the information lost in erasures we consider sources and channels with memory observed through erasure channels in particular we examine the impact of sporadic erasures on the fundamental limits of lossless data compression lossy data compression channel coding and denoising we define the erasure entropy of a collection of random variables as the sum of entropies of the individual variables conditioned on all the rest the erasure entropy measures the information content carried by each symbol knowing its context the erasure entropy rate is shown to be the minimal amount of bits per erasure required to recover the lost information in the limit of small erasure probability when we allow recovery of the erased symbols within a prescribed degree of distortion the fundamental tradeoff is described by the erasure rate distortion function which we characterize we show that in the regime of sporadic erasures knowledge at the encoder of the erasure locations does not lower the rate required to achieve a given distortion when no additional encoded information is available the erased information is reconstructed solely on the basis of its context by a denoiser connections between erasure entropy and discrete denoising are developed the decrease of the capacity of channels with memory due to sporadic memoryless erasures is also characterized in wide generality

fuzzy relational inequalities and equations fuzzy quasi orders closures and openings of fuzzy sets the paper deals with systems of fuzzy relation equations known in the literature as eigen fuzzy set equations as well as with systems of related fuzzy relation inequalities our main results are algorithms for computing the greatest and the smallest solutions to the considered systems of fuzzy relation inequalities and algorithms for computing the greatest solutions to the considered systems of fuzzy relation equations the systems are studied in the framework of complete residuated lattices as the structure of membership values by means of fuzzy quasi orders and closures and openings on a collection of fuzzy sets

a zero delay sequential scheme for lossy coding of individual sequences we consider adaptive sequential lossy coding of bounded individual sequences when the performance is measured by the sequentially accumulated mean squared distortion the encoder and the decoder are connected via a noiseless channel of capacity r and both are assumed to have zero delay no probabilistic assumptions are made on how the sequence to be encoded is generated for any bounded sequence of length n the distortion redundancy is defined as the normalized cumulative distortion of the sequential scheme minus the normalized cumulative distortion of the best scalar quantizer of rate r which is matched to this particular sequence we demonstrate the existence of a zero delay sequential scheme which uses common randomization in the encoder and the decoder such that the normalized maximum distortion redundancy converges to zero at a rate n sup 1 5 log n as the length of the encoded sequence n increases without bound

a parallel implicit method for the direct numerical simulation of wall bounded compressible turbulence a new second order accurate implicit temporal numerical scheme for the direct numerical simulation of turbulent flows is presented the formulation of the implicit method and the corresponding tunable parameters are introduced the numerical simulation results are compared with the results given by explicit runge kutta schemes theoretical results and published experimental and numerical data an assessment of the accuracy and performance of the method to simulate turbulent flows is made for temporally decaying isotropic turbulence and subsonic and supersonic turbulent boundary layers whereas no significant advantage over typical explicit time integration methods are found for the incompressible flows it is shown that the implicit scheme yields significant reduction in computer cost while assuring time accurate solutions for compressible turbulence simulations

multidimensional incremental parsing for universal source coding a multidimensional incremental parsing algorithm mdip for multidimensional discrete sources as a generalization of the lempel ziv coding algorithm is investigated it consists of three essential component schemes maximum decimation matching hierarchical structure of multidimensional source coding and dictionary augmentation as a counterpart of the longest match search in the lempel ziv algorithm two classes of maximum decimation matching are studied also an underlying behavior of the dictionary augmentation scheme for estimating the source statistics is examined for an m dimensional source m augmentative patches are appended into the dictionary at each coding epoch thus requiring the transmission of a substantial amount of information to the decoder the property of the hierarchical structure of the source coding algorithm resolves this issue by successively incorporating lower dimensional coding procedures in the scheme in regard to universal lossy source coders we propose two distortion functions the local average distortion and the local minimax distortion with a set of threshold levels for each source symbol for performance evaluation we implemented three image compression algorithms based upon the mdip one is lossless and the others are lossy the lossless image compression algorithm does not perform better than the lempel ziv welch coding but experimentally shows efficiency in capturing the source structure the two lossy image compression algorithms are implemented using the two distortion functions respectively the algorithm based on the local average distortion is efficient at minimizing the signal distortion but the images by the one with the local minimax distortion have a good perceptual fidelity among other compression algorithms our insights inspire future research on feature extraction of multidimensional discrete sources

fixed points of functions with max weighted quasi arithmetic mean operator abstract let 0 1 and f be a continuous strictly monotone real valued function the weighted quasi arithmetic mean of two numbers a b is defined by a b f 1 f a 1 f b let a a i j be an n n real matrix and x x 1 x 2 x n t r n we construct a function a 1 a 2 a n a r n r n by j a x max 1 l n x l a l j for all j 1 2 n in this paper we show that a has a unique fixed point x a moreover it can be shown that for each x r n the sequence x a k generated by the following iterative scheme x a 0 x and x a k a x a k 1 for all k 1 converges to the unique fixed point x a besides some properties of the fixed point are derived as an application our results imply that the max weighted quasi arithmetic mean powers of any matrix are always convergent the continuity of the function m n n r r n defined by a x a is proposed as well

