an iterative scheme for a class of quasi variational inequalities an iterative scheme is given to obtain the approximate solution of a class of quasi variational inequalities it is shown that the approximate solution obtained by the iterative scheme converges strongly in the hilbert space to the exact solution as a special case we obtain the corresponding iterative scheme for variational inequalities

partial non gaussian state space summary in this paper we suggest the use of simulation techniques to extend the applicability of the usual gaussian state space filtering and smoothing techniques to a class of nongaussian time series models this allows a fully bayesian or maximum likelihood analysis of some interesting models including outlier models discrete markov chain components multiplicative models and stochastic variance models finally we discuss at some length the use of a non gaussian model to seasonally adjust the published money supply figures

thermoacoustic tomography for an integro differential wave equation modeling attenuation abstract in this article we study the inverse problem of thermoacoustic tomography tat on a medium with attenuation represented by a time convolution or memory term and whose consideration is motivated by the modeling of ultrasound waves in heterogeneous tissue via fractional derivatives with spatially dependent parameters under the assumption of being able to measure data on the whole boundary we prove uniqueness and stability and propose a convergent reconstruction method for a class of smooth variable sound speeds by a suitable modification of the time reversal technique we obtain a neumann series reconstruction formula

analytic explanation of spatial resolution related to bandwidth and detector aperture size in thermoacoustic or photoacoustic reconstruction an analytic explanation of the spatial resolution in thermoacoustic or photoacoustic reconstruction is presented three types of specific recording geometries including spherical planar and cylindrical surface as well as other general cases are investigated analytic expressions of the point spread functions psf s as a function of the bandwidth of the measurement system and the finite size of the detector aperture are derived based on rigorous reconstruction formulas the analyses clearly reveal that the dependence of the psf s on the bandwidth of all recording geometries shares the same space invariant expression while the dependence on the aperture size of the detector differs the bandwidth affects both axial and lateral resolutions in contrast the detector aperture blurs the lateral resolution greatly but the axial resolution only slightly

inversion of the elliptical radon transform arising in migration imaging using the regular radon transform abstract in recent years many types of elliptical radon transforms that integrate functions over various sets of ellipses ellipsoids have been considered relating to studies in bistatic synthetic aperture radar ultrasound reflection tomography radio tomography and migration imaging in this article we consider the transform that integrates a given function in r n over a set of ellipses when n 2 or ellipsoids of rotation when n 3 with foci restricted to a hyperplane we show a relation between this elliptical radon transform and the regular radon transform and provide the inversion formula for the elliptical radon transform using this relation numerical simulations are performed to demonstrate the suggested algorithms in two dimensions and these simulations are also provided in this article

injectivity sets for the radon transform over circles and complete systems of radial functions abstract a necessary and sufficient characterization is given that specifies which sets of sums of translations of radial functions are dense in the set of continuous functions in the plane this problem is shown to be equivalent to inversion for the radon transform on circles centered on restricted subsets of the plane the proofs rest on the geometry of zero sets for harmonic polynomials and the microlocal analysis of this circular radon transform a characterization of nodal sets for the heat and wave equation in the plane are consequences of our theorems and questions of pinkus and ehrenpreis are answered

likelihood analysis of non gaussian measurement time series summary in this paper we provide methods for estimating non gaussian time series models these techniques rely on markov chain monte carlo to carry out simulation smoothing and bayesian posterior analysis of parameters and on importance sampling to estimate the likelihood function for classical inference the time series structure of the models is used to ensure that our simulation algorithms are efficient

curve driven based acoustic inversion for photoacoustic tomography the computation of model matrix in the iterative imaging reconstruction process is crucial for the quantitative photoacoustic tomography pat however it is challenging to establish an outstanding model matrix to improve the overall imaging quality in pat due to the noisy signal acquisition and inevitable artifacts in this work we present a novel method named as the curve driven based model matrix inversion cdmmi to calculate the model matrix for tomographic reconstruction in photoacoustic imaging it eliminated the use of interpolation techniques and thus avoided all interpolation related errors the conventional interpolated matrix model inversion immi method was applied to evaluate its performance in numerical simulation tissue mimicking phantom and in vivo small animal studies results demonstrated that cdmmi achieved better reconstruction accuracy until immi kept increasing discrete points to 10000 furthermore the proposed method can suppress the negative influence of noise and artifacts effectively which benefited the overall imaging quality of photoacoustic tomography

