parameter estimation of delay dynamical system from a scalar time series under external noise we introduce an adaptive learning rules for estimating all unknown parameters of delay dynamical system using a scalar time series sufficient condition for synchronization is derived using krasovskii lyapunov theory this scheme is highly applicable in secure communication since multiple messages can be transmitted through multiple parameter modulations one of the advantage of this method is that parameter estimation is also possible even when only one time series of the transmitter is available we present numerical examples for mackey glass system with periodic delay time which are used to illustrate the validity of this scheme the corresponding numerical results and the effect of external noise are also studied

trans dimensional geoacoustic inversion this paper develops a general trans dimensional bayesian methodology for geoacoustic inversion trans dimensional inverse problems are a generalization of fixed dimensional inversion that includes the number and type of model parameters as unknowns in the problem by extending the inversion state space to multiple subspaces of different dimensions the posterior probability density quantifies the state of knowledge regarding inversion parameters including effects due to limited knowledge about appropriate parametrization of the environment and error processes the inversion is implemented here using a reversible jump markov chain monte carlo algorithm and the seabed is parametrized using a partition model unknown data errors are addressed by including a data error model jumps between dimensions are implemented with a birth death methodology that allows transitions between dimensions by adding or removing interfaces while maintaining detailed balance in the markov chain trans dimensional inversion results in an inherently parsimonious solution while partition modeling provides a naturally self regularizing algorithm based on data information content not on subjective regularization functions together this results in environmental estimates that quantify appropriate seabed structure as supported by the data allowing sharp discontinuities while approximating smooth transitions where needed this approach applies generally to geoacoustic inversion and is illustrated here with seabed reflection coefficient data

uncertain population forecasting abstract errors in population forecasts arise from errors in the jump off population and errors in the predictions of future vital rates the propagation of these errors through the linear leslie growth model is studied and prediction intervals for future population are developed for u s national forecasts the prediction intervals are compared with the u s census bureau s high low intervals to assess the accuracy of the predictions of future vital rates we derive the predictions from a parametric statistical model and estimate the extent of model misspecification and errors in parameter estimates subjective expert opinion so important in real forecasting is incorporated with the technique of mixed estimation a robust regression model is used to assess the effects of model misspecification

efficient navigation of parameter landscapes optimization techniques can have difficulty navigating long valleys that are oriented obliquely to the parameter axes efficiency may be improved by rotating coordinates so that the most prominent valleys are optimally aligned with the parameter axes the rotated axes are parallel to the eigenvectors of the covariance matrix of the gradient of the cost function which may be estimated efficiently by monte carlo integration the information in the covariance matrix may also be used to obtain an improved parametrization which corresponds to the rotated coordinates associated with the largest eigenvalues the approach is illustrated for the inverse problem of estimating ocean bottom parameters from acoustic data using simulated annealing for multifrequency inverse problems the resolution for each frequency is optimized

regularized iterative image restoration with ringing reduction linear space invariant image restoration algorithms often introduce ringing effects near sharp intensity transitions it is shown that these artifacts are attributable to the regularization of the ill posed image restoration problem two possible methods to reduce the ringing effects in restored images are proposed the first method incorporates deterministic a priori knowledge about the original image into the restoration algorithm the second method locally regulates the severity of the noise magnification and the ringing phenomenon depending on the edge information in the image a regularized iterative image restoration algorithm is proposed in which both ringing reduction methods are included by making use of the theory of the projections onto convex sets and the concept of norms in a weighted hilbert space both the numerical performance and the visual evaluation of the results are improved by the use of ringing reduction

restoration of blurred color images with impulse noise restoration of images degraded by blurring and impulse noise has received considerable attention recently guo et al 2009 proposed a fast l 1 total variation algorithm for grayscale image restoration with impulse noise in this paper we extend their idea for deblurring color images with impulse noise an alternating iteration scheme is adopted for solving the corresponding problem more importantly we employ the five point property to analyze the convergence of the proposed alternating algorithm numerical experiments demonstrate that the proposed method could deblur color images with good quality

markov chain monte carlo methods for high dimensional inversion in remote sensing summary we discuss the inversion of the gas profiles ozone no3 no2 aerosols and neutral density in the upper atmosphere from the spectral occultation measurements the data are produced by the global ozone monitoring of occultation of stars instrument on board the envisat satellite that was launched in march 2002 the instrument measures the attenuation of light spectra at various horizontal paths from about 100 km down to 10 20 km the new feature is that these data allow the inversion of the gas concentration height profiles a short introduction is given to the present operational data management procedure with examples of the first real data inversion several solution options for a more comprehensive statistical inversion are presented a direct inversion leads to a non linear model with hundreds of parameters to be estimated the problem is solved with an adaptive single step markov chain monte carlo algorithm another approach is to divide the problem into several non linear smaller dimensional problems to run parallel adaptive markov chain monte carlo chains for them and to solve the gas profiles in repetitive linear steps the effect of grid size is discussed and we present how the prior regularization takes the grid size into account in a way that effectively leads to a grid independent inversion

adaptive approximation method for joint parameter estimation and identical synchronization of chaotic systems we introduce a numerical approximation method for estimating an unknown parameter of a primary chaotic system which is partially observed through a scalar time series specifically we show that the recursive minimization of a suitably designed cost function that involves the dynamic state of a fully observed secondary system and the observed time series can lead to the identical synchronization of the two systems and the accurate estimation of the unknown parameter the salient feature of the proposed technique is that the only external input to the secondary system is the unknown parameter which needs to be adjusted we present numerical examples for the lorenz system which show how our algorithm can be considerably faster than some previously proposed methods

comments on least squares restoration of multichannel images for original article see galatsanos et al ieee trans signal processing vol 39 p 2222 36 oct 1991 in this correspondence we give the correct matrix formulation arising from the constrained optimization of the least squares restoration of multichannel images in galatsanos et al