fuzzy relational equations and the inverse problem abstract the inverse problem concerned with fuzzy relations is investigated the conditions for the existence of a solution are shown and an analytical solution is given a method for the improvement of the solution is proposed

overlap and channel errors in adaptive vector quantization for image coding adaptive vector quantization avq is a flexible adaptive single pass image compression method with fast decompression time for which practical compression achieved compares favorably with existing methods such as the jpeg standard and traditional trained vq in this paper we analyze its asymptotic performance for the lossless case and present variations to limit the effect of transmission errors on the decoding image

on the information rates of the plenoptic function the plenoptic function describes the visual information available to an observer at any point in space and time samples of the plenoptic function pof are seen in video and in general visual content images mosaics panoramic scenes etc and represent large amounts of information in this paper we propose a stochastic model to study the compression limits of a simplified version of the plenoptic function in the proposed framework we isolate the two fundamental sources of information in the pof the one representing the camera motion and the other representing the information complexity of the reality being acquired and transmitted the sources of information are combined generating a stochastic process that we study in detail we first propose a model for ensembles of realities that do not change over time the proposed model is simple in that it enables us to derive precise coding bounds in the information theoretic sense that are sharp in a number of cases of practical interest for this simple case of static realities and camera motion our results indicate that coding practice is in accordance with optimal coding from an information theoretic standpoint the model is further extended to account for visual realities that change over time we derive bounds on the lossless and lossy information rates for this dynamic reality model stating conditions under which the bounds are tight examples with synthetic sources suggest that within our proposed model common hybrid coding using motion displacement estimation with dpcm performs considerably suboptimally relative to the true rate distortion bound

twofold universal prediction schemes for achieving the finite state predictability of a noisy individual binary sequence the problem of predicting the next outcome of an individual binary sequence corrupted by noise using finite memory is considered the conditional finite state fs predictability of an infinite individual sequence given its noisy version is defined as the minimum fraction of errors that can be made by any fs predictor fed by the noisy version it is proved that the conditional fs predictability can be attained almost surely by universal sequential prediction schemes in the case where the noisy version is the output of a binary symmetric channel bsc whose input is the clean individual sequence in particular universal predictors of the original noise free setting which operate on the noisy sequence have this property moreover these universal predictors do not depend on the crossover probability characterizing the bsc it is seen that the noisy setting gives rise to additional criteria by which the performance of prediction schemes can be assessed finally a closer look is taken at the conditional fs predictability and this quantity is proposed as an additional measure of the complexity of a sequence perhaps finer and more informative than the predictive complexity of the noise free setting

an adaptive implicit explicit scheme for the dns and les of compressible flows on unstructured grids an adaptive implicit explicit scheme for direct numerical simulation dns and large eddy simulation les of compressible turbulent flows on unstructured grids is developed the method uses a node based finite volume discretization with summation by parts sbp property which in conjunction with simultaneous approximation terms sat for imposing boundary conditions leads to a linearly stable semi discrete scheme the solution is marched in time using an implicit explicit runge kutta imex rk time advancement scheme a novel adaptive algorithm for splitting the system into implicit and explicit sets is developed the method is validated using several canonical laminar and turbulent flows load balance for the new scheme is achieved by a dual constraint domain decomposition algorithm the scalability and computational efficiency of the method is investigated and memory savings compared with a fully implicit method is demonstrated a notable reduction of computational costs compared to both fully implicit and fully explicit schemes is observed

image analysis using space filling curves and 1d wavelet bases images are transformed into signals using a peano hilbert space filling curve this continuous mapping captures local informations when hilbert s curve is wandering inside the image then the obtained signal is analysed using 1 d one dimensional wavelet orthogonal bases the spaces of details of smaller and smaller scales are considered they are built from a scaling function an image can be computed by selecting wavelet coefficients corresponding to one or several scales and using the inverse peano hilbert procedure due to the good localization of wavelet analysis local and global patterns can be detected and global ones can be reinforced so the edge detection of global edges is prepared and easier with mathematical morphology

on the power sequence of a fuzzy matrix with convex combination of max product and max min operations in the literature the powers of a fuzzy matrix with max min max product max archimedean t norm max t norm max arithmetic mean compositions have been studied it turns out that the limiting behavior of the powers of a fuzzy matrix depends on the composition involved in this paper we consider the powers of a fuzzy matrix with convex combination of max product and max min operations we show that the powers of a fuzzy matrix a with such operations are asymptotical p period if and only if the powers of an associated boolean matrix a are p periodic moreover necessary and sufficient conditions for such a fuzzy matrix to be nilpotent are proposed