inversion of spherical means and the wave equation in even dimensions we establish inversion formulas of the so called filtered back projection type to recover a function supported in the ball in even dimensions from its spherical means over spheres centered on the boundary of the ball we also find several formulas to recover initial data of the form f 0 or 0 g for the free space wave equation in even dimensions from the trace of the solution on the boundary of the ball provided that the initial data has support in the ball

recovering functions from the spherical mean transform with limited radii data by expansion into spherical harmonics abstract the aim of the article is to generalize the method presented in 3 theorem 1 by g ambartsoumian r gouia zarrad and m lewis for recovering functions from their spherical mean transform with limited radii data from the two dimensional case to the general n dimensional case the idea behind the method is to expand each function in question into spherical harmonics and then obtain for each term in the expansion an integral equation of volterra s type that can be solved iteratively we show also how this method can be modified for the spherical case of recovering functions from the spherical transform with limited radii data lastly we solve the analogous problem for the case of the funk transform by again using expansion into spherical harmonics and then obtain an abel type integral equation which can be inverted by a method introduced in 14

on gibbs sampling for state space models summary we show how to use the gibbs sampler to carry out bayesian inference on a linear state space model with errors that are a mixture of normals and coefficients that can switch over time our approach simultaneously generates the whole of the state vector given the mixture and coefficient indicator variables and simultaneously generates all the indicator variables conditional on the state vectors the states are generated efficiently using the kalman filter we illustrate our approach by several examples and empirically compare its performance to another gibbs sampler where the states are generated one at a time the empirical results suggest that our approach is both practical to implement and dominates the gibbs sampler that generates the states one at a time

discretization and simulation of the zakai equation this paper is concerned with numerical approximations for a class of nonlinear stochastic partial differential equations zakai equation of nonlinear filtering problem and mckean vlasov type equations the approximation scheme is based on the re pre sentation of the solutions as weighted conditional distributions we first accurately analyse the error caused by an euler type scheme of time discretization sharp error bounds are calculated we show that the rate of convergence is in general of order sqrt delta delta is the time step but in the case when there is no correlation between the signal and the observation for the zakai equation the order of convergence becomes delta this result is obtained by carefully employing techniques of malliavin calculus in a second step we propose a simulation of the time discretization euler scheme by a quantization approach this formally consists in an approximation of the weighted conditional distribution by a conditional discrete distribution on finite supports we provide error bounds and rate of convergence in terms of the number n of the grids of this support these errors are minimal at some optimal grids which are computed by a recursive method based on monte carlo simulations finally we illustrate our results with some numerical experiments arising from correlated kalman bucy filter and burgers equation

non gaussian state space modeling of nonstationary time series abstract a non gaussian state space approach to the modeling of nonstationary time series is shown the model is expressed in state space form where the system noise and the observational noise are not necessarily gaussian recursive formulas of prediction filtering and smoothing for the state estimation and identification of the non gaussian state space model are given also given is a numerical method based on piecewise linear approximation to the density functions for realizing these formulas significant merits of non gaussian modeling and the wide range of applicability of the method are illustrated by some numerical examples a typical application of this non gaussian modeling is the smoothing of a time series that has mean value function with both abrupt and gradual changes simple gaussian state space modeling is not adequate for this situation here the model with small system noise variance cannot detect jump whereas the one with large system noise variance yields unfavorable wiggle to work

monte carlo smoothing for nonlinear time series we develop methods for performing smoothing computations in general state space models the methods rely on a particle representation of the filtering distributions and their evolution through time using sequential importance sampling and resampling ideas in particular novel techniques are presented for generation of sample realizations of historical state sequences this is carried out in a forward filtering backward smoothing procedure that can be viewed as the nonlinear non gaussian counterpart of standard kalman filter based simulation smoothers in the linear gaussian case convergence in the mean squared error sense of the smoothed trajectories is proved showing the validity of our proposed method the methods are tested in a substantial application for the processing of speech signals represented by a time varying autoregression and parameterized in terms of time varying partial correlation coefficients comparing the results of our algorithm with those from a simple smoother based on the filte