markov chain monte carlo method in bayesian reconstruction of dynamical systems from noisy chaotic time series the presence of a noise component in the time series generated by a dynamical system ds results in finite accuracy of reconstruction of the evolution operator eo any model that can be constructed will generally speaking differ from the original system one of the ways to take this fact into consideration is to describe parameters of the model eo as random quantities 1 two limiting cases may be distinguished 2 the perfect model scenario when the form of the operator describing the ds evolution is reliably known and the imperfect model scenario when eo is unknown the perfect model scenario is realized for instance when the problem of hidden information transmission is solved using chaotic time series ts generated by the known ds 3 in this case we are interested in the characteristics of the system perfect model parameters the most probable value mean dispersion distribution in investigations of many natural atmospheric oceanic tectonic biological systems the eo is unknown which corresponds to the imperfect model scenario then information about model parameters is of no value as the physical meaning of the parameters is unknown and we are interested in the properties of the model defined by these parameters and reflecting the properties of the reconstructed ds nevertheless in this case too evaluation of statistical characteristics of model parameters is the key element without which the problem of reconstructing a ds generating the original ts cannot be solved the mathematical body used to reconstruct the ds is determined by a specific application for example for finding the most probable set of model perfect or imperfect parameters it suffices to determine the maximum of posterior probability density of model parameters 4 6 however it should be remembered that in the presence of noise the inverse problem of reconstruction becomes ill posed i e it admits an infinite set of solutions selection of the most correct solutions demands regularization that is a physically justified constraint on admissible values of parameters based solely on a priori information 7 this approach is usually called bayesian within the bayesian approach there are methods which make it possible to estimate dispersions and mathematical expectations of the model parameters 8 a significant advantage of such methods is their relatively low computational resource requirements however due to the model nonlinearity the form of parameter distribution may differ strongly from the normal one in this case estimation of expectation and dispersion is insufficient to construct a correct model and one must use the bayesian approach in full in other words we must construct models which include distributions of parameters and take a priori information about the system into account correctly in this formulation the problem can be solved using the markov chain monte carlo mcmc algorithms 9 however in the case of reconstruction of dss by noisy chaotic time series computational resources required for these algorithms strongly depend on distribution dimensionality this limits applicability of the algorithms to a narrow class of problems e g the case of short ts 10 the method proposed in this paper makes it possible to expand the applicability domain of the mcmc algorithms to the case of arbitrarily long ts

optimal design of multichannel equalizers for the structural similarity index the optimization of multichannel equalizers is studied for the structural similarity ssim criteria the closed form formula is provided for the optimal equalizer when the mean of the source is zero the formula shows that the equalizer with maximal ssim index is equal to the one with minimal mean square error mse multiplied by a positive real number which is shown to be equal to the inverse of the achieved ssim index the relation of the maximal ssim index to the minimal mse is also established for given blurring filters and fixed length equalizers an algorithm is also presented to compute the suboptimal equalizer for the general sources various numerical examples are given to demonstrate the effectiveness of the results

parameter estimation through ignorance dynamical modeling lies at the heart of our understanding of physical systems its role in science is deeper than mere operational forecasting in that it allows us to evaluate the adequacy of the mathematical structure of our models despite the importance of model parameters there is no general method of parameter estimation outside linear systems a relatively simple method of parameter estimation for nonlinear systems is introduced based on variations in the accuracy of probability forecasts it is illustrated on the logistic map the henon map and the 12 dimensional lorenz96 flow and its ability to outperform linear least squares in these systems is explored at various noise levels and sampling rates as expected it is more effective when the forecast error distributions are non gaussian the method selects parameter values by minimizing a proper local skill score for continuous probability forecasts as a function of the parameter values this approach is easier to implement in practice than alternative nonlinear methods based on the geometry of attractors or the ability of the model to shadow the observations direct measures of inadequacy in the model the implied ignorance and the information deficit are introduced

image sequence filtering in quantum limited noise with applications to low dose fluoroscopy clinical angiography requires hundreds of x ray images putting the patients and particularly the medical staff at risk dosage reduction involves an inevitable sacrifice in image quality in this work the latter problem is addressed by first modeling the signal dependent poisson distributed noise that arises as a result of this dosage reduction the commonly utilized noise model for single images is shown to be obtainable from the new model stochastic temporal filtering techniques are proposed to enhance clinical fluoroscopy sequences corrupted by quantum mottle the temporal versions of these filters as developed here are more suitable for filtering image sequences as correlations along the time axis can be utilized for these dynamic sequences the problem of displacement field estimation is treated in conjunction with the filtering stage to ensure that the temporal correlations are taken along the direction of motion to prevent object blur

a generalized matrix krylov subspace method for tv regularization abstract this paper presents efficient algorithms to solve both tv l1 and tv l2 models of images contaminated by blur and noise the unconstrained structure of the problems suggests that one can solve a constrained optimization problem by transforming the original unconstrained minimization problem to an equivalent constrained minimization one an augmented lagrangian method is developed to handle the constraints when the model is given with matrix variables and an alternating direction method adm is used to iteratively find solutions of the subproblems the solutions of some subproblems are belonging to subspaces generated by application of successive orthogonal projections onto a class of generalized matrix krylov subspaces of increasing dimension we give some theoretical results and report some numerical experiments to show the effectiveness of the proposed algorithms

fuzzy prediction of chaotic time series based on singular value decomposition for dynamic systems with complex ill conditioned or nonlinear characteristics the modeling method based on fuzzy sets is very effective to describe the properties of the systems in this paper a fuzzy modeling method based on singular value decomposition svd is proposed first a fuzzy clustering method is used to confirm the input space of fuzzy model then the recursive least square algorithm with singular value decomposition is applied to estimate the consequent parameters of fuzzy model in order to avoid error delivery and error accumulation furthermore the parameters of fuzzy model are also optimized by the presented algorithm to demonstrate the performance of this modeling method simulations on mackey glass time series and lorenz chaotic system are performed the results show that this method provides effective and accurate prediction

asymptotically optimal blind estimation of multichannel images optimal estimation of a two dimensional 2 d multichannel signal ideally decorrelates the data in both channel and space and weights the resulting coefficients according to their snr many scenarios exist where the required second order signal and noise statistics are not known in which the decorrelation is difficult or expensive to calculate an asymptotically optimal estimation scheme proposed here uses a 2 d discrete wavelet transform to approximately decorrelate the signal in space and the discrete fourier transform to decorrelate between channels the coefficient weighting is replaced with a wavelet domain thresholding operation to result in an efficient estimation scheme for both stationary and nonstationary signals in contrast to optimal estimation this new scheme does not require second order signal statistics making it well suited to many applications in addition to providing vastly improved visual quality the new estimator typically yields signal to noise ratio gains 12 db or higher for hyperspectral imagery and functional magnetic resonance images

scalable posterior approximations for large scale bayesian inverse problems via likelihood informed parameter and state reduction two major bottlenecks to the solution of large scale bayesian inverse problems are the scaling of posterior sampling algorithms to high dimensional parameter spaces and the computational cost of forward model evaluations yet incomplete or noisy data the state variation and parameter dependence of the forward model and correlations in the prior collectively provide useful structure that can be exploited for dimension reduction in this setting both in the parameter space of the inverse problem and in the state space of the forward model to this end we show how to jointly construct low dimensional subspaces of the parameter space and the state space in order to accelerate the bayesian solution of the inverse problem as a byproduct of state dimension reduction we also show how to identify low dimensional subspaces of the data in problems with high dimensional observations these subspaces enable approximation of the posterior as a product of two factors i a projection of the posterior onto a low dimensional parameter subspace wherein the original likelihood is replaced by an approximation involving a reduced model and ii the marginal prior distribution on the high dimensional complement of the parameter subspace we present and compare several strategies for constructing these subspaces using only a limited number of forward and adjoint model simulations the resulting posterior approximations can rapidly be characterized using standard sampling techniques e g markov chain monte carlo two numerical examples demonstrate the accuracy and efficiency of our approach inversion of an integral equation in atmospheric remote sensing where the data dimension is very high and the inference of a heterogeneous transmissivity field in a groundwater system which involves a partial differential equation forward model with high dimensional state and parameters

