wavelets and filter banks theory and design the wavelet transform is compared with the more classical short time fourier transform approach to signal analysis then the relations between wavelets filter banks and multiresolution signal processing are explored a brief review is given of perfect reconstruction filter banks which can be used both for computing the discrete wavelet transform and for deriving continuous wavelet bases provided that the filters meet a constraint known as regularity given a low pass filter necessary and sufficient conditions for the existence of a complementary high pass filter that will permit perfect reconstruction are derived the perfect reconstruction condition is posed as a bezout identity and it is shown how it is possible to find all higher degree complementary filters based on an analogy with the theory of diophantine equations an alternative approach based on the theory of continued fractions is also given these results are used to design highly regular filter banks which generate biorthogonal continuous wavelet bases with symmetries

constrained linear quadratic regulation the paper is a contribution to the theory of the infinite horizon linear quadratic regulator lqr problem subject to inequality constraints on the inputs and states extending an approach first proposed by sznaier and damborg 1987 a solution algorithm is presented which requires solving a finite number of finite dimensional positive definite quadratic programs the constrained lqr outlined does not feature the undesirable mismatch between open loop and closed loop nominal system trajectories which is present in the other popular forms of model predictive control mpc that can be implemented with a finite quadratic programming algorithm the constrained lqr is shown to be both optimal and stabilizing the solution algorithm is guaranteed to terminate in finite time with a computational cost that has a reasonable upper bound compared to the minimal cost for computing the optimal solution inherent to the approach is the removal of a tuning parameter the control horizon which is present in other mpc approaches and for which no reliable tuning guidelines are available two examples are presented that compare constrained lqr and two other popular forms of mpc the examples demonstrate that constrained lqr achieves significantly better performance than the other forms of mpc on some plants and the computational cost is not prohibitive for online implementation

a remark concerning m divisibility and the discrete logarithm in the divisor class group of curves the aim of this paper is to show that the computation of the discrete logarithm in the m torsion part of the divisor class group of a curve x over a finite field ko with char ko prime to m or over a local field k with residue field ko can be reduced to the computation of the discrete logarithm in k0 4m for this purpose we use a variant of the tame tate pairing for abelian varieties over local fields in the same way the problem to determine all linear combinations of a finite set of elements in the divisor class group of a curve over k or ko which are divisible by m is reduced to the computation of the discrete logarithm in ko cm

jpeg2000 coded image error concealment exploiting convex sets projections transmission errors in jpeg2000 can be grouped into three main classes depending on the affected area ll high frequencies at the lower decomposition levels and high frequencies at the higher decomposition levels the first type of errors are the most annoying but can be concealed exploiting the signal spatial correlation like in a number of techniques proposed in the past the second are less annoying but more difficult to address the latter are often imperceptible in this paper we address the problem of concealing the second class or errors when high bit planes are damaged by proposing a new approach based on the theory of projections onto convex sets accordingly the error effects are masked by iteratively applying two procedures low pass lp filtering in the spatial domain and restoration of the uncorrupted wavelet coefficients in the transform domain it has been observed that a uniform lp filtering brought to some undesired side effects that negatively compensated the advantages this problem has been overcome by applying an adaptive solution which exploits an edge map to choose the optimal filter mask size simulation results demonstrated the efficiency of the proposed approach

constrained mpc algorithm for uncertain time varying systems with state delay in this note we present a model predictive control mpc algorithm for uncertain time varying systems with input constraints and state delay uncertainty is assumed to be polytopic and delay is assumed to be unknown but with a known upper bound for a memoryless state feedback mpc law we define an optimization problem that minimizes a cost function and relaxes it to two other optimization problems by finding an upper bound of the cost function one is solvable and the other is not we prove equivalence and feasibilities of the two optimization problems under a certain assumption on the weighting matrix based on these properties and optimality we show that feasible mpc from the optimization problems stabilizes the closed loop system then we present an improved mpc algorithm that includes relaxation procedures of the assumption on the weighting matrix and stabilizes the closed loop system finally a numerical example illustrates the performance of the proposed algorithm

improved pollard rho method for computing discrete logarithms over finite extension fields it is clear that the distinctive feature of the normal basis representations namely the p th power of an element is just the cyclic shift of its normal basis representation where p is the characteristic of the underlying field can be used to speed up the computation of discrete logarithms over finite extension fields f p m we propose a variant of the pollard rho method to take advantage of this feature and achieve the speedup by a factor of m rather than 3p 34p 3m the previous result reported in the literature besides the theoretical analysis we also compare the performances of the new method with the previous algorithm in experiments and the result confirms our analysis due to the mov reduction our method can be applied to paring based cryptosystems over binary or ternary fields

classified vector quantization of images vector quantization vq provides many attractive features for image coding with high compression ratios however initial studies of image coding with vq have revealed several difficulties most notably edge degradation and high computational complexity we address these two problems and propose a new coding method classified vector quantization cvq which is based on a composite source model blocks with distinct perceptual features such as edges are generated from different subsources i e belong to different classes in cvq a classifier determines the class for each block and the block is then coded with a vector quantizer designed specifically for that class we obtain better perceptual quality with significantly lower complexity with cvq when compared to ordinary vq we demonstrate with cvq visual quality which is comparable to that produced by existing coders of similar complexity for rates in the range 0 6 1 0 bits pixel

adaptive map error concealment for dispersively packetized wavelet coded images in this paper we present an adaptive maximum a posteriori map error concealment algorithm for dispersively packetized wavelet coded images we model the subbands of a wavelet coded image as markov random fields and use the edge characteristics in a particular subband and regularity properties of subband wavelet samples across scales to adapt the potential functions locally the resulting adaptive map estimation gives psnr advantages of up to 0 7 db compared to the competing algorithms the advantage is most evident near the edges which helps improve the visual quality of the reconstructed images

subband filters optimized for lost coefficient reconstruction transmission of digital subband coded images over lossy packet networks presents a reconstruction problem at the decoder this correspondence addresses the design of a family of quadrature mirror filters qmfs that minimize the mean squared error of mean reconstructed low frequency subband coefficients the resulting filters perform well as qmfs as well as provide the desired reconstruction properties in the event of loss