a mollification approach for inverting the spherical mean radon transform the filtered backprojection algorithm is still one of the most important reconstruction methods in computed tomography it is based on explicit formulas for recovering mollified versions of the original unknown function in this paper we derive such formulas for the spherical mean radon transform with centers restricted to the boundary of a ball in two spatial dimensions we present an efficient implementation strategy that leads to a stable reconstruction algorithm of filtered backprojection type

a reconstruction algorithm for photoacoustic imaging based on the nonuniform fft fourier reconstruction algorithms significantly outperform conventional backprojection algorithms in terms of computation time in photoacoustic imaging these methods require interpolation in the fourier space domain which creates artifacts in reconstructed images we propose a novel reconstruction algorithm that applies the one dimensional nonuniform fast fourier transform to photoacoustic imaging it is shown theoretically and numerically that our algorithm avoids artifacts while preserving the computational effectiveness of fourier reconstruction

inversion of circular means and the wave equation on convex planar domains we study the problem of recovering the initial data of the two dimensional wave equation from values of its solution on the boundary w of a smooth convex bounded domain w r 2 as a main result we establish back projection type inversion formulas that recover any initial data with support in w modulo an explicitly computed smoothing integral operator k w for circular and elliptical domains the operator k w is shown to vanish identically and hence we establish exact inversion formulas of the back projection type in these cases similar results are obtained for recovering a function from its mean values over circles with centers on w both reconstruction problems are amongst others essential for the hybrid imaging modalities photoacoustic and thermoacoustic tomography

on a regularization scheme for linear operators in distribution spaces with an application to the spherical radon transform this article provides a framework to regularize operator equations of the first kind where the underlying operator is linear and continuous between distribution spaces the dual spaces of smooth functions to regularize such a problem the authors extend louis method of approximate inverse from hilbert spaces to distribution spaces the idea is to approximate the exact solution in the weak topology by a smooth function where the smooth function is generated by a mollifier the resulting regularization scheme consists of the evaluation of the given data at so called reconstruction kernels which solve the dual operator equation with the mollifier as right hand side a nontrivial example of such an operator is given by the spherical radon transform which maps a function to its mean values over spheres centered on a line or plane this transform is one of the mathematical models in sonar and radar after establishing the theory of the approximate inverse for distributions we apply it to the spherical radon

sampling conditions for the circular radon transform recovering a function from circular or spherical mean values is the basis of many modern imaging technologies such as photo and thermoacoustic computed tomography or ultrasound reflection tomography recently much progress has been made concerning the problem of recovering a function from its circular mean values its circular radon transform in particular theoretically exact inversion formulas of the back projection type have been discovered using continuously sampled data in practical applications however only a discrete number of circular mean values can be collected in this paper we address this issue in the context of the shannon sampling theory we derive sharp sampling conditions for the number of angular and radial samples such that any essentially b0 bandlimited function can be recovered from a finite number of such circular mean values

adaptive meshfree backward sde filter an adaptive meshfree approach is proposed to solve the nonlinear filtering problem based on forward backward stochastic differential equations the algorithm relies on the fact that the solution of the forward backward stochastic differential equations is the unnormalized filtering density as required in the nonlinear filtering problem adaptive space points are constructed in a stochastic manner to improve the efficiency of the algorithm we also introduce a markov chain monte carlo resampling method to address the degeneracy problem of the adaptive space points numerical experiments are carried out against the auxiliary particle filter method in the rugged double well potential problem as well as the multitarget tracking problem to demonstrate the superior performance of our algorithm

bayesian inference in cyclical component dynamic linear models abstract dynamic linear models dlm s with time varying cyclical components are developed for the analysis of time series with persistent though time varying cyclical behavior the development covers inference on wavelengths of possibly several persistent cycles in nonstationary time series permitting explicit time variation in amplitudes and phases of component waveforms decomposition of stochastic inputs into purely observational noise and innovations that impact on the waveform characteristics with extensions to incorporate ranges of time varying time series and regression terms wihin the standard dlm context bayesian inference via iterative stochastic simulation methods is developed and illustrated some indications of model extensions and generalizations are given in addition to the specific focus on cyclical component models the development provides the basis for bayesian inference via stochastic simulation for state evolution matrix parameters and variance components in dlm s building o

