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

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

interframe predictive coding of images using hybrid vector quantization the temporal and spatial redundancies of image sequences can be reduced by prediction and vector quantization respectively the robustness of the coder is increased through the use of a hybrid two stage vector quantizer the first stage is of the linde buzo gray type the second stage encodes the residual error of the first stage using a lattice vector quantizer

a pyramid vector quantizer the geometric properties of a memoryless laplacian source are presented and used to establish a source coding theorem motivated by this geometric structure a pyramid vector quantizer pvq is developed for arbitrary vector dimension the pvq is based on the cubic lattice points that lie on the surface of an l dimensional pyramid and has simple encoding and decoding algorithms a product code version of the pvq is developed and generalized to apply to a variety of sources analytical expressions are derived for the pvq mean square error mse and simulation results are presented for pvq encoding of several memoryless sources for large rate and dimension pvq encoding of memoryless laplacian gamma and gaussian sources provides rose improvements of 5 64 8 40 and 2 39 db respectively over the corresponding optimum scalar quantizer although suboptimum in a rate distortion sense because the pvq can encode large dimensional vectors it offers significant reduction in rose distortion compared with the optimum lloyd max scalar quantizer and provides an attractive alternative to currently available vector quantizers

a fast mmse encoding technique for vector quantization the authors present a very efficient minimum mean squared error mmse encoding method useful for vector quantization using this method results in a considerable reduction in the number of multiplications and additions the increase in the number of comparisons is moderate and therefore the overall saving in the number of operations is still considerable very little precomputation and extra storage is required

two fast nearest neighbor searching algorithms for image vector quantization in this paper two efficient codebook searching algorithms for vector quantization vq are presented the first fast search algorithm utilizes the compactness property of signal energy on transform domain and the geometrical relations between the input vector and every codevector to eliminate those codevectors that have no chance to be the closest codeword of the input vector it achieves a full search equivalent performance as compared with other fast methods of the same kind this algorithm requires the fewest multiplications and the least total times of distortion measurements then a suboptimal searching method which sacrifices the reconstructed signal quality to speed up the search of nearest neighbor is presented this algorithm performs the search process on predefined small subcodebooks instead of the whole codebook for the closest codevector experimental results show that this method not only needs less cpu time to encode an image but also encounters less loss of reconstructed signal quality than tree structured vq does

on axis and far field sound radiation from resilient flat and dome shaped radiators on axis and far field series expansions are developed for the sound pressure due to an arbitrary circular symmetric velocity distribution on a flat radiator in an infinite baffle these expansions are obtained by expanding the velocity distributions in terms of orthogonal polynomials r 2n 0 sigma a p n 2 sigma a 2 1 with p n the legendre polynomials the terms r 2n 0 give rise to a closed form expression for the pressure on axis as well as for the far field pressure furthermore for a large number of velocity profiles including those associated with the rigid piston the simply supported radiator and the clamped radiators as well as gaussian radiators there are closed form expressions for the required expansion coefficients in particular for the rigid simply supported and clamped radiators this results in explicit finite series expressions for both the on axis and far field pressures in the reverse direction a method of estimating velocity distributions from measured on axis pressures by matching in terms of expansion coefficients is proposed together with the forward far field computation scheme this yields a method for far field loudspeaker assessment from on axis data generalized keele scheme the forward computation scheme is extended to dome shaped radiators with arbitrary velocity distributions

a generalization of holder s inequality and some probability inequalities the main result of this article is a generalization of the generalized holder inequality for functions or random variables defined on lowerdimensional subspaces of n dimensional product spaces it will be seen that various other inequalities are included in this approach for example it allows the calculation of upper bounds for the product measure of n dimensional sets with the help of product measures of lower dimensional marginal sets furthermore it yields an interesting inequality for various cumulative distribution functions depending on a parameter n e n 1 introduction we first recall the generalized holder inequality in terms of a measure theoretic approach let fq x t be a measure space and let lp fb a but be the set of p integrable 1 1 with e i lp 1 1 and let f elp fvf jm 1 m