optimization of packetization masks for image coding based on an objective cost function for desired packet spreading in image communication over lossy packet networks e g cell phone communication packet loss errors lead to damaged images damaged images can be repaired with passive error concealment methods which use neighboring coefficient or pixel values to estimate the missing ones neighboring image data should thus be spread over different packets this paper presents a novel robust packetization method for the transmission of image content in lossy packet networks we first define novel criteria for a good packetization based on these properties we propose a cost function for packetization masks we then use stochastic optimization to calculate optimal packetization masks we test our packetization technique on both wavelet coding and dct coding compared to other packetization techniques we are able to achieve the same or better mean quality of the reconstructed images but with less fluctuation in quality which is important for the viewer experience in this way we significantly increase the worst case quality especially for high packet loss rates this leads to visually more pleasing images in case of a passive reconstruction

motion estimation methods for overlapped block motion compensation an extension of conventional block motion compensation bmc overlapped block motion compensation obmc has been shown to reduce residual errors and blocking effects in motion compensated video however the overlap creates a noncausal spatial dependence between blocks and complicates motion estimation me for obmc iterative methods have traditionally been employed for overlapped block motion estimation obme for compression the rate for the motion vector field mvf may also be constrained this work considers several rate constrained obme algorithms both iterative and noniterative experiments demonstrate that a simple raster scan algorithm is effective as a suboptimal noniterative solution with comparable or better rate distortion performance and computational complexity than iterative obme algorithms depending on the application either this method or a simple block matching algorithm plus iteration are the most attractive of the tested obme schemes

design of regular nonseparable bidimensional wavelets using grobner basis techniques the design of two dimensional 2 d filter banks yielding orthogonality and linear phase filters and generating regular wavelet bases is a difficult task involving the algebraic properties of multivariate polynomials using cascade forms implies dealing with nonlinear optimization we turn the issue of optimizing the orthogonal linear phase cascade from kovacevic and vetterli 1992 into a polynomial problem and solve it using grobner basis techniques and computer algebra this leads to a complete description of maximally flat wavelets among the orthogonal linear phase family proposed by kovacevic and vetterli we obtain up to five degrees of flatness for a 16 spl times 16 filter bank whose sobolev exponent is 2 11 making this wavelet the most regular orthogonal linear phase nonseparable wavelet to the authors knowledge

output feedback predictive control with one free control move for nonlinear systems represented by a takagi sugeno model this paper addresses the output feedback predictive control for a takagi sugeno t s fuzzy system like many existing results the controller optimizes an infinite horizon objective function respecting input constraint the infinite horizon control moves are parameterized as a free control move followed by an output feedback based on the prespecified state estimator while the use of a free control move is well practiced in the existing research works of model predictive control mpc it was not previously applied in the output feedback mpc when 1 the future model parameters are uncertain and 2 the recursive feasibility and closed loop stability are guaranteed a key point for us to overcome this difficulty is to introduce a formula for refreshing the bound of the estimation error a numerical example is given to illustrate the effectiveness of the proposed output feedback controller

explicit mpc for lpv systems stability and optimality this paper considers high speed control of constrained linear parameter varying systems using model predictive control existing model predictive control schemes for control of constrained linear parameter varying systems typically require the solution of a semi definite program at each sampling instance recently variants of explicit model predictive control were proposed for linear parameter varying systems with polytopic representation decreasing the online computational effort by orders of magnitude depending on the mathematical structure of the underlying system the constrained finite time optimal control problem can be solved optimally or close to optimal solutions can be computed constraint satisfaction recursive feasibility and asymptotic stability can be guaranteed a priori by an appropriate selection of the terminal state constraints and terminal cost the paper at hand gathers previous developments and provides new material such as a proof for the optimality of the solution or in the case of close to optimal solutions a procedure to determine a bound on the suboptimality of the solution

adaptive transforms for image coding using spatially varying wavelet packets we introduce a novel adaptive image representation using spatially varying wavelet packets wps our adaptive representation uses the fast double tree algorithm introduced previously herley et al 1993 to optimize an operational rate distortion r d cost function as is appropriate for the lossy image compression framework this involves jointly determining which filter bank tree wp frequency decomposition to use and when to change the filter bank tree spatial segmentation for optimality the spatial and frequency segmentations must be done jointly not sequentially due to computational complexity constraints we consider quadtree spatial segmentations and binary wp frequency decompositions corresponding to two channel filter banks for application to image coding we present results verifying the usefulness and versatility of this adaptive representation for image coding using both a first order entropy rate measure based coder as well as a powerful space frequency quantization based spq based wavelet coder introduced by xiong et al 1993

output feedback robust mpc with one free control move for the linear polytopic uncertain system with bounded disturbance in this paper a previous approach for the robust model predictive control mpc for a linear polytopic uncertain system is extended to the case with bounded disturbance and unmeasurable state the controller on line optimizes a free control move followed by an output feedback control law based on the pre specified state estimator a key technique for this controller is an appropriate formulation of the estimation error bound which accounts for recursive feasibility of the optimization problem the quadratic boundedness qb of the augmented state is guaranteed by the proposed approach a numerical example is given to illustrate the effectiveness of the proposed controller

constrained robust model predictive control for time delay systems with polytopic description this paper considers an infinite horizon min max model predictive control mpc problem for time delay discrete systems with a polytopic uncertainty description which has rarely been addressed in the literature several new solutions to this problem are proposed which are inter complementary if there is an input delay then the single state feedback solution requires all the system matrices to be stable this deficiency can be removed by adding free control moves before a modified state feedback law if there is no input delay then a computationally efficient off line state feedback solution can be applied in order to obtain desirable region of attraction while at the same time preserve reasonably low on line computational effort one can choose the standard solution simulation results are given to illustrate these new solutions

piecewise affinity of min max mpc with bounded additive uncertainties and a quadratic criterion this brief shows how a min max mpc with bounded additive uncertainties and a quadratic cost function results in a piecewise affine and continuous control law proofs based on properties of the cost function and the optimization problem are given the boundaries of the regions in which the state space can be partitioned are also treated the results are illustrated by an example

