efficient encoding of colored pictures in r g b components the encoding of colored pictures in components has attracted a lot of attention in this paper for their efficient transmission in the 2 3 bit pel range the direct encoding of the red r green g and blue b primaries is investigated differential pcm with vector quantization is used and the encoding efficiencies are compared to the similar result obtained using the properly converted luminance y and chrominance i q component signals a new quantization scheme is proposed for rgb encoding to improve the picture quality as a result it is shown that rgb encoding can attain a comparable or slightly higher encoding efficiency as compared to yiq encoding and a higher resolution can be obtained for strong color edges defined by the primary colors but the resulting picture quality is much noisier thus it is better suited for such applications in which the edges of primary colors play important roles such as in graphics materials an adaptive vector quantization is introduced in order to apply the proposed rgb encoding scheme to a wider range of pictures the quantity called activity is introduced considering the form of the predictor used the optimum adaptive scheme is derived and its effectiveness is verified through simulations

bandpass correlator analysis for general input assumptions corresp for general assumptions concerning bandpass signal and noise inputs previous analyses of analog cross correlators have yielded very complicated expressions for the probability density function pdf of the correlator output the inherent computational difficulties therefore limited the application of these pdf s almost exclusively to special cases of equal noise powers and noise spectrums symmetric about the signal s frequency in this correspondence it is shown that for general bandpass inputs the correlator output can always be expressed as the difference of two scaled independent noncentral chi squared variables if a certain matrix transformation of variables is employed the characteristic function method is then used to derive the pdf which is as readily computed as for the case of special assumptions

percolation on infinite graphs and isoperimetric inequalities we consider the bernoulli bond percolation process with parameter p on infinite graphs and we give a general criterion for bounded degree graphs to exhibit a non trivial percolation threshold based either on a single isoperimetric inequality if the graph has a bi infinite geodesic or two isoperimetric inequalities if the graph has not a bi infinite geodesic this new criterion extends previous criteria and brings together a large class of amenable graphs such as regular lattices and non amenable graphs such trees we also study the finite connectivity in graphs satisfying the new general criterion and show that graphs in this class with a bi infinite geodesic always have finite connectivity functions with exponential decay when p is sufficiently close to one on the other hand we show that there are graphs in the same class with no bi infinite geodesic for which the finite connectivity decays sub exponentially down to polynomially in the highly supercritical phase even for p arbitrarily close to one

the covariance matrix of the potts model a random cluster analysis we consider the covariance matrix g mm q2 of thed dimensionalq states potts model rewriting it in the random cluster representation of fortuin and kasteleyn in any of theq ordered phases we identify the eigenvalues of this matrix both in terms of representations of the unbroken symmetry group of the model and in terms of random cluster connectivities and covariances thereby attributing algebraic significance to these stochastic geometric quantities we also show that the correlation length corresponding to the decay rate of one of the eigenvalues is the same as the inverse decay rate of the diameter of finite clusers for dimensiond 2 we show that this correlation length and the correlation length of the two point function with free boundary conditions at the corresponding dual temperature are equal up to a factor of two for systems with first order transitions this relation helps to resolve certain inconsistencies between recent exact and numerical work on correlation lengths at the self dual point o for systems with second order transitions this relation implies the equality of the correlation length exponents from above and below threshold as well as an amplitude ratio of two in the course of proving the above results we establish several properties of independent interest including left continuity of the inverse correlation length with free boundary conditions and upper semicontinuity of the decay rate for finite clusters in all dimensions and left continuity of the two dimensional free boundary condition percolation probability at o we also introduce dlr equations for the random cluster model and use them to establish ergodicity of the free measure in order to prove these results we introduce a new class of events which we call decoupling events and two inequalities for these events the first is similar to the fkg inequality but holds for events which are neither increasing nor decreasing the second is similar to the van den berg kesten inequality in standard percolation both inequalities hold for an arbitrary fkg measure

