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

ergodicity of markov channels a markov channel is a discrete information channel that includes as special cases the finite state channels and finite state codes of information theory kieffer and rahe proved that one sided and two sided markov channels have the following property if the input source to a markov channel is asymptotically mean stationary ams then so is the resulting input output process and hence the ergodic theorem and the shannon mcmillan breiman theorem hold for the input output process kieffer and rahe also provided a sufficient condition for any ams ergodic source to yield an ams ergodic input output process new conditions for a markov channel to have this ergodicity property are presented and discussed here several relations are developed among various classes of channels including weakly ergodic indecomposable and strongly mixing channels some connections between markov channels and the theory of nonhomogeneous markov chains are also discussed

vector quantization of speech and speech like waveforms an algorithm for the design of vector quantizers that are locally optimum in the sense of minimizing an average quantitative distortion measure is used to design 1 and 2 bit sample vector quantizers for both real sampled speech and a simulated speech like auto regressive random process both weighted and unweighted squared error distortion measures are considered several comparisons are made and discussed based on the average distortions of the vector quantization schemes the results for the simulated speech are compared to mathematical performance bounds from information theory to provide an indication of how nearly globally optimal vector quantization is for such highly correlated sources a comparison of the results for the real speech and the simulated speech provides a quantitative measure of the accuracy of such models and hence of the applicability of information theory bounds and code designs based on probabilistic models the signal to quantization noise ratios of vector quantizers designed to minimize squared error distortion are compared to those of several popular speech waveform coding systems of similar rates

a faffa mlfma algorithm for electromagnetic scattering based on the multilevel fast multipole algorithm mlfma an efficient method is proposed to accelerate the solution of the combined field integral equation in electromagnetic scattering and radiation where the fast far field approximation faffa is combined with mlfma the translation between groups in mlfma is expensive because spherical hankel functions and legendre polynomials are involved and the translator is defined on an eward sphere with many k spl circ directions when two groups are in the far field region however the translation can be greatly simplified by faffa where only a single k spl circ direction is involved in the translator the condition for using faffa and the way to efficiently incorporate faffa with mlfma are discussed complexity analysis illustrates that the computational cost in faffa mlfma can be asymptotically cut by half compared to the conventional mlfma numerical results are given to verify the efficiency of the algorithm

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

multigrid optimization in applications abstract iterative techniques are a key methodology for the numerical solution of optimization problems in differential equations in two practical application problems with different characteristics this paper shows how multigrid methods can be applied efficiently to this problem class problem formulations solution approaches as well as numerical results are presented

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

antenna characterization in the time domain a theory for a complete far field transmit receive system characterization of short pulse antennas is derived in the time domain the transmit receive antenna system is characterized by a set of cascaded operators which transform the source waveform and power into similar quantities at the receiving antenna terminals two such sets are defined the first one is phrased in terms of the wave type time dependent effective height operator while the second one is defined in terms of the energy type gain operator both definitions fit within a complete transmit receive system description the latter being equivalent to the frequency domain friis equation however these operators are derived entirely in the context of the time domain field equation the starting point in the time domain analysis of the effective height is the slant stack transform sst of the time dependent current distribution in a manner equivalent to the spatial fourier transform used in the frequency domain the vector autocorrelation of the transmitting effective height is then used to define the time dependent gain operator under impulsive source excitation time domain reciprocity leads to the definitions of antenna parameters under receiving conditions and the corresponding equivalent circuit the parameters defined in this way fit within a consistent transmit receive convolution operator operating on the autocorrelation of the input signal this independent time domain representation is thus similar to the frequency domain representation however unlike the conventional frequency domain circuit parameters which relate voltage and current amplitudes the time domain circuit representation is based on incident and reflected wave type constituents in addition the use of appropriate norms facilitates the transformation of our operators to stand alone figures of merits the general concepts developed are demonstrated for a short dipole antenna

on the convergence of recursive trust region methods for multiscale nonlinear optimization and applications to nonlinear mechanics we prove new convergence results for a class of multiscale trust region algorithms originally introduced by gratton sartenaer and toint in siam j optim 19 2008 pp 414 444 to solve unconstrained minimization problems within the euclidean space mathbb r n we will state less restrictive assumptions on the objective function and on the iteratively computed trust region corrections which allow for proving first order convergence moreover we propose a novel projection approach for obtaining the initial coarse level iterates which are needed within the nonlinear multiscale iteration we show the efficiency and robustness of our approach by means of numerical examples from nonlinear continuum mechanics where stored energy functions for materials of ogden type and for materials with visco plastic behavior are minimized

