efficient scalar quantization of exponential and laplacian random variables this paper presents solutions to the entropy constrained scalar quantizer ecsq design problem for two sources commonly encountered in image and speech compression applications sources having the exponential and laplacian probability density functions we use the memoryless property of the exponential distribution to develop a new noniterative algorithm for obtaining the optimal quantizer design we show how to obtain the optimal ecsq either with or without an additional constraint on the number of levels in the quantizer in contrast to prior methods which require a multidimensional iterative solution of a large number of nonlinear equations the new method needs only a single sequence of solutions to one dimensional nonlinear equations in some laplacian cases one additional two dimensional solution is needed as a result the new method is orders of magnitude faster than prior ones we show that as the constraint on the number of levels in the quantizer is relaxed the optimal ecsq becomes a uniform threshold quantizer utq for exponential but not for laplacian sources we then further examine the performance of the utq and optimal ecsq and also investigate some interesting alternatives to the utq including a uniform reconstruction quantizer urq and a constant dead zone ratio quantizer cdzrq

existence uniqueness and asymptotic behavior of solutions to a class of zakai equations with unbounded coefficients conditions are given to guarantee the existence and uniqueness of solutions to the zakai equation associated with the nonlinear filtering of diffusion processes the conditions permit stronger than polynomial growth of the coefficients and depend instead on the relative growth rates the results are derived by adapting through a sequence of exponential transformations the classical existence and uniqueness theorems for parabolic pde s due to besala to the robust form of the zakai equation in this process we also obtain sharp estimates for the tail behavior of the conditional density examples including observations through a polynomial sensor and estimation of the state of a bilinear system are worked out in detail our results are compared to those of fleming and mitter pardoux and sussmann who among others have obtained existence and uniqueness theorems for a more limited class of problems by different methods

a delay decomposition approach to h admissibility for discrete time singular delay systems abstract this paper considers the problem of delay dependent admissibility condition and h performance analysis for discrete time singular delay systems by utilizing the delay decomposition approach an improved delay dependent admissibility condition is presented in terms of linear matrix inequalities lmis this admissibility condition is much less conservative than some existing results and includes those as its special cases based on the proposed condition a new delay dependent bounded real lemma is also given which guarantees the admissibility and the h performance numerical examples are given to illustrate the effectiveness of the proposed method

on the new control functions for linear discrete delay systems new control functions are derived for linear difference equations with delay which can be used to construct a nontrivial solution of a boundary value problem with zero boundary conditions later a special case of invariant linear subspace is considered and corresponding control functions are constructed results for weakly nonlinear problems are also discussed

analysis of low bit rate image transform coding calculations based on high resolution quantizations prove that the distortion rate d r of an image transform coding is proportional to 2 sup 2r when r is large enough in wavelet and block cosine bases we show that if r 1 bit pixel then d r varies like r sup 1 2 spl gamma where spl gamma remains of the order of 1 for most natural images the improved performance of embedded codings in wavelet bases is analyzed at low bit rates we show that the compression performance of an orthonormal basis depends mostly on its ability to approximate images with a few nonzero vectors

on the relation of zakai s and mortensen s equations the problem of optimal control for partially observable diffusion processes is studied by the dynamic programming in function space approach first proposed by r e mortensen the density of the conditional distribution of the unobservable signal given past and present observations which satisfies the zakai equation of nonlinear filtering is viewed as the new state of the system a verification result is established for the corresponding bellman hamilton jacobi equation known as mortensen s equation

delay dependent exponential stabilization of positive 2d switched state delayed systems in the roesser model this paper deals with the controller synthesis for a class of positive two dimensional 2d switched delay systems described by the roesser model this kind of systems has the property that the states take nonnegative values whenever the initial boundaries are nonnegative some delay dependent sufficient conditions for the exponential stability of positive 2d switched systems with state delays are given furthermore the design of positive state feedback controller under which the resulting closed loop system meets the requirements of positivity and exponential stability is presented in terms of linear matrix inequalities lmis an example is included to illustrate the effectiveness of the proposed approach

entropy based algorithms for best basis selection adapted waveform analysis uses a library of orthonormal bases and an efficiency functional to match a basis to a given signal or family of signals it permits efficient compression of a variety of signals such as sound and images the predefined libraries of modulated waveforms include orthogonal wavelet packets and localized trigonometric functions and have reasonably well controlled time frequency localization properties the idea is to build out of the library functions an orthonormal basis relative to which the given signal or collection of signals has the lowest information cost the method relies heavily on the remarkable orthogonality properties of the new libraries all expansions in a given library conserve energy and are thus comparable several cost functionals are useful one of the most attractive is shannon entropy which has a geometric interpretation in this context

controllability of linear discrete systems with constant coefficients and pure delay the purpose of this contribution is to develop a controllability method for linear discrete systems with constant coefficients and with pure delay to do this a representation of solutions with the aid of a discrete matrix delayed exponential is used such an approach leads to new conditions of controllability except for a criterion of relative controllability a control function is constructed as well

on local stability of stochastic delay nonlinear discrete systems with state dependent noise abstract we examine the local stability of solutions of a delay stochastic nonlinear difference equation with deterministic and state dependent gaussian perturbations we apply the degenerate lyapunov krasovskii functional technique and construct a sequence of events each term of which is defined by a bound on a normally distributed random variable local stability holds on the intersection of these events which has probability at least 1 0 1 this probability can be made arbitrarily high by choosing the initial value sufficiently small we also present a generalization to systems where a condition for stability is expressed in terms of the diagonal part of the unperturbed system and computer simulations which illustrate our results

partially observable nonlinear risk sensitive control problems dynamic programming and verification theorems in this paper we consider continuous time partially observable optimal control problems with exponential of integral cost criteria we derive a rigorous verification theorem when the state and control enter nonlinear in the dynamics in addition we show that the quadratic sensor problem is estimation solvable with respect to a certain cost criterion the framework relies on dynamic programming and the hamilton jacobi theory

a finite dimensional risk sensitive control problem a partially observed stochastic control problem with exponential running cost is considered the dynamics are linear and the running cost is quadratic although the control may enter nonlinearly explicit solutions are found to a modified zakai equation and a backward adjoint equation this enables the problem to be expressed in terms of observable finite dimensional dynamics and a separation principle to be applied

hierarchical segmentation based image coding using hybrid quad binary trees a novel segmentation based image approximation and coding technique is proposed a hybrid quad binary qb tree structure is utilized to efficiently model and code geometrical information within images compared to other tree based representation such as wedgelets the proposed qb tree based method is more efficient for a wide range of contour features such as junctions corners and ridges especially at low bit rates

classes of nonlinear partially observable stochastic optimal control problems with explicit optimal control laws this paper introduces certain nonlinear partially observable stochastic optimal control problems which are equivalent to completely observable control problems with finite dimensional state space in some cases the optimal control laws are analogous to linear exponential quadratic gaussian and linear quadratic gaussian tracking problems the problems discussed allow nonlinearities to enter the unobservable dynamics as gradients of potential functions the methodology is based on explicit solutions of a modified duncan mortensen zakai equation

maximum likelihood parameter estimation from incomplete data via the sensitivity equations the continuous time case this paper deals with maximum likelihood ml parameter estimation of continuous time nonlinear partially observed stochastic systems via the expectation maximization em algorithm it is shown that the em algorithm can be executed efficiently provided the unnormalized conditional density of nonlinear filtering is either explicitly solvable or numerically implemented the methodology exploits the relationships between incomplete and complete data log likelihood and its gradient

fast adaptive wavelet packet image compression wavelets are ill suited to represent oscillatory patterns rapid variations of intensity can only be described by the small scale wavelet coefficients which are often quantized to zero even at high bit rates our goal is to provide a fast numerical implementation of the best wavelet packet algorithm in order to demonstrate that an advantage can be gained by constructing a basis adapted to a target image emphasis is placed on developing algorithms that are computationally efficient we developed a new fast two dimensional 2 d convolution decimation algorithm with factorized nonseparable 2 d filters the algorithm is four times faster than a standard convolution decimation an extensive evaluation of the algorithm was performed on a large class of textured images because of its ability to reproduce textures so well the wavelet packet coder significantly out performs one of the best wavelet coder on images such as barbara and fingerprints both visually and in term of psnr