dynamic finite state vector quantization of digital images a vector quantization vq scheme with finite memory called dynamic finite state vector quantization dfsvq is presented the encoder consists of a large codebook so called super codebook where for each input vector a fixed number of its codevectors are chosen to generate a much smaller codebook sub codebook this sub codebook represents the best matching codevectors that could be found in the super codebook for encoding the current input vector the choice for the codevectors in the sub codebook is based on the information obtained from the previously encoded blocks where directional conditional block probability histogram matrices are used in the selection of the codevectors the index of the best matching codevector in the sub codebook is transmitted to the receiver an adaptive dfsvq scheme is also proposed in which when encoding an input vector first the sub codebook is searched for a matching codevector to satisfy a pre specified waveform distortion if such a codevector is not found in tile current sub codebook then the whole super codebook is checked for a better match if a better match is found then a signaling flag along with the corresponding index of the codevector is transmitted to the receiver both the dfsvq encoder and its adaptive version are implemented experimental results for several monochrome images with a super codebook size of 256 or 512 and different sub codebook sizes are presented

image compression using address vector quantization a novel vector quantization scheme called the address vector quantizer a vq is proposed it is based on exploiting the interblock correlation by encoding a group of blocks together using an address codebook the address codebook consists of a set of address codevectors where each codevector represents a combination of addresses indexes each element of this codevector is an address of an entry in the lbg codebook representing a vector quantized block the address codebook consists of two regions one is the active addressable region and the other is the inactive nonaddressable region during the encoding process the codevectors in the address codebook are reordered adaptively in order to bring the most probable address codevectors into the active region when encoding an address codevector the active region of the address codebook is checked and if such an address combination exist its index is transmitted to the receiver otherwise the address of each block is transmitted individually the quality snr value of the images encoded by the proposed a vq method is the same as that of a memoryless vector quantizer but the bit rate would be reduced by a factor of approximately two when compared to a memoryless vector quantizer

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

optimization of partition based weighted sum filters and their application to image denoising partition based weighted sum p ws filtering is an effective method for processing nonstationary signals especially those with regularly occurring structures such as images p ws filters were originally formulated as hard partition weighted sum hp ws filters and were successfully applied to image denoising this formulation relied on intuitive arguments to generate the filter class here we present a statistical analysis that justifies the use of weighted sum filters after observation space partitioning unfortunately the hp ws filters are nondifferentiable and an analytical solution for their global optimization is therefore difficult to obtain a two stage suboptimal training procedure has been reported in the literature but prior to this research no evaluation on the optimality of this approach has been reported here a genetic algorithm ga hp ws optimization procedure is developed that in simulations shows that the simpler two stage training procedure yields near optimal results also developed in this paper are soft partition weighted sum sp ws filters the sp ws filters utilize soft or fuzzy partitions that yield a differentiable filtering operation enabling the development of gradient based optimization procedures image denoising simulation results are presented comparing hp ws and sp ws filters their optimization procedures and wavelet based image denoising these results show that p ws filters in general outperform traditional and wavelet based image filters and sp ws filters utilizing soft partitioning not only allow for simple optimization but also yields improved performance

adaptive vector quantization with codebook updating based on locality and history we propose two techniques that are applicable to any adaptive vector quantization avq systems the first one is called the locality based codebook updating when performing a codebook updating we update the operational codebook using not only the current input vector but also the codewords at all positions within a selected neighboring area called the locality while the operational codebook is organized in a cache manner this technique is rationalized by the high correlation cross neighboring vectors that facilitates a more efficient coding of the indices of the codewords chosen from the codebook the second technique is called the history aid which makes use of the information of previously coded vectors to quantize the current input vector if it is used to update the operational codebook a more effective avq system is obtained by combining together the history aid and the locality based updating extensive simulations are carried out to demonstrate the improved results achieved by our avq systems particularly when the operational codebook size is relatively small the improvement over a benchmark avq system the generalized threshold replenishment gtr is drastic for example when the size is 32 testing on a nonstationary signal containing frames from different video sequences ordered in the concatenating or interleaving format shows that the combination of history aid and locality based updating offers more than 4 db gain over gtr at 0 5 bpp

fuzzy vector quantization algorithms and their application in image compression this paper presents the development and evaluation of fuzzy vector quantization algorithms these algorithms are designed to achieve the quality of vector quantizers provided by sophisticated but computationally demanding approaches while capturing the advantages of the frequently used in practice k means algorithm such as speed simplicity and conceptual appeal the uncertainty typically associated with clustering tasks is formulated in this approach by allowing the assignment of each training vector to multiple clusters in the early stages of the iterative codebook design process a training vector assignment strategy is also proposed for the transition from the fuzzy mode where each training vector can be assigned to multiple clusters to the crisp mode where each training vector can be assigned to only one cluster such a strategy reduces the dependence of the resulting codebook on the random initial codebook selection the resulting algorithms are used in image compression based on vector quantization this application provides the basis for evaluating the computational efficiency of the proposed algorithms and comparing the quality of the resulting codebook design with that provided by competing techniques

