estimation and control of systems with unknown covariance and multiplicative noise the problem of estimation and control for systems with multiplicative noise and unknown second order statistics is considered conditions are found for the existence of a solution based on game theoretic ideas the conditions for the existence of a saddle point for the time invariant filtering problem are necessary and sufficient whereas for all other cases only necessary the central idea of the solution is to convert the stochastic problem to a deterministic optimal control problem whose minimax point is sought with respect to the control filter and unknown statistics parameters the results that are derived show that the problem of estimation for systems with unknown covariances depends on the costate matrix which in turn is a function of the performance measure thus the filter loses one of its best known properties that of independence of the performance functional this property holds not only for the classical kalman filter but also for multiplicative systems

nonlocal discrete regularization on weighted graphs a framework for image and manifold processing we introduce a nonlocal discrete regularization framework on weighted graphs of the arbitrary topologies for image and manifold processing the approach considers the problem as a variational one which consists of minimizing a weighted sum of two energy terms a regularization one that uses a discrete weighted dirichlet energy and an approximation one this is the discrete analogue of recent continuous euclidean nonlocal regularization functionals the proposed formulation leads to a family of simple and fast nonlinear processing methods based on the weighted laplace operator parameterized by the degree of regularity the graph structure and the graph weight function these discrete processing methods provide a graph based version of recently proposed semi local or nonlocal processing methods used in image and mesh processing such as the bilateral filter the tv digital filter or the nonlocal means filter it works with equal ease on regular 2 d and 3 d images manifolds or any data we illustrate the abilities of the approach by applying it to various types of images meshes manifolds and data represented as graphs

finite element method for one dimensional and two dimensional time dependent problems with b splines abstract one dimensional and two dimensional time dependent problems have been solved by the galerkin method with cubic b splines as basis functions the redefining of basis functions has been done for two dimensional problems for the dirichlet type boundary conditions resulting in a non homogeneous part in the approximation the equidistribution of the error principle given by carl de boor for one dimensional problems has been extended to two dimensional problems the solutions for nonlinear problems are obtained as the limit of solutions of a sequence of linear problems generated by the quasilinearization technique the method developed with these features compares favourably with the methods available in literature

algorithms for optimal discontinuous piecewise linear and constant l 2 fits to continuous functions with adjustable nodes in one and two dimensions in this paper a direct variational approach with nonstandard variations is used to generate algorithms to determine optimal discontinuous piecewise linear and piecewise constant l2 fits to a continuous function of one or two variables with adjustable nodes in the one variable case the algorithm is fast and robust the mesh cannot tangle and the resulting fits are continuous a e in the two variable case on an adjustable triangular grid the algorithm is less robust but gives good results for particular functions possessing a single steep feature the extension to higher dimensions is straightforward

robust soft decision interpolation using weighted least squares soft decision adaptive interpolation sai provides a powerful framework for image interpolation the robustness of sai can be further improved by using weighted least squares estimation instead of least squares estimation in both of the parameter estimation and data estimation steps to address the mismatch issue of geometric duality during parameter estimation the residuals prediction errors are weighted according to the geometric similarity between the pixel of interest and the residuals the robustness of data estimation can be improved by modeling the weights of residuals with the well known bilateral filter experimental results show that there is a 0 25 db increase in peak signal to noise ratio psnr for a sample set of natural images after the suggested improvements are incorporated into the original sai the proposed algorithm produces the highest quality in terms of psnr and subjective quality among sophisticated algorithms in the literature

super resolution of multi observed rgb d images based on nonlocal regression and total variation there is growing demand for accuracy in image processing and visualization and the super resolution sr technique for multi observed rgb d images has become popular because it provides space redundant information and produces a detailed reconstruction even with a large magnification factor this technique has been thoroughly investigated in recent years nevertheless technical challenges remain such as finding sub pixel correspondences with low resolution lr observations exploiting space redundant information formulating space homogeneity constraints and leveraging cross image similarities in structures to address these challenges this paper proposes a unified optimization framework to estimate both the super resolved rgb image and the super resolved depth image from the multi observed lr rgb d images using their correlations using depth assisted cross image correspondences the rgb image sr problem is formulated as an effective regularization function by incorporating the normalized bilateral total variation regularizer and it is efficiently solved by a first order primal dual algorithm the depth image sr estimate can be obtained by minimizing a nonlocal regression based energy which integrates the structural cues of the super resolved rgb image in a detail preserving fashion essentially our unified optimization framework uses the rgb image and depth image as a priori knowledge that the sr process uses for better accuracy our extensive experiments on public rgb d benchmarks and real data and our quantitative comparison with several state of the art methods demonstrate the superiority of our method in terms of accuracy versatility and reliability of details and sharp feature preservation

