prediction using asymmetric loss functions abstract estimators and predictors that are optimal relative to varian s asymmetric linex loss function are derived for a number of well known models their risk functions and bayes risks are derived and compared with those of usual estimators and predictors it is shown that some usual estimators for example a scalar sample mean or a scalar least squares regression coefficient estimator are inadmissible relative to asymmetric linex loss by providing alternative estimators that dominate them uniformly in terms of risk

information geometric measure for neural spikes this study introduces information geometric measures to analyze neural firing patterns by taking not only the second order but also higher order interactions among neurons into account information geometry provides useful tools and concepts for this purpose including the orthogonality of coordinate parameters and the pythagoras relation in the kullback leibler divergence based on this orthogonality we show a novel method for analyzing spike firing patterns by decomposing the interactions of neurons of various orders as a result purely pairwise triple wise and higher order interactions are singled out we also demonstrate the benefits of our proposal by using several examples

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

information theoretic active polygons for unsupervised texture segmentation curve evolution models used in image segmentation and based on image region information usually utilize simple statistics such as means and variances hence can not account for higher order nature of the textural characteristics of image regions in addition the object delineation by active contour methods results in a contour representation which still requires a substantial amount of data to be stored for subsequent multimedia applications such as visual information retrieval from databases polygonal approximations of the extracted continuous curves are required to reduce the amount of data since polygons are powerful approximators of shapes for use in later recognition stages such as shape matching and coding the key contribution of this paper is the development of a new active contour model which nicely ties the desirable polygonal representation of an object directly to the image segmentation process this model can robustly capture texture boundaries by way of higher order statistics of the data and using an information theoretic measure and with its nature of the ordinary differential equations this new variational texture segmentation model is unsupervised since no prior knowledge on the textural properties of image regions is used another contribution in this sequel is a new polygon regularizer algorithm which uses electrostatics principles this is a global regularizer and is more consistent than a local polygon regularization in preserving local features such as corners