conditional entropy coding of vq indexes for image compression block sizes of practical vector quantization vq image coders are not large enough to exploit all high order statistical dependencies among pixels therefore adaptive entropy coding of vq indexes via statistical context modeling can significantly reduce the bit rate of vq coders for given distortion address vq was a pioneer work in this direction in this paper we develop a framework of conditional entropy coding of vq indexes cecovi based on a simple bayesian type method of estimating probabilities conditioned on causal contexts cecovi is conceptually cleaner and algorithmically more efficient than address vq with address vq technique being its special case it reduces the bit rate of address vq by more than 20 for the same distortion and does so at only a tiny fraction of address vq s computational cost

tight bounds on rician type error probabilities and some applications consider the classic problem of evaluating the probability that one rician random variable exceeds another possibly correlated rician random variable this probability is given by stein 1964 in terms of the marcum s q function which requires numerical integration on the computer for its evaluation to facilitate application in many digital communication problems we derive here tight upper and lower bounds on this probability the bounds are motivated by a classic result in communication theory namely the error probability performance of binary orthogonal signaling over the gaussian channel with unknown carrier phase various applications of the bounds are reported including the evaluation of the bit error probabilities of mdpsk and mpsk with differential detection and generalized differential detection respectively the bounds prove to be tight in all cases further applications will be reported in the future

least squares quantization in pcm it has long been realized that in pulse code modulation pcm with a given ensemble of signals to handle the quantum values should be spaced more closely in the voltage regions where the signal amplitude is more likely to fall it has been shown by panter and dite that in the limit as the number of quanta becomes infinite the asymptotic fractional density of quanta per unit voltage should vary as the one third power of the probability density per unit voltage of signal amplitudes in this paper the corresponding result for any finite number of quanta is derived that is necessary conditions are found that the quanta and associated quantization intervals of an optimum finite quantization scheme must satisfy the optimization criterion used is that the average quantization noise power be a minimum it is shown that the result obtained here goes over into the panter and dite result as the number of quanta become large the optimum quautization schemes for 2 b quanta b 1 2 cdots 7 are given numerically for gaussian and for laplacian distribution of signal amplitudes

ber expressions for differentially detected spl pi 4 dqpsk modulation closed form bit error rate ber expressions for differentially detected spl pi 4 shifted differentially encoded quadrature phase shift keying qpsk modulation spl pi 4 dqpsk are derived for both additive white gaussian noise awgn and rayleigh fading channels the derivations are carried out in an exact and most general manner in that in phase i and quadrature q channel bit error probabilities p sub cl and p sub cq are separately obtained in terms of the same quadrature and cross quadrature noise correlation functions including a measure of noise nonstationarity we then specialize the general expressions for uncorrelated noise and equal noise powers in successive symbol periods to obtain a useful bit error probability expression for the awgn channel in the form p sub e spl ap q spl radic 1 1716 spl middot e sub b n sub 0 where q spl middot is the gaussian distribution q function and e sub b n sub 0 is the bit energy to noise density ratio exact ber expressions for the rayleigh fading channel that involve the noise parameters are also given and are extended to the case of l fold diversity combining

a successive approximation vector quantizer for wavelet transform image coding a coding method for wavelet coefficients of images using vector quantization called successive approximation vector quantization sa w vq is proposed in this method each vector is coded by a series of vectors of decreasing magnitudes until a certain distortion level is reached the successive approximation using vectors is analyzed and conditions for convergence are derived it is shown that lattice codebooks are an efficient tool for meeting these conditions without the need for very large codebooks regular lattices offer the extra advantage of fast encoding algorithms in sa w vq distortion equalization of the wavelet coefficients can be achieved together with high compression ratio and precise bit rate control the performance of sa w vq for still image coding is compared against some of the most successful image coding systems reported in the literature the comparison shows that sa w vq performs remarkably well at several bit rates and in various test images

