a review of geometric transformations for nonrigid body registration this paper provides a comprehensive and quantitative review of spatial transformations models for nonrigid image registration it explains the theoretical foundation of the models and classifies them according to this basis this results in two categories physically based models described by partial differential equations of continuum mechanics e g linear elasticity and fluid flow and basis function expansions derived from interpolation and approximation theory e g radial basis functions b splines and wavelets recent work on constraining the transformation so that it preserves the topology or is diffeomorphic is also described the final section reviews some recent evaluation studies the paper concludes by explaining under what conditions a particular transformation model is appropriate

kalman filtering with intermittent observations on the boundedness of the expected error covariance this paper addresses the stability of a kalman filter when measurements are intermittently available due to constraints in the communication channel between the sensor and the estimator we give a necessary condition and a sufficient condition with a trivial gap between them for the boundedness of the expected value of the estimation error covariance these conditions are more general than the existing ones in the sense that they only require the state matrix of the system to be diagonalizable and the sequence of packet losses to be a stationary finite order markov process hence we extend the class of systems for which these conditions are known in two directions namely by including degenerate systems and by considering network models more general than i i d and gilbert elliott we show that these conditions recover known results from the literature when evaluated for non degenerate systems under the assumption of i i d or gilbert elliott packet loss models

optimal estimation and control for lossy network stability convergence and performance in this paper we study the problems of optimal estimation and control i e the linear quadratic gaussian lqg control for systems with packet losses but without acknowledgment such acknowledgment is a signal sent by the actuator to inform the estimator of the incidence of control packet losses for such system which is usually called as a user datagram protocol udp like system the optimal estimation is nonlinear and its calculation is time consuming making its corresponding optimal lqg problem complicated we first propose two conditions 1 the sensor has some computation abilities and 2 the control command exerted to the plant is known to the sensor for a udp like system satisfying these two conditions we derive the optimal estimation by constructing the finite and infinite product probability measure spaces for the estimation error covariances eec we give the stability condition for the expected eec and show the existence of a measurable function to which the eec converges in distribution and propose some practical methods to evaluate the estimation performance finally the lqg controllers are derived and the conditions for the mean square stability of the closed loop system are established

variational methods for multimodal image matching matching images of different modalities can be achieved by the maximization of suitable statistical similarity measures within a given class of geometric transformations handling complex nonrigid deformations in this context turns out to be particularly difficult and has attracted much attention in the last few years the thrust of this paper is that many of the existing methods for nonrigid monomodal registration that use simple criteria for comparing the intensities e g ssd can be extended to the multimodal case where more complex intensity similarity measures are necessary to this end we perform a formal computation of the variational gradient of a hierarchy of statistical similarity measures and use the results to generalize a recently proposed and very effective optical flow algorithm l alvarez j weickert and j sanchez 2000 technical report and ijcv 39 1 41 56 to the case of multimodal image registration our method readily extends to the case of locally computed similarity measures thus providing the flexibility to cope with spatial non stationarities in the way the intensities in the two images are related the well posedness of the resulting equations is proved in a complementary work o d faugeras and g hermosillo 2001 technical report 4235 inria using well established techniques in functional analysis we briefly describe our numerical implementation of these equations and show results on real and synthetic data

stability of mmse state estimators over lossy networks using linear coding this paper studies the state estimation problem for a stochastic discrete time system over a lossy channel where the packet loss is modeled as an independent and identically distributed binary process to counter the effect of random packet loss we propose a linear coding method to preprocess the measured output and prove that the coded output is information preserving when packet loss is void and is information enhancing when packet loss is present an optimal state estimator under the minimum mean square error mmse criterion is derived for the coded output when subject to packet loss the maximum packet loss rate for ensuring a stable estimator is then derived and shown to be very close to a well known lower bound also considered is a compressed linear coding method where the measured output is first compressed onto a lower dimensional space before encoding and it is shown that the similar packet rate condition for stability holds