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

the acoustic power of a vibrating clamped circular plate revisited in the wide low frequency range using expansion into the radial polynomials this study deals with the classical problem of sound radiation of an excited clamped circular plate embedded into a flat rigid baffle the system of the two coupled differential equations is solved one for the excited and damped vibrations of the plate and the other one the helmholtz equation an approach using the expansion into radial polynomials leads to results for the modal impedance coefficients useful for a comprehensive numerical analysis of sound radiation the results obtained are accurate and efficient in a wide low frequency range and can easily be adopted for a simply supported circular plate the fluid loading is included providing accurate results in resonance

btc image coding using vector quantization this paper describes source encoding of the outputs of a block truncation coder btc namely the overhead statistical information and the truncated block the statistical overhead and the truncated block exhibit properties which can be effectively used for their quantization as vectors vector quantization of these btc outputs results into reduction of the bit rate of the coder the bit rate reduces up to 1 5 bits pel if vector quantization is used on one of the outputs i e either the overhead information or the truncated block by vector quantizing both the btc outputs the bit rate can he reduced up to 1 0 bits pel without introducing many perceivable errors in the reconstructed output

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

improved batch fuzzy learning vector quantization for image compression in this paper we develop a batch fuzzy learning vector quantization algorithm that attempts to solve certain problems related to the implementation of fuzzy clustering in image compression the algorithm s structure encompasses two basic components first a modified objective function of the fuzzy c means method is reformulated and then is minimized by means of an iterative gradient descent procedure second the overall training procedure is equipped with a systematic strategy for the transition from fuzzy mode where each training vector is assigned to more than one codebook vectors to crisp mode where each training vector is assigned to only one codebook vector the algorithm is fast and easy to implement finally the simulation results show that the method is efficient and appears to be insensitive to the selection of the fuzziness parameter

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

a complexity reduction technique for image vector quantization a technique for reducing the complexity of spatial domain image vector quantization vq is proposed the conventional spatial domain distortion measure is replaced by a transform domain subspace distortion measure due to the energy compaction properties of image transforms the dimensionality of the subspace distortion measure can be reduced drastically without significantly affecting the performance of the new quantizer a modified lbg algorithm incorporating the new distortion measure is proposed unlike conventional transform domain vq the codevector dimension is not reduced and a better image quality is guaranteed the performance and design considerations of a real time image encoder using the techniques are investigated compared with spatial domain a speed up in both codebook design time and search time is obtained for mean residual vq and the size of fast ram is reduced by a factor of four degradation of image quality is less than 0 4 db in psnr

the maximum familywise error rate of fisher s least significant difference test abstract in this article an investigation is made of the maximum familywise error rate mfwer of fisher s least significant difference lsd test for testing the equality of k population means in a one way layout an exact expression for the mfwer is derived see theorem 1 for all balanced models and for an unbalanced model with k 3 populations type i models a close upper bound for the mfwer is derived for all unbalanced models with four or more populations type ii models these expressions are used to illustrate that the mfwer may greatly exceed the nominal size of the lsd test in addition a simple modification of the lsd test is proposed to control the mfwer this modified procedure has mfwer equal to the nominal level for type i models and no greater than for type ii models theorem 2 and is therefore recommended as an improvement over the lsd test the key to the analysis is two theorems concerning the ranges of independent normal random variables which are contained in the append

multiple testing in clinical trials the basic ideas of multiple testing are outlined and the problem of how to control the probability of erroneous decisions is discussed the main emphasis is on the concept of the multiple level of significance controlling the experiment or family error in the strong sense which can be achieved by applying the principle of closed tests various practical situations encountered in multiple testing in clinical trials are considered more than one end point more than two treatments such as comparisons with a single control comparisons using ordered alternatives all pairwise comparisons and contrast methods and more than one trial tests based on global statistics the union intersection principle and other criteria are discussed the application of the multiple test concept in sequential sampling is investigated finally some comments are made on multiple power multiple confidence intervals and directed decisions

on a monotonicity problem in step down multiple test procedures abstract we consider a monotonicity problem concerning the critical values in stepwise multiple test procedures for comparing k parameters this problem will be solved for a large class of distributional settings by means of an inequality for cumulative distribution functions of test statistics satisfying a simple monotonicity condition

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

a vector distribution model and an effective nearest neighbor search method for image vector quantization in this correspondence a modified version of hunt s 1980 image model is used to interpret the distribution of image data vectors the model suggests that the diagonal line of the coordinates system is a good approximation of the principal axis of the image data vector set the validity of the model is supported by experiments following this suggestion an effective nearest neighbor search method for vector quantization of image data is developed the method is based on partitioning the vector space using hyperplanes which are perpendicular to the diagonal direction of the coordinate system the validity of the method is assessed by analyzing its complexity and comparing its performance to those of existing algorithms on a number of images