subband coded image reconstruction for lossy packet networks transmission of digital subband coded images over lossy packet networks presents a reconstruction problem at the decoder this paper presents two techniques for reconstruction of lost subband coefficients one for low frequency coefficients and one for high frequency coefficients the low frequency reconstruction algorithm is based on inherent properties of the hierarchical subband decomposition to maintain smoothness and exploit the high intraband correlation a cubic interpolative surface is fit to known coefficients to interpolate lost coefficients accurate edge placement crucial for visual quality is achieved by adapting the interpolation grid in both the horizontal and vertical directions as determined by the edges present an edge model is used to characterize the adaptation and a quantitative analysis of this model demonstrates that edges can be identified by simply examining the high frequency bands without requiring any additional processing of the low frequency band high frequency reconstruction is performed using linear interpolation which provides good visual performance as well as maintains properties required for edge placement in the low frequency reconstruction algorithm the complete algorithm performs well on loss of single coefficients vectors and small blocks and is therefore applicable to a variety of source coding techniques

image coding using wavelet transform a scheme for image compression that takes into account psychovisual features both in the space and frequency domains is proposed this method involves two steps first a wavelet transform used in order to obtain a set of biorthogonal subclasses of images the original image is decomposed at different scales using a pyramidal algorithm architecture the decomposition is along the vertical and horizontal directions and maintains constant the number of pixels required to describe the image second according to shannon s rate distortion theory the wavelet coefficients are vector quantized using a multiresolution codebook to encode the wavelet coefficients a noise shaping bit allocation procedure which assumes that details at high resolution are less visible to the human eye is proposed in order to allow the receiver to recognize a picture as quickly as possible at minimum cost a progressive transmission scheme is presented it is shown that the wavelet transform is particularly well adapted to progressive transmission

on constrained infinite time linear quadratic optimal control abstract this work presents a solution to the infinite time linear quadratic optimal control itlqoc problem with state and control constraints it is shown that a single finite dimensional convex program of known size can yield this solution properties of the resulting value function with respect to initial conditions are also established and are shoen to be useful in determining the aforementioned problem size an example illustrating the method is finally presented

factorization of the eighth fermat number we describe a monte carlo factorization algorithm which was used to factorize the fermat number f8 2256 1 previously f8 was known to be composite but its factors were unknown comments only the abstract is given here the full paper appeared as 2 for a succinct proof of primality of the larger factor q8 of f8 see 3 at the time of this paper lenstra s elliptic curve method ecm had not been invented thus a modification of pollard s rho method 1 was used to factor f8 and several mersenne numbers 4 for the factorization of a larger fermat number by ecm see 5 the smaller factor of f8 is 1238926361552897 the epigram i am now entirely persuaded to employ the method a handy trick on gigantic composite numbers may appeal to readers who wish to memorize this factor

robust receding horizon control of constrained nonlinear systems we present a method for the construction of a robust dual mode receding horizon controller which can be employed for a wide class of nonlinear systems with state and control constraints and model error the controller is dual mode in a neighborhood of the origin the control action is generated by a linear feedback controller designed for the linearized system outside this neighborhood receding horizon control is employed existing receding horizon controllers for nonlinear continuous time systems which are guaranteed to stabilize the nonlinear system to which they are applied require the exact solution at every instant of an optimal control problem with terminal equality constraints these requirements are considerably relaxed in the dual mode receding horizon controller presented in this paper stability is achieved by imposing a terminal inequality rather than an equality constraint only approximate minimization is required a variable time horizon is permitted robustness is achieved by employing conservative state and stability constraint sets thereby permitting a margin of error the resultant dual mode controller requires considerably less online computation than existing receding horizon controllers for nonlinear constrained systems

rate distortion optimized tree structured compression algorithms for piecewise polynomial images this paper presents novel coding algorithms based on tree structured segmentation which achieve the correct asymptotic rate distortion r d behavior for a simple class of signals known as piecewise polynomials by using an r d based prune and join scheme for the one dimensional case our scheme is based on binary tree segmentation of the signal this scheme approximates the signal segments using polynomial models and utilizes an r d optimal bit allocation strategy among the different signal segments the scheme further encodes similar neighbors jointly to achieve the correct exponentially decaying r d behavior d r spl sim c sub 0 2 sup c1r thus improving over classic wavelet schemes we also prove that the computational complexity of the scheme is of o nlogn we then show the extension of this scheme to the two dimensional case using a quadtree this quadtree coding scheme also achieves an exponentially decaying r d behavior for the polygonal image model composed of a white polygon shaped object against a uniform black background with low computational cost of o nlogn again the key is an r d optimized prune and join strategy finally we conclude with numerical results which show that the proposed quadtree coding scheme outperforms jpeg2000 by about 1 db for real images like cameraman at low rates of around 0 15 bpp

brief robust one step receding horizon control of discrete time markovian jump uncertain systems this paper proposes a receding horizon control scheme for a set of uncertain discrete time linear systems with randomly jumping parameters described by a finite state markov process whose jumping transition probabilities are assumed to belong to some convex sets the control scheme for the underlying systems is based on the minimization of the worst case one step finite horizon cost with a finite terminal weighting matrix at each time instant this robust receding horizon control scheme has a more general structure than the existing robust receding horizon control for the underlying systems under the same design parameters the proposed controller is obtained using semidefinite programming

optimal bit allocation via the generalized bfos algorithm p h westerink et al 1988 developed an optimal bit allocation algorithm that is simplified when all operational distortion rate functions which are referred to as quantizer functions are convex this algorithm is restated using the generalized breiman friedman olshen and stone bfos algorithm a recently developed technique for variable rate vector quantizer design for both cases of convex and nonconvex quantizer functions qfs and its complexity is analyzed the use of the generalized bfos algorithm for optimal bit allocation is analysed it is shown that if each source has a convex quantizer function then the complexity of the algorithm is low

output feedback model predictive control for lpv systems based on quasi min max algorithm this paper proposes a robust output feedback model predictive control mpc scheme for linear parameter varying lpv systems based on a quasi min max algorithm this approach involves an off line design of a robust state observer for lpv systems using linear matrix inequality lmi and an on line robust output feedback mpc algorithm using the estimated state the proposed mpc method for lpv systems is applicable for a variety of systems with constraints and guarantees the robust stability of the output feedback systems a numerical example for an lpv system subject to input constraints is given to demonstrate its effectiveness