indices and periods of incline matrices abstract inclines are the additively idempotent semirings in which products are less than or equal to factors thus inclines generalize boolean algebra fuzzy algebra and distributive lattice and the boolean matrices the fuzzy matrices and the lattice matrices are the prototypical examples of the incline matrices i e the matrices over inclines this paper studies the power sequence of incline matrices in detail a necessary and sufficient condition for the incline matrix to have index is given and the indices of some incline matrices with indices are estimated it is proved that the period of n n incline matrix with index is a divisor of n and that the set of periods of n n incline matrices with indices is not bounded from above in the sense of a power of n for all n an equivalent condition and some sufficient conditions for the incline matrix to converge in finite steps are established the stability of the orbits of an incline matrix is considered and a theorem in fuzzy sets and systems 81 1996 227 is pointed out being false the results in the present paper include some previous results in the literatures which were obtained for the boolean matrices the fuzzy matrices and the lattice matrices among their special cases

some theoretical aspects of fuzzy relation equations describing fuzzy systems abstract this paper contains some theoretical results on fuzzy relation equations and applications to analysis of fuzzy systems as well as identification and control problems if ai 1 i k are fuzzy inputs b is a fuzzy output and r is a fuzzy relation describing the system the above problems are illustrated by means of a max min multidimensional equation of type b a 1 a k r furthermore we investigate some properties of fuzzy systems described by fuzzy relation equations focusing our attention on energy and entropy measures of fuzziness of solutions of the class of equations under discussion

fused trees and some new approaches to source coding the concept of fusion partition for the node set of a tree and the concept of a fused tree corresponding to it are discussed a fused tree requires in principle significantly less memory for storage than the original tree yet allows the recovery of the original hence it makes sense to store a tree in a fused form furthermore if labels from an ordered set c are assigned to the branches of the original tree so that a lexographic alphabetic order on the set of terminal nodes is induced a fused tree still enables the execution of direct and inverse enumeration algorithms a fusion algorithm to produce the completely fused tree for a given tree is presented some approaches to data compression problems related to the algorithms given are discussed

on the sequence of consecutive powers of a fuzzy matrix with max archimedean t norms in the literature the limiting behavior of powers of a fuzzy matrix has been studied with max product composition pang and guu proposed a simple and effective characterization for the limiting behavior with the notion of asymptotic period in this paper we shall extend pang and guu s work to the realm with the max archimedean t norm composition to which the max product belongs moreover some sufficient conditions for the powers to converge in finitely many steps will be established

convergence of max arithmetic mean powers of a fuzzy matrix fuzzy matrices provide convenient representations for fuzzy relations on finite universes in the literature the powers of a fuzzy matrix with max min max product max archimedean t norm compositions have been studied it turns out that the limiting behavior of the powers of a fuzzy matrix depends on the composition involved in this paper the max arithmetic mean composition is considered for the fuzzy relations we show that the max arithmetic mean powers of a fuzzy matrix always are convergent

discrete denoising with shifts we introduce s dude a new algorithm for denoising discrete memoryless channel dmc corrupted data the algorithm which generalizes the recently introduced dude discrete universal denoiser aims to compete with a genie that has access in addition to the noisy data also to the underlying clean data and that can choose to switch up to m times between sliding window denoisers in a way that minimizes the overall loss when the underlying data form an individual sequence we show that the s dude performs essentially as well as this genie provided that m is sublinear in the size of the data when the clean data are emitted by a piecewise stationary process we show that the s dude achieves the optimum distribution dependent performance provided that the same sublinearity condition is imposed on the number of switches to further substantiate the universal optimality of the s dude we show that when the number of switches is allowed to grow linearly with the size of the data any sequence of scheme s fails to compete in the above sense using dynamic programming we derive an efficient implementation of the s dude which has complexity time and memory growing linearly with the data size and the number of switches m preliminary experimental results are presented suggesting that s dude has the capacity to improve on the performance attained by the original dude in applications where the nature of the data abruptly changes in time or space as is often the case in practice

textbook efficiency multigrid solver for three dimensional unsteady compressible navier stokes equations implicit time integration techniques are envisioned to be the methods of choice for direct numerical simulations dns for flows at high reynolds numbers therefore the computational efficiency of implicit flow solvers becomes critically important the textbook multigrid efficiency tme which is the optimal efficiency of a multigrid method is achieved if accurate solutions of the governing equations are obtained with the total computational work that is a small less than 10 multiple of the operation count in one residual evaluation in this paper we present a tme solver for unsteady subsonic compressible navier stokes equations in three dimensions discretized with an implicit second order accurate in both space and time unconditionally stable and non conservative scheme a semi lagrangian approach is used to discretize the time dependent convection part of the equations viscous terms and the pressure gradient are discretized on a staggered grid the tme solver for the implicit equations is applied at each time level the computational efficiency of the solver is designed to be independent of the reynolds number our tests show that the proposed solver maintains its optimal efficiency at high reynolds numbers and for large time steps