kalman filtering with intermittent observations tail distribution and critical value in this paper we analyze the performance of kalman filtering for discrete time linear gaussian systems where packets containing observations are dropped according to a markov process modeling a gilbert elliot channel to address the challenges incurred by the loss of packets we give a new definition of non degeneracy which is essentially stronger than the classical definition of observability but much weaker than one step observability which is usually used in the study of kalman filtering with intermittent observations we show that the trace of the kalman estimation error covariance under intermittent observations follows a power decay law moreover we are able to compute the exact decay rate for non degenerate systems finally we derive the critical value for non degenerate systems based on the decay rate improving upon the state of the art

diffeomorphisms groups and pattern matching in image analysis in a previous paper it was proposed to see the deformations of a common pattern as the action of an infinite dimensional group we show in this paper that this approac h can be applied numerically for pattern matching in image analysis of digital images using lie group ideas we construct a distance between deformations defined through a metric given the cost of infinitesimal deformations then we propose a numerical scheme to solve a variational problem involving this distance and leading to a sub optimal gradient pattern matching its links with fluid models are established

registration of 4d cardiac ct sequences under trajectory constraints with multichannel diffeomorphic demons we propose a framework for the nonlinear spatiotemporal registration of 4d time series of images based on the diffeomorphic demons dd algorithm in this framework the 4d spatiotemporal registration is decoupled into a 4d temporal registration defined as mapping physiological states and a 4d spatial registration defined as mapping trajectories of physical points our contribution focuses more specifically on the 4d spatial registration that should be consistent over time as opposed to 3d registration that solely aims at mapping homologous points at a given time point first we estimate in each sequence the motion displacement field which is a dense representation of the point trajectories we want to register then we perform simultaneously 3d registrations of corresponding time points with the constraints to map the same physical points over time called the trajectory constraints under these constraints we show that the 4d spatial registration can be formulated as a multichannel registration of 3d images to solve it we propose a novel version of the diffeomorphic demons dd algorithm extended to vector valued 3d images the multichannel diffeomorphic demons mdd for evaluation this framework is applied to the registration of 4d cardiac computed tomography ct sequences and compared to other standard methods with real patient data and synthetic data simulated from a physiologically realistic electromechanical cardiac model results show that the trajectory constraints act as a temporal regularization consistent with motion whereas the multichannel registration acts as a spatial regularization finally using these trajectory constraints with multichannel registration yields the best compromise between registration accuracy temporal and spatial smoothness and computation times a prospective example of application is also presented with the spatiotemporal registration of 4d cardiac ct sequences of the same patient before and after radiofrequency ablation rfa in case of atrial fibrillation af the intersequence spatial transformations over a cardiac cycle allow to analyze and quantify the regression of left ventricular hypertrophy and its impact on the cardiac function

determining optical flow for irregular domains by minimizing quadratic functionals of a certain class snyder 1989 has recently classified all smoothness terms which involve first order derivatives of the flowfield u x t and of the image grey value function g x t the physically plausible smoothness terms belonging to this class are known from the work of horn and schunck 1981 and nagel 1987 in this paper we discuss the possibilities of approximating the solutions to the minimization problems of horn schunk 1981 and nagel 1987 in particular it is shown that these solutions exist are unique and depend continuously on the input data these properties make it possible while taking into consideration arbitrary models of the grey value function to approximate efficiently the weak solutions of the associated boundary value problems in irregularly shaped domains with a sufficiently smooth boundary using finite elements experiments with image sequences from synthetic as well as outdoor scenes show how the orientation dependency of the smoothness term in nagel s approach influences the results

a general framework for low level vision we introduce a new geometrical framework based on which natural flows for image scale space and enhancement are presented we consider intensity images as surfaces in the x i space the image is thereby a two dimensional 2 d surface in three dimensional 3 d space for gray level images and 2 d surfaces in five dimensions for color images the new formulation unifies many classical schemes and algorithms via a simple scaling of the intensity contrast and results in new and efficient schemes extensions to multidimensional signals become natural and lead to powerful denoising and scale space algorithms