the universal back projection formula for spherical means and the wave equation on certain quadric hypersurfaces abstract in many tomographic applications and elsewhere there arises a need to reconstruct a function from the data on the boundary of some domain given either by the spherical means of the function or by the corresponding solution of the free space wave equation in this paper we show that the so called universal back projection formulas provide exact recovery of the unknown function with compact support for data on any quadric hypersurfaces that can be approximated by elliptic hypersurfaces these quadric hypersurfaces include elliptic paraboloid as well as parabolic and elliptic cylinders

effective one dimensional approach to the source reconstruction problem of three dimensional inverse optoacoustics the direct problem of optoacoustic signal generation in biological media consists of solving an inhomogeneous three dimensional 3d wave equation for an initial acoustic stress profile in contrast the more defiant inverse problem requires the reconstruction of the initial stress profile from a proper set of observed signals in this article we consider an effectively 1d approach based on the assumption of a gaussian transverse irradiation source profile and plane acoustic waves in which the effects of acoustic diffraction are described in terms of a linear integral equation the respective inverse problem along the beam axis can be cast into a volterra integral equation of the second kind for which we explore here efficient numerical schemes in order to reconstruct initial stress profiles from observed signals constituting a methodical progress of computational aspects of optoacoustics in this regard we explore the validity as well as the limits of the inversion scheme via numerical experiments with parameters geared toward actual optoacoustic problem instances the considered inversion input consists of synthetic data obtained in terms of the effectively 1d approach and more generally a solution of the 3d optoacoustic wave equation finally we also analyze the effect of noise and different detector to sample distances on the optoacoustic signal and the reconstructed pressure profiles

the inversion problem and applications of the generalized radon transform we prove that under certain conditions the inversion problem for the generalized radon transform reduces to solving a fredholm integral equation and we obtain the asymptotic expansion of the symbol of the integral operator in this equation we consider applications of the generalized radon transform to partial differential equations with variable coefficients and provide a solution to the inversion problem for the attenuated and exponential radon transforms

dynamic conditional independence models and markov chain monte carlo methods abstract in dynamic statistical modeling situations observations arise sequentially causing the model to expand by progressive incorporation of new data items and new unknown parameters for example in clinical monitoring patients and data arrive sequentially and new patient specific parameters are introduced with each new patient markov chain monte carlo mcmc might be used for continuous updating of the evolving posterior distribution but would need to be restarted from scratch at each expansion stage thus mcmc methods are often too slow for real time inference in dynamic contexts by combining mcmc with importance resampling we show how real time sequential updating of posterior distributions can be effected the proposed dynamic sampling algorithms use posterior samples from previous updating stages and exploit conditional independence between groups of parameters to allow samples of parameters no longer of interest to be discarded such as when a patient dies or is discharged we apply the

sampling in fan beam tomography in fan beam tomography functions in mathbb r 2 are constructed from integrals along straight lines emanating from a finite number of sources sitting on a circle around the reconstruction region using a sampling theorem for periodic functions and asymptotic estimates for the fourier transform of the fan beam transform the exact sampling conditions are found for standard fan beam scanning necessary to obtain a certain resolution new efficient sampling schemes and corresponding reconstruction algorithms are also found these sampling schemes need significantly less data to obtain a certain resolution than a standard fan beam geometry the correctness of the sampling conditions for standard fan beam scanning and the superiority of the new schemes are shown by computer simulations

inversion formulas and stability estimates of the wave operator on the hyperplane abstract one of the mathematical problems arising in photoacoustic tomography pat a novel and promising technology in medical imaging is to recover the initial function from the solution of the wave equation on a surface where the detectors of pat are located we define the wave operator as the transform assigning to a given function f the solution of the wave equation on the detector surface where the detectors are located with the initial function f here we study many properties of this wave operator including the inversion formulas and stability estimates assuming that the detector surface is a hyperplane

sequential imputations and bayesian missing data problems abstract for missing data problems tanner and wong have described a data augmentation procedure that approximates the actual posterior distribution of the parameter vector by a mixture of complete data posteriors their method of constructing the complete data sets is closely related to the gibbs sampler both required iterations and similar to the em algorithm convergence can be slow we introduce in this article an alternative procedure that involves imputing the missing data sequentially and computing appropriate importance sampling weights in many applications this new procedure works very well without the need for iterations sensitivity analysis influence analysis and updating with new data can be performed cheaply bayesian prediction and model selection can also be incorporated examples taken from a wide range of applications are used for illustration