a joint wavenumber time domain technique to determine the transient acoustic radiation loading on planar vibrators abstract a new method is presented to determine the transient radiation loading on planar vibrators mounted on rigid infinite baffles by using a wave vector time domain technique the specified non uniform velocity of the vibrator is expressed as a time dependent modal expansion where the modes are solutions to the homogeneous problem the time dependent acoustic modal forces can then be expressed as a sum of the modal radiation impulse responses convolved with the modal velocities in order to evaluate the radiation impulse responses the relationship between the fourier and hankel transforms of circular symmetric functions is first used to express the green s function for the problem as an integral over wave vector space the integral form of the green s function is then used to reduce the expression for the radiation impulse responses from a double surface integral over the vibrator to an integral over the wave vector space in contrast to the double surface integral which is difficult to evaluate the integral over the wave vector space can be evaluated easily numerical results are presented for clamped circular plates and simply supported square plates

on the structure of vector quantizers vector quantization is intrinsically superior to predictive coding transform coding and other suboptimal and em ad hoc procedures since it achieves optimal rate distortion performance subject only to a constraint on memory or block length of the observable signal segment being encoded the key limitation of existing techniques is the very large randomly generated code books which must be stored and the computational complexity of the associated encoding procedures the quantization operation is decomposed into its rudimentary structural components this leads to a simple and elegant approach to derive analytical properties of optimal quantizers some useful properties of quantizers and algorithmic approaches are given which are relevant to the complexity of both storage and processing in the encoding operation highly disordered quantizers which have been designed using a clustering algorithm are considered finally lattice quantizers are examined which circumvent the need for a code book by using a highly structured code based on lattices the code vectors are algorithmically generated in a simple manner rather than stored in a code book and fast algorithms perform the encoding algorithm with negligible complexity

the effect of different combinations of boundary conditions on the average radiation efficiency of rectangular plates the boundary conditions of a vibrating plate are known to have an influence on its sound radiation for frequencies below the critical frequency to investigate this effect in a systematic way the average radiation efficiency and radiated power are calculated for a rectangular plate set in an infinite baffle using a modal summation approach whereas analytical expressions exist for simply supported boundary conditions a numerical approach is required for other cases nine combinations of boundary conditions are considered consisting of simply supported clamped and free edges on different plate edges the structural vibration is approximated by using independent beam functions in orthogonal directions allowing simple approximate formulae for mode shapes and natural frequencies this assumption is checked against a finite element model and shown to give reliable results it is shown that a free plate has the lowest radiation efficiency and a clamped plate the highest for most frequencies between the fundamental panel natural frequency and the critical frequency other combinations of boundary condition give intermediate results according to the level of constraint introduced the differences depend on frequency excluding the extreme case of a fully free plate all the other boundary conditions give results within a range of 8 db in the middle part of the short circuiting region decreasing towards the critical frequency at low frequency the differences can be even greater in some cases up to 20 db these conclusions are shown to hold for a range of plate thicknesses and dimensions

transform and hybrid transform dpcm coding of images using pyramid vector quantization the transform and hybrid transform dpcm methods of image coding are generalized to allow pyramid vector quantization of the transform coefficients an asymptotic mean squared error performance expression is derived for the pyramid vector quantizer and used to determine the optimum rate assignment for encoding the various transform coefficients coding simulations for two images at average rates of 0 5 1 bit pixel demonstrate a 1 3 db improvement in signal to noise ratio for the vector quantization approach in the hybrid coding with more modest improvements in signal to noise ratio in the transform coding however this improvement is quite noticeable in image quality particularly in reducing blockiness in the low bit rate encoded images

a fast method of designing better codebooks for image vector quantization a maximum descent md method is proposed as an alternative to the generalized lloyd lbg algorithm for vector quantization codebook generation compared with the lbg algorithm the md algorithm requires far less computation and generates codebooks that are superior in quality this paper investigates and compares the performances of various partition techniques in the md algorithm in image vector quantization the md algorithm can produce codebooks with about 1 db improvement in peak signal to noise ratio in less than 1 100 of the time required by the lbg algorithm

some new inequalities for the range distribution with application to the determination of optimum significance levels of multiple range tests abstract a problem arising in multiple range tests is the monotonicity of the defining critical values which ws first treated by lehmann and shaffer 1977 this article proves a general inequality for the distribution function of the range which guarantees the monotonicity of a special set of critical values it also discusses the relation to some other inequalities the importance of these inequalities is pointed out in considering some concepts of admissibility and optimality of multiple range tests