a combined transform coding ctc scheme for medical images a combined transform coding ctc scheme is proposed to reduce the blocking artifact of conventional block transform coding and hence to improve the subjective performance the proposed ctc scheme is described and its information theoretic properties are investigated computer simulation results for a class of chest x ray images are presented a comparison between the ctc scheme and the conventional discrete cosine transform dct and discrete walsh hadamard transform dwht demonstrates the performance improvement of the proposed scheme in addition combined coding can also be used in noiseless coding yielding a slight improvement in the compression performance if it is used properly

efficient adaptive algorithms and minimax bounds for zero delay lossy source coding zero delay lossy source coding schemes are considered for both individual sequences and random sources performance is measured by the distortion redundancy which is defined as the difference between the normalized cumulative mean squared distortion of the scheme and the normalized cumulative distortion of the best scalar quantizer of the same rate that is matched to the entire sequence to be encoded by improving and generalizing a scheme of linder and lugosi weissman and merhav showed the existence of a randomized scheme that for any bounded individual sequence of length n achieves a distortion redundancy o n sup 1 3 logn however both schemes have prohibitive complexity both space and time which makes practical implementation infeasible in this paper we present an algorithm that computes weissman and merhav s scheme efficiently in particular we introduce an algorithm with encoding complexity o n sup 4 3 and distortion redundancy o n sup 1 3 logn the complexity can be made linear in the sequence length n at the price of increasing the distortion redundancy to o n sup 1 4 spl radic logn we also consider the problem of minimax distortion redundancy in zero delay lossy coding of random sources by introducing a simplistic scheme and proving a lower bound we show that for the class of bounded memoryless sources the minimax expected distortion redundancy is upper and lower bounded by constant multiples of n sup 1 2

a methodology for modeling the distributions of medical images and their stochastic properties the probabilistic distribution properties of a set of medical images are studied it is shown that the generalized gaussian function provides a good approximation to the distribution of ap chest radiographs based on this result and a goodness of fit test a generalized gaussian autoregressive model ggar is proposed its properties and limitations are also discussed it is expected that the ggar model will be useful in describing the stochastic characteristics of some classes of medical images and in image data compression and other applications

universal prediction of individual binary sequences in the presence of noise the problem of predicting the next outcome of an individual binary sequence based on noisy observations of the past is considered the goal of the predictor is to perform for each individual sequence almost as well as the best in a set of experts where performance is evaluated using a general loss function a comprehensive approach to prediction in this noisy setting is presented and proven generally efficient under appropriate conditions as an illustration of the applicability of the approach suggested for concrete situations two important special cases are explicitly treated the first is the case where the data corrupting noise process is binary valued where the observed bit is the bitwise xor of the clean bit and the noise bit the second case is that of real valued additive noise it is shown that even in this more challenging situation where the information available to the predictor regarding the past sequence is incomplete a predictor can be guaranteed to successfully compete with a whole set of experts in considerably strong senses

universal filtering via prediction we consider the filtering problem where a finite alphabet individual sequence is corrupted by a discrete memoryless channel and the goal is to causally estimate each sequence component based on the past and present noisy observations we establish a correspondence between the filtering problem and the problem of prediction of individual sequences which leads to the following result given an arbitrary finite set of filters there exists a filter which performs with high probability essentially as well as the best in the set regardless of the underlying noiseless individual sequence we use this relationship between the problems to derive a filter guaranteed of attaining the finite state filterability of any individual sequence by leveraging results from the prediction problem

pattern matching and lossy data compression on random fields we consider the problem of lossy data compression for data arranged on two dimensional arrays such as images or more generally on higher dimensional arrays such as video sequences several of the most commonly used algorithms are based on pattern matching given a distortion level d and a block of data to be compressed the encoder first finds a d close match of this block into some database and then describes the data by describing the position of the match we consider two idealized versions of this scenario in the first the database is taken to be a collection of independent realizations of the same size and from the same distribution as the original data in the second the database is assumed to be a single long realization from the same source as the data we show that the compression rate achieved in either version is no worse than r d 2 bits per symbol where r d is the rate distortion function this is proved under the assumptions that 1 the data is generated by a gibbs distribution and 2 the distortion measure is a metric generalizing the corresponding one dimensional bound of steinberg and gutman 1993 using large deviations results by dembo and kontoyiannis see ibid vol 48 p 1590 15 2000 and by chi 2001 we are able to give short proofs for the present results

image registration by compression abstract image registration consists in finding the transformation that brings one image into the best possible spatial correspondence with another image in this paper we present a new framework for image registration based on compression the basic idea underlying our approach is the conjecture that two images are correctly registered when we can maximally compress one image given the information in the other the contribution of this paper is twofold first we show that image registration can be formulated as a compression problem second we demonstrate the good performance of the similarity metric introduced by li et al in image registration two different approaches for the computation of this similarity metric are described the kolmogorov version computed using standard real world compressors and the shannon version calculated from an estimation of the entropy rate of the images