universal back projection algorithm for photoacoustic computed tomography we report results of a reconstruction algorithm for three dimensional photoacoustic computed tomography a universal back projection formula is presented for three types of imaging geometries planar spherical and cylindrical surfaces a solid angle weighting factor is introduced in the back projection formula to compensate for the variations of detection views a method for implementing this algorithm is described numerical simulation is used to demonstrate the performance of the algorithm

variable background born inversion by wavefield backpropagation the inverse scattering problem for an acoustic medium is formulated by using the variable background born approximation a constant density acoustic medium is probed by a wide band point source and the scattered field is observed along a curved receiver array located outside the region where the medium velocity is different from the assumed background velocity function the solution proposed relies on the introduction of a backpropagated field this field is obtained by using a finite difference scheme backward in time to backpropagate into the medium the scattered field observed along the receiver array the backpropagated field is imaged at the source travel times giving an image of the same type as obtained by reverse time finite difference migration techniques the gradient of this image is then taken along rays linking the source to points in the medium and after scaling this gives the reconstructed potential to relate the reconstructed potential to the true scattering potential high frequency

exact and approximative imaging methods for photoacoustic tomography using an arbitrary detection surface two universal reconstruction methods for photoacoustic also called optoacoustic or thermoacoustic computed tomography are derived applicable to an arbitrarily shaped detection surface in photoacoustic tomography acoustic pressure waves are induced by illuminating a semitransparent sample with pulsed electromagnetic radiation and are measured on a detection surface outside the sample the imaging problem consists in reconstructing the initial pressure sources from those measurements the first solution to this problem is based on the time reversal of the acoustic pressure field with a second order embedded boundary method the pressure on the arbitrarily shaped detection surface is set to coincide with the measured data in reversed temporal order in the second approach the reconstruction problem is solved by calculating the far field approximation a concept well known in physics where the generated acoustic wave is approximated by an outgoing spherical wave with the reconstruction point as center numerical simulations are used to compare the proposed universal reconstruction methods with existing algorithms

general nonlinear variational inequalities abstract the fixed point technique is used to prove the existence of a unique solution of a new unified and general class of nonlinear variational inequalities several special cases which can be obtained from our main result are also discussed

a new slant on seismic imaging migration and integral geometry a new approach to seismic migration formalizes the classical diffraction or common tangent stack by relating it to linearized seismic inversion and the generalized radon transform this approach recasts migration as the problem of reconstructing the earth s acoustic scattering potential from its integrals over isochron surfaces the theory rests on a solution of the wave equation with the geometrical optics green function and an approximate inversion formula for the generalized radon transform the method can handle both complex velocity models and nearly arbitrary configurations of sources and receivers in this general case the method can be implemented as a weighted diffraction stack with the weights determined by tracing rays from image points to the experiment s sources and receivers when tested on a finite difference simulation of a deviated well vertical seismic profile a hybrid experiment which is difficult to treat with conventional wave equation methods the algorithm accurately reconstructed faulted earth models analytical reconstruction formulas are derived from the general formula for zero offset and fixed offset surface experiments in which the background velocity is constant the zero offset inversion formula resembles standard kirchhoff migration our analysis provides a direct connection between the experimental setup source and receiver positions source wavelet background velocity and the spatial resolution of the reconstruction synthetic examples illustrate that the lateral resolution in seismic images is described well by the theory and is improved greatly by combining surface data and borehole data the best resolution is obtained from a zero offset experiment that surrounds the region to be imaged

is a curved flight path in sar better than a straight one in the plane we study the transform r gamma f of integrating an unknown function f over circles centered at a given curve gamma this is a simplified model of synthetic aperture radar sar when the radar is not directed but has other applications like thermoacoustic tomography for example we study the problem of recovering the wave front set wf f if the visible singularities of f hit gamma once we show that wf f cannot be recovered i e the artifacts cannot be resolved if gamma partial omega is the boundary of a strictly convex domain omega we show that this is still true on the other hand in the latter case if f is known a priori to have singularities in a compact set then we show that one can recover wf f omega and moreover this can be done in a simple explicit way using backpropagation for the wave equation