minimax linear observers and regulators for stochastic systems with uncertain second order statistics the problem of minimax design of linear observers and regulators for linear time varying multivariable stochastic systems with uncertain models of their second order statistics is treated in this paper general classes of allowable covariance matrices and means of the process and observation noises and of the random initial condition are considered a game formulation of the problem is adopted and it is shown that the optimal filter for the least favorable set of covariances is minimax robust for each of the filtering situations analyzed conditions satisfied by the saddle point solutions are given and their utility for finding the worst case covariances is illustrated by way of several examples of uncertainty classes of practical interest

on minimax robustness a general approach and applications the minimax approach to the design of systems that are robust with respect to modeling uncertainties is studied using a game theoretic formulation in which the performance functional and the sets of modeling uncertainties and admissible design policies are arbitrary the existence and characterization of minimax robust solutions that form saddle points are discussed through various methods that take into account several common features of the games encountered in applications in particular it is shown that if the performance functional and the uncertainty set are convex then a certain type of regularity condition on the functional is sufficient to ensure that the optimal strategy for a least favorable element of the uncertainty set is minimax robust the efficacy of the methods proposed for a general game is tested in the problems of matched filtering wiener filtering quadratic detection and output energy filtering in which uncertainties in their respective signal and noise models are assumed to exist these problems are analyzed in a common hilbert space framework and they serve to point out the advantages and limitations of the proposed techniques

a multiloop generalization of the circle criterion for stability margin analysis in order to provide a theoretical tool well suited for use in characterizing the stability margins e g gain and phase margins of multiloop feedback systems multiloop input output stability results generalizing the circle stability criterion are considered generalized conic sectors with centers and radii determined by linear dynamical operators are employed to enable an engineer to specify the stability margins which he desires as a frequency dependent convex set of modeling errors including nonlinearities gain variations and phase variations which the system must be able to tolerate in each feedback loop without instability the resulting stability criterion gives sufficient conditions for closed loop stability in the presence of such frequency dependent modeling errors even when the modeling errors occur simultaneously in all loops so for example stability is assured as loop gains and phases vary throughout a set of nonzero measure whose boundaries are frequency dependent the stability conditions yield an easily interpreted scalar measure of the amount by which a muitiloop system exceeds or falls short of its stability margin specifications

single image super resolution via adaptive high dimensional non local total variation and adaptive geometric feature single image super resolution sr is very important in many computer vision systems however as a highly ill posed problem its performance mainly relies on the prior knowledge among these priors the non local total variation nltv prior is very popular and has been thoroughly studied in recent years nevertheless technical challenges remain because nltv only exploits a fixed non shifted target patch in the patch search process a lack of similar patches is inevitable in some cases thus the non local similarity cannot be fully characterized and the effectiveness of nltv cannot be ensured based on the motivation that more accurate non local similar patches can be found by using shifted target patches a novel multishifted similar patch search msps strategy is proposed with this strategy nltv is extended as a newly proposed super high dimensional nltv shnltv prior to fully exploit the underlying non local similarity however as shnltv is very high dimensional applying it directly to sr is very difficult to solve this problem a novel statistics based dimension reduction strategy is proposed and then applied to shnltv thus shnltv becomes a more computationally effective prior that we call adaptive high dimensional non local total variation ahnltv in ahnltv a novel joint weight strategy that fully exploits the potential of the msps based non local similarity is proposed to further boost the performance of ahnltv the adaptive geometric duality agd prior is also incorporated finally an efficient split bregman iteration based algorithm is developed to solve the ahnltv agd driven minimization problem extensive experiments validate the proposed method achieves better results than many state of the art sr methods in terms of both objective and subjective qualities

minimax quadratic filtering of uncertain linear stochastic systems with partial fourth order information a minimax filtering problem for a class of uncertain linear stochastic systems is studied uncertainties involving fourth order moments of the noise distribution and of the initial state are considered under the hypothesis that the second order statistics are known hence the linear filter is available the quadratic minimax filter is found moreover it is shown that the minimax filter gives a worst case error variance even less than the exact error variance of the linear filter numerical simulations show that this improvement is meaningful also in cases of great uncertainty regarding the higher order statistics

single image super resolution using local geometric duality and non local similarity super resolution sr from a single image plays an important role in many computer vision applications it aims to estimate a high resolution hr image from an input low resolution lr image to ensure a reliable and robust estimation of the hr image we propose a novel single image sr method that exploits both the local geometric duality gd and the non local similarity of images the main principle is to formulate these two typically existing features of images as effective priors to constrain the super resolved results in consideration of this principle the robust soft decision interpolation method is generalized as an outstanding adaptive gd agd based local prior to adaptively design weights for the agd prior a local non smoothness detection method and a directional standard deviation based weights selection method are proposed after that the agd prior is combined with a variational framework based non local prior furthermore the proposed algorithm is speeded up by a fast gd matrices construction method which primarily relies on the selective pixel processing the extensive experimental results verify the effectiveness of the proposed method compared with several state of the art sr algorithms