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

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

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

a propagating plane wave based near field transmission equation for antenna gain determination from irregular measurement samples in order to accurately determine the far field gain of an antenna under test from near field measurements a general transmission equation between the ports of a transmitting and a receiving antenna is derived the formulation is based on a propagating plane wave expansion of the electric field and allows one to use a derivation based on far field concepts separately for all entries of the plane wave spectrum it is shown that the equation is a generalization of the friis transmission equation to the near field case and the equation is compared with spherical multipole based transmission equations for single and multiple antenna systems the new transmission equation is integrated into the fast irregular antenna field transformation algorithm which now allows one to determine the antenna gain pattern not only from canonical measurement surfaces as planes and spheres but also from highly irregular sample distributions examples using near field data from both simulations and measurements are given to prove the validity of the formulation and to illustrate the capabilities of the implementation in particular it is also shown that accurate gain determination is possible from incomplete near field measurements and that appropriate probe correction is important

encoding of correlated observations an important class of engineering problems involves sensing an environment and making estimates based on the phenomena sensed in the traditional model of this problem the sensors observations are available to the estimator without alteration there is growing interest in em distributed sensing systems in which several observations are communicated to the estimator over channels of limited capacity the observations must be separately encoded so that the target can be estimated with minimum distortion two questions are addressed for a special case of this problem wherein there are two sensors which observe noisy data and communicate with a single estimator 1 if the encoder is unlimited in complexity what communication rates and distortions can be achieved 2 if the encoder must be a quantizer a mapping of a single observation sample into a digital output how can it be designed for good performance the first question is treated by the techniques of information theory it is proved that a given combination of rates and distortion is achievable if there exist degraded versions of the observations that satisfy certain formulas the second question is treated by two approaches in the first the outputs of the quantizers undergo a second stage of encoding which exploits their correlation to reduce the output rate algorithms which design the second stage are presented and tested the second approach is based on the em distributional distance a measure of dissimilarity between two probability distributions an algorithm to modify a quantizer for increased distributional distance is derived and tested

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

polynomial approximation and vector quantization a region based integration the paper presents an adaptive scheme for image data compression it is a region based approach that suitably integrates two different approaches to image coding vector quantization vq and polynomial approximation pa the scheme is adaptive from the point of view of the human observer the perceptually most significant areas are those near edges or details in smoothed areas pa can be used with notable results but there vq must be employed to ensure high fidelity the two techniques exhibit a complementarity in both advantages and drawbacks pa is not efficient in compressing high frequency areas but yields the best results when applied to highly correlated data vq is unable to reach high compression ratios because of its low adaptability but is quite suitable for compressing uncorrelated data the means to achieve the integration of the two techniques is a control image containing information about edge and texture locations in the paper edge encoding and restoration are also addressed which are closely related to the proposed hybrid scheme block prediction is also utilized to further reduce the residual redundancy between vq blocks the exploitation of the best features of both approaches results in high compression factors and in perceivable good quality in particular bit rates range from 0 15 to 0 07 bpp main applications of this compression scheme are in the areas of very low bit rate image transmission and image archiving

model problems for the multigrid optimization of systems governed by differential equations we discuss a multigrid approach to the optimization of systems governed by differential equations such optimization problems appear in many applications and are of a different nature than systems of equations our approach uses an optimization based multigrid algorithm in which the multigrid algorithm relies explicitly on nonlinear optimization models as subproblems on coarser grids our goal is not to argue for a particular optimization based multigrid algorithm but instead to demonstrate how multigrid can be used to accelerate nonlinear programming algorithms furthermore using several model problems we give evidence both theoretical and numerical that the optimization setting is well suited to multigrid algorithms some of the model problems show that the optimization problem may be more amenable to multigrid than the governing differential equation in addition we relate the multigrid approach to more traditional optimization methods as further justification for the use of an optimization based multigrid algorithm

a multilevel nonlinear method a multilevel nonlinear method mnm for the numerical solution of nonlinear partial differential equations is developed the mnm algorithm is motivated and analyzed using a simplified model which retains the essential features of the new approach it is thereby shown to combine the advantages of the two classical multigrid approaches to nonlinear problems the analysis is supported by numerical tests for nonlinear differential equations in one and two dimensions