fast geodesic active fields for image registration based on splitting and augmented lagrangian approaches in this paper we present an efficient numerical scheme for the recently introduced geodesic active fields gaf framework for geometric image registration this framework considers the registration task as a weighted minimal surface problem hence the data term and the regularization term are combined through multiplication in a single parametrization invariant and geometric cost functional the multiplicative coupling provides an intrinsic spatially varying and data dependent tuning of the regularization strength and the parametrization invariance allows working with images of nonflat geometry generally defined on any smoothly parametrizable manifold the resulting energy minimizing flow however has poor numerical properties here we provide an efficient numerical scheme that uses a splitting approach data and regularity terms are optimized over two distinct deformation fields that are constrained to be equal via an augmented lagrangian approach our approach is more flexible than standard gaussian regularization since one can interpolate freely between isotropic gaussian and anisotropic tv like smoothing in this paper we compare the geodesic active fields method with the popular demons method and three more recent state of the art algorithms nl optical flow mrf image registration and landmark enhanced large displacement optical flow thus we can show the advantages of the proposed fastgaf method it compares favorably against demons both in terms of registration speed and quality over the range of example applications it also consistently produces results not far from more dedicated state of the art methods illustrating the flexibility of the proposed framework

on solvability of boundary value problems for higher order nonlinear hyperbolic equations abstract in the rectangle 0 a 0 b for the nonlinear hyperbolic equation u m n i 0 m 1 h 1 i x u i n k 0 n 1 h 2 k y u m k f x y u u m 1 n 1 the boundary value problems of the type l 1 i u y 0 i 1 m l 2 k u x 0 k 1 n are considered where l 1 i c m 1 0 a r i 1 m and l 2 k c n 1 0 b r k 1 n are linear bounded functionals sufficient conditions of solvability and unique solvability of the general problem and its particular cases nicoletti type dirichlet lidstone and periodic problems are established

a theoretical framework for convex regularizers in pde based computation of image motion many differential methods for the recovery of the optic flow field from an image sequence can be expressed in terms of a variational problem where the optic flow minimizes some energy typically these energy functionals consist of two terms a data term which requires e g that a brightness constancy assumption holds and a regularizer that encourages global or piecewise smoothness of the flow field in this paper we present a systematic classification of rotation invariant convex regularizers by exploring their connection to diffusion filters for multichannel images this taxonomy provides a unifying framework for data driven and flow driven isotropic and anisotropic as well as spatial and spatio temporal regularizers while some of these techniques are classic methods from the literature others are derived here for the first time we prove that all these methods are well posed they posses a unique solution that depends in a continuous way on the initial data an interesting structural relation between isotropic and anisotropic flow driven regularizers is identified and a design criterion is proposed for constructing anisotropic flow driven regularizers in a simple and direct way from isotropic ones its use is illustrated by several examples

reliable estimation of dense optical flow fields with large displacements in this paper we show that a classic optical flow technique by nagel and enkelmann 1986 ieee trans pattern anal mach intell vol 8 pp 565 593 can be regarded as an early anisotropic diffusion method with a diffusion tensor we introduce three improvements into the model formulation that i avoid inconsistencies caused by centering the brightness term and the smoothness term in different images ii use a linear scale space focusing strategy from coarse to fine scales for avoiding convergence to physically irrelevant local minima and iii create an energy functional that is invariant under linear brightness changes applying a gradient descent method to the resulting energy functional leads to a system of diffusion reaction equations we prove that this system has a unique solution under realistic assumptions on the initial data and we present an efficient linear implicit numerical scheme in detail our method creates flow fields with 100 density over the entire image domain it is robust under a large range of parameter variations and it can recover displacement fields that are far beyond the typical one pixel limits which are characteristic for many differential methods for determining optical flow we show that it performs better than the optical flow methods with 100 density that are evaluated by barron et al 1994 int j comput vision vol 12 pp 43 47 our software is available from the internet