correlation lengths for oriented percolation oriented percolation has two correlation lengths one in the space and one in the time direction in this paper we define these quantities for the two dimensional model in terms of the exponential decay of suitably chosen quantities and study the relationship between the various definitions the definitions are used in a companion paper to prove inequalities between critical exponents

test of universal finite size scaling in two dimensional site percolation traditional two scale factor universality concerning the number of clusters within a correlation volume near the percolation threshold is reconfirmed by a comparison of site percolation on square and triangular lattices we also test universality at the threshold e g of the ratio where is the correlation length and l the lattice size at the threshold the result is sensitive to the system s shape and aspect ratio boundary conditions the algorithm the detailed units measuring and l and possibly other factors as yet unexplored

a fast vq codebook generation algorithm using codeword displacement in this paper we present a fast codebook generation algorithm called cgaucd codebook generation algorithm using codeword displacement by making use of the codeword displacement between successive partition processes by implementing a fast search algorithm named mfaupi modified fast algorithm using projection and inequality for vq encoding in the partition step of cgaucd the codebook generation time can be further reduced significantly using mfaupi the computing time of cgaucd can be reduced by a factor of 4 7 7 6 compared to generalized lloyd algorithm gla our proposed method can reduce the codebook generation time by a factor of 35 9 121 2 compared to the best codebook generation algorithm to our knowledge our approach can further reduce the corresponding computing time by 26 0 32 8 it is noted that our proposed algorithm can generate the same codebook as that produced by the gla the superiority of our method is more remarkable when a larger codebook is generated

percolation and cluster structure parameters the radius of gyration the squared radius of gyration of percolation clusters are determined in terms of the clusters second spatial moments using the enhanced hoshen kopelman algorithm for square and triangular lattices containing sites correlation length exponents and related exponents as well as their corresponding amplitudes are calculated in terms of the squared radius of gyration above and below the percolation threshold a coefficient for cluster compactness that is based on the squared radius of gyration of a cluster is introduced that coefficient is compared with a similar coefficient of compactness that is based on the cluster cyclomatic number

a fuzzy vector quantization approach to image compression the use of fuzzy clustering analysis in the early stages of a vector quantization process is able to make this process less sensitive to initialization this is justified by the fact that fuzzy clustering provides a framework for the quantitative formulation of the uncertainty typically involved in a training vector space this paper proposes a fuzzy clustering based vector quantization algorithm which employs an effective vector assignment strategy for the transition from fuzzy mode where each training vector is assigned to more than one clusters to crisp mode where each training vector is assigned to only one cluster this transition is controlled by analytical conditions that are obtained by minimizing a modified objective function for the fuzzy c means algorithm the application to image compression shows that the proposed approach is able to achieve a very efficient performance while maintaining the computational capabilities of other methods reported in the literature

on the calculation of the generalized q function via parl s method corresp parl has previously given error bounds suitable for calculating marcum s q function however it is shown that additional terms in the error bound are necessary for accurate calculations of the generalized q function q m alpha beta the values of m alpha and beta that result in successful algorithm completion are examined numerical results are presented for calculations of the noncentral chi square distribution and the probability of detection for a classical multiobservation detection problem

bit error probabilities mdpsk over the nonselective rayleigh fading channel with diversity reception data transmission using m ary differential phase shift keying mdpsk over the nonselective rayleigh fading channel with diversity reception is considered while previous studies on error probability mostly assume no fading fluctuation the author considers exclusively the case in which the fading process fluctuates from one symbol interval to the next exact bit error probability results for 2 4 and 8 dpsk as well as tight upper bounds are derived some applications of the results are discussed

image compression using adaptive vector quantization the paper demonstrates the application of adaptive vector quantization techniques to the coding of monochromatic and color pictures codebooks of representative vectors are generated for different portions of the image by means of extensive simulations the performance of the coder for monochrome images is estimated as a function of the various coding parameters vector dimensionality number of representative vectors and degree of adaptivity it is shown that for a vector size of dimension 4 there is a zone of operation ranging from 1 0 to 1 5 bits pixel where adaptive vector quantization is advantageous despite the simplicity of the decoder the performance of the adaptive vector quantizer is found to be comparable with block transform coding schemes for both monochrome and color pictures