finite difference schemes for long time integration a general method for constructing finite difference schemes for longtime integration problems is presented it is demonstrated for discretizations of first and second space derivatives however the approach is not limited to these cases the schemes are constructed so as to minimize the global truncation error taking into account the initial data the resulting second order compact schemes can be used for integration times fourfold or more longer than previously studied schemes with similar computational complexity a similar approach was used to obtain improved integration schemes

new fuzzy learning model with recursive estimation for dynamic systems abstract a systematic design technique for a discrete time self learning fuzzy model based on fuzzy relational equations is presented with some novel features firstly the model utilizes a probabilistic fuzzy relation obtained from referential fuzzy sets on the input and output spaces secondly the conventional input output formulation of the fuzzy relation is extended by introducing internal fuzzy states in order to model the internal dynamics of the given dynamic system thirdly the fuzzy relation is used to estimate the output as a response to a given stimulus by means of the compositional rule of inference extended to include recursive estimation of the internal fuzzy state as a result the new model is shown to be a fuzzy automaton first and second order versions of the fuzzy model are validated by means of a well known set of industrial data

standard eigenvectors of incline matrices abstract inclines are the additively idempotent semirings in which products are less than or equal to either factor thus inclines generalize boolean algebra fuzzy algebra and distributive lattice this paper studies the standard eigenvectors of incline matrices i e matrices over inclines in detail as the main results for an incline matrix with index and for a lattice matrix the structures of all the standard eigenvectors are given and the greatest standard eigenvector is determined also it is proved that for an incline matrix with index the set of all the standard eigenvectors of it coincides with the set of all the standard eigenvectors of its transitive closure the power convergence of an incline matrix with index is characterized in terms of the sets of standard eigenvectors the results in the present paper include some previous results for the boolean matrices the fuzzy matrices and the lattice matrices among their special cases

two dimensional encoding by finite state encoders distortion free compressibility of individual pictures by finite state encoders is investigated in a recent paper see ieee trans inform theory vol 32 no 1 p 1 8 1986 the compressibility of a given picture i was defined and shown to be the asymptotically attainable lower bound on the compression ratio that can be achieved for i by any finite state encoder here a different and more direct approach is taken to prove similar results which are summarized in a converse to coding theorem and a constructive coding theorem that leads to a universal asymptotically optimal compression algorithm

hidden markov processes an overview of statistical and information theoretic aspects of hidden markov processes hmps is presented an hmp is a discrete time finite state homogeneous markov chain observed through a discrete time memoryless invariant channel in recent years the work of baum and petrie 1966 on finite state finite alphabet hmps was expanded to hmps with finite as well as continuous state spaces and a general alphabet in particular statistical properties and ergodic theorems for relative entropy densities of hmps were developed consistency and asymptotic normality of the maximum likelihood ml parameter estimator were proved under some mild conditions similar results were established for switching autoregressive processes these processes generalize hmps new algorithms were developed for estimating the state parameter and order of an hmp for universal coding and classification of hmps and for universal decoding of hidden markov channels these and other related topics are reviewed

on the symmetric information rate of two dimensional finite state isi channels we derive a pair of bounds upper and lower on the symmetric information rate of a two dimensional finite state intersymbol interference isi channel model for channels with small impulse response support they can be estimated via a modified forward recursion of the bahl cocke jelinek raviv bcjr algorithm the convergence of the bounds is also analyzed to relax the constraint on the size of the impulse response a new upper bound is proposed which allows the tradeoff of the computational complexity and the tightness of the bound these bounds are further extended to d dimensional d 2 isi channels

on the max contraction powers of a fuzzy matrix abstract in the literature the powers of a fuzzy matrix with max arithmetic mean convex combination of max min and max arithmetic mean convex combination of max product and max min compositions have been studied it turns out that the limiting behavior of the powers of a fuzzy matrix depends on the composition involved in this paper we consider the max contraction powers of a fuzzy matrix which is an extension of the max arithmetic mean convex combination of max min and max arithmetic mean convex combination of max product and max arithmetic mean operation we show that the powers of such a fuzzy matrix are always convergent and the limit matrix has the feature that all elements of each column are identical

convergence eigen fuzzy sets and stability analysis of relational matrices abstract if stable control applications are formulated with a max product composition then instability in the relational matrix under any conditions is undesirable this paper reviews the stability analysis of relational matrices combined with the max min composition 19 and then presents an analysis of the stability of relational matrices combined with the max product composition this analysis includes results defining the convergence properties of the relational matrix determination of the eigen fuzzy sets of the stable matrices and algorithmic solutions for several important cases a method is also presented to stabilize unstable relational matrices for some control applications

on the metric properties of discrete space filling curves a space filling curve is a linear traversal of a discrete finite multidimensional space in order for this traversal to be useful in many applications the curve should preserve locality we quantify locality and bound the locality of multidimensional space filling curves classic hilbert space filling curves come close to achieving optimal locality