optimal pruning with applications to tree structured source coding and modeling an algorithm introduced by l breiman et al 1984 in the context of classification and regression trees is reinterpreted and extended to cover a variety of applications in source coding and modeling in which trees are involved these include variable rate and minimum entropy tree structured vector quantization minimum expected cost decision trees variable order markov modeling optimum bit allocation and computer graphics and image processing using quadtrees a concentration on the first of these and a detailed analysis of variable rate tree structured vector quantization are provided it is found that variable rate tree structured vector quantization outperforms not only the fixed rate variety but also full search vector quantization the successive approximation character of variable rate tree structured vector quantization permits it to degrade gracefully if the rate is reduced at the encoder this has applications to the problem of buffer overflow

structures factorizations and design criteria for oversampled paraunitary filterbanks yielding linear phase filters we present here a special class of oversampled filterbanks fbs namely paraunitary fbs with linear phase filters we propose some necessary conditions for the existence of such banks based on the repartition between type i ii and type ii iv linear phase filters in the bank for a subset of these fbs we develop a factorization that leads to a minimal implementation as well as a direct parameterization of the fbs in terms of elementary rotation angles this factorization is applied to some design examples with two different optimization criteria coding gain and reconstructibility of lost coefficients

robust constrained model predictive control using linear matrix inequalities abstract the primary disadvantage of current design techniques for model predictive control mpc is their inability to deal explicitly with plant model uncertainty in this paper we present a new approach for robust mpc synthesis that allows explicit incorporation of the description of plant uncertainty in the problem formulation the uncertainty is expressed in both the time and frequency domains the goal is to design at each time step a state feedback control law that minimizes a worst case infinite horizon objective function subject to constraints on the control input and plant output using standard techniques the problem of minimizing an upper bound on the worst case objective function subject to input and output constraints is reduced to a convex optimization involving linear matrix inequalities lmis it is shown that the feasible receding horizon state feedback control design robustly stabilizes the set of uncertain plants several extensions such as application to systems with time delays problems involving constant set point tracking trajectory tracking and disturbance rejection which follow naturally from our formulation are discussed the controller design is illustrated with two examples

tube based model predictive control for linear parameter varying systems with bounded rate of parameter variation abstract this paper introduces a tube based model predictive control mpc for linear parameter varying lpv systems which exploits knowledge about bounds on the parameters rate of change to extrapolate its admissible values over the prediction horizon this information is used to construct state tubes to which the future trajectories of the state are confined the tubes are consequently used for constraint tightening then an mpc optimization problem subject to tightened sets for the state and control constraints is solved for only a nominal system corresponding to a nominal trajectory of the scheduling parameter starting from its current value recursive feasibility and asymptotic stability are proven and two numerical examples are given to demonstrate the effectiveness of the proposed approach

model predictive control for linear parameter varying constrained systems using ellipsoidal set prediction this paper proposes a new model predictive control mpc method for linear parameter varying systems with bounded parameter variation subject to input constraints the method adopts closed loop prediction and constructs ellipsoidal sets to predict the future states with reasonable computational effort then the information on the parameter variation rate is exploited to improve the accuracy of the prediction furthermore a relaxed terminal condition which guarantees the stability for infinite horizon is introduced to enlarge the stabilizable region it is shown that the feasibility of the mpc problem at the initial step ensures the stability of the closed loop system finally a simulation result illustrates the effectiveness of the proposed method

tilings of the time frequency plane construction of arbitrary orthogonal bases and fast tiling algorithms the authors consider expansions which give arbitrary orthonormal tilings of the time frequency plane these differ from the short time fourier transform wavelet transform and wavelet packets tilings in that they change over time they show how this can be achieved using time varying orthogonal tree structures which preserve orthogonality even across transitions the method is based on the construction of boundary and transition filters these allow us to construct essentially arbitrary tilings time varying modulated lapped transforms are a special case where both boundary and overlapping solutions are possible with filters obtained by modulation they present a double tree algorithm which for a given signal decides on the best binary segmentation in both time and frequency that is it is a joint optimization of time and frequency splitting the algorithm is optimal for additive cost functions e g rate distortion and results in time varying best bases the main application of which is for compression of nonstationary signals experiments on test signals are presented

image coding with an l sup spl infin norm and confidence interval criteria a new image coding technique based on an l sup spl infin norm criterion and exploiting statistical properties of the reconstruction error is investigated the original image is preprocessed quantized encoded and reconstructed within a given confidence interval two important classes of preprocessing namely linear prediction and iterated filterbanks are used the approach is also shown to be compatible with previous techniques the approach allows a great flexibility in that it can perform lossless coding as well as a controlled lossy one specifications are typically that only p the reconstructed pixels are different from the original ones

elliptic curve cryptosystems we discuss analogs based on elliptic curves over finite fields of public key cryptosystems which use the multiplicative group of a finite field these elliptic curve cryptosystems may be more secure because the analog of the discrete logarithm problem on elliptic curves is likely to be harder than the classical discrete logarithm problem especially over gf 2 we discuss the question of primitive points on an elliptic curve modulo p and give a theorem on nonsmoothness of the order of the cyclic subgroup generated by a global point

improving the parallelized pollard lambda search on anomalous binary curves the best algorithm known for finding logarithms on an elliptic curve e is the parallelized pollard lambda collision search we show how to apply a pollard lambda search on a set of equivalence classes derived from e which requires fewer iterations than the standard approach in the case of anomalous binary curves over f 2 m the new approach speeds up the standard algorithm by a factor of 2m

vector quantization for entropy coding of image subbands vector quantization for entropy coding of image subbands is investigated rate distortion curves are computed with mean square error as a distortion criterion the authors show that full search entropy constrained vector quantization of image subbands results in the best performance but is computationally expensive lattice quantizers yield a coding efficiency almost indistinguishable from optimum full search entropy constrained vector quantization orthogonal lattice quantizers were found to perform almost as well as lattice quantizers derived from dense sphere packings an optimum bit allocation rule based on a lagrange multiplier formulation is applied to subband coding coding results are shown for a still image