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

computing modified newton directions using a partial cholesky factorization the effectiveness of newton s method for finding an unconstrained minimizer of a strictly convex twice continuously differentiable function has prompted the proposal of various modified newton methods for the nonconvex case linesearch modified newton methods utilize a linear combination of a descent direction and a direction of negative curvature if these directions are sufficient in a certain sense and a suitable linesearch is used the resulting method will generate limit points that satisfy the second order necessary conditions for optimality the authors propose an efficient method for computing a descent direction and a direction of negative curvature that is based on a partial cholesky factorization of the hessian this factorization not only gives theoretically satisfactory directions but also requires only a partial pivoting strategy i e the equivalent of only two rows of the schur complement needs to be examined at each step

steplength optimization and linear multigrid methods recently steplength parameters have been used in linear multigrid methods in this paper we give a theoretical analysis of the effects of steplength optimization in a rather general framework which covers two different implementations of steplength optimization in standard multigrid methods

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

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

a multigrid approach to sdp relaxations of sparse polynomial optimization problems we propose a multigrid approach for the global optimization of polynomial optimization problems with sparse support the problems we consider arise from the discretization of infinite dimensional optimization problems such as pde optimization problems boundary value problems and some global optimization applications in many of these applications the level of discretization can be used to obtain a hierarchy of optimization models that capture the underlying infinite dimensional problem at different degrees of fidelity this approach inspired by multigrid methods has been successfully used for decades to solve large systems of linear equations however multigrid methods are difficult to apply to semidefinite programming sdp relaxations of polynomial optimization problems the main difficulty is that the information between grids is lost when the original problem is approximated via an sdp relaxation despite the loss of information we develop a multigrid approach and propose prolongation operator

global and uniform convergence of subspace correction methods for some convex optimization problems this paper gives some global and uniform convergence estimates for a class of subspace correction based on space decomposition iterative methods applied to some unconstrained convex optimization problems some multigrid and domain decomposition methods are also discussed as special examples for solving some nonlinear elliptic boundary value problems

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

a line search multigrid method for large scale nonlinear optimization we present a line search multigrid method for solving discretized versions of general unconstrained infinite dimensional optimization problems at each iteration on each level the algorithm computes either a direct search direction on the current level or a recursive search direction from coarser level models introducing a new condition that must be satisfied by a backtracking line search procedure the recursive search direction is guaranteed to be a descent direction global convergence is proved under fairly minimal requirements on the minimization method used at all grid levels using a limited memory bfgs quasi newton method to produce the direct search direction preliminary numerical experiments show that our line search multigrid approach is promising

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

rate distortion speech coding with a minimum discrimination information distortion measure an information theory approach to the theory and practice of linear predictive coded lpc speech compression systems is developed it is shown that a traditional lpc system can be viewed as a minimum distortion or nearest neighbor system where the distortion measure is a minimum discrimination information between a speech process model and an observed frame of actual speech this distortion measure is used in an algorithm for computer aided design of block source codes subject to a fidelity criterion to obtain a 750 bits s speech compression system that resembles an lpc system but has a much lower rate a larger memory requirement and requires no on line lpc analysis quantitative and informal subjective comparisons are made among our system and lpc systems

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

a new finite state vector quantizer with optimized state space and derailment free operation a new finite state vector quantization fsvq algorithm is developed based on state space optimization and the derailment prevention requirement the proposed derailment free fsvq df fsvq achieves good performance through i state space reduction which allows a practical implementation of high order fsvq and ii derailment free state transitions experimental results show that our approach outperforms other known fsvq schemes in terms of performance system complexity and processing speed especially at low bit rate image coding

a multilevel proximal gradient algorithm for a class of composite optimization problems composite optimization models consist of the minimization of the sum of a smooth not necessarily convex function and a nonsmooth convex function such models arise in many applications where in addition to the composite nature of the objective function a hierarchy of models is readily available it is common to take advantage of this hierarchy of models by first solving a low fidelity model and then using the solution as a starting point to a high fidelity model we adopt an optimization point of view and show how to take advantage of the availability of a hierarchy of models in a consistent manner we do not use the low fidelity model just for the computation of promising starting points but also for the computation of search directions we establish the convergence and convergence rate of the proposed algorithm our numerical experiments on large scale image restoration problems and the transition path problem suggest that for certain classes of problems the proposed algorithm is significantly fas

projection multilevel methods for quasilinear elliptic partial differential equations theoretical results the goal of this paper is to introduce a new multilevel solver for two dimensional elliptic systems of nonlinear partial differential equations pdes where the nonlinearity is of the type u partial v the incompressible navier stokes equations are an important representative of this class and are the target of this study using a first order system least squares fosls approach and introducing a new variable for partial v for this class of pdes we obtain a formulation in which the nonlinearity appears as a product of two different dependent variables the result is a system that is linear within each variable but nonlinear in the cross terms in this paper we introduce a new multilevel method that treats the nonlinearities directly this approach is based on a projection multilevel pml method s f mccormick multilevel projection methods for partial differential equations siam philadelphia 1992 applied to the fosls functional the implementation of the discretization process relaxation coarse grid correction and cycling strategies is discussed and optimal performance is established numerically a companion paper t a manteuffel s f mccormick and o rohrle siam j numer anal 44 2006 pp 139 152 establishes a two level convergence proof for this new multilevel method

a diagonalized multilevel fast multipole method with spherical harmonics expansion of the k space integrals diagonalization of the fast multipole method fmm for the helmholtz equation is usually achieved by expanding the multipole representation in propagating plane waves the resulting k space integral over the ewald sphere is numerically evaluated storing the k space quadrature samples of the method of moments mom basis functions constitutes a large portion of the overall memory requirements of the resulting algorithm for solving the integral equations of scattering and radiation problems in this paper it is proposed to expand the k space representation of the basis functions by spherical harmonics in order to reduce the sampling redundancy introduced by numerical quadrature rules aggregations plane wave translations and disaggregations in the realized multilevel fast multipole method mlfmm are carried out using the k space samples of a numerical quadrature rule however the incoming plane waves on the finest mlfmm level are expanded in spherical harmonics again thus due to the orthonormality of spherical harmonics the testing integrals for the individual testing functions are simplified into series over products of spherical harmonics expansion coefficients overall the resulting mlfmm can save a considerable amount of memory without compromising accuracy and numerical speed

next state functions for finite state vector quantization in this paper the finite state vector quantization scheme called dynamic finite state vector quantization dfsvq is investigated with regard to its subcodebook construction in dfsvq each input block is encoded by a small codebook called subcodehook which is created from a much larger codebook called supercodebook each subcodebook is constructed by selecting using a reordering procedure a set of appropriate codevectors from the supercodebook the performance of the dfsvq depends on this reordering procedure therefore several reordering procedures are introduced and their performances are evaluated in this paper the reordering procedures that are investigated are based on the conditional histogram of the codevectors index prediction vector prediction nearest neighbor design and frequency usage of the code vectors the performances of the reordering procedures are evaluated by comparing their hit ratios the number of blocks encoded by the subcodebook and their computational complexity experimental results are presented and it is found that the reordering procedure based on the vector prediction performs the best when compared with the other reordering procedures

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

efficient near field far field transformation for nonredundant sampling representation on arbitrary surfaces in near field antenna measurements a nonredundant sampling representation on arbitrary surfaces in near field antenna measurements together with a direct near field far field transformation is described the utilized sampling criterion depends on the electrical size of the antenna under test aut along with the separation between the aut and the measurement surface the minimum number of samples required is directly linked with the number of unknowns in the linear system of equations derived considering spherical expansion of radiated aut fields equivalent plane wave sources are used to represent the aut fields plane wave translations can be directly performed for any arbitrary measurement grid with the same efficiency thus nonredundant sampling representations can be utilized on any scan surface in contrast other fast field transformation techniques would lose their efficiency the proposed sampling is applied to near field measurements and synthetic data using a variety of antennas and the results are compared to the case of standard sampling remarkable decrease in the number of measurement points is observed with a negligible change in the accuracy of the transformed pattern thereby greatly reducing the measurement time and the computational effort