optimal control of partially observable stochastic systems with an exponential of integral performance index the stochastic control problem with linear stochastic differential equations driven by brownian motion processes and as cost functional the exponential of a quadratic form is considered the soluti

stability switches in linear delay difference equations the paper discusses necessary and sufficient conditions for the asymptotic stability of the zero solution of the linear delay difference equation y n 1 email protected n email protected n k where a b are complex numbers and k is a positive integer compared to the case when a b are real numbers the stability behavior of this equation turns out to be much richer in particular if a b 1 then as k monotonously increases the equation may switch finite times from asymptotic stability to instability and vice versa we describe an interesting structure of the set of these stability switches their explicit values and apply the obtained results to some important delay difference equations and their systems

stability and exponential stability of linear discrete systems with constant coefficients and single delay this paper investigates the exponential stability and exponential estimate of the norms of solutions to a linear system of difference equations with single delay x k 1 a x k b x k m k 0 1 where a b are square constant matrices and m n sufficient conditions for exponential stability are derived using the method of lyapunov functions and its efficiency is demonstrated by examples

best wavelet packet bases in a rate distortion sense a fast rate distortion r d optimal scheme for coding adaptive trees whose individual nodes spawn descendents forming a disjoint and complete basis cover for the space spanned by their parent nodes is presented the scheme guarantees operation on the convex hull of the operational r d curve and uses a fast dynamic programing pruning algorithm to markedly reduce computational complexity applications for this coding technique include r coefman et al s yale univ 1990 generalized multiresolution wavelet packet decomposition iterative subband coders and quadtree structures applications to image processing involving wavelet packets as well as discrete cosine transform dct quadtrees are presented

representation of solutions of discrete delayed system x k 1 ax k bx k m f k with commutative matrices abstract in the investigation performed we give on half infinity discrete intervals formulas for solution of initial problem of linear discrete systems x k 1 a x k b x k m f k with constant square matrices a b such that a b b a det a 0 and with a vector function f k corresponding representations are obtained with the aid of so called discrete matrix delayed exponential which permits to represent solutions in a matrix form similarly as for ordinary differential systems with constant matrices or as well as for differential systems with constant matrices and constant delay

sparse representation in structured dictionaries with application to synthetic aperture radar sparse signal representations and approximations from overcomplete dictionaries have become an invaluable tool recently in this paper we develop a new heuristic graph structured sparse signal representation algorithm for overcomplete dictionaries that can be decomposed into subdictionaries and whose dictionary elements can be arranged in a hierarchy around this algorithm we construct a methodology for advanced image formation in wide angle synthetic aperture radar sar defining an approach for joint anisotropy characterization and image formation additionally we develop a coordinate descent method for jointly optimizing a parameterized dictionary and recovering a sparse representation using that dictionary the motivation is to characterize a phenomenon in wide angle sar that has not been given much attention before migratory scattering centers i e scatterers whose apparent spatial location depends on aspect angle finally we address the topic of recovering solutions that are sparse in more than one objective domain by introducing a suitable sparsifying cost function we encode geometric objectives into sar image formation through sparsity in two domains including the normal parameter space of the hough transform

the asymptotic stability of xn 1 axn bxn k 0 we obtain necessary and sufficient conditions for the asymptotic stability of the difference equation xn 1 axn bxn k 0 n 0 1 2 where the coefficients a and b are real numbers and the delay k is a nonnegative integer

general finite dimensional risk sensitive problems and small noise limits for a risk sensitive partially observed stochastic control problem the modified zakai equation includes an extra term related to the exponential running cost the finite dimensional solutions of this modified zakai equation are obtained these are analogs of the kalman and benes filters the small noise limits of the finite dimensional risk sensitive problems are then obtained these lead to differential games with deterministic disturbances

multilayered image representation application to image compression the main contribution of this work is a new paradigm for image representation and image compression we describe a new multilayered representation technique for images an image is parsed into a superposition of coherent layers piecewise smooth regions layer textures layer etc the multilayered decomposition algorithm consists in a cascade of compressions applied successively to the image itself and to the residuals that resulted from the previous compressions during each iteration of the algorithm we code the residual part in a lossy way we only retain the most significant structures of the residual part which results in a sparse representation each layer is encoded independently with a different transform or basis at a different bitrate and the combination of the compressed layers can always be reconstructed in a meaningful way the strength of the multilayer approach comes from the fact that different sets of basis functions complement each others some of the basis functions will give reasonable account of the large trend of the data while others will catch the local transients or the oscillatory patterns this multilayered representation has a lot of beautiful applications in image understanding and image and video coding we have implemented the algorithm and we have studied its capabilities

representation of solutions of delayed difference equations with linear parts given by pairwise permutable matrices via z transform in the present paper a system of nonhomogeneous linear difference equations with any finite number of constant delays and linear parts given by pairwise permutable matrices is considered representation of its solution is derived in a form of a matrix polynomial using the z transform so the recent results for one and two delays and an inductive formula for multiple delays are unified the representation is suitable for theoretical as well as practical computations

variational denoising of partly textured images by spatially varying constraints denoising algorithms based on gradient dependent regularizers such as nonlinear diffusion processes and total variation denoising modify images towards piecewise constant functions although edge sharpness and location is well preserved important information encoded in image features like textures or certain details is often compromised in the process of denoising we propose a mechanism that better preserves fine scale features in such denoising processes a basic pyramidal structure texture decomposition of images is presented and analyzed a first level of this pyramid is used to isolate the noise and the relevant texture components in order to compute spatially varying constraints based on local variance measures a variational formulation with a spatially varying fidelity term controls the extent of denoising over image regions our results show visual improvement as well as an increase in the signal to noise ratio over scalar fidelity term processes this type of processing can be used for a variety of tasks in partial differential equation based image processing and computer vision and is stable and meaningful from a mathematical viewpoint

image compression with adaptive local cosines a comparative study the goal of this work is twofold first we demonstrate that an advantage can be gained by using local cosine bases over wavelets to encode images that contain periodic textures we designed a coder that outperforms one of the best wavelet coders on a large number of images the coder finds the optimal segmentation of the image in terms of local cosine bases the coefficients are encoded using a scalar quantizer optimized for laplacian distributions this new coder constitutes the first concrete contribution of the paper second we used our coder to perform an extensive comparison of several optimized bells in terms of rate distortion and visual quality for a large collection of images this study provides for the first time a rigorous evaluation in realistic conditions of these bells our experiments show that bells that are designed to reproduce exactly polynomials of degree 1 resulted in the worst performance in terms of the psnr however a visual inspection of the compressed images indicates that these bells often provide reconstructed images with very few visual artifacts even at low bit rates the bell with the most narrow fourier transform gave the best results in terms of the psnr on most images this bell tends however to create annoying visual artifacts in very smooth regions at low bit rate

the stability of stochastic coupled systems with time delays and time varying coupling structure this paper is concerned with the pth moment exponential stability of stochastic coupled systems with time delays and time varying coupling structure sctvcs the coupling structure is time varying first second the method of graph theory has been generalized from a system established on a digraph with constant coupling structure to a digraph with time varying coupling structure successfully combining graph theory with lyapunov method a systematic method is given to construct a lyapunov function for sctvcs several pth moment exponential stability criteria are presented including a lyapunov type theorem and some sufficient criteria in the form of coefficients furthermore the theoretical conclusions are applied to the stochastic coupled oscillators with time varying coupling structure and two stability criteria are obtained finally we give two numerical examples to illustrate the effectiveness of our results

exponential stability of descriptor systems with large delay period based on a switching method this paper addresses the problem of exponential stability for a class of descriptor systems with interval time varying delays the time varying delays contain a large delay period ldp which is often present in practical control systems such descriptor system with ldp has been modeled as a switched descriptor system with delay which may include an unstable subsystem caused by large delay bound by adopting the switching technique and constructing a novel lyapunov krasovskii functional stability criteria are proposed under the restriction frequency and the rate of ldp to ensure that the descriptor system is regular impulse free and exponentially stable finally an integrated circuit example and a numerical simulation are given to illustrate the effectiveness and applicability of the proposed method