stochastic population forecasts for the united states beyond high medium and low abstract conventional population projections use high medium and low scenarios to indicate uncertainty but probability interpretations are rarely given and in any event the resulting ranges for vital rates births deaths age groups sizes age ratios and population size cannot possibly be probabilistically consistent with one another this article presents and implements a new method for making stochastic population forecasts that provide consistent probability intervals we blend mathematical demography and statistical time series methods to estimate stochastic models of fertility and mortality based on u s data back to 1900 and then use the theory of random matrix products to forecast various demographic measures and their associated probability intervals to the year 2065 our expected total population sizes agree quite closely with the census medium projections and our 95 percent probability intervals are close to the census high and low scenarios but census intervals in 2065 for ages 65

ocean acoustic inversion with estimation of a posteriori probability distributions inversion methods are applied in ocean acoustics to infer parameters which characterize the environment the objective of this paper is to provide such estimates and means of evaluating the inherent uncertainty of the parameter estimates in a bayesian approach the result of inversion is the a posteriori probability density for the estimated parameters from which all information such as mean higher moments and marginal distributions can be extracted these are multidimensional integrals of the a posteriori probability density which are complicated to evaluate for many parameters various sampling options are examined and it is suggested that importance sampling based on a directed monte carlo method such as genetic algorithms is the preferred method the formulation of likelihood functions and maximum likelihood objective functions for multifrequency data on a vertical array is discussed a priori information about the parameters may be used in the formulation shallow water acoustic data obtain

inferential framework for nonstationary dynamics i theory a general bayesian framework is introduced for the inference of time varying parameters in nonstationary nonlinear stochastic dynamical systems its convergence is discussed the performance of the method is analyzed in the context of detecting signaling in a system of neurons modeled as fitzhugh nagumo fhn oscillators it is assumed that only fast action potentials for each oscillator mixed by an unknown measurement matrix can be detected it is shown that the proposed approach is able to reconstruct unmeasured hidden variables of the fhn oscillators to determine the model parameters to detect stepwise changes of control parameters for each oscillator and to follow continuous evolution of the control parameters in the adiabatic limit

matched field inversion of broadband data using the freeze bath method this paper presents a statistical freeze bath method for geoacoustic inversion that emphasizes the search for a distribution of models that fit the data well contrary to simulated annealing optimization the freeze bath samples the multidimensional model parameter space at constant freeze probability corresponding to fixed temperatures for each parameter the sampling process uses a heat bath algorithm as a boltzmann sampling tool to carry out a global search over the model parameter space the conventional heat bath algorithm is modified to sample on a fuzzy grid in order to access the entire range of parameter values the inversion provides a set of good models that indicates how well the model parameters are constrained by the data and reveals the degree of correlation between parameters the efficiency of the search process is improved by reparameterizing the original model parameters to a new set based on the eigenvectors of the model covariance matrix the inversion performance of the freeze bath

an efficient tvl1 algorithm for deblurring multichannel images corrupted by impulsive noise we extend the alternating minimization algorithm recently proposed in y wang j yang w yin and y zhang siam j imag sci 1 2008 pp 248 272 j yang w yin y zhang and y wang siam j imag sci 2 2009 pp 569 592 to the case of recovering blurry multichannel color images corrupted by impulsive rather than gaussian noise the algorithm minimizes the sum of a multichannel extension of total variation and a data fidelity term measured in the ell 1 norm and is applicable to both salt and pepper and random valued impulsive noise we derive the algorithm by applying the well known quadratic penalty function technique and prove attractive convergence properties including finite convergence for some variables and q linear convergence rate under periodic boundary conditions the main computational requirements of the algorithm are fast fourier transforms and a low complexity gaussian elimination procedure numerical results on images with different blurs and impulsive noise are presented to demonstrate the efficiency of the algorithm in addition it is numerically compared to the least absolute deviation method h y fu m k ng m nikolova and j l barlow siam j sci comput 27 2006 pp 1881 1902 and the two phase method j f cai r chan and m nikolova aims j inverse problems and imaging 2 2008 pp 187 204 for recovering grayscale images we also present results of recovering multichannel images

properties of a simple bilinear stochastic model estimation and predictability we analyze the properties of arguably the simplest bilinear stochastic multiplicative process proposed as a model of financial returns and of other complex systems combining both nonlinearity and multiplicative noise by construction it has no linear predictability zero two point correlation but a certain nonlinear predictability non zero three point correlation it can thus be considered as a paradigm for testing the existence of a possible nonlinear predictability in a given time series we present a rather exhaustive study of the process including its ability to produce fat tailed distributions from gaussian innovations the unstable characteristics of the inversion of the key nonlinear parameters and of the two initial conditions necessary for the implementation of a prediction scheme and an analysis of the associated super exponential sensitivity of the inversion of the innovations in the presence of a large impulse our study emphasizes the conditions under which a degree of predictability can be achieved and describe a number of different attempts which overall illuminates the properties of the process in conclusion notwithstanding its remarkable simplicity the bilinear stochastic process exhibits remarkably rich and complex behavior which makes it a serious candidate for the modeling of financial time series among others

inversion of acoustic data using a combination of genetic algorithms and the gauss newton approach an inversion procedure for obtaining speeds attenuation densities and thicknesses for a layered medium is described the inversion is carried out using the least squares technique and the forward modeling is based on safari the optimization is a hybrid method combining the global genetic algorithms and the local gauss newton method this is done by taking several gradient steps between each update of the object function for each individual in the population the gradients for the gauss newton method are computed analytically this makes the computation faster and more stable than computing the gradients by numerical differentiation the combination of a global and a local method makes the hybrid method faster and it gets closer to the global minimum than a pure global method examples based on both real and synthetic data in wave number frequency and range frequency domains show that the method works well

efficient total variation minimization methods for color image restoration in this paper we consider and study a total variation minimization model for color image restoration in the proposed model we use the color total variation minimization scheme to denoise the deblurred color image an alternating minimization algorithm is employed to solve the proposed total variation minimization problem we show the convergence of the alternating minimization algorithm and demonstrate that the algorithm is very efficient our experimental results show that the quality of restored color images by the proposed method are competitive with the other tested methods