on universal types the universal type class of a sequence xn is defined in analogy to the notion underlying the classical method of types two sequences of the same length are said to be of the same universal lz type if and only if they yield the same dictionary or equivalently parsing tree in the incremental parsing of ziv and lempel 1978 it is shown that for any finite order k the variational distance between the kth order empirical probability distributions of two sequences of the same universal type vanishes as the sequence length tends to infinity consequently for any k and any kth order probability assignment the difference between the normalized logarithms of the probabilities assigned to two sequences of the same universal type also vanishes asymptotically the size of a universal type class is studied and it is shown that its asymptotic behavior parallels that of the conventional counterpart with the lz78 code length playing the role of the empirical entropy the number of universal types for sequences of length n is estimated and shown to be of the form exp 1 o 1 gamman logn for a well characterized constant gamma algorithms for enumerating the sequences in a universal type class and for drawing a sequence from the class with uniform probability are described as an application the problem of universal simulation of individual sequences is considered a sequence drawn with uniform probability from the universal type class of xn is an optimal simulation of xn in a well defined mathematical sense

space filling approach for fast window query on compressed images based on the space filling approach this paper presents a fast algorithm for window query on compressed images given a query window of size n sub 1 spl times n sub 2 the proposed algorithm takes o n sub 1 logt p time to perform the window query where n sub 1 max n sub 1 n sub 2 and t spl times t is the image size p is the number of outputted codes the proposed algorithm improves the naive algorithm which needs o n sub 1 n sub 2 log t p time significantly some experimentations are carried out to demonstrate the computational advantage of the proposed algorithm from the experimental results it is observed that the proposed algorithm has about 72 98 time improvement when compared to the naive algorithm

sequential prediction of individual sequences under general loss functions we consider adaptive sequential prediction of arbitrary binary sequences when the performance is evaluated using a general loss function the goal is to predict on each individual sequence nearly as well as the best prediction strategy in a given comparison class of possibly adaptive prediction strategies called experts by using a general loss function we generalize previous work on universal prediction forecasting and data compression however here we restrict ourselves to the case when the comparison class is finite for a given sequence we define the regret as the total loss on the entire sequence suffered by the adaptive sequential predictor minus the total loss suffered by the predictor in the comparison class that performs best on that particular sequence we show that for a large class of loss functions the minimax regret is either spl theta log n or spl omega spl radic spl lscr log n depending on the loss function where n is the number of predictors in the comparison class and spl lscr is the length of the sequence to be predicted the former case was shown previously by vovk 1990 we give a simplified analysis with an explicit closed form for the constant in the minimax regret formula and give a probabilistic argument that shows this constant is the best possible some weak regularity conditions are imposed on the loss function in obtaining these results we also extend our analysis to the case of predicting arbitrary sequences that take real values in the interval 0 1

an algorithm for source coding subject to a fidelity criterion based on string matching a practical suboptimal universal block source coding scheme subject to a fidelity criterion is proposed the algorithm is an extension of the lempel ziv algorithm and is based on string matching with distortion it is shown that given average distortion d 0 the algorithm achieves a rate of exceeding r d 2 for a large class of sources and distortion measures tighter bounds on the rate are derived for discrete memoryless sources and for memoryless gaussian sources

mutual information and minimum mean square error in gaussian channels this paper deals with arbitrarily distributed finite power input signals observed through an additive gaussian noise channel it shows a new formula that connects the input output mutual information and the minimum mean square error mmse achievable by optimal estimation of the input given the output that is the derivative of the mutual information nats with respect to the signal to noise ratio snr is equal to half the mmse regardless of the input statistics this relationship holds for both scalar and vector signals as well as for discrete time and continuous time noncausal mmse estimation this fundamental information theoretic result has an unexpected consequence in continuous time nonlinear estimation for any input signal with finite power the causal filtering mmse achieved at snr is equal to the average value of the noncausal smoothing mmse achieved with a channel whose snr is chosen uniformly distributed between 0 and snr

structural information in two dimensional patterns entropy convergence and excess entropy we develop information theoretic measures of spatial structure and pattern in more than one dimension as is well known the entropy density of a two dimensional configuration can be efficiently and accurately estimated via a converging sequence of conditional entropies we show that the manner in which these conditional entropies converge to their asymptotic value serves as a measure of global correlation and structure for spatial systems in any dimension we compare and contrast entropy convergence with mutual information and structure factor techniques for quantifying and detecting spatial structure

compression of two dimensional data distortion free compressibility of individual pictures i e two dimensional arrays of data by finite state encoders is investigated for every individual infinite picture i a quantity rho i is defined called the compressibility of i which is shown to be the asymptotically attainable lower bound on the compression ratio that can be achieved for i by any finite state information lossless encoder this is demonstrated by means of a constructive coding theorem and its converse that apart from their asymptotic significance might also provide useful criteria for finite and practical data compression tasks the proposed picture compressibility is also shown to possess the properties that one would expect and require of a suitably defined concept of two dimensional entropy for arbitrary probabilistic ensembles of infinite pictures while the definition of rho i allows the use of different machines for different pictures the constructive coding theorem leads to a universal compression scheme that is asymptotically optimal for every picture the results are readily extendable to data arrays of any finite dimension