time reversal for photoacoustic tomography based on the wave equation of nachman smith and waag one goal of photoacoustic tomography pat is to estimate an initial pressure function from pressure data measured at a boundary surrounding the object of interest this paper is concerned with a time reversal method for pat that is based on the dissipative wave equation of nachman smith and waag j acoust soc am 88 1584 1990 this equation is a correction of the thermoviscous wave equation such that its solution has a finite wave front speed and in contrast it can model several relaxation processes in this sense it is more accurate than the thermoviscous wave equation for simplicity we focus on the case of one relaxation process we derive an exact formula for the time reversal image i which depends on the relaxation time 1 and the compressibility 1 of the dissipative medium and show i 1 1 for 1 0 this implies that i holds in the dissipation free case and that i is similar to for sufficiently small compressibility 1 moreover we show for tissue similar to water that the small wave number approximation i 0 of the time reversal image satisfies i 0 0 x with over 0 k const for k 1 c 0 1 where denotes the initial pressure function for such tissue our theoretical analysis and numerical simulations show that the time reversal image i is very similar to the initial pressure function and that a resolution of 0 036mm is feasible for exact measurement data

bayesian inference and prediction for mean and variance shifts in autoregressive time series abstract this article is concerned with statistical inference and prediction of mean and variance changes in an autoregressive time series we first extend the analysis of random mean shift models to random variance shift models we then consider a method for predicting when a shift is about to occur this involves appending to the autoregressive model a probit model for the probability that a shift occurs given a chosen set of explanatory variables the basic computational tool we use in the proposed analysis is the gibbs sampler for illustration we apply the analysis to several examples

discrete radon transform this paper describes the discrete radon transform drt and the exact inversion algorithm for it similar to the discrete fourier transform dft the drt is defined for periodic vector sequences and studied as a transform in its own right casting the forward transform as a matrix vector multiplication the key observation is that the matrix although very large has a block circulant structure this observation allows construction of fast direct and inverse transforms moreover we show that the drt can be used to compute various generalizations of the classical radon transform rt and in particular the generalization where straight lines are replaced by curves and weight functions are introduced into the integrals along these curves in fact we describe not a single transform but a class of transforms representatives of which correspond in one way or another to discrete versions of the rt and its generalizations an interesting observation is that the exact inversion algorithm cannot be obtained directly from radon s inversion formula given the fact that the rt has no nontrivial one dimensional analog exact invertibility makes the drt a useful tool geared specifically for multidimensional digital signal processing exact invertibility of the drt flexibility in its definition and fast computational algorithm affect present applications and open possibilities for new ones some of these applications are discussed in the paper

an inversion formula for the spherical mean transform with data on an ellipsoid in two and three dimensions abstract in the articles 1 and 2 of d finch m haltmeier s patch and d rakesh inversion formulas were found in any dimension greater than or equal to 2 for recovering a smooth function with compact support in the unit ball from spherical means centered on the unit sphere the aim of this article is to show that the methods used in 1 2 can be modified in order to get similar inversion formulas from spherical means centered on an ellipsoid in two and three dimensional spaces

to local reconstruction from the spherical mean radon transform abstract the article suggests a new approach using the so called consistency method for the inversion of the spherical mean radon transform in 2d with detectors on a line we present a new iterative formula which gives an algorithm to recover an unknown function supported completely on one side of a line l from its spherical means over circles centered on the line l our reconstruction formula has the benefit of being local such an inversion is required in problems of thermo and photo acoustic tomography ultrasound reflection tomography radar imaging and a few other

particle filtering for partially observed gaussian state space models summary solving bayesian estimation problems where the posterior distribution evolves over time through the accumulation of data has many applications for dynamic models a large number of algorithms based on particle filtering methods also known as sequential monte carlo algorithms have recently been proposed to solve these problems we propose a special particle filtering method which uses random mixtures of normal distributions to represent the posterior distributions of partially observed gaussian state space models this algorithm is based on a marginalization idea for improving efficiency and can lead to substantial gains over standard algorithms it differs from previous algorithms which were only applicable to conditionally linear gaussian state space models computer simulations are carried out to evaluate the performance of the proposed algorithm for dynamic tobit and probit models

unobserved component time series models with arch disturbances abstract this paper considers how arch effects may be handled in time series models formulated in terms of unobserved components a general model is formulated but this includes as special cases a random walk plus noise model with both disturbances subject to arch effects an arch m model with a time varying parameter and a latent factor model with arch effects in the factors although the model is not conditionally gaussian an approximate filter can be obtained and used as the basis for estimation the performance of this method is examined on real data sets and monte carlo experiments are carried out the method is extended to handle garch and a latent factor model based on the t distribution