nonlocally centralized sparse representation for image restoration sparse representation models code an image patch as a linear combination of a few atoms chosen out from an over complete dictionary and they have shown promising results in various image restoration applications however due to the degradation of the observed image e g noisy blurred and or down sampled the sparse representations by conventional models may not be accurate enough for a faithful reconstruction of the original image to improve the performance of sparse representation based image restoration in this paper the concept of sparse coding noise is introduced and the goal of image restoration turns to how to suppress the sparse coding noise to this end we exploit the image nonlocal self similarity to obtain good estimates of the sparse coding coefficients of the original image and then centralize the sparse coding coefficients of the observed image to those estimates the so called nonlocally centralized sparse representation ncsr model is as simple as the standard sparse representation model while our extensive experiments on various types of image restoration problems including denoising deblurring and super resolution validate the generality and state of the art performance of the proposed ncsr algorithm

grading functions and mesh redistribution we consider the problem of determining an appropriate grading of a mesh for piecewise polynomial interpolation and for approximate solution of two point boundary value problems by finite difference or finite element methods an analysis of optimality of the mesh and optimal grading functions in various norms and seminorms for the interpolation problem leads to the formulation of an adaptive mesh redistribution algorithm for boundary value problems in one dimension error estimates are given and numerical results presented to demonstrate the performance of the scheme and compare alternative redistribution criteria

optimal robust linear quadratic regulator for systems subject to uncertainties in this technical note a robust recursive regulator for linear discrete time systems which are subject to parametric uncertainties is proposed the main feature of the optimal regulator developed is the absence of tuning parameters in online applications to achieve this purpose a quadratic cost function based on the combination of penalty function and robust weighted least squares methods is formulated the convergence and stability proofs for the stationary system and a numerical comparative study among the standard linear quadratic regulator guaranteed cost and h controllers are provided

stability robustness of the continuous time lqg system under plant perturbation and noise uncertainty abstract in this paper the robustness of the continuous time lqg problem is studied the system to be controlled is described by the usual state space formulation that includes the structure of plant parameter perturbations and noise uncertainty a simple method is given to prove the saddle point inequality of the closed loop system performance to cope with noise uncertainty one sufficient condition which is applicable to general linear systems for system stability robustness under plant perturbation is presented

on autocovariance least squares method for noise covariance matrices estimation the technical note focuses on the estimation of the noise covariance matrices of the state space models stress is laid on the autocovariance least squares method providing unbiased estimates of the noise covariance matrices of linear systems in particular two topics are discussed first selection of the predictor gain as a key parameter of the method second generalization of the method for linear systems with a time varying measurement equation the theoretical results are illustrated in numerical examples

the kalman bucy filter accuracy in the guaranteed parameter estimation problem with uncertain statistics the guaranteed parameter estimation problem for a linear dynamical system with uncertain disturbance statistics is considered the estimate of the kalman bucy filter nonoptimality degree is constructed it is based on the duality theory this estimate is determined by the kalman bucy filter characteristics only and can be calculated without knowledge of the accurate solution of the optimal guaranteed estimation problem

the polynomial approach to the lq non gaussian regulator problem a new approach for the solution of the regulator problem for linear discrete time dynamical systems with non gaussian disturbances is proposed this approach generalizes a previous result concerning the definition of the quadratic optimal regulator it consists of the definition of the polynomial optimal algorithm of an order spl nu for the solution of the linear quadratic non gaussian stochastic regulator problem for systems with partial state information the validity of the separation principle has also been proved in this case numerical simulations show the high performance of the proposed method with respect to the classical linear regulation techniques

moving finite elements i we present new and general numerical methods for dealing with problems whose solutions develop sharp transition layers or near shocks these methods allow many nodes automatically to concentrate in the critical regions and move with them for clarity of exposition we concentrate on the space of piecewise linear functions with movable nodes with burgers equation as our test equation but the generalization to much more general spaces and equations including even certain previous moving vorticity blobs of the first author and s doss for the navier stokes equations becomes clear in this paper we present the theoretical and computational details of our scheme along with computational trial runs for burgers equation showing that the nodes do concentrate sharply and move with the shocks as desired the conclusiveness of these preliminary numerical trials is marred somewhat by the fact that we never successfully debugged a newton s method for our implicit stiff ode solver and were thus limited to ver