event triggered maximum likelihood state estimation the event triggered state estimation problem for linear time invariant systems is considered in the framework of maximum likelihood ml estimation in this paper we show that the optimal estimate is parameterized by a special time varying riccati equation and the computational complexity increases exponentially with respect to the time horizon for ease in implementation a one step event based ml estimation problem is further formulated and solved and the solution behaves like a kalman filter with intermittent observations for the one step problem the calculation of upper and lower bounds of the communication rates from the process side is also briefly analyzed an application example to sensorless event based estimation of a dc motor system is presented and the benefits of the obtained one step event based estimator are demonstrated by comparative simulations

asymptotic behavior of recursive state estimations with intermittent measurements convergence rate and stationary distribution approximation are investigated in this paper for both the covariance matrix of the kalman filter and the pseudo covariance matrix of a robust recursive state estimator developed by us when the measurement dropping process is described by a markov chain and an associated plant is both controllable and observable it is proved that if the dropping probability is less than 1 these two matrices converge exponentially to a stationary distribution independent of its initial values moreover when they are initialized with the stabilizing solution of an associated algebraic riccati equation both of them are shown to converge to an ergodic process based on these results two approximations are derived for their stationary probability distributions as well as a bound of approximation errors it has been made clear that rather than the delta function suggested by kar and moura a series of delta functions give a more accurate approximation and replacement of these estimators update gain by a constant matrix usually deteriorates their steady estimation accuracy a numerical example is provided to illustrate the obtained theoretical results

robust recursive state estimation with random measurement droppings a recursive state estimation procedure is derived for a linear time varying system with both parametric uncertainties and stochastic measurement droppings this estimator has a similar form as that of kalman filter with intermittent observations but its parameters should be adjusted when a plant output measurement arrives a new recursive form is derived for the pseudo covariance matrix of estimation errors based on a riemannian metric for positive definite matrices some necessary and sufficient conditions have been obtained for the strict contractiveness of this recursion it has also been proved that under some controllability and observability conditions as well as some weak requirements on measurement arrival probability the update gain of this recursive robust state estimator and the mean of its squared estimation errors converge in probability one respectively to a corresponding stationary distribution numerical simulation results show that estimation accuracy of the suggested procedure is more robust against parametric modelling errors than kalman filter

kalman filtering with intermittent observations motivated by navigation and tracking applications within sensor networks we consider the problem of performing kalman filtering with intermittent observations when data travel along unreliable communication channels in a large wireless multihop sensor network the effect of communication delays and loss of information in the control loop cannot be neglected we address this problem starting from the discrete kalman filtering formulation and modeling the arrival of the observation as a random process we study the statistical convergence properties of the estimation error covariance showing the existence of a critical value for the arrival rate of the observations beyond which a transition to an unbounded state error covariance occurs we also give upper and lower bounds on this expected state error covariance

well posedness of nonlocal boundary value problems with integral condition for the system of hyperbolic equations abstract a nonlocal boundary value problem with integral condition for a system of hyperbolic equations is considered relationship with the family of boundary value problems for ordinary differential equations is established sufficient and necessary conditions of well posedness of nonlocal boundary value problems with integral condition for a system of hyperbolic equations are obtained

large displacement optical flow descriptor matching in variational motion estimation optical flow estimation is classically marked by the requirement of dense sampling in time while coarse to fine warping schemes have somehow relaxed this constraint there is an inherent dependency between the scale of structures and the velocity that can be estimated this particularly renders the estimation of detailed human motion problematic as small body parts can move very fast in this paper we present a way to approach this problem by integrating rich descriptors into the variational optical flow setting this way we can estimate a dense optical flow field with almost the same high accuracy as known from variational optical flow while reaching out to new domains of motion analysis where the requirement of dense sampling in time is no longer satisfied