output tracking of constrained nonlinear processes with offset free input to state stable fuzzy predictive control this paper develops an efficient offset free output feedback predictive control approach to nonlinear processes based on their approximate fuzzy models as well as an integrating disturbance model the estimated disturbance signals account for all the plant model mismatch and unmodeled plant disturbances an augmented piecewise observer constructed by solving some linear matrix inequalities is used to estimate the system states and the lumped disturbances based on the reference from an online constrained target generator the fuzzy model predictive control law can be easily obtained by solving a convex semi definite programming optimization problem subject to several linear matrix inequalities the resulting closed loop system is guaranteed to be input to state stable even in the presence of observer estimation error the zero offset output tracking property of the proposed control approach is proved and subsequently demonstrated by the simulation results on a strongly nonlinear benchmark plant

reducing elliptic curve logarithms to logarithms in a finite field elliptic curve cryptosystems have the potential to provide relatively small block size high security public key schemes that can be efficiently implemented as with other known public key schemes such as rsa and discrete exponentiation in a finite field some care must be exercised when selecting the parameters involved in this case the elliptic curve and the underlying field specific classes of curves that give little or no advantage over previously known schemes are discussed the main result of the paper is to demonstrate the reduction of the elliptic curve logarithm problem to the logarithm problem in the multiplicative group of an extension of the underlying finite field for the class of supersingular elliptic curves the reduction takes probabilistic polynomial time thus providing a probabilistic subexponential time algorithm for the former problem

passive error concealment for wavelet coded i frames with an inhomogeneous gauss markov random field model in video communication over lossy packet networks e g the internet packet loss errors can severely damage the transmitted video the damaged video can largely be repaired with passive error concealment where neighboring information is used to estimate missing information we address the problem of passive error concealment for wavelet coded data with dispersive packetization the reported techniques of this kind have many problems and usually fail in the reconstruction of high frequency content this paper presents a novel locally adaptive error concealment method for subband coded i frames based on an inhomogeneous gaussian markov random field model we estimate the parameters of this model from a local context of each lost coefficient and we interpolate the lost coefficients accordingly the results demonstrate a significant improvement over the reported related methods both in terms of objective performance measures and visually the biggest improvement of the proposed method compared to the state of the art in the field is the correct reconstruction of high frequency information such as textures and edges

subband coding of images subband coding has become quite popular for the source encoding of speech this paper presents a simple yet efficient extension of this concept to the source coding of images we specify the constraints for a set of two dimensional quadrature mirror filters qmf s for a particular frequency domain partition and show that these constraints are satisfied by a separable combination of one dimensional qmf s bits are then optimally allocated among the subbands to minimize the mean squared error for dpcm coding of the subbands also an adaptive technique is developed to allocate the bits within each subband by means of a local variance mask optimum quantization is employed with quantizers matched to the laplacian distribution subband coded images are presented along with their signal to noise ratios snr s the snr performance of the subband coder is compared to that of the adaptive discrete cosine transform dct vector quantization and differential vector quantization for bit rates of 0 67 1 0 and 2 0 bits per pixel for 256 256 monochrome images the adaptive subband coder has the best snr performance

an improved moving horizon control scheme through lagrange duality this paper presents a computationally tractable moving horizon control scheme where the to be on line solved minimax problem is relaxed to a minimization problem by lagrange duality this helps the avoidance of infeasibility and reduction of conservation caused by the ellipsoid evaluation of time domain constraints disturbance attenuation with performance adaptation is achieved by on line monitoring of the dissipation level and accumulating the energy reserve from performance relaxations that are necessary for the satisfaction of time domain constraints simulation and comparison results confirm the advantages of the proposed algorithm

absolute optimal time frequency basis a research tool the paper presents a method for finding the absolute best basis out of the library of bases offered by the wavelet packet decomposition of a discrete signal data adaptive optimality is achieved with respect to an objective function e g minimizing entropy and concerns the choice of the heisenberg rectangles tiling the time frequency domain over which the energy of the signal is distributed it is also shown how optimizing a concave objective function is equivalent to concentrating maximal energy into a few basis elements signal adaptive basis selection algorithms currently in use do not generally find the absolute best basis and moreover have an asymmetric time frequency adaptivity although a complete wavepacket decomposition comprises a symmetric set of tilings with respect to time and frequency the higher adaptivity in frequency than in time can lead to ignoring frequencies that exist over short time intervals short as compared to the length of the whole signal not to the period corresponding to these frequencies revealing short lived frequencies to the investigator can bring up important features of the studied process such as the presence of coherent persistent structures in a time series

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

a fast ellipsoidal mpc scheme for discrete time polytopic linear parameter varying systems this paper proposes a fast ellipsoidal model predictive control mpc strategy to address feedback regulation problems for constrained polytopic linear parameter varying lpv systems subject to bounded disturbances in order to deal with the specific non convex structure of the state prediction tubes arising in lpv contexts a new convexification procedure is proposed and based on the off line computation of a sequence of inner ellipsoidal approximations of exact one step controllable sets a computationally low demanding mpc algorithm is presented comparisons with state of the art mpc control algorithms for lpv systems are reported in a final numerical example where several methods are contrasted in terms of achievable domains of attraction control performance numerical burdens and memory requirements

fast algorithms for multidimensional dct to dct computation between a block and its associated subblocks in this paper we first propose an efficient algorithm for computing one dimensional 1 d discrete cosine transform dct for a signal block given its two adjacent subblocks in the dct domain and then introduce several algorithms for the fast computation of multidimensional m d dct with size n sub 1 spl times n sub 2 spl times spl times n sub m given 2 sup m subblocks of dct coefficients with size n sub 1 2 spl times n sub 2 2 spl times spl times n sub m 2 where n sub i i 1 2 m are powers of 2 obviously the row column method which employs the most efficient algorithms along each dimension reduces the computational complexity considerably compared with the traditional method which employs only the one dimensional 1 d fast dct and inverse dct idct algorithms however when m spl ges 2 the traditional method which employs the most efficient multidimensional dct idct algorithms has lower computational complexity than the row column method besides we propose a direct method by dividing the data into 2 sup m parts for independent fast computation in which only two steps of r dimensional r 1 2 m idct and additional multiplications and additions are required if all the dimensional sizes are the same the number of multiplications required for the direct method is only 2 sup m 1 m2 sup m 1 times of that required for the row column method and if n spl ges 2 sup 2m 1 the computational efficiency of the direct method is surely superior to that of the traditional method which employs the most efficient multidimensional dct idct algorithms