scanning and sequential decision making for multidimensional data part i the noiseless case we investigate the problem of scanning and prediction ldquoscandiction rdquo for short of multidimensional data arrays this problem arises in several aspects of image and video processing such as predictive coding for example where an image is compressed by coding the error sequence resulting from scandicting it thus it is natural to ask what is the optimal method to scan and predict a given image what is the resulting minimum prediction loss and whether there exist specific scandiction schemes which are universal in some sense specifically we investigate the following problems first modeling the data array as a random field we wish to examine whether there exists a scandiction scheme which is independent of the field s distribution yet asymptotically achieves the same performance as if this distribution were known this question is answered in the affirmative for the set of all spatially stationary random fields and under mild conditions on the loss function we then discuss the scenario where a nonoptimal scanning order is used yet accompanied by an optimal predictor and derive bounds on the excess loss compared to optimal scanning and prediction this paper is the first part of a two part paper on sequential decision making for multidimensional data it deals with clean noiseless data arrays the second part deals with noisy data arrays namely with the case where the decision maker observes only a noisy version of the data yet it is judged with respect to the original clean data

an identification algorithm in fuzzy relational systems abstract the paper presents an effective identification method in fuzzy relational systems we propose an algorithm for constructing models on the basis of fuzzy and nonfuzzy data with the aid of fuzzy discretization and clustering techniques the usefulness of the method provided is demonstrated by means of two numerical examples also a possible way of generating a linguistic decision making algorithm is discussed

scan predictive vector quantization of multispectral images conventional vector quantization vq based techniques partition an image into nonoverlapping blocks that are then raster scanned and quantized image blocks that contain an edge result in high frequency vectors the coarse representation of such vectors leads to visually annoying degradations in the reconstructed image the authors present a solution to the edge degradation problem based on some earlier work on scan models the approach reduces the number of vectors with abrupt intensity variations by using an appropriate scan to partition an image into vectors they show how their techniques can be used to enhance the performance of vq of multispectral data sets comparisons with standard techniques are presented and shown to give substantial improvements

design of fuzzy logic controllers based on generalized t operators abstract since zadeh first proposed the basic principle of fuzzy logic controllers in 1968 the min and max operators have been popular in the design of fuzzy logic controllers in this paper the general concept of t operators is introduced into the conventional design methods for fuzzy logic controllers so that a general and flexible methodology for the design of these fuzzy logic controllers is available then by computer simulations studies are made so as to determine the relations between the various t operators and the performance of a fuzzy logic controller it is concluded that the performance of the fuzzy logic controller for a given class of plants very much depends upon the choice of the t operators

computational mechanics pattern and prediction structure and simplicity computational mechanics an approach to structural complexity defines a process s causal states and gives a procedure for finding them we show that the causal state representation an machine is the minimal one consistent with accurate prediction we establish several results on machine optimality and uniqueness and on how machines compare to alternative representations further results relate measures of randomness and structural complexity obtained from machines to those from ergodic and information theories

on universal quantization the quantization of n dimensional vectors in r n with an arbitrary probability measure under a mean square error constraint is discussed it is demonstrated that a uniform one dimensional quantizer followed by a noiseless digital variable rate encoder entropy encoding can yield a rate that is for any n no more than 0 754 bit per sample higher than the rate associated with the optimal n dimensionai quantizer regardless of the probabilistic characterization of the input n vector for the allowable mean square error

an analysis of some common scanning techniques for lossless image coding though most image coding techniques use a raster scan to order pixels prior to coding hilbert and other scans have been proposed as having better performance due to their superior locality preserving properties however a general understanding of the merits of various scans has been lacking this paper develops an approach for quantitatively analyzing the effect of pixel scan order for context based predictive lossless image compression and uses it to compare raster hilbert random and hierarchical scans specifically for a quantized gaussian image model and a given scan order it shows how the encoding rate can be estimated from the frequencies with which various pixel configurations are available as previously scanned contexts and from the corresponding conditional differential entropies formulas are derived for such context frequencies and entropies assuming an isotropic image model and contexts consisting of previously scanned adjacent pixels it is found that the raster scan is better than the hilbert scan which is often used in compression applications due to its locality preserving properties the hierarchical scan is better still though it is based on nonadjacent contexts the random scan is the worst of the four considered extensions and implications of the results to lossy coding are also discussed

a mach sensitive implicit explicit scheme adapted to compressible multi scale flows abstract the method presented below focuses on the numerical approximation of the euler compressible system it pursues a two fold objective being able to accurately follow slow material waves as well as strong shock waves in the context of low mach number flows the resulting implicit explicit imex fractional step approach leans on a dynamic splitting designed to react to the time fluctuations of the maximal flow mach number when the latter rises suddenly the imex scheme so far driven by a material wave courant number turn into a time explicit approximate riemann solver constrained by an acoustic wave courant number it is also possible to enrich the dynamic splitting in order to capture high pressure jumps even when the flow mach number is low one dimensional low mach number test cases involving single or multiple waves confirm that the present approach is as accurate and efficient as an imex lagrange projection method besides numerical results suggest that the stability of the present method holds for any mach number if the courant number related to the convective subsystem arising from the splitting is of order unity