state estimation with probability constraints this paper considers a state estimation problem for a discrete time linear system driven by a gaussian random process the second order statistics of the input process and state initial condition are uncertain however the probability that the state and input satisfy linear constraints during the estimation interval is known a minimax estimation problem is formulated to determine an estimator that minimises the worst case mean square error criterion over the uncertain second order statistics subject to the probability constraints it is shown that a solution to this constrained state estimation problem is given by a kalman filter for appropriately chosen input and initial condition models these models are obtained from a finite dimensional convex optimisation problem the application of this estimator to an aircraft tracking problem quantifies the improvement in estimation accuracy obtained from the inclusion of probability constraints in the minimax formulation

addendum b spline interpolation in medical image processing analyzes b spline interpolation techniques of degree 2 4 and 5 with respect to all criteria that have been applied to evaluate various interpolation schemes in a recently published survey on image interpolation in medical imaging lehmann et al 1999 it is shown that high degree b spline interpolation has superior fourier properties smallest interpolation error and reasonable computing times therefore high degree b splines are preferable interpolators for numerous applications in medical image processing particularly if high precision is required if no aliasing occurs this result neither depends on the geometric transform applied for the tests nor the actual content of images

restricted risk bayes linear state estimation the problem of state estimation with stochastic uncertainties in the initial state model noise and measurement noise is considered using the restricted risk bayes approach it is assumed that the a priori distributions of these quantities are not perfectly known but that some information about them may be available while offering robustness the restricted risk bayes approach incorporates the available a priori information to give less conservative state estimators than the gamma minimax approach popular in the literature when attention is restricted to linear estimators based on a quadratic loss function a systematic method to derive restricted risk bayes estimators is proposed applying to the filtering problem the restricted risk bayes approach provides us with a robust method to calibrate the kalman filter kf considering the presence of stochastic uncertainties this method is illustrated with a target tracking example and a wireless channel tracking example for which the bayes minimax and restricted risk bayes estimators are derived and their performance is compared

constrained restoration and the recovery of discontinuities the linear image restoration problem is to recover an original brightness distribution x sup 0 given the blurred and noisy observations y kx sup 0 b where k and b represent the point spread function and measurement error respectively this problem is typical of ill conditioned inverse problems that frequently arise in low level computer vision a conventional method to stabilize the problem is to introduce a priori constraints on x sup 0 and design a cost functional h x over images x which is a weighted average of the prior constraints regularization term and posterior constraints data term the reconstruction is then the image x which minimizes h a prominent weakness in this approach especially with quadratic type stabilizers is the difficulty in recovering discontinuities the authors therefore examine prior smoothness constraints of a different form which permit the recovery of discontinuities without introducing auxiliary variables for marking the location of jumps and suspending the constraints in their vicinity in this sense discontinuities are addressed implicitly rather than explicitly

optimal quadratic solution for the non gaussian finite horizon regulator problem in this paper the problem of the optimal quadratic regulator for non gaussian discrete time stochastic systems with a quadratic cost function is considered the main result here obtained is that such optimal control can be derived from the classical lqg solution by substituting the linear filtering part with a quadratic optimal filter numerical results show high performance of this method

lqg optimal control system design under plant perturbation and noise uncertainty a state space approach abstract in this paper the stochastic linear dynamic system with uncertain parametric perturbations and uncertain noise covariances is studied based on minimax theory and the bellman gronwall inequality a sufficient condition for robust stability is derived finally a robust lqg optimal control design technique is employed to treat this problem

minimax control of linear stochastic systems with noise uncertainty the problem of linear quadratic gaussian control of multivariable linear stochastic systems with uncertain second order statistical properties is considered uncertainty is modeled by allowing process and observation noise spectral density matrices to vary arbitrarily within given classes and a minimax control formulation is applied to the quadratic objective functional general theorems proving the existence and characterization of saddle point solutions to this problem are presented and the relationship of these results to earlier results on minimax state estimation are discussed to illustrate the analytical results the specific example of regulating a double integrator plant is treated in detail

robustness results in linear quadratic gaussian based multivariable control designs the robustness of control systems with respect to model uncertainty is considered using simple frequency domain criteria available and new results are derived under a common framework in which the minimum singular value of the return differences transfer matrix is the key quantity in particular robustness results associated with multivariable control systems designed on the basis of linear quadratic lq and the linear quadratic gaussian lqg design methodologies are presented

robust filtering and prediction for linear systems with uncertain dynamics a game theoretic approach we examine the existence and behavior of game theoretic solutions for robust linear filters and predictors our basic uncertainty class includes m th order time varying discrete time systems with uncertain dynamics uncertain initial state covariance and uncertain nonstationary input and observation noise covariance our results include recursive kalman filter predictor realizations for the resulting robust procedures our approach is based on saddle point theory we emphasize the notion of a least favorable prior distribution for the uncertain parameter values to obtain a worst case design technique in this paper we highlight the role such distributions with finite support play in these decision models in particular we demonstrate that in these decision models the least favorable prior distribution is always discrete