regularization of inverse visual problems involving discontinuities inverse problems such as the reconstruction problems that arise in early vision tend to be mathematically ill posed through regularization they may be reformulated as well posed variational principles whose solutions are computable standard regularization theory employs quadratic stabilizing functionals that impose global smoothness constraints on possible solutions discontinuities present serious difficulties to standard regularization however since their reconstruction requires a precise spatial control over the smoothing properties of stabilizers this paper proposes a general class of controlled continuity stabilizers which provide the necessary control over smoothness these nonquadratic stabilizing functionals comprise multiple generalized spline kernels combined with noncontinuous continuity control functions in the context of computational vision they may be thought of as controlled continuity constraints these generic constraints are applicable to visual reconstruction problems that involve both continuous regions and discontinuities for which global smoothness constraints fail

optimal sampling schemes for the gaussian hypothesis testing problem a class of sampling designs for a continuous time gaussian hypothesis testing problem is discussed this problem arises frequently in systems where it is necessary to sample the continuous time signal to produce discrete time data for computer processing a class of periodic nonuniform sampling designs which optimizes performance under an asymptotic probability of error criterion is investigated a design algorithm for the optimal sampler is presented

better nonlinear models from noisy data attractors with maximum likelihood a new approach to nonlinear modelling is presented which by incorporating the global behaviour of the model lifts shortcomings of both least squares and total least squares parameter estimates although ubiquitous in practice a least squares approach is fundamentally flawed in that it assumes independent normally distributed ind forecast errors nonlinear models will not yield ind errors even if the noise is ind a new cost function is obtained via the maximum likelihood principle superior results are illustrated both for small data sets and infinitely long data streams

on a recursive method for the estimation of unknown parameters of partially observed chaotic systems we investigate a recently proposed method for on line parameter estimation and synchronization in chaotic systems this novel technique has been shown effective to estimate a single unknown parameter of a primary chaotic system with known functional form that is only partially observed through a scalar time series it works by periodically updating the parameter of interest in a secondary system with the same functional form as the primary one but no explicit coupling between their dynamic variables in order to minimize a suitably defined cost function in this paper we review the basics of the method and investigate its robustness and new extensions in particular we study the performance of the novel technique in the presence of noise either observational i e an additive contamination of the observed time series or dynamical i e a random perturbation of the system dynamics and when there is a mismatch between the primary and secondary systems numerical results including comparisons with other techniques are presented finally we investigate the extension of the original method to perform the estimation of two unknown parameters and illustrate its effectiveness by means of computer simulations

a fast parallel algorithm for blind estimation of noise variance a blind noise variance algorithm that recovers the variance of noise in two steps is proposed the sample variances are computed for square cells tessellating the noise image several tessellations are applied with the size of the cells increasing fourfold for consecutive tessellations the four smallest sample variance values are retained for each tessellation and combined through an outlier analysis into one estimate the different tessellations thus yield a variance estimate sequence the value of the noise variance is determined from this variance estimate sequence the blind noise variance algorithm is applied to 500 noisy 256 256 images in 98 of the cases the relative estimation error was less than 0 2 with an average error of 0 06 application of the algorithm to differently sized images is also discussed

statistical methods of parameter estimation for deterministically chaotic time series we discuss the possibility of applying some standard statistical methods the least square method the maximum likelihood method and the method of statistical moments for estimation of parameters to deterministically chaotic low dimensional dynamic system the logistic map containing an observational noise a segmentation fitting maximum likelihood ml method is suggested to estimate the structural parameter of the logistic map along with the initial value x 1 considered as an additional unknown parameter the segmentation fitting method called piece wise ml is similar in spirit but simpler and has smaller bias than the multiple shooting previously proposed comparisons with different previously proposed techniques on simulated numerical examples give favorable results at least for the investigated combinations of sample size n and noise level besides unlike some suggested techniques our method does not require the a priori knowledge of the noise variance we also clarify the nature of the inherent difficulties in the statistical analysis of deterministically chaotic time series and the status of previously proposed bayesian approaches we note the trade off between the need of using a large number of data points in the ml analysis to decrease the bias to guarantee consistency of the estimation and the unstable nature of dynamical trajectories with exponentially fast loss of memory of the initial condition the method of statistical moments for the estimation of the parameter of the logistic map is discussed this method seems to be the unique method whose consistency for deterministically chaotic time series is proved so far theoretically not only numerically

exact image deconvolution from multiple fir blurs we address the problem of restoring an image from its noisy convolutions with two or more blur functions channels deconvolution from multiple blurs is in general better conditioned than from a single blur and can be performed without regularization for moderate noise levels we characterize the problem of missing data at the image boundaries and show that perfect reconstruction is impossible even in the no noise case almost surely unless there are at least three channels conversely when there are at least three channels we show that perfect reconstruction is not only possible almost surely in the absence of noise but also that it can be accomplished by finite impulse response fir filtering such fir reconstruction is vastly more efficient computationally than the least squares solution and is suitable for low noise levels even in the high noise case the estimates obtained by fir filtering provide useful starting points for iterative least squares algorithms we present results on the minimum possible sizes of such deconvolver filters we derive expressions for the mean square errors in the fir reconstructions and show that performance comparable to that of the least squares reconstruction may be obtained with relatively small deconvolver filters finally we demonstrate the fir reconstruction on synthetic and real data

quantifying uncertainty in geoacoustic inversion ii application to broadband shallow water data this paper applies the new method of fast gibbs sampling fgs to estimate the uncertainties of seabed geoacoustic parameters in a broadband shallow water acoustic survey with the goal of interpreting the survey results and validating the method for experimental data fgs applies a bayesian approach to geoacoustic inversion based on sampling the posterior probability density to estimate marginal probability distributions and parameter covariances this requires knowledge of the statistical distribution of the data errors including both measurement and theory errors which is generally not available invoking the simplifying assumption of independent identically distributed gaussian errors allows a maximum likelihood estimate of the data variance and leads to a practical inversion algorithm however it is necessary to validate these assumptions i e to verify that the parameter uncertainties obtained represent meaningful estimates to this end fgs is applied to a geoacoustic experiment carried out at a site off the west coast of italy where previous acoustic and geophysical studies have been performed the parameter uncertainties estimated via fgs are validated by comparison with i the variability in the results of inverting multiple independent data sets collected during the experiment ii the results of fgs inversion of synthetic test cases designed to simulate the experiment and data errors and iii the available geophysical ground truth comparisons are carried out for a number of different source bandwidths ranges and levels of prior information and indicate that fgs provides reliable and stable uncertainty estimates for the geoacoustic inverse problem