on the max nilpotent t norm powers of a fuzzy matrix fuzzy matrices have been proposed to represent fuzzy relations in finite universes various studies have evaluated the powers of a fuzzy matrix with max min max product max archimedean t norm max t norm max arithmetic mean compositions indicating that the limiting behavior of the powers of a fuzzy matrix depends on its composition in this paper max nilpotent composition is considered for the fuzzy relations we demonstrate that the max nilpotent powers of a fuzzy matrix either converge or oscillate in a finite period moreover the max nilpotent t norm powers of a fuzzy matrix a are p periodic if and only if the powers of an associated boolean matrix a c are p periodic finally necessary and sufficient conditions are proposed for nilpotent fuzzy matrices that exhibit max nilpotent composition

on the wyner ziv problem for individual sequences we consider a variation of the wyner ziv w z problem pertaining to lossy compression of individual sequences using finite state encoders and decoders there are two main results in this paper the first characterizes the relationship between the performance of the best m state encoder decoder pair to that of the best block code of size lscr for every input sequence and shows that the loss of the latter relative to the former in terms of both rate and distortion never exceeds the order of logm lscr independently of the input sequence thus in the limit of large m the best rate distortion performance of every infinite source sequence can be approached universally by a sequence of block codes which are also implementable by finite state machines while this result assumes an asymptotic regime where the number of states is fixed and only the length n of the input sequence grows without bound we then consider the case where the number of states m mn is allowed to grow concurrently with n our second result is then about the critical growth rate of mn such that the rate distortion performance of mn state encoder decoder pairs can still be matched by a universal code we show that this critical growth rate of mn is linear in n

data parallel lower upper relaxation method for reacting flows the implicit lower upper symmetric gauss seidel lu sgs method of yoon and jameson is modified for use on massively parallel computers the method has been implemented on the thinking machines cm s and the maspar mp 1 and mp 2 where large percentages of the theoretical peak floating point performance are obtained it is shown that the new data parallel lu relaxation method has better convergence properties than the original method for two different inviscid compressible flow simulations the convergence is also improved for five species reacting air computations the performance of the method on various partitions of the cm s and on the maspar computers is discussed the new method shows promise for the efficient simulation of very large perfect gas and reacting flows

writing sequences on the plane the problem of arranging two dimensional arrays of data into one dimensional sequences comes up in image processing color quantization and optical and magnetic data recording a good arrangement should enable the one dimensional sequences to be modeled as markov chains or shifts of finite type since this is not possible in general two dimensional data is most commonly scanned by rows columns or diagonals we look into three unusual ways to write a sequence in the plane by penrose tilings by space filling curves and by cylindrical and spiral lattices we show how penrose tilings can be used to record information and how some spiral lattices can be used for quantization of color spaces

color quantization and processing by fibonacci lattices color quantization is sampling of three dimensional 3 d color spaces such as rgb or lab which results in a discrete subset of colors known as a color codebook or palette it is extensively used for display transfer and storage of natural images in internet based applications computer graphics and animation we propose a sampling scheme which provides a uniform quantization of the lab space the idea is based on several results from number theory and phyllotaxy the sampling algorithm is very much systematic and allows easy design of universal image independent color codebooks for a given set of parameters the codebook structure allows fast quantization and ordered dither of color images the display quality of images quantized by the proposed color codebooks is comparable with that of image dependent quantizers most importantly the quantized images are more amenable to the type of processing used for grayscale ones methods for processing grayscale images cannot be simply extended to color images because they rely on the fact that each gray level is described by a single number and the fact that a relation of full order can be easily established on the set of those numbers color spaces such as rgb or lab are on the other hand 3 d the proposed color quantization i e color space sampling and numbering of sampled points makes methods for processing grayscale images extendible to color images we illustrate possible processing of color images by first introducing the basic average and difference operations and then implementing edge detection and compression of color quantized images

occam filters for stochastic sources with application to digital images an occam filter employs lossy data compression to separate signal from noise previously it was shown that occam filters can filter random noise from deterministic signals here we show that occam filters can also separate two stochastic sources depending on their relative compressibility we also compare the performance of occam filters and wavelet based denoising on digital images

universal prediction of individual sequences the problem of predicting the next outcome of an individual binary sequence using finite memory is considered the finite state predictability of an infinite sequence is defined as the minimum fraction of prediction errors that can be made by any finite state fs predictor it is proven that this fs predictability can be achieved by universal sequential prediction schemes an efficient prediction procedure based on the incremental parsing procedure of the lempel ziv data compression algorithm is shown to achieve asymptotically the fs predictability some relations between compressibility and predictability are discussed and the predictability is proposed as an additional measure of the complexity of a sequence