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

optimal nonlinear interpolative vector quantization a process by which a reduced dimensionality feature vector can be extracted from a high dimensionality signal vector and then vector quantized with lower complexity than direct quantization of the signal vector is discussed in this procedure a receiver must estimate or interpolate the signal vector from the quantized features the task of recovering a high dimensional signal vector from a reduced dimensionality feature vector can be viewed as a generalized form of interpolation or prediction a way in which optimal nonlinear interpolation can be achieved with negligible complexity eliminating the need for ad hoc linear or nonlinear interpolation techniques is presented the range of applicability of nonlinear interpolative vector quantization is illustrated with examples in which optimal nonlinear estimation from quantized data is needed for efficient signal compression

product code vector quantizers for waveform and voice coding memory and computation requirements imply fundamental limitations on the quality that can be achieved in vector quantization systems used for speech waveform coding and linear predictive voice coding lpc one approach to reducing storage and computation requirements is to organize the set of reproduction vectors as the cartesian product of a vector codebook describing the shape of each reproduction vector and a scalar codebook describing the gain or energy such shape gain vector quantizers can be applied both to waveform coding using a quadratic error distortion measure and to voice coding using an itakura saito distortion measure in each case the minimum distortion reproduction vector can be found by first selecting a shape code word and then based on that choice selecting a gain codeword several algorithms are presented for the design of shape gain vector quantizers based on a traning sequence of data or a probabilistic model the algorithms are used to design shape gain vector quantizers for both the waveform coding and voice coding application the quantizers are simulated and their performance is compared to that of previously reported vector quantization systems

a new vector quantization clustering algorithm the pairwise nearest neighbor pnn algorithm is presented as an alternative to the linde buzo gray 1980 lbg generalized lloyd 1982 algorithm for vector quantization clustering the pnn algorithm derives a vector quantization codebook in a diminishingly small fraction of the time previously required without sacrificing performance in addition the time needed to generate a codebook grows only o n log n in training set size and is independent of the number of code words desired using this method one can either minimize the number of code words needed subject to a maximum rate the pnn algorithm can be used with squared error and weighted squared error distortion measure simulations on a variety of images encoded at 1 2 b pixel indicate that pnn codebooks can be developed in roughly 5 of the time required by the lbg algorithm

adaptive dimensionality reduction techniques for tree structured vector quantization abstruct it is well known that the exorbitant complexity of vector quantization s codebook design and encoding process have hindered the vector quantization based coding systems for real time implementations he structured vector quantization tsvq is one of the most efficient techniques to solve these problems however the encoder s memory requirement has increased as compared with the conventional full search vector quantization to tackle this drawback and further reduce the searching complexity of tsvq new multisubspace tree structured vector quantization design and encoding techniques are proposed in this paper during the tree codebook generation process each nonterminal node of the tree is associated with a partition or region and the child nodes are generated by further partitioning of these regions individually thus different distortion measures can be used in different partitions for the node splitting based on this idea the proposed multisubspace tsvq design algorithms perform the vector quantization in spatial domain while using specially designed subspace distortions in transform domain as cost functions in the optimization process due to the energy compaction property of orthonormal transforms dimensionality reduction is permitted by disregarding the components of minimal energy the conventional euclidean distortion is therefore adaptively replaced by dimension reduced transform domain subspace distortions based on the local statistics of the partition experimental results show that exceptionally low subspace dimension can be used in multisubspace tsvq based on a fixed transform domain to obtain a similar performance as the conventional tsvq or single subspace tsvq for example a 256 level and 4x4 image multisubspace tsvq using binary tree and 1 dimensional subspace distortions achieved almost 63 times computational reduction and 5 times storage reduction when compared with conventional full search vector quantization in addition the proposed generalized multisubspace tsvq design algorithm is a general tsvq design algorithm and which can also be utilized as a fast codebook design algorithm

closure of the newman keuls multiple comparisons procedure abstract closure of the family of hypotheses tested by the newman keuls procedure has been proposed in order to avoid excessive type i errors this proposal is examined in some detail and a practical procedure for carrying it out is described and programmed in fortran the relation of such closure to other multiple comparison procedures is discussed and its relatively high power is pointed out

vector quantizers and predictive quantizers for gauss markov sources low rate vector quantizers are designed and simulated for highly correlated gauss markov sources and the resulting performance is compared with arnstein s optimized predictive quantizer and with huang and schultheiss optimized transform coder two implementations of vector quantizers are considered full search vector quantizers which are optimal but require large codebook searches and tree searched vector quantizers which are suboptimal but require far less searching the various systems are compared on the basis of performance complexity and generality of design techniques