an optimal triangulation for second order elliptic problems abstract let be a polygonal domain in r n h an associated triangulation and uh the finite element solution of a well posed second order elliptic problem on h let m mi p qi 1 be the set of nodes which defines the vertices of the triangulation h for each i m i x i l 1 l n in rn the object of this paper is to provide a computational tool to approximate the best set of positions m of the nodes and hence the best triangulation gt h which minimizes the solution error in the natural norm associated with the problem the main result of this paper are theorems which provide explicit expressions for the partial derivatives of the associated energy functional with respect to the coordinates xil 1 l n of each of the variable nodes mi i 1 p

quasi deadbeat minimax filters for deterministic state space models in this note a quasi deadbeat property is introduced and a quasi deadbeat minimax filter dmf is proposed as a new class of filters for deterministic discrete time state space models constraints such as linearity quasi deadbeat property and independence of the initial state information will be required in advance in addition to a new performance index of the worst case gain between the disturbance and the current estimation error the proposed dmf is obtained by directly minimizing the new performance index with above constraints finite impulse response fir and infinite impulse response iir structures are suggested with emphasis on the fir structure the proposed dmf is represented first in a standard batch form and then in an iterative form it is shown that the dmf with fir and iir structures for deterministic systems are similar in form to the existing receding horizon unbiased fir filter rhuff and the kalman filter respectively for stochastic systems

stability robustness of the discrete time lqg system under plant perturbation and noise uncertainty in this paper the robustness of discrete time lqg problems is studied the system to be controlled is described by the usual state space formulation but includes the structure of plant parameter perturbations and noise uncertainty a simple and direct way is given to derive a saddle point inequality of the closed loop system performance to cope with noise uncertainty and one sufficient condition for system stability robustness under plant perturbation is presented

moving mesh partial differential equations mmpdes based on the equidistribution principle this paper considers several moving mesh partial differential equations that are related to the equidistribution principle several of these are new and some correspond to discrete moving mesh equations that have been used by others their stability is analyzed and it is seen that a key term for most of these moving mesh pdes is a source like term that measures the level of equidistribution it is shown that under weak assumptions mesh crossing cannot occur for most of them finally numerical experiments for these various moving mesh pdes are performed to study their relative properties

review of some adaptive node movement techniques in finite element and finite difference solutions of partial differential equations abstract this article summarizes the results of a literature search for adaptive numerical methods of solving partial differential equations the methods discussed involve the adaptive movement of nodes so as to obtain a low level of solution truncation error while minimizing the number of nodes used in the calculation such methods are applicable to the solution of nonstationary flow problems that contain moving regions of rapid change in the flow variables surrounded by regions of relatively smooth variation flows with shock waves contact surfaces slip streams phase change interfaces and boundary layers can be modelled with great precision by these methods it will be shown that significant economies of execution can be attained if nodes are moved so that they remain concentrated in regions of rapid variation of the flow variables

a simple adaptive grid method in two dimensions this paper gives an interpretation of the concept of equidistribution in the context of adaptive grid generation for multidimensional problems it is shown that the equidistribution principle cannot be satisfied throughout the domain of the problem and based on this recognition a local equidistribution principle is developed a discrete formulation is described for grid generation in two space dimensions and a smoothing mechanism is presented for improving mesh quality the adaptive grid method that is constructed contains three grid quality parameters numerical examples illustrate adaptive grid generation using a prescribed monitor function and grid generation for numerical solution of partial differential equations results show that the method produces high quality grids and that it is fairly insensitive to the choice of parameters

intrinsically bayesian robust kalman filter an innovation process approach in many contemporary engineering problems model uncertainty is inherent because accurate system identification is virtually impossible owing to system complexity or lack of data on account of availability time or cost the situation can be treated by assuming that the true model belongs to an uncertainty class of models in this context an intrinsically bayesian robust ibr filter is one that is optimal relative to the cost function in the classical sense and the prior distribution over the uncertainty class in the bayesian sense ibr filters have previously been found for both wiener and granulometric morphological filtering in this paper we derive the ibr kalman filter that performs optimally relative to an uncertainty class of state space models introducing the notion of bayesian innovation process and the bayesian orthogonality principle we show how the problem of designing an ibr kalman filter can be reduced to a recursive system similar to the classical kalman recursive equations except with effective counterparts such as the effective kalman gain matrix after deriving the recursive ibr kalman equations for discrete time we use the limiting method to obtain the ibr kalman bucy equations for continuous time finally we demonstrate the utility of the proposed framework for two real world problems sensor networks and gene regulatory network inference