low rank separated representation surrogates of high dimensional stochastic functions application in bayesian inference this study introduces a non intrusive approach in the context of low rank separated representation to construct a surrogate of high dimensional stochastic functions e g pdes odes in order to decrease the computational cost of markov chain monte carlo simulations in bayesian inference the surrogate model is constructed via a regularized alternative least square regression with tikhonov regularization using a roughening matrix computing the gradient of the solution in conjunction with a perturbation based error indicator to detect optimal model complexities the model approximates a vector of a continuous solution at discrete values of a physical variable the required number of random realizations to achieve a successful approximation linearly depends on the function dimensionality the computational cost of the model construction is quadratic in the number of random inputs which potentially tackles the curse of dimensionality in high dimensional stochastic functions furthermore this vector valued separated representation based model in comparison to the available scalar valued case leads to a significant reduction in the cost of approximation by an order of magnitude equal to the vector size the performance of the method is studied through its application to three numerical examples including a 41 dimensional elliptic pde and a 21 dimensional cavity flow

a new look to multichannel blind image deconvolution the aim of this paper is to propose a new look to mbid examine some known approaches and provide a new mc method for restoring blurred and noisy images first the direct image restoration problem is briefly revisited then a new method based on inverse filtering for perfect image restoration in the noiseless case is proposed the noisy case is addressed by introducing a regularization term into the objective function in order to avoid noise amplification second the filter identification problem is considered in the mc context a new robust solution to the degradation matrix filter is then derived and used in conjunction with a total variation approach to restore the original image simulation results and performance evaluations using recent image quality metrics are provided to assess the effectiveness of the proposed methods

modeling and forecasting u s mortality abstract time series methods are used to make long run forecasts with confidence intervals of age specific mortality in the united states from 1990 to 2065 first the logs of the age specific death rates are modeled as a linear function of an unobserved period specific intensity index with parameters depending on age this model is fit to the matrix of u s death rates 1933 to 1987 using the singular value decomposition svd method it accounts for almost all the variance over time in age specific death rates as a group whereas e 0 has risen at a decreasing rate over the century and has decreasing variability k t declines at a roughly constant rate and has roughly constant variability facilitating forecasting k t which indexes the intensity of mortality is next modeled as a time series specifically a random walk with drift and forecast the method performs very well on within sample forecasts and the forecasts are insensitive to reductions in the length of the base period from 90 to 30

seeker optimization algorithm for parameter estimation of time delay chaotic systems time delay chaotic systems have some very interesting properties and their parameter estimation has received increasing interest in the recent years it is well known that parameter estimation of a chaotic system is a nonlinear multivariable and multimodal optimization problem for which global optimization techniques are required in order to avoid local minima in this work a seeker optimization algorithm soa based method is proposed to address this issue in the soa search direction is based on the empirical gradients by evaluating the response to the position changes and step length is based on uncertainty reasoning by using a simple fuzzy rule the performance of the algorithm is evaluated on two typical test systems moreover two state of the art algorithms i e particle swarm optimization and differential evolution are also considered for comparison the simulation results show that the proposed algorithm is better than or at least as good as the other two algorithms and can effectively solve the parameter estimation problem of time delay chaotic systems

least squares restoration of multichannel images multichannel restoration using both within and between channel deterministic information is considered a multichannel image is a set of image planes that exhibit cross plane similarity existing optimal restoration filters for single plane images yield suboptimal results when applied to multichannel images since between channel information is not utilized multichannel least squares restoration filters are developed using the set theoretic and the constrained optimization approaches a geometric interpretation of the estimates of both filters is given color images three channel imagery with red green and blue components are considered constraints that capture the within and between channel properties of color images are developed issues associated with the computation of the two estimates are addressed a spatially adaptive multichannel least squares filter that utilizes local within and between channel image properties is proposed experiments using color images are described

multichannel restoration of single channel images using a wavelet based subband decomposition we present a new matrix vector formulation of a wavelet based subband decomposition this formulation allows for the decomposition of both the convolution operator and the signal in the subband domain with this approach any single channel linear space invariant filtering problem can be cast into a multichannel framework we apply this decomposition to the linear space invariant image restoration problem and propose a family of multichannel linear minimum mean square error lmmse restoration filters these filters explicitly incorporate both within and between subband channel relations of the decomposed image since only within channel stationarity is assumed in the image model this approach presents a new method for modeling the nonstationarity of images experimental results are presented which test the proposed multichannel lmmse filters these experiments show that if accurate estimates of the subband statistics are available the proposed multichannel filters provide major improvements over the traditional single channel filters

evaluation of nonlinearity and validity of nonlinear modeling for complex time series even if an original time series exhibits nonlinearity it is not always effective to approximate the time series by a nonlinear model because such nonlinear models have high complexity from the viewpoint of information criteria therefore we propose two measures to evaluate both the nonlinearity of a time series and validity of nonlinear modeling applied to it by nonlinear predictability and information criteria through numerical simulations we confirm that the proposed measures effectively detect the nonlinearity of an observed time series and evaluate the validity of the nonlinear model the measures are also robust against observational noises we also analyze some real time series the difference of the number of chickenpox and measles patients the number of sunspots five japanese vowels and the chaotic laser we can confirm that the nonlinear model is effective for the japanese vowel a the difference of the number of measles patients and the chaotic laser

inversion of seismoacoustic data using genetic algorithms and a posteriori probability distributions the goal of many underwater acoustic modeling problems is to find the physical parameters of the environment with the increase in computer power and the development of advanced numerical models it is now feasible to carry out multiparameter inversion the inversion is posed as an optimization problem which is solved by a directed monte carlo search using genetic algorithms the genetic algorithm presented in this paper is formulated by steady state reproduction without duplicates for the selection of parents the object function is scaled according to a boltzmann distribution with a temperature equal to the fitness of one of the members in the population the inversion would be incomplete if not followed by an analysis of the uncertainties of the result when using genetic algorithms the response from many environmental parameter sets has to be computed in order to estimate the solution the many samples of the models are used to estimate the a posteriori probabilities of the model parameters t

simultaneous recursive displacement estimation and restoration of noisy blurred image sequences we develop a recursive model based maximum a posteriori map estimator that simultaneously estimates the displacement vector field dvf and the intensity field from a noisy blurred image sequence current motion compensated spatio temporal noise filters treat the estimation of the dvf as a preprocessing step generally no attempt is made to verify the accuracy of these estimates prior to their use in the filter by simultaneously estimating these two fields we establish a link between the two estimators it is through this link that the dvf estimate and its corresponding accuracy information are shared with the other intensity estimator and vice versa to model the dvf and the intensity field we use coupled gauss markov cgm models a cgm model consists of two levels an upper level which is made up of several submodels with various characteristics and a lower level or line field which governs the transitions between the submodels the cgm models are well suited for estimating the displacement and intensity fields since the resulting estimates preserve the boundaries between the stationary areas present in both fields detailed line fields are proposed for the modeling of these boundaries which also take into account the correlations that exist between these two fields a kalman type estimator results followed by a decision criterion for choosing the appropriate set of line fields several experiments using noisy and noisy blurred image sequences demonstrate the superior performance of the proposed algorithm with respect to prediction error and mean square error