supercritical percolation on nonamenable graphs isoperimetry analyticity and exponential decay of the cluster size distribution let g be a connected locally finite transitive graph and consider bernoulli bond percolation on g we prove that if g is nonamenable and p p c g then there exists a positive constant c p such that begin aligned mathbf p p n le k infty le e c p n end aligned for every n ge 1 where k is the cluster of the origin we deduce the following two corollaries

an algorithm for the design of labeled transition finite state vector quantizers a finite state vector quantizer fsvq is a switched vector quantizer where the sequence of quantizers selected by the encoder can be tracked by the decoder it can be viewed as an adaptive vector quantizer with backward estimation a vector generalization of an aqb system recently a family of algorithms for the design of fsvq s for waveform coding application has been introduced these algorithms first design an initial set of vector quantizers together with a next state function giving the rule by which the next quantizer is selected the codebooks of this initial fsvq are then iteratively improved by a natural extension of the usual memoryless vector quantizer design algorithm the next state function however is not modified from its initial form in this paper we present two extensions of the fsvq design algorithms first the algorithm for fsvq design for waveform coders is extended to fsvq design of linear predictive coded lpc speech parameter vectors using an itakura saito distortion measure second we introduce a new technique for the iterative improvement of the next state function based on an algorithm from adaptive stochastic automata theory the design algorithms are simulated for an lpc fsvq and the results are compared with each other and to ordinary memoryless vector quantization several open problems suggested by the simulation results are presented

image sequence coding using vector quantization in this paper a new interframe coding technique based upon vector quantization is presented this algorithm has as its basis twodimensional block vector quantization at the frame level onto which is grafted the concept of adaptive codebook replenishment and frame replenishment this algorithm includes three strategies label replenishment label replenishment with mean shift and label replenishment with mean shift and selective codeword replacement the last two strategies efficiently update the codebook to track the changes in local statistics on a frame basis compared with three dimensional block vector quantization 16 for bit rates between 0 5 and 0 65 the normalized mean squared error nmse is reduced by a factor ranging between 2 and 2 5 by the use of replenishment

anisotropic diffusion of multivalued images with applications to color filtering a general framework for anisotropic diffusion of multivalued images is presented we propose an evolution equation where at each point in time the directions and magnitudes of the maximal and minimal rate of change in the vector image are first evaluated these are given by eigenvectors and eigenvalues of the first fundamental form in the given image metric then the image diffuses via a system of coupled differential equations in the direction of minimal change the diffusion strength is controlled by a function that measures the degree of dissimilarity between the eigenvalues we apply the proposed framework to the filtering of color images represented in cie l a b space

a novel encoding algorithm for vector quantization using transformed codebook in this paper a novel encoding algorithm for vector quantization is presented our method uses a set of transformed codewords and partial distortion rejection to determine the reproduction vector of an input vector experimental results show that our algorithm is superior to other methods in terms of the computing time and number of distance calculations compared with available approaches our method can reduce the computing time and number of distance calculations significantly compared with the available best method of reducing the number of distance computations our approach can reduce the number of distance calculations by 32 3 67 1 compared with the best encoding algorithm for vector quantization our method can also further reduce the computing time by 19 7 23 9 the performance of our method is better when a larger codebook is used and is weakly correlated to codebook size

approximate expressions for the output signal to noise ratios for two types of cross correlators with correlated bandpass inputs thus far analytical expressions have not been developed for the output signal to noise ratio of a polarity coincidence correlator when the noise is correlated between the input channels approximate expressions are developed here for the output signal to noise ratios for two types of cross correlator systems one being the polarity coincidence correlator with a hard limiter in each input channel and the other variation of this correlator having a hard limiter in only one input channel the approximation scheme is based upon the known output signal to noise characteristics of a limiter and that of the standard analog correlator with no limiters the derived expressions are applicable for the case of deterministic sine waves plus narrow band gaussian noise in each input channel where the noise between channels may be correlated for the case of uncorrelated noise between input channels good agreement is found between the approximate formulas and known exact results finally asymptotic expressions are developed for certain limiting cases of input signal to noise ratios having extreme values in one or both input channels

large deviations for the chemical distance in supercritical bernoulli percolation the chemical distance d x y is the length of the shortest open path between two points x and y in an infinite bernoulli percolation cluster in this work we study the asymptotic behavior of this random metric and we prove that for an appropriate norm depending on the dimension and the percolation parameter the probability of the event 0 x d 0 x x 1 e 1 e exponentially decreases when x 1 tends to infinity from this bound we also derive a large deviation inequality for the corresponding asymptotic shape result