optimal discretizations in adaptive finite element electromagnetics one of the primary objectives of adaptive finite element analysis research is to determine how to effectively discretize a problem in order to obtain a sufficiently accurate solution efficiently therefore the characterization of optimal finite element solution properties could have significant implications on the development of improved adaptive solver technologies ultimately the analysis of optimally discretized systems in order to learn about ideal solution characteristics can lead to the design of better feedback refinement criteria for guiding practical adaptive solvers towards optimal solutions efficiently and reliably a theoretical framework for the qualitative and numerical study of optimal finite element solutions to differential equations of macroscopic electromagnetics is presented in this study for one two and three dimensional systems the formulation is based on variational aspects of optimal discretizations for helmholtz systems that are closely related to the underlying stationarity principle used in computing finite element solutions to continuum problems in addition the theory is adequately general and appropriate for the study of a range of electromagnetics problems including static and time harmonic phenomena moreover finite element discretizations with arbitrary distributions of element sizes and degrees of approximating functions are assumed so that the implications of the theory for practical h p hp and r type finite element adaption in multidimensional analyses may be examined copyright 2001 john wiley sons ltd

lqg controller synthesis with plant and noise spectral uncertainties in this paper we consider the problem of robust controller synthesis with plant and noise spectral uncertainties in lqg optimal systems we frame an algorithm for synthesizing the robust controller to minimize the least favourable cost functional j via specifying the weighting matrices q and r the wiener hopf technique in the lqg optimal system the saddle point theory and a property of the contractive operator are employed to solve this problem

the problem of the selection of an a posteriori error indicator based on smoothening techniques abstract this paper addresses the problem of assessing the quality of an a posteriori error estimate of a finite element solution an error estimate based on local l projections is analyzed in the case of translation invariant meshes it is shown that for general meshes this technique does not lead to an asymptotically exact estimator the problem is analyzed in detail in the one dimensional setting it is shown that an asymptotically exact estimator is not the optimal one when the solution is not sufficiently smooth an optimal estimator for adaptively constructed meshes is given finally a general mathematical framework for the quality assessment of estimators is introduced

voronoi cell finite difference method for the diffusion operator on arbitrary unstructured grids voronoi cells and the notion of natural neighbours are used to develop a finite difference method for the diffusion operator on arbitrary unstructured grids natural neighbours are based on the voronoi diagram which partitions space into closest point regions the sibson and the laplace non sibsonian interpolants which are based on natural neighbours have shown promise within a galerkin framework for the solution of partial differential equations in this paper we focus on the laplace interpolant with a two fold objective first to unify the previous developments related to the laplace interpolant and to indicate its ties to some well known numerical methods and secondly to propose a voronoi cell finite difference scheme for the diffusion operator on arbitrary unstructured grids a conservation law in integral form is discretized on voronoi cells to derive a finite difference scheme for the diffusion operator on irregular grids the proposed scheme can also be viewed as a point collocation technique a detailed study on consistency is conducted and the satisfaction of the discrete maximum principle stability is established owing to symmetry of the laplace weight a symmetric positive definite stiffness matrix is realized which permits the use of efficient linear solvers on a regular rectangular or hexagonal grid the difference scheme reduces to the classical finite difference method numerical examples for the poisson equation with dirichlet boundary conditions are presented to demonstrate the accuracy and convergence of the finite difference scheme copyright 2003 john wiley sons ltd

noncausal minimax linear state estimation for systems with uncertain second order statistics this note considers the problem of minimax state estimation of the states of a linear time invariant system which is driven by and observed in the presence of noise processes with uncertain second order statistics when the process noise and observations are scalars the problem is shown to be equivalent to a scalar minimax estimation problem the existence of a minimax solution is thereby established and the minimax filter is shown to be a linear transformation of the minimax filter for the scalar problem

brief state estimation of continuous time radial basis function networks this paper presents state estimators for previously trained rbf networks based on a minimax approach the uncertainty class is characterized in terms of an approximation error vector minimizing the objective function over this uncertainty class is used to obtain state estimates the initial portion of the paper presents the derivation and properties of such a minimax state estimator for rbf networks in the later portion this is extended to the problem of minimax adaptive state estimation this approach is useful in the cases where the pretrained rbf network is to be used in state estimation since the latest information is used in improving estimates of the rbf weights a special class of estimators for the appended state estimation problem is also considered where a constant gain estimator matrix can be obtained this section gives sufficient conditions for the existence of such an observer and follows directly from the structure of the rbf networks finally example applications of the minimax and adaptive minimax estimation for nonlinear problems are presented the results show the accuracy of state estimation using the proposed minimax estimator

right half plane poles and zeros and design tradeoffs in feedback systems this paper expresses limitations imposed by right half plane poles and zeros of the open loop system directly in terms of the sensitivity and complementary sensitivity functions of the closed loop system the limitations are determined by integral relationships which must be satisfied by these functions the integral relationships are interpreted in the context of feedback design