failure of maximum likelihood methods for chaotic dynamical systems the maximum likelihood method is a basic statistical technique for estimating parameters and variables and is the starting point for many more sophisticated methods like bayesian methods this paper shows that maximum likelihood fails to identify the true trajectory of a chaotic dynamical system because there are trajectories that appear to be far more infinitely more likely than truth this failure occurs for unbounded noise and for bounded noise when it is sufficiently large and will almost certainly have consequences for parameter estimation in such systems the reason for the failure is rather simple in chaotic dynamical systems there can be trajectories that are consistently closer to the observations than the true trajectory being observed and hence their likelihood dominates truth the residuals of these truth dominating trajectories are not consistent with the noise distribution they would typically have too small standard deviation and many outliers and hence the situation may be remedied by using methods that examine the distribution of residuals and are not entirely maximum likelihood based

evaluation of decay times in coupled spaces reliability analysis of bayeisan decay time estimation this paper discusses quantitative tools to evaluate the reliability of decay time estimates and inter relationships between multiple decay times for estimates made within a bayesian framework previous works xiang and goggans j acoust soc am 110 1415 1424 2001 113 2685 2697 2003 have applied bayesian framework to cope with the demanding tasks in estimating multiple decay times from schroeder decay functions measured in acoustically coupled spaces a parametric model of schroeder decay function xiang j acoust soc am 98 2112 2121 1995 has been used for the bayesian model based analysis the relevance of this work is that architectural acousticians need to know how well determined are the estimated decay times calculated within bayesian framework using schroeder decay function data this paper will first address the estimation of global variance of the residual errors between the schroeder function data and its model moreover this paper discusses how the landscape shape of the posterior probability density function over the decay parameter space influences the individual decay time estimates their associated variances and their inter relationships this paper uses experimental results from measured room impulse responses in real halls to describe a model based sampling method for an efficient estimation of decay times and their individual variances these parameters along with decay times are relevant decay parameters for evaluation and understanding of acoustically coupled spaces

a general framework for frequency domain multi channel signal processing the authors provide a general framework for performing processing of stationary multichannel mc signals that is linear shift invariant within channel and shift varying across channels emphasis is given to the restoration of degraded signals it is shown that by utilizing the special structure of semiblock circulant and block diagonal matrices mc signal processing can be easily carried out in the frequency domain the generalization of many frequency domain single channel sc signal processing techniques to the mc case is presented it is shown that in mc signal processing each frequency component of a signal and system is presented respectively by a small vector and a matrix of size equal to the number of channels while in sc signal processing each frequency component in both cases is a scalar

markov chain monte carlo estimation of nonlinear dynamics from time series abstract much of nonlinear time series analysis is concerned with inferring unmeasured quantities e g system parameters the shape of attractors in state space from a noisy measured time series from a bayesian perspective the time series is a vector sample picked at random from a probability density the density reflects the system dynamics and our subjective uncertainty about system parameters the measurement function dynamical noise and measurement noise the conditional probability density of the system parameters given the measured data is the basis of a bayesian estimate of the system parameters using illustrative chaotic systems with large amplitude dynamical and measurement noise we show here that it is feasible to use the markov chain monte carlo mcmc technique to generate the bayesian conditional probabilities the resulting parameter estimates are markedly superior to those based on conventional least squares methods the mcmc based estimates are unbiased and allow estimates of dynamical parameters on unmeasured components of the state vector in addition the mcmc method enables de noised attractors to be reconstructed not just in an embedding based on lags of measured variables but in the state space that includes unmeasured components of the dynamics state vector the general purpose mcmc technique effectively combines techniques of nonlinear noise reduction and nonlinear parameter estimation

error models for official mortality forecasts abstract the office of the actuary u s social security administration produces alternative forecasts of mortality to reflect uncertainty about the future appropriate probabilistic interpretations of the intervals have not been provided however because explicit stochastic models are not used in this article we identify the components and assumptions of the official forecasts and approximate them by stochastic parametric models we estimate parameters of the models from past data derive statistical intervals for the forecasts and compare them with the official high low intervals we use the models to evaluate the forecasts rather than to develop different predictions of the future analysis of data from 1972 to 1985 shows that the official intervals for mortality forecasts for males or females aged 45 70 have approximately a 95 chance of including the true mortality rate in any year for other ages the chances are much less than 95 the office of the actuary s interval estimates of age and cause

generalized multichannel image filtering structures recent works in multispectral image processing advocate the employment of vector approaches for this class of signals vector processing operators that involve the minimization of a suitable error criterion have been proposed and shown appropriate for this task in this framework two main classes of vector processing filters have been reported in the literature astola et al 1990 introduce the well known class of vector median filters vmf which are derived as maximum likelihood ml estimates from exponential distributions trahanias et al see ibid vol 2 no 4 p 528 34 1993 and vol 5 no 6 p 868 80 1996 study the processing of color image data using directional information considering the class of vector directional filters vdf we introduce a new filter structure the directional distance filters ddf which combine both vdf and vmf in a novel way we show that ddf are robust signal estimators under various noise distributions they have the property of chromaticity preservation and finally compare favorably to other multichannel image processing filters

stochastic modeling and estimation of multispectral image data multispectral images consist of multiple channels each containing data acquired from a different band within the frequency spectrum since most objects emit or reflect energy over a large spectral bandwidth there usually exists a significant correlation between channels due to often harsh imaging environments the acquired data may be degraded by both blur and noise simply applying a monochromatic restoration algorithm to each frequency band ignores the cross channel correlation present within a multispectral image a gibbs prior is proposed for multispectral data modeled as a markov random field containing both spatial and spectral cliques spatial components of the model use a nonlinear operator to preserve discontinuities within each frequency band while spectral components incorporate nonstationary cross channel correlations the multispectral model is used in a bayesian algorithm for the restoration of color images in which the resulting nonlinear estimates are shown to be quantitatively and visually superior to linear estimates generated by multichannel wiener and least squares restoration

consistent nonlinear dynamics identifying model inadequacy empirical modelling often aims for the simplest model consistent with the data a new technique is presented which quantifies the consistency of the model dynamics as a function of location in state space as is well known traditional statistics of nonlinear models like root mean square rms forecast error can prove misleading testing consistency is shown to overcome some of the deficiencies of rms error both within the perfect model scenario and when applied to data from several physical systems using previously published models in particular testing for consistent nonlinear dynamics provides insight towards i identifying when a delay reconstruction fails to be an embedding ii allowing state dependent model selection and iii optimising local neighbourhood size it also provides a more relevant state dependent threshold for identifying false nearest neighbours