generalized cost measure based address predictive vector quantization address predictive vector quantization apvq exploits the interblock dependency by jointly encoding the addresses of the codewords associated with spatially close blocks it profiles the same image quality as memoryless vq for a much lesser bit rate br and the same computational complexity in the generalized cost measure based apvq the two steps of the encoding process namely vq and predictive address encoding are carried out jointly by minimizing a generalized cost measure which takes into account both the br and the distortion computer simulations show that a significant improvement can be obtained with respect to apvq in terms of both br and distortion compared with memoryless vq a bit rate reduction of almost 60 is obtained for the same image quality

exponent inequalities for the bulk conductivity of a hierarchical model the bulk conductivity p of the bond lattice in d is considered where the bonds have conductivity 1 with probabilityp or e 0 with probability 1 p various representations of the derivatives of p are developed these representations are used to analyze the behavior of p for e 0 near the percolation thresholdp c when the conducting backbone is assumed to have a hierarchical node link blob nlb structure this model has loops on arbitrarily many length scales and contains both singly and multiply connected bonds exact asymptotics of frac d 2 sigma dp 2 for the nlb model are proven under some technical assumptions the proof employs a novel technique whereby frac d 2 sigma dp 2 for the nlb model with e 0 andp nearp c is computed using perturbation theory for p for two and three component resistor lattices aroundp 1 with a sequence of e s converging to 1 as one goes deeper in the hierarchy these asymptotics establish convexity of p for the nlb model nearp c and that its critical exponentt obeys the inequalities 1 t 2 ford 2 3 while 2 t 3 ford 4 the upper boundt 2 ind 3 which is realizable in the nlb class virtually coincides with two very recent numerical estimates obtained from simulation and series expansion for the original model

new expressions for the pdf and cdf of the filtered output of an analog cross correlator corresp a general expression is derived for the probability density function pdf associated with the filtered output of an analog cross correlator the inputs of which consist of deterministic signals having the same frequency plus correlated stationary gaussian noise processes the correlator is composed of input bandpass filters a multiplier and a zonal iowpass filter the noise components in each channel have distinct variances and obey no spectral symmetry condition using the derived expression for the pdf the cumulative distribution function cdf under the same general conditions is calculated all previous known special cases are subsequently deduced from the general expressions given here the general results derived here are more suitable for numerical computations than comparable previous results found in the literature due to the fact that expressions here do not involve multiple infinite series lastly asymptotic formulas are developed for both the pdf and cdf which may be helpful in certain calculations

the probability of a large finite cluster in supercritical bernoulli percolation we consider standard bernoulli site percolation on zd with probability p for each site to be occupied c denotes the occupied cluster of the origin and ici its cardinality we show that for p critical probability of the halfspacezd l x 7 one has pp ici n 0 this improves a recent result of chayes chayes and newman the proof is based on a peierls argument which shows exponential decay of the distribution of the size of an exterior boundary of c

mean field theory for percolation models of the ising type the q 2 random cluster model is studied in the context of two mean field models the bethe lattice and the complete graph for these systems the critical exponents that are defined in terms of finite clusters have some anomalous values as the critical point is approached from the high density side which vindicates the results of earlier studies in particular the exponent which characterizes the divergence of the average size of finite clusters is 1 2 and the exponent associated with the length scale of finite clusters is 1 4 the full collection of exponents indicates an upper critical dimension of 6 the standard mean field exponents of the ising system are also present in this model 1 2 1 which implies in particular the presence of two diverging length scales furthermore the finite cluster exponents are stable to the addition of disorder which near the upper critical dimension may have interesting implications concerning the generality of the disordered system correlation length bounds

a new dynamic finite state vector quantization algorithm for image compression the picture quality of conventional memory vector quantization techniques is limited by their supercodebooks this paper presents a new dynamic finite state vector quantization dfsvq algorithm which provides better quality than the best quality that the supercodebook can offer the new dfsvq exploits the global interblock correlation of image blocks instead of local correlation in conventional dfsvqs for an input block we search the closest block from the previously encoded data using the side match technique the closest block is then used as the prediction of the input block or used to generate a dynamic codebook the input block is encoded by the closest block dynamic codebook or supercodebook searching for the closest block from the previously encoded data is equivalent to expand the codevector space thus the picture quality achieved is not limited by the supercodebook experimental results reveal that the new dfsvq reduces bit rate significantly and provides better visual quality as compared to the basic vq and other dfsvqs