layer stripping solutions of multidimensional inverse scattering problems a layer stripping procedure for solving three dimensional schrodinger equation inverse scattering problems is developed this method operates by recursively reconstructing the potential from the jump in the scattered field at the wave front and then using the reconstructed potential to propagate the wave front and the scattered field further into the inhomogeneous region it is thus a generalization of algorithms that have been developed for one dimensional inverse scattering problems although the procedure has not yet been numerically tested the corresponding one dimensional algorithms have performed well on synthetic data the procedure is applied to a two dimensional inverse seismic problem connections between simplifications of this method and born approximation inverse scattering methods are also noted

the spherical radon transform with centers on cylindrical surfaces abstract recovering a function from its spherical radon transform with centers of spheres of integration restricted to a hypersurface is at the heart of several modern imaging technologies including sar ultrasound imaging and photo and thermoacoustic tomography in this paper we study an inversion of the spherical radon transform with centers of integration restricted to cylindrical surfaces of the form r m where is a hypersurface in r n we show that this transform can be decomposed into two lower dimensional spherical radon transforms one with centers on and one with a planar center set in r m 1 together with explicit inversion formulas for the spherical radon transform with a planar center set and existing algorithms for inverting the spherical radon transform with a center set this yields reconstruction procedures for general cylindrical domains in the special case of spherical or elliptical cylinders we obtain novel explicit inversion formulas for three spatial dimensions these inversion formulas can be implemented efficiently by backprojection type algorithms only requiring o n 4 3 floating point operations where n is the total number of unknowns to be recovered we present numerical results demonstrating the efficiency of the derived algorithms

filtering via simulation auxiliary particle filters this article analyses the recently suggested particle approach to filtering time series we suggest that the algorithm is not robust to outliers for two reasons the design of the simulators and the use of the discrete support to represent the sequentially updating prior distribution here we tackle the first of these problems

inversion of n dimensional spherical averages in this paper we give a simple inversion formula for determining the even part of a function from its averages over the surfaces of spheres in mathbb r n centered on a hyperplane y 0 we emphasize the relation between the backprojection approximation to the function and the full inversion result a simple necessary and sufficient condition for data to correspond to the spherical averages of a function is given

markov chain monte carlo in conditionally gaussian state space models summary a bayesian analysis is given for a state space model with errors that are finite mixtures of normals and with coefficients that can assume a finite number of different values a sequence of indicator variables determines which components the errors belong to and the values of the coefficients the computation is carried out using markov chain monte carlo with the indicator variables generated without conditioning on the states previous approaches use the gibbs sampler to generate the indicator variables conditional on the states in many problems however there is a strong dependence between the indicator variables and the states causing the gibbs sampler to converge unacceptably slowly or even not to converge at all the new sampler is implemented in o n operations where n is the sample size permitting an exact bayesian analysis of problems that previously had no computationally tractable solution we show empirically that the new sampler can be much more efficient than previous approaches and illustrate its applicability to robust nonparametric regression with discontinuities and to a time series change point problem

a galerkin least squares approach for photoacoustic tomography the development of fast and accurate image reconstruction algorithms is a central aspect of computed tomography in this paper we address this issue for photoacoustic computed tomography in circular geometry we investigate the galerkin least squares method for that purpose for approximating the function to be recovered we use subspaces of translation invariant spaces generated by a single function this includes many systems that have previously been employed in photoacoustic tomography such as generalized kaiser bessel basis functions or the natural pixel basis by exploiting an isometry property of the forward problem we are able to efficiently set up the galerkin equation for a wide class of generating functions and devise efficient algorithms for its solution we establish a convergence analysis and present numerical simulations that demonstrate the efficiency and accuracy of the derived algorithm

the calculation of posterior distributions by data augmentation comment a noniterative sampling importance resampling alternative to the data augmentation algorithm for creating a few imputations when fractions of missing information are modest the sir algorithm

a class of singular fourier integral operators in synthetic aperture radar imaging in this article we analyze the microlocal properties of the linearized forward scattering operator f and the normal operator f f where f is the l 2 adjoint of f which arises in synthetic aperture radar imaging for the common midpoint acquisition geometry when f is applied to the scattered data artifacts appear we show that f f can be decomposed as a sum of four operators each belonging to a class of distributions associated to two cleanly intersecting lagrangians i p l 0 1 thereby explaining the latter artifacts