fuzzy constrained min max model predictive control based on piecewise lyapunov functions this paper proposes two novel stable fuzzy model predictive controllers based on piecewise lyapunov functions and the min max optimization of a quasi worst case infinite horizon objective function the main idea is to design state feedback control laws that minimize the worst case objective function based on fuzzy model prediction and thus to obtain the optimal transient control performance which is of great importance in industrial process control moreover in both of these predictive controllers piecewise lyapunov functions have been used in order to reduce the conservatism of those existent predictive controllers based on common lyapunov functions it is shown that the asymptotic stability of the resulting closed loop discrete time fuzzy predictive control systems can be established by solving a set of linear matrix inequalities moreover the controller designs of the closed loop control systems with desired decay rate and input constraints are also considered simulations on a numerical example and a highly nonlinear benchmark system are presented to demonstrate the performance of the proposed fuzzy predictive controllers

maximally smooth image recovery in transform coding the authors consider the reconstruction of images from partial coefficients in block transform coders and its application to packet loss recovery in image transmission over asynchronous transfer mode atm networks the proposed algorithm uses the smoothness property of common image signals and produces a maximally smooth image among all those with the same coefficients and boundary conditions it recovers each damaged block by minimizing the intersample variation within the block and across the block boundary the optimal solution is achievable through two linear transformations where the transform matrices depend on the loss pattern and can be calculated in advance the reconstruction of contiguously damaged blocks is accomplished iteratively using the previous solution as the boundary conditions in each new step this technique is applicable to any unitary block transform and is effective for recovering the dc and low frequency coefficients when applied to still image coders using the discrete cosine transform dct high quality images are reconstructed in the absence of many dc and low frequency coefficients over spatially adjacent blocks when the damaged blocks are isolated by block interleaving satisfactory results have been obtained even when all the coefficients are missing

receding horizon control strategies for constrained lpv systems based on a class of nonlinearly parameterized lyapunov functions in this technical note we present a receding horizon control rhc design method for linear parameter varying lpv systems subject to input and or state constraints based on a class of nonlinearly parameterized lyapunov functions recently introduced by guerra and vermeiren as it will be made clear their use gives rise to less conservative stabilizability conditions w r t those arising from quadratic lyapunov functions a workable convex optimization procedure is first presented for control design purposes which allows the synthesis of stabilizing scheduling state feedback control laws complying with the prescribed constraints this control design method is then arranged into a receding horizon framework and its feasibility and stability properties are carefully analyzed numerical comparisons with existing rhc methods for lpv systems are reported in the final example

robust model predictive control for discrete time takagi sugeno fuzzy systems with structured uncertainties and persistent disturbances in this paper robust model predictive control for uncertain discrete time takagi sugeno t s fuzzy systems with input constraints and persistent disturbances is considered the robust positively invariant set for t s fuzzy systems is investigated based on this result computation of the terminal constraint set is proposed which is of crucial importance in the robust predictive controller design a zero step predictive controller is discussed first which has a time varying terminal constraint set the recursive feasibility and input to state stability can be ensured then a novel controller with n step prediction is further proposed which can be used to deal with the case of fixed terminal constraint set the implementation of the n step controller involves both online and offline computations it is shown that a sequence of approximating robust one step sets can be computed offline then bisection searches are carried out online as well as a constrained convex optimization problem the n step controller guarantees that the system state can be steered to the terminal constraint set in less than n steps if the initial state lies in a specific region simulation results are finally presented to show the effectiveness of the proposed controllers

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

a feedback min max mpc algorithm for lpv systems subject to bounded rates of change of parameters a novel closed loop model based predictive control mpc strategy for input saturated polytopic linear parameter varying lpv discrete time systems is proposed it is postulated that the plant belongs to a polytopic family of linear systems each member of which being parameterized by the value that a parameter vector assumes in the unit simplex such a parameter can be measured online and used for feedback while a bound on its rate of change is known and exploited for predictions the paper extends the mpc scheme presented by lu et al 2000 for the restricting case of 1 step long control horizons to the general case of control horizons of arbitrary length n this is done by suitably modifying the robust mpc scheme presented by casavola et al 2000 for uncertain polytopic systems the feasibility and closed loop stability of this strategy are proved and a numerical example is also presented in order to show how the freedom of extending the control horizon and knowledge of the parameter is significant in order to improve the performance of the control strategy

matching wavelet packets to gaussian random processes we consider the problem of approximating a set of arbitrary discrete time gaussian random processes by a single representative wavelet based gaussian process we measure the similarity between the original processes and the wavelet based process with the bhattacharyya 1943 coefficient by manipulating the bhattacharyya coefficient we reduce the task of defining the representative process to finding an optimal unitary matrix of wavelet based eigenvectors an associated diagonal matrix of eigenvalues and a mean vector the matching algorithm we derive maximizes the nonadditive bhattacharyya coefficient in three steps a migration algorithm that determines the best basis by searching through a wavelet packet tree for the optimal unitary matrix of wavelet based eigenvectors and two separate fixed point algorithms that derive an appropriate set of eigenvalues and a mean vector we illustrate the method with two different classes of processes first order markov and bandlimited the technique is also applied to the problem of robust terrain classification in polarimetric sar images

region adaptive subband image coding we present a region adaptive subband image coding scheme using the statistical properties of image subbands for various subband decompositions motivated by analytical results obtained when the input signal to the subband decomposition is a unit step function we analyze the energy packing properties toward the lower frequency subbands edges and the dependency of energy distribution on the orientation of the edges in subband decomposed images based on these investigations and ideal analysis synthesis filtering done in the frequency domain the region adaptive subband image coding scheme extracts suitably shaped regions in each subband and then uses adaptive entropy constrained quantizers for different regions under the assumption of a generalized gaussian distribution for the image subbands we also address the problem of determining an optimal subband decomposition among all possible decompositions experimental results show that visual degradations in the reconstructed image are negligible at a bit rate of 1 0 b pel and reasonable quality images are obtainable at rates as low as 0 25 b pel