on bayesian adaptive video super resolution although multiframe super resolution has been extensively studied in past decades super resolving real world video sequences still remains challenging in existing systems either the motion models are oversimplified or important factors such as blur kernel and noise level are assumed to be known such models cannot capture the intrinsic characteristics that may differ from one sequence to another in this paper we propose a bayesian approach to adaptive video super resolution via simultaneously estimating underlying motion blur kernel and noise level while reconstructing the original high resolution frames as a result our system not only produces very promising super resolution results outperforming the state of the art but also adapts to a variety of noise levels and blur kernels to further analyze the effect of noise and blur kernel we perform a two step analysis using the cramer rao bounds we study how blur kernel and noise influence motion estimation with aliasing signals how noise affects super resolution with perfect motion and finally how blur kernel and noise influence super resolution with unknown motion our analysis results confirm empirical observations in particular that an intermediate size blur kernel achieves the optimal image reconstruction results

an edge guided image interpolation algorithm via directional filtering and data fusion preserving edge structures is a challenge to image interpolation algorithms that reconstruct a high resolution image from a low resolution counterpart we propose a new edge guided nonlinear interpolation technique through directional filtering and data fusion for a pixel to be interpolated two observation sets are defined in two orthogonal directions and each set produces an estimate of the pixel value these directional estimates modeled as different noisy measurements of the missing pixel are fused by the linear minimum mean square error estimation lmmse technique into a more robust estimate using the statistics of the two observation sets we also present a simplified version of the lmmse based interpolation algorithm to reduce computational cost without sacrificing much the interpolation performance experiments show that the new interpolation techniques can preserve edge sharpness and reduce ringing artifacts

robust stability analysis of kalman bucy filter under parametric and noise uncertainties the linear kalman bucy filter with both uncertain second order statistical noise properties and uncertain system model parameters is considered we investigate the conditions for robust stability based on the upper norm bound of noise and parametrical uncertainties saddlepoint theory and the gronwall lemma are employed to solve this problem

an estimator for uncertain output matrix systems a linear time invariant optimal estimator for uncertain output matrix systems is considered uncertainty of the output matrix is represented by a set of multiple parameters and the optimal estimator is introduced by minimizing the expected cost function of the estimation error when the number of measured variables is small the order of the optimal estimator does not depend on the number of models and meeting the computational demand becomes quite feasible

intrinsically optimal bayesian robust filtering when designing optimal filters it is often unrealistic to assume that the statistical model is known perfectly the issue is then to design a robust filter that is optimal relative to an uncertainty class of processes robust filter design has been treated from minimax best worst case performance and bayesian best average performance perspectives heretofore the bayesian approach has involved finding a model specific optimal filter one that is optimal for some model in the uncertainty class lifting this constraint we optimize over the full class from which the original optimal filters were obtained for instance over all linear filters by extending the original characteristics determining the filter such as the power spectral density to effective characteristics that apply across the uncertainty class we demonstrate for both linear and morphological filtering that an intrinsically optimal bayesian robust filter can be represented in the same form as the standard solution to the optimal filter except via the effective characteristics solutions for intrinsic bayesian robust filters are more transparent and intuitive than solutions for model specific filters and also less tedious because effective characteristics push through the spectral theory into the bayesian setting whereas solutions in the model specific case depend on grinding out the optimization

minimax robust deconvolution filters under stochastic parametric and noise uncertainties the author consider the design of robust deconvolution filters for linear discrete time systems with stochastic parameter and noise uncertainties it is assumed that some large but bounded uncertainties exist in the driving and measurement noise covariances as well as the second order statistics of stochastic parameters and initial conditions three kinds of minimax sensitivity criteria are used to develop the techniques to the synthesis of minimax deconvolution filters under uncertain linear stochastic systems their approach is based on saddle point theory and the sensitivity analysis of kalman filters the design algorithms give the recursive realization of the minimax deconvolution filters for the time varying uncertain systems under fairly general conditions for the time invariant uncertain case the existence and solutions of steady state deconvolution filters are further developed finally the utility of the minimax design approaches and the properties of the resulting minimax deconvolution filters are illustrated by a numerical example

minimax robust discrete time matched filters the problem of designing finite length discrete time matched filters is considered for situations in which exact knowledge of the input signal and or noise characteristics is not available such situations arise in many applications due to channel distortion incoherencies nonlinear effects and other modeling uncertainties in such cases it is often of interest to design a minimax robust matched filter i e a nonadaptive filter with an optimum level of worst case performance for the expected uncertainty class this problem is investigated here for three types of uncertainty models for the input signal namely the mean absolute mean square and maximum absolute distortion classes and for a wide generality of norm deviation models for the noise covariance matrix some numerical examples illustrate the robustness properties of the proposed designs