an on line universal lossy data compression algorithm via continuous codebook refinement i basic results a new on line universal lossy data compression algorithm is presented for finite memoryless sources with unknown statistics its performance asymptotically approaches the fundamental rate distortion limit the codebook is generated on the fly and continuously adapted by simple rules there is no separate codebook training or codebook transmission candidate codewords are randomly generated according to an arbitrary and possibly suboptimal distribution through a carefully designed gold washing or information theoretic sieve mechanism good codewords and only good codewords are promoted to permanent status with high probability we also determine the rate at which our algorithm approaches the fundamental limit

image coding using vector quantization a review a review of vector quantization techniques used for encoding digital images is presented first the concept of vector quantization is introduced then its application to digital images is explained spatial predictive transform hybrid binary and subband vector quantizers are reviewed the emphasis is on the usefulness of the vector quantization when it is combined with conventional image coding techniques or when it is used in different domains

interpolative vector quantization of color images interpolative vector quantization has been devised to alleviate the visible block structure of coded images plus the sensitive codebook problems produced by a simple vector quantizer in addition the problem of selecting color components for color picture vector quantization is discussed computer simulations demonstrate the success of this coding technique for color image compression at approximately 0 3 b pel some background information on vector quantization is provided

the correlation length for the high density phase of bernoulli percolation l auteur examine 2 types standards de fonctions de connectivite dans la phase de densite elevee de filtration de bernoulli du plus proche voisin il demontre que les 2 quantites decroissent exponentiellement avec le meme taux constant la reciproque de cette constante definit donc une longueur de correlation pour laquelle on n arrive pas a montrer qu elle est finie au dessus d une densite critique associee a la transition de phases des proprietes de semicontinuite et de convexite sont montrees pour cette longueur de correlation et on obtient des resultats analogues a ceux concernant le modele d ising en deux dimensions

comparison of generalized q function algorithms corresp several methods have been proposed for calculating the generalized q function q m alpha beta but only isolated comparisons of the various techniques have been reported the accuracy range and execution time of prominent methods for computing the q function are compared and limitations of the algorithms are identified

fast searching algorithm for vector quantization using projection and triangular inequality in this paper a new and fast searching algorithm for vector quantization is presented two inequalities one used for terminating the searching process and the other used to delete impossible codewords are presented to reduce the distortion computations our algorithm makes use of a vector s features mean value edge strength and texture strength to reject many unlikely codewords that cannot be rejected by other available approaches experimental results show that our algorithm is superior to other algorithms in terms of computing time and the number of distortion calculations compared with available approaches our method can reduce the computing time and the number of distortion computations significantly compared with the best method of reducing distortion computation our algorithm can further reduce the number of distortion calculations by 29 to 58 4 compared with the best encoding algorithm for vector quantization our approach also further reduces the computing time by 8 to 47 7

the wulff construction and asymptotics of the finite cluster distribution for two dimensional bernoulli percolation we consider two dimensional bernoulli percolation at densityp p c and establish the following results

lossless compression of vq index with search order coding in memoryless vector quantization vq for images each block is quantized independently and its corresponding index is sent to the decoder this paper presents a new lossless algorithm that exploits the interblock correlation in the index domain we compare the current index with previous indices in a predefined search path and then send the corresponding search order to the decoder the new algorithm achieves significant reduction of bit rates without introducing extra coding distortion when compared to memoryless vq it is very simple and computationally efficient

a theoretical and experimental comparison of output signal to noise ratios of three types of cross correlators the output signal to noise ratio as a function of input signal to noise ratios is compared for three different types of cross correlators 1 the standard analog cross correlator consisting of bandpass filters multiplier and low pass filter 2 the polarity coincidence correlator pcc which incorporates hard limiters in each analog input channel and 3 a modified type of pcc wherein only one of the analog channels utilizes a hard limiter some of the previous theoretical work on the pcc is extended to include new expressions for the output signal to noise ratio from which computations can more readily be made in addition discrete circuits were fabricated that closely approximate idealized elements so as to experimentally verify the theoretical results in almost all cases tested the experimental results were in close agreement with the math models