spherical demons fast diffeomorphic landmark free surface registration we present the spherical demons algorithm for registering two spherical images by exploiting spherical vector spline interpolation theory we show that a large class of regularizors for the modified demons objective function can be efficiently approximated on the sphere using iterative smoothing based on one parameter subgroups of diffeomorphisms the resulting registration is diffeomorphic and fast the spherical demons algorithm can also be modified to register a given spherical image to a probabilistic atlas we demonstrate two variants of the algorithm corresponding to warping the atlas or warping the subject registration of a cortical surface mesh to an atlas mesh both with more than 160 k nodes requires less than 5 min when warping the atlas and less than 3 min when warping the subject on a xeon 3 2 ghz single processor machine this is comparable to the fastest nondiffeomorphic landmark free surface registration algorithms furthermore the accuracy of our method compares favorably to the popular freesurfer registration algorithm we validate the technique in two different applications that use registration to transfer segmentation labels onto a new image 1 parcellation of in vivo cortical surfaces and 2 brodmann area localization in ex vivo cortical surfaces

catadioptric projective geometry catadioptric sensors are devices which utilize mirrors and lenses to form a projection onto the image plane of a camera central catadioptric sensors are the class of these devices having a single effective viewpoint in this paper we propose a unifying model for the projective geometry induced by these devices and we study its properties as well as its practical implications we show that a central catadioptric projection is equivalent to a two step mapping via the sphere the second step is equivalent to a stereographic projection in the case of parabolic mirrors conventional lens based perspective cameras are also central catadioptric devices with a virtual planar mirror and are thus covered by the unifying model we prove that for each catadioptric projection there exists a dual catadioptric projection based on the duality between points and line images conics it turns out that planar and parabolic mirrors build a dual catadioptric projection pair as a practical example we describe a procedure to estimate focal length and image center from a single view of lines in arbitrary position for a parabolic catadioptric system

alignment by maximization of mutual information a new information theoretic approach is presented for finding the pose of an object in an image the technique does not require information about the surface properties of the object besides its shape and is robust with respect to variations of illumination in our derivation few assumptions are made about the nature of the imaging process as a result the algorithms are quite general and may foreseeably be used in a wide variety of imaging situations experiments are presented that demonstrate the approach registering magnetic resonance mr images aligning a complex 3d object model to real scenes including clutter and occlusion tracking a human head in a video sequence and aligning a view based 2d object model to real images the method is based on a formulation of the mutual information between the model and the image as applied here the technique is intensity based rather than feature based it works well in domains where edge or gradient magnitude based methods have difficulty yet it is more robust than traditional correlation additionally it has an efficient implementation that is based on stochastic approximation

an improved stability condition for kalman filtering with bounded markovian packet losses in this paper we consider the peak covariance stability of kalman filtering subject to packet losses the length of consecutive packet losses is governed by a time homogeneous finite state markov chain we establish a sufficient condition for peak covariance stability and show that this stability check can be recast as a linear matrix inequality lmi feasibility problem compared with the literature the stability condition given in this paper is invariant with respect to similarity state transformations moreover our condition is proved to be less conservative than the existing results numerical examples are provided to demonstrate the effectiveness of our result

geodesic active fields a geometric framework for image registration in this paper we present a novel geometric framework called geodesic active fields for general image registration in image registration one looks for the underlying deformation field that best maps one image onto another this is a classic ill posed inverse problem which is usually solved by adding a regularization term here we propose a multiplicative coupling between the registration term and the regularization term which turns out to be equivalent to embed the deformation field in a weighted minimal surface problem then the deformation field is driven by a minimization flow toward a harmonic map corresponding to the solution of the registration problem this proposed approach for registration shares close similarities with the well known geodesic active contours model in image segmentation where the segmentation term the edge detector function is coupled with the regularization term the length functional via multiplication as well as a matter of fact our proposed geometric model is actually the exact mathematical generalization to vector fields of the weighted length problem for curves and surfaces introduced by caselles kimmel sapiro the energy of the deformation field is measured with the polyakov energy weighted by a suitable image distance borrowed from standard registration models we investigate three different weighting functions the squared error and the approximated absolute error for monomodal images and the local joint entropy for multimodal images as compared to specialized state of the art methods tailored for specific applications our geometric framework involves important contributions firstly our general formulation for registration works on any parametrizable smooth and differentiable surface including nonflat and multiscale images in the latter case multiscale images are registered at all scales simultaneously and the relations between space and scale are intrinsically being accounted for second this method is to the best of our knowledge the first reparametrization invariant registration method introduced in the literature thirdly the multiplicative coupling between the registration term i e local image discrepancy and the regularization term naturally results in a data dependent tuning of the regularization strength finally by choosing the metric on the deformation field one can freely interpolate between classic gaussian and more interesting anisotropic tv like regularization

stability of kalman filtering with markovian packet losses we consider kalman filtering in a network with packet losses and use a two state markov chain to describe the normal operating condition of packet delivery and transmission failure based on the sojourn time of each visit to the failure or successful packet reception state we analyze the behavior of the estimation error covariance matrix and introduce the notion of peak covariance as an estimate of filtering deterioration caused by packet losses which describes the upper envelope of the sequence of error covariance matrices p t t 1 for the case of an unstable scalar model we give sufficient conditions for the stability of the peak covariance process in the general vector case and obtain a sufficient and necessary condition for the scalar case finally the relationship between two different types of stability notions is discussed

group actions homeomorphisms and matching a general framework this paper constructs metrics on the space of images cal i defined as orbits under group actions cal g the groups studied include the finite dimensional matrix groups and their products as well as the infinite dimensional diffeomorphisms examined in trouve 1999 quaterly of applied math and dupuis et al 1998 quaterly of applied math left invariant metrics are defined on the product cal g times cal i thus allowing the generation of transformations of the background geometry as well as the image values examples of the application of such metrics are presented for rigid object matching with and without signature variation curves and volume matching and structural generation in which image values are changed supporting notions such as tissue creation in carrying one image to another

on a stochastic sensor selection algorithm with applications in sensor scheduling and sensor coverage in this note we consider the following problem suppose a set of sensors is jointly trying to estimate a process one sensor takes a measurement at every time step and the measurements are then exchanged among all the sensors what is the sensor schedule that results in the minimum error covariance we describe a stochastic sensor selection strategy that is easy to implement and is computationally tractable the problem described above comes up in many domains out of which we discuss two in the sensor selection problem there are multiple sensors that cannot operate simultaneously e g sonars in the same frequency band thus measurements need to be scheduled in the sensor coverage problem a geographical area needs to be covered by mobile sensors each with limited range thus from every position the sensors obtain a different view point of the area and the sensors need to optimize their trajectories the algorithm is applied to these problems and illustrated through simple examples

the integral operator method for finding almost periodic solutions of nonlinear wave equations on considere une equation d onde autonome semilineaire de la forme u tt u x x a u x b u t c u f u x t r 2 ou a b c sont des constantes et f u est une fonction continue dans r on cherche une solution non constante satisfaisant la condition presque periodique par rapport a x t

jacobi iteration in implicit difference schemes for the wave equation it is shown how a jacobi iteration can be used to approximate the linear algebra required by a class of implicit finite difference element schemes for a linear hyperbolic pde while preserving the important properties of the implicit scheme in particular it is shown that order of accuracy stability energy conservation and isotropy of the implicit scheme are all carried over into the new scheme in general the new scheme is much more efficient than the implicit scheme it is derived from for problems in more than one space variable and can be vectorized and or parallelized quite easily furthermore it is shown that a modification of the technique can be used to improve some properties of the underlying implicit scheme at little or no extra cost

minimax estimation with intermittent observations this paper considers a problem of minimax or h state estimation with intermittent observations in this setting the disturbance in the dynamical system and the sensor noise are controlled by adversaries and the estimator receives the sensor measurements only sporadically with the availability governed by an independent and identically distributed bernoulli process we cast this problem within the framework of stochastic zero sum dynamic games we first obtain a corresponding stochastic minimax state estimator smse and an associated generalized stochastic riccati equation gsre whose evolutions depend on two parameters one that governs the random measurement arrivals and another one that quantifies the level of h disturbance attenuation we then analyze the asymptotic behavior of the sequence generated by the gsre in the expectation sense and its weak convergence specifically we obtain threshold type conditions above which the sequence generated by the gsre can be bounded both below and above in the expectation sense moreover we show that under some conditions the norm of the sequence generated by the gsre converges weakly to a unique stationary distribution finally we prove that when the disturbance attenuation parameter goes to infinity our asymptotic results are equivalent to the corresponding results from the literature on kalman filtering with intermittent observations we provide simulations to illustrate the results