optimization of linear filters under power spectral density stabilization geometric mean filters compose a family of filters indexed by a parameter k varying between 0 and 1 they have been used to provide frequency based filtering that mitigates the noise suppression of the optimal linear wiener filter in the blurred signal plus noise model for k 0 and k 1 the geometric mean filter gives the inverse filter and the wiener filter for the model respectively the geometric mean for k 1 2 has previously been derived as the optimal linear filter for the model under power spectral density psd equalization this constraint requires the psd of the filtered signal to be equal to the psd of the uncorrupted signal that it estimates this paper defines the notion of psd stabilization in which the psd of the restored signal is equal to a predetermined function times the psd of the uncorrupted signal a particular parameterized stabilization function yields the geometric mean family as the optimal linear filter for the model under psd stabilization relative to unconstrained optimization geometric means are suboptimal however we consider a parameterized model for which the noise is such that the geometric mean filters provide optimal linear filtering in the altered signal plus noise model for which the geometric mean is optimal the blur is the same as the original model in which the geometric mean is defined but the noise psd is a function of the fourier transform of the blur and the psd of the original noise since the altered model depends on k we consider a robustness question what kind of suboptimality results from applying the geometric mean for k sub 1 to the model fur which the geometric mean for k sub 2 is optimal

l_2 e fir filters for deterministic continuous time state space signal models in this paper a new l2 e performance criterion is introduced which is represented as a gain between the disturbance during the recent time interval and the current estimation error based on the l2 e performance criterion the l2 e finite impulse response fir filter leff is proposed for deterministic continuous time state space signal models without requiring the stochastic information such as variances and means the leff is designed to minimize the maximum value of the l2 e performance criterion together with prior constraints such as linearity unbiased property in the deterministic sense and fir structure simultaneously via simulation the leff is compared with other deterministic infinite impulse response iir filters such as the hinfin and l2 linfin filters

image super resolution via sparse representation this paper presents a new approach to single image superresolution based upon sparse signal representation research on image statistics suggests that image patches can be well represented as a sparse linear combination of elements from an appropriately chosen over complete dictionary inspired by this observation we seek a sparse representation for each patch of the low resolution input and then use the coefficients of this representation to generate the high resolution output theoretical results from compressed sensing suggest that under mild conditions the sparse representation can be correctly recovered from the downsampled signals by jointly training two dictionaries for the low and high resolution image patches we can enforce the similarity of sparse representations between the low resolution and high resolution image patch pair with respect to their own dictionaries therefore the sparse representation of a low resolution image patch can be applied with the high resolution image patch dictionary to generate a high resolution image patch the learned dictionary pair is a more compact representation of the patch pairs compared to previous approaches which simply sample a large amount of image patch pairs reducing the computational cost substantially the effectiveness of such a sparsity prior is demonstrated for both general image super resolution sr and the special case of face hallucination in both cases our algorithm generates high resolution images that are competitive or even superior in quality to images produced by other similar sr methods in addition the local sparse modeling of our approach is naturally robust to noise and therefore the proposed algorithm can handle sr with noisy inputs in a more unified framework

multiple models multiplicative noise and linear quadratic control algorithmic aspects numerical solution of certain linear quadratic lq control problems for robust design is addressed an iterative method is suggested and analysed for solving a minimax multiple model lq control problem a convergent iterative method is studied for finding the constant feedback gains of a given linear controller so as to solve a spectral radius functional minimization problem for multiple plants furthermore a convergent iterative method is proposed for solving the maximum entropy parametric lq control problem with multiplicative noise

quantifying the objective cost of uncertainty in complex dynamical systems real world problems often involve complex systems that cannot be perfectly modeled or identified and many engineering applications aim to design operators that can perform reliably in the presence of such uncertainty in this paper we propose a novel bayesian framework for objective based uncertainty quantification uq which quantifies the uncertainty in a given system based on the expected increase of the operational cost that it induces this measure of uncertainty called mocu mean objective cost of uncertainty provides a practical way of quantifying the effect of various types of system uncertainties on the operation of interest furthermore the proposed uq framework provides a general mathematical basis for designing robust operators and it can be applied to diverse applications including robust filtering classification and control we demonstrate the utility and effectiveness of the proposed framework by applying it to the problem of robust structural intervention of gene regulatory networks an important application in translational genomics

state estimation with initial state uncertainty the problem of state estimation with initial state uncertainty is approached from a statistical decision theory point of view the initial state is regarded as deterministic and unknown it is only known that the initial state vector belongs to a specified parameter set the frequentist risk is considered as the performance measure and the minimax approach is adopted minimax estimators are derived for some important cases of unbounded parameter sets if the parameter set is bounded a method of finding estimators whose maximum risk is arbitrarily close to that of a minimax estimator is provided this method is illustrated with an example in which an estimator whose maximum risk is at most 3 larger than that of a minimax estimator is derived