effective discretization of direct reconstruction schemes for photoacoustic imaging in spherical geometries recently kernel methods for the recovery of a function from its spherical means in spherical acquisition geometry have been proposed we present efficient algorithms for these formulas in the two and three dimensional cases our scheme applies fourier techniques for certain convolution type integrals and discretizes physical space on a polar and a spherical grid respectively

particle filter with a mode tracker for visual tracking across illumination changes in this correspondence our goal is to develop a visual tracking algorithm that is able to track moving objects in the presence of illumination variations in the scene and that is robust to occlusions we treat the illumination and motion x y translation and scale parameters as the unknown state sequence the observation is the entire image and the observation model allows for occasional occlusions modeled as outliers the nonlinearity and multimodality of the observation model necessitate the use of a particle filter pf due to the inclusion of illumination parameters the state dimension increases thus making regular pfs impractically expensive we show that the recently proposed approach using a pf with a mode tracker can be used here since even in most occlusion cases the posterior of illumination conditioned on motion and the previous state is unimodal and quite narrow the key idea is to importance sample on the motion states while approximating importance sampling by posterior mode tracking for estimating illumination experiments demonstrate the advantage of the proposed algorithm over existing pf based approaches for various face and vehicle tracking we are also able to detect illumination model changes e g those due to transition from shadow to sunlight or vice versa by using the generalized expected log likelihood statistics and successfully compensate for it without ever loosing track

on the determination of a function from an elliptical radon transform abstract in recent years radon type transforms that integrate functions over various sets of ellipses ellipsoids have been considered in synthetic aperture radar ultrasound reflection tomography and radio tomography in this paper we consider the transform that integrates a given function in r n over a set of solid ellipses when n 2 or solid ellipsoids of rotation when n 3 with a fixed eccentricity and foci restricted to a hyperplane inversion formulas are obtained for appropriate classes of functions that are even with respect to the hyperplane stability estimates and local uniqueness results are also provided

blind deconvolution via sequential imputations abstract the sequential imputation procedure is applied to adaptively and sequentially reconstruct discrete input signals that are blurred by an unknown linear moving average channel and contaminated by additive gaussian noises a problem known as blind deconvolution in digital communication a rejuvenation procedure for improving the efficiency of sequential imputation is introduced and theoretically justified the proposed method does not require the channel to be nonminimum phase and can be used in real time signal restoration two simulated systems are studied to illustrate the proposed method our result shows that the ideas of multiple imputations and flexible simulation techniques are as powerful in engineering as in survey sampling

range descriptions for the spherical mean radon transform abstract the transform considered in the paper averages a function supported in a ball in r n over all spheres centered at the boundary of the ball this radon type transform arises in several contemporary applications e g in thermoacoustic tomography and sonar and radar imaging range descriptions for such transforms are important in all these areas for instance when dealing with incomplete data error correction and other issues four different types of complete range descriptions are provided some of which also suggest inversion procedures necessity of three of these appropriately formulated conditions holds also in general domains while the complete discussion of the case of general domains would require another publication

a note on general algorithm for variational inequalities in this note we introduce and study a new general strongly quasivariational inequality problem which includes as special cases a number of known classes of variational inequalities studied previously by many authors in this field a general and unified iterative algorithm for finding the approximate solution to this problem is constructed by the projection method we prove the existence of the solution for this problem and the convergence of the iterative sequence generated by this algorithm

the calculation of posterior distributions by data augmentation abstract the idea of data augmentation arises naturally in missing value problems as exemplified by the standard ways of filling in missing cells in balanced two way tables thus data augmentation refers to a scheme of augmenting the observed data so as to make it more easy to analyze this device is used to great advantage by the em algorithm dempster laird and rubin 1977 in solving maximum likelihood problems in situations when the likelihood cannot be approximated closely by the normal likelihood maximum likelihood estimates and the associated standard errors cannot be relied upon to make valid inferential statements from the bayesian point of view one must now calculate the posterior distribution of parameters of interest if data augmentation can be used in the calculation of the maximum likelihood estimate then in the same cases one ought to be able to use it in the computation of the posterior distribution it is the purpose of this article to explain how this can be done the basic idea