a quasi infinite horizon nonlinear model predictive control scheme with guaranteed stability we present in this paper a novel nonlinear model predictive control scheme that guarantees asymptotic closed loop stability the scheme can be applied to both stable and unstable systems with input constraints the objective functional to be minimized consists of an integral square error ise part over a finite time horizon plus a quadratic terminal cost the terminal state penalty matrix of the terminal cost term has to be chosen as the solution of an appropriate lyapunov equation furthermore the setup includes a terminal inequality constraint that forces the states at the end of the finite prediction horizon to lie within a prescribed terminal region if the jacobian linearization of the nonlinear system to be controlled is stabilizable we prove that feasibility of the open loop optimal control problem at time t 0 implies asymptotic stability of the closed loop system the size of the region of attraction is only restricted by the requirement for feasibility of the optimization problem due to the input and terminal inequality constraints and is thus maximal in some sense

quasi min max mpc algorithms for lpv systems in this paper a new model predictive controller mpc is developed for polytopic linear parameter varying lpv systems we adopt the paradigm used in gain scheduling and assume that the time varying parameters are measured on line but their future behavior is uncertain and contained in a given polytope at each sampling time optimal control action is computed by minimizing the upper bound on the quasi worst case value of an infinite horizon quadratic objective function subject to constraints on inputs and outputs the mpc algorithm is called quasi because the first stage cost can be computed without any uncertainty this allows the inclusion of the first move u k k separately from the rest of the control moves governed by a feedback law and is shown to reduce conservatism and improve feasibility characteristics with respect to input and output constraints proposed optimization problems are solved by semi definite programming involving linear matrix inequalities it is shown that closed loop stability is guaranteed by the feasibility of the linear matrix inequalities a numerical example demonstrates the unique features of the mpc design

constrained rhc for lpv systems with bounded rates of parameter variations this paper studies a stabilization problem of polytopically uncertain linear parameter varying systems with input constraints and bounded rates of parameter variations in the framework of finite receding horizon control rhc a system containing parameter uncertainties is modified into a system with parameter incremental uncertainties within each horizon for the system modified in this manner a robust rhc is designed by solving an optimization problem at each time instant based on the feasibility of the problem and the optimality of its solution the closed loop system stability is guaranteed a numerical example is included to illustrate the validity of the results

orthonormal bases of compactly supported wavelets we construct orthonormal bases of compactly supported wavelets with arbitrarily high regularity the order of regularity increases linearly with the support width we start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction the construction then follows from a synthesis of these different approaches

output feedback robust mpc for lpv system with polytopic model parametric uncertainty and bounded disturbance abstractthe output feedback robust model predictive control mpc for the linear parameter varying lpv system with norm bounded disturbance is addressed where the model parametric matrices are only known to be bounded within a polytope the previous techniques of norm bounding technique quadratic boundedness qb dynamic output feedback and ellipsoid true state bound tsb refreshment formula for guaranteeing recursive feasibility are fused into the newly proposed approaches in the notion of qb the full lyapunov matrix is applied for the first time in this context the single step dynamic output feedback robust mpc where the infinite horizon control moves are parameterised as a dynamic output feedback law is the main topic of this paper while the multi step method is also suggested in order to strictly guarantee the physical constraints the outer bound of the true state replaces the true state itself so tightness of this bound has a major effect on the control performance in order to ti

brief optimizing the end point state weighting matrix in model based predictive control in this paper a linear model based predictive control mpc algorithm is presented for which nominal closed loop stability is guaranteed the input is obtained by minimizing a quadratic performance index over a finite horizon plus an end point state eps penalty subject to input state and output constraints under certain conditions the weighting matrix in the eps penalty enables one to specify an invariant ellipsoid in which the input state and output constraints are satisfied in existing mpc algorithms this weighting matrix is calculated off line the main contribution of this paper is to incorporate the calculation of the eps weighting matrix into the on line optimization problem of the controller the main advantage of this approach is that a natural and automatic trade off between feasibility and optimality is obtained this is demonstrated in a simulation example

design of receding horizon controls for constrained time varying systems in this note we propose a generalized stabilizing receding horizon control scheme for input state constrained linear discrete time varying systems that improves feasibility and on line computation on the constrained finite horizon optimization problem compared with existing schemes the control scheme is based on a time varying horizon cost function with time varying terminal weighting matrices which can easily be implemented via linear matrix inequality technique we discuss modifications of the proposed scheme that improve feasibility or on line computation time through simulation examples we illustrate the results of these schemes

a feasible moving horizon cal h _ infty control scheme for constrained uncertain linear systems this note presents a robust moving horizon hinfin control scheme that achieves disturbance attenuation with performance adaptation or for a prescribed level the on line solved optimization problem is a lagrange relaxation of the constrained minimax problem with the benefit of achieving feasibility in the moving horizon implementation uncertainties are incorporated by the use of the full block multiplier technique simulation and comparison results are given

image subband coding using context based classification and adaptive quantization adaptive compression methods have been a key component of many proposed subband or wavelet image coding techniques this paper deals with a particular type of adaptive subband image coding where we focus on the image coder s ability to adjust itself on the fly to the spatially varying statistical nature of image contents this backward adaptation is distinguished from more frequently used forward adaptation in that forward adaptation selects the best operating parameters from a predesigned set and thus uses considerable amount of side information in order for the encoder and the decoder to operate with the same parameters specifically we present backward adaptive quantization using a new context based classification technique which classifies each subband coefficient based on the surrounding quantized coefficients we couple this classification with online parametric adaptation of the quantizer applied to each class a simple uniform threshold quantizer is employed as the baseline quantizer for which adaptation is achieved our subband image coder based on the proposed adaptive classification quantization idea exhibits excellent rate distortion performance in particular at very low rates for popular test images it is comparable or superior to most of the state of the art coders in the literature