kalman filtering with relays over wireless fading channels this note studies the use of relays to improve the performance of kalman filtering over packet dropping links packet reception probabilities are governed by time varying fading channel gains and the sensor and relay transmit powers we consider situations with multiple sensors and relays where each relay can either forward one of the sensors measurements to the gateway fusion center or perform a simple linear network coding operation on some of the sensor measurements using an expected error covariance performance measure we consider optimal and suboptimal methods for finding the best relay configuration and power control problems for optimizing the kalman filter performance our methods show that significant performance gains can be obtained through the use of relays network coding and power control with at least 30 40 less power consumption for a given expected error covariance specification

scale space analysis and active contours for omnidirectional images a new generation of optical devices that generate images covering a larger part of the field of view than conventional cameras namely catadioptric cameras is slowly emerging these omnidirectional images will most probably deeply impact computer vision in the forthcoming years provided that the necessary algorithmic background stands strong in this paper we propose a general framework that helps define various computer vision primitives we show that geometry which plays a central role in the formation of omnidirectional images must be carefully taken into account while performing such simple tasks as smoothing or edge detection partial differential equations pdes offer a very versatile tool that is well suited to cope with geometrical constraints we derive new energy functionals and pdes for segmenting images obtained from catadioptric cameras and show that they can be implemented robustly using classical finite difference schemes various experimental results illustrate the potential of these new methods on both synthetic and natural images

robust stabilization subject to structured uncertainties and mean power constraint abstract this paper deals with a robust stabilization problem for discrete time systems subject to multiple disturbances occurring in controller and actuating channel where both linear structured uncertainties and white gaussian noises are included the desired control law is aimed to robustly stabilize the system and to satisfy some pre specified mean power constraint simultaneously by the philosophy of the mixed h 2 h control a solvability condition is first derived for single input systems that reveals the intrinsic relation between the unstable poles of the plant and the disturbance parameters together with two cross coupled algebraic riccati equations the result is further generalized to multiple input systems with a sufficient condition given again by the unstable poles of the plant an example is included to illustrate the current results

periodic solutions of hyperbolic partial differential equations abstract constructive methods by obtaining multiple solutions of first and second order nonlinear hyperbolic periodic boundary value problems are given appropriate partial differential inequalities are developed and are then employed to derive the iterative schemes which yield the desired solutions the advantage of these methods is that the solutions of the given nonlinear problems are constructed as uniform limits of monotone iterates these iterates being solutions of linear problems are explicitly computable

on kalman filtering for detectable systems with intermittent observations we consider the problem of kalman filtering when observations are available according to a bernoulli process it is known that there exists a critical probability pc such that if measurements are available with probability greater than pc then the expected prediction covariance is bounded for all initial conditions otherwise it is unbounded for some initial conditions we show that when the system observation matrix restricted to the observable subspace is invertible the known lower bound on pc is in fact the exact critical probability this result is based on a novel decomposition of positive semidefinite matrices

multi sensor kalman filtering with intermittent measurements in this paper we extend the stability theory on kalman filtering with intermittent measurements from the scenario of one single sensor to the one of multiple sensors consider that a group of sensors take measurement of the states of a process and then send the data to a remote estimator the estimator receives the measurements intermittently which may be caused by the fact that the channels have packet dropouts or that the sensors schedule the data transmission stochastically based on the received measurements the estimator computes the estimates of the process states by multi sensor kalman filtering because of the intermittent measurements the estimator may be unstable this stability issue is mainly investigated in this paper a notion of transmission capacity which is related to the communication rates of sensors is proposed it is shown that the expected estimation error covariance diverges for all feasible communication rates collections of the sensors when the transmission capacity is below a certain value meanwhile when the transmission capacity is above another certain value there exists a feasible communication rates collection such that the expected estimation error covariance is bounded