nonlinear dynamical system identification with dynamic noise and observational noise in this paper we consider the problem of whether a nonlinear system has dynamic noise and then estimate the level of dynamic noise to add to any model we build the method we propose relies on a nonlinear model and an improved least squares method recently proposed on the assumption that observational noise is not large we do not need any a priori knowledge for systems to be considered and we can apply the method to both maps and flows we demonstrate with applications to artificial and experimental data the results indicate that applying the proposed method can detect presence or absence of dynamic noise from scalar time series and give a reliable level of dynamic noise to add to the model built in some cases

convergence of adaptive and interacting markov chain monte carlo algorithms adaptive and interacting markov chain monte carlo algorithms mcmc have been recently introduced in the literature these novel simulation algorithms are designed to increase the simulation efficiency to sample complex distributions motivated by some recently introduced algorithms such as the adaptive metropolis algorithm and the interacting tempering algorithm we develop a general methodological and theoretical framework to establish both the convergence of the marginal distribution and a strong law of large numbers this framework weakens the conditions introduced in the pioneering paper by roberts and rosenthal j appl probab 44 2007 458 475 it also covers the case when the target distribution is sampled by using markov transition kernels with a stationary distribution that differs from

blind identification of multichannel fir blurs and perfect image restoration despite its practical importance in image processing and computer vision blind blur identification and blind image restoration have so far been addressed under restrictive assumptions such as all pole stationary image models blurred by zero or minimum phase point spread functions relying upon diversity availability of a sufficient number of multiple blurred images we develop blind fir blur identification and order determination schemes apart from a minimal persistence of the excitation condition also present with nonblind setups the inaccessible input image is allowed to be deterministic or random and of unknown color of distribution with the blurs satisfying a certain co primeness condition in addition we establish existence and uniqueness results which guarantee that single input multiple output fir blurred images can be restored blindly though perfectly in the absence of noise using linear fir filters results of simulations employing the blind order determination blind blur identification and blind image restoration algorithms are presented when the snr is high direct image restoration is found to yield better results than indirect image restoration which employs the estimated blurs in low snr indirect image restoration performs well while the direct restoration results vary with the delay but improve with larger equalizer orders

proximal admm for multi channel image reconstruction in spectral x ray ct the development of spectral x ray computed tomography ct using binned photon counting detectors has received great attention in recent years and has enabled selective imaging of contrast agents loaded with k edge materials a practical issue in implementing this technique is the mitigation of the high noise levels often present in material decomposed sinogram data in this work the spectral x ray ct reconstruction problem is formulated within a multi channel mc framework in which statistical correlations between the decomposed material sinograms can be exploited to improve image quality specifically a mc penalized weighted least squares pwls estimator is formulated in which the data fidelity term is weighted by the mc covariance matrix and sparsity promoting penalties are employed this allows the use of any number of basis materials and is therefore applicable to photon counting systems and k edge imaging to overcome numerical challenges associated with use of the full covariance matrix as a data fidelity weight a proximal variant of the alternating direction method of multipliers is employed to minimize the mc pwls objective function computer simulation and experimental phantom studies are conducted to quantitatively evaluate the proposed reconstruction method

validation of statistical estimation of transmission loss in the presence of geoacoustic inversion uncertainty often the ocean acoustic environment is not well known and sonar performance prediction will be affected by this uncertainty here a method for estimating transmission loss tl is proposed which incorporates these environmental uncertainties specifically we derive an approach for the statistical estimation of tl based on the posterior probability density of environmental parameters obtained from the geoacoustic inversion process first a markov chain monte carlo procedure is employed in the inversion process to sample the posterior probability density of the geoacoustic parameters then these sampled parameters are mapped to the transmission loss domain where a full multidimensional probability distribution of tl as a function of range and depth is obtained in addition tl is also characterized by its summary statistics including the median percentiles and correlation coefficients the approach is illustrated using a data set obtained from the asiaex 2001 east china sea experiment based on the geoacoustic inversion results the predicted tl and its variability are estimated and then compared with the measured tl in general there is a good agreement with the percentage of observed number of data points inside the credibility interval

directional processing of color images theory and experimental results the processing of color image data using directional information is studied the class of vector directional filters vdf which was introduced by the authors in a previous work is further considered the analogy of vdf to the spherical median is shown and their relation to the spatial median is examined moreover their statistical and deterministic properties are studied which demonstrate their appropriateness in image processing vdf result in optimal estimates of the image vectors in the directional sense this is very important in the case of color images where the vectors direction signifies the chromaticity of a given color issues regarding the practical implementation of vdf are also considered in addition efficient filtering schemes based on vdf are proposed which include adaptive and or double window structures experimental and comparative results in image filtering show very good performance measures when the error is measured in the l a b space l a b is known as a space where equal color differences result in equal distances and therefore it is very close to the human perception of colors moreover an indication of the chromaticity error is obtained by measuring the error on the maxwell triangle the results demonstrate that vdf are very accurate chromaticity estimators

regularization parameter estimation for non negative hyperspectral image deconvolution this paper aims at studying a method to automatically estimate the regularization parameters of non negative hyperspectral image deconvolution methods the deconvolution problem is formulated as a multi objective optimization problem and the properties of the corresponding response surface are studied based on these properties the minimum distance criterion mdc and the maximum curvature criterion mcc are proposed to estimate regularization parameters especially for the non negativity constrained deconvolution problem mdc has good theoretical properties convexity and uniqueness but requires to choose a reference point on the contrary mcc does not need to choose any reference point but does not have interesting theoretical properties a grid search based approach to minimize the computational cost of mdc and mcc is proposed it results in fast approaches to estimate the regularization parameters based on simulated 2d images the proposed approaches are compared with the state of the art methods confirming the effectiveness of the mdc and mcc for the non negativity constrained image deconvolution problem in the case of non negative hyperpsectral image deconvolution the fast mdc yields better performances than the fast mcc an application to real world hyperspectral fluorescence microscopy images is also provided it confirms the superiority of mdc

structured total least squares for color image restoration the problem of 3 x 3 color mixing image restoration is considered the blurring matrices as well as the observed image are contaminated by noise therefore the total least squares tls method is employed to restore the original image since the blurring matrices are also structured we apply the structured total least squares stls method j b rosen h park and j glick siam j matrix anal appl 17 1996 pp 110 126 the blurring matrices are generally ill conditioned thus tikhonov s regularization is used to stabilize the solution since neumann boundary conditions are used in the restoration process the discrete cosine transform dct based preconditioner is effective for the linear systems encountered in our stls algorithm

bayesian multichannel image restoration using compound gauss markov random fields we develop a multichannel image restoration algorithm using compound gauss markov random fields cgmrf models the line process in the cgmrf allows the channels to share important information regarding the objects present in the scene in order to estimate the underlying multichannel image two new iterative algorithms are presented and their convergence is established they can be considered as extensions of the classical simulated annealing and iterative conditional methods experimental results with color images demonstrate the effectiveness of the proposed approaches

comparisons of laboratory scale measurements of three dimensional acoustic propagation with solutions by a parabolic equation model in this paper laboratory scale measurements of long range across slope acoustic propagation in a three dimensional 3 d wedge like environment are compared to numerical solutions in a previous work it was shown that the experimental data contain strong 3 d effects like mode shadow zones and multiple mode arrivals in qualitative agreement with theoretical and numerical predictions in the present work the experimental data are compared with numerical solutions obtained using a fully 3 d parabolic equation based model a subspace inversion approach is used for the refinement of some of the parameters describing the model experiment the inversion procedure is implemented in a bayesian framework based on the exhaustive search over the parameter space the comparisons are performed both in the time and in the frequency domain using the maximum a posteriori estimates of the refined parameters as input in the 3 d model a very good quantitative agreement is achieved between the numerical predictions provided by the 3 d parabolic equation model and the experimental data

fast spatio temporal image reconstruction for dynamic pet in tomographic imaging dynamic images are typically obtained by reconstructing the frames of a time sequence independently one by one a disadvantage of this frame by frame reconstruction approach is that it fails to account for temporal correlations in the signal ideally one should treat the entire image sequence as a single spatio temporal signal however the resulting reconstruction task becomes computationally intensive fortunately as the authors show in this paper the spatio temporal reconstruction problem call be greatly simplified by first applying a temporal karhunen loeve kl transformation to the imaging equation the authors show that if the regularization operator is chosen to be separable into space and time components penalized weighted least squares reconstruction of the entire image sequence is approximately equivalent to frame by frame reconstruction in the space kl domain by this approach spatio temporal reconstruction can be achieved at reasonable computational cost one can achieve further computational savings by discarding high order kl components to avoid reconstructing them performance of the method is demonstrated through statistical evaluations of the bias variance tradeoff obtained by computer simulation reconstruction

choice of dynamical variables for global reconstruction of model equations from time series the success of modeling from an experimental time series is determined to a significant extent by the choice of dynamical variables we propose a method for preliminary investigation of a time series whose purpose is to find out whether a global dynamical model with smooth functions can be constructed for the chosen variables the method consists in the estimation of single valuedness and continuity of relations between dynamical variables and variables to enter left hand sides of model equations the method is explained with numerical examples its efficiency is demonstrated by modeling a real nonlinear electric circuit

simultaneous multichannel image restoration and estimation of the regularization parameters in this correspondence a constrained least squares multichannel image restoration approach is proposed in which no prior knowledge of the noise variance at each channel or the degree of smoothness of the original image is required the regularization functional for each channel is determined by incorporating both within channel and cross channel information it is shown that the proposed smoothing functional has a global minimizer

the effect of source amplitude and phase in matched field source localization traditional matched field processing is typically employed for localization of a source with unknown amplitude and phase at transmission the spectral information of the source is estimated via maximum likelihood and is used for localization with the bartlett processor maximum a posteriori estimation of the spectrum of the source is here proposed along with the estimation of source location and noise variance where the joint posterior probability distribution of all parameters is computed with gibbs sampling it is shown that the proposed method has a higher probability of correct localization than the traditional approach

quantifying uncertainty in geoacoustic inversion i a fast gibbs sampler approach this paper develops a new approach to estimating seabed geoacoustic properties and their uncertainties based on a bayesian formulation of matched field inversion in bayesian inversion the solution is characterized by its posterior probability density ppd which combines prior information about the model with information from an observed data set to interpret the multi dimensional ppd requires calculation of its moments such as the mean covariance and marginal distributions which provide parameter estimates and uncertainties computation of these moments involves estimating multi dimensional integrals of the ppd which is typically carried out using a sampling procedure important goals for an effective bayesian algorithm are to obtain efficient unbiased sampling of these moments and to verify convergence of the sample this is accomplished here using a gibbs sampler gs approach based on the metropolis algorithm which also forms the basis for simulated annealing sa although gs can be computationally slow in its basic form just as modifications to sa have produced much faster optimization algorithms the gs is modified here to produce an efficient algorithm referred to as the fast gibbs sampler fgs an automated convergence criterion is employed based on monitoring the difference between two independent fgs samples collected in parallel comparison of fgs gs and monte carlo integration for noisy synthetic benchmark test cases indicates that fgs provides rigorous estimates of ppd moments while requiring orders of magnitude less computation time

evaluation of decay times in coupled spaces an efficient search algorithm within the bayesian framework this paper discusses an efficient method for evaluating multiple decay times within the bayesian framework previous works n xiang and p m goggans j acoust soc am 110 1415 1424 2001 113 2685 2697 2003 n xiang p m goggans t jasa and m kleiner 117 3707 3715 2005 have applied the bayesian inference to cope with demanding tasks in estimating multiple decay times from schroeder decay functions measured or calculated in acoustically coupled spaces since then a number of recent works call for efficient estimation methods within the bayesian framework an efficient analysis is of practical significance for better understanding and modeling the sound energy decay process in acoustically coupled spaces or even in single spaces for reverberation time estimation this paper will first formulate the bayesian posterior probability distribution function ppdf in a matrix form to reduce the dimensionality as applied to the decay time evaluation based on existence of only global extremes o

stochastic joint inversion of 2d seismic and seismoelectric signals in linear poroelastic materials a numerical investigation the interpretation of seismoelectrical signals is a difficult task because coseismic and seismoelectric converted signals are recorded simultaneously and the seismoelectric conversions are typically several orders of magnitude smaller than the coseismic electrical signals the seismic and seismoelectric signals are modeled using a finite element code with perfectly matched layer boundary conditions assuming a linear poroelastic body we present a stochastic joint inversion of the seismic and seismoelectrical data based on the adaptive metropolis algorithm to obtain the posterior probability density functions of the material properties of each geologic unit this includes the permeability porosity electrical conductivity bulk modulus of the dry porous frame bulk modulus of the fluid bulk modulus of the solid phase and shear modulus of the formations a test of this approach is performed with a synthetic model comprising two horizontal layers and a reservoir partially saturated with oil which is embedded in the second layer the result of the joint inversion shows that we can invert the permeability of the reservoir and its mechanical properties

efficient multiframe wiener restoration of blurred and noisy image sequences computationally efficient multiframe wiener filtering algorithms that account for both intraframe spatial and interframe temporal correlations are proposed for restoring image sequences that are degraded by both blur and noise one is a general computationally efficient multiframe filter the cross correlated multiframe ccmf wiener filter which directly utilizes the power and cross power spectra of only n n matrices where n is the number of frames used in the restoration in certain special cases the ccmf lends itself to a closed form solution that does not involve any matrix inversion a special case is the motion compensated multiframe mcmf filter where each frame is assumed to be a globally shifted version of the previous frame in this case the interframe correlations can be implicitly accounted for using the estimated motion information thus the mcmf filter requires neither explicit estimation of cross correlations among the frames nor matrix inversion performance and robustness results are given