stochastic model predictive control of lpv systems via scenario optimization a stochastic receding horizon control approach for constrained linear parameter varying discrete time systems is proposed in this paper it is assumed that the time varying parameters have stochastic nature and that the system s matrices are bounded but otherwise arbitrary nonlinear functions of these parameters no specific assumption on the statistics of the parameters is required by using a randomization approach a scenario based finite horizon optimal control problem is formulated where only a finite number m of sampled predicted parameter trajectories scenarios are considered this problem is convex and its solution is a priori guaranteed to be probabilistically robust up to a user defined probability level p the p level is linked to m by an analytic relationship which establishes a tradeoff between computational complexity and robustness of the solution then a receding horizon strategy is presented involving the iterated solution of a scenario based finite horizon control problem at each time step our key result is to show that the state trajectories of the controlled system reach a terminal positively invariant set in finite time either deterministically or with probability no smaller than p the features of the approach are illustrated by a numerical example

mpc for lpv systems with bounded parameter variations this article deals with the model predictive control mpc design problem for systems which are linearly dependent on a time varying parameter the main novelty is that motivated by practical issues the bounds on the rate of variation of the parameters are taken into account in the control design moreover a lyapunov function depending multiaffinely on the parameters computed at a set of instants of time and a parameter dependent control gain are used to provide an upper bound to a quadratic performance index the solution is obtained by means of a semidefinite programming algorithm examples illustrate the efficiency of the proposed approach

quasi min max fuzzy model predictive control of direct methanol fuel cells abstract direct methanol fuel cells dmfcs are known as a promising power source in future in this paper we consider steering a dmfc plant to a desired operating point while optimizing the transient performance according to a quadratic cost function quasi min max fuzzy model predictive control fmpc with input constraints is proposed for the dmfc in order to reduce the computational burden for real time implementation a partial off line quasi min max fmpc is also proposed in this case a bank of invariant sets together with the corresponding feedback control laws are obtained by solving some linear matrix inequalities lmis off line leaving the online part a bisection search and a much simplified constrained optimization problem online computation complexity for both the quasi min max fmpc and the partial off line one is also analyzed simulation results are given to show the effectiveness of the proposed controllers

wavelet footprints theory algorithms and applications wavelet based algorithms have been successful in different signal processing tasks the wavelet transform is a powerful tool because it manages to represent both transient and stationary behaviors of a signal with few transform coefficients discontinuities often carry relevant signal information and therefore they represent a critical part to analyze we study the dependency across scales of the wavelet coefficients generated by discontinuities we start by showing that any piecewise smooth signal can be expressed as a sum of a piecewise polynomial signal and a uniformly smooth residual theorem 1 we then introduce the notion of footprints which are scale space vectors that model discontinuities in piecewise polynomial signals exactly we show that footprints form an overcomplete dictionary and develop efficient and robust algorithms to find the exact representation of a piecewise polynomial function in terms of footprints this also leads to efficient approximation of piecewise smooth functions finally we focus on applications and show that algorithms based on footprints outperform standard wavelet methods in different applications such as denoising compression and nonblind deconvolution in the case of compression we also prove that at high rates footprint based algorithms attain optimal performance theorem 3

output feedback model predictive control for lpv systems using parameter dependent lyapunov function in this paper we consider a robust dynamic output feedback model predictive controller mpc design for linear parameter varying lpv systems according to the proposed mpc algorithm the control law is computed based on linear matrix inequality lmi at each sampling time by solving convex optimization problem also a new parameter dependent lyapunov function is proposed to get a less conservative condition for stability of the system the effectiveness of the result proposed is verified via a numerical example

an efficient model predictive controller with pole placement for model predictive control mpc of constrained systems enlarging the feasible region is usually in conflict with improving the dynamic performance to resolve the conflict we proposed an efficient model predictive controller with pole placement for a class of discrete time linear systems by specifying a group of circular regions that contain the desired closed loop poles appropriate terminal weighting matrices and local controllers are calculated to construct a time varying terminal convex set which is a significant constraint for the online optimization problem during the online optimization the size of the terminal convex set can adjust itself according to the actual state at each sampling time in this way a large initial feasible region can be achieved while maintaining the good dynamic performance an illustrative example is used to show the effectiveness of the proposed approach

an ellipsoidal off line model predictive control strategy for linear parameter varying systems with applications in chemical processes abstract in this paper a novel off line model predictive control strategy for linear parameter varying systems is presented the on line computational burdens are reduced by pre computing off line the sequences of state feedback gains corresponding to the sequences of nested ellipsoids the number of sequences of nested ellipsoids constructed is equal to the number of vertices of the polytope at each sampling instant the smallest ellipsoid containing the currently measured state is determined in each sequence of ellipsoids and the scheduling parameter is measured the real time state feedback gain is calculated by linear interpolation between the corresponding state feedback gains an overall algorithm is proved to guarantee robust stability the controller design is illustrated with two examples of continuous stirred tank reactors

performances of linear tools and models for error detection and concealment in subband image transmission we investigate the performances of gaussian modeling and linear prediction tools for error detection and concealment in the transmission of still images we consider the transmission of subband encoded images through two types of channels we model the residual correlation between subband coefficients by considering them as jointly gaussian variables the first transmission medium considered is a packet oriented channel where some packets are lost during transmission the problem is to estimate the values of missing coefficients in this case particular care must be taken while evaluating correlation matrices from incomplete data the other system considered is based on a discrete memoryless noisy channel affecting the data being transmitted the challenge is here first to determine the locations of the errors which is done through hypotheses tests and then to replace them by estimates based on their neighbors the reconstruction via linear prediction is shown to give better results than median filtering based reconstruction error detection through this gaussian model also shows promising results in particular when channel statistics are taken into account in a joint source channel decoding framework

a robust mpc for input output lpv models in this note a discrete time robust model predictive control mpc design approach is proposed to control systems described by linear parameter varying models in input output form subject to constraints to ensure the stability of the closed loop system a quadratic terminal cost along with an ellipsoidal terminal constraint are included in the control optimization problem the mpc design problem is formulated as a linear matrix inequality problem the proposed mpc scheme is applied on a continuously stirred tank reactor as an illustrative example

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed