multiple emitter location and signal parameter estimation processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions the general problem considers sensors with arbitrary locations and arbitrary directional characteristics gain phase polarization in a noise interference environment of arbitrary covariance matrix this report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution a description is given of the multiple signal classification music algorithm which provides asymptotically unbiased estimates of 1 number of incident wavefronts present 2 directions of arrival doa or emitter locations 3 strengths and cross correlations among the incident waveforms 4 noise interference strength examples and comparisons with methods based on maximum likelihood ml and maximum entropy me as well as conventional beamforming are included an example of its use as a multiple frequency estimator operating on time series is included

robust hypothesis testing with alpha divergence a robust minimax test for two composite hypotheses which are determined by the neighborhoods of two nominal distributions with respect to a set of distances called alpha divergence distances is proposed sion s minimax theorem is adopted to characterize the saddle value condition least favorable distributions the robust decision rule and the robust likelihood ratio test are derived if the nominal probability distributions satisfy a symmetry condition the design procedure is shown to be simplified considerably the parameters controlling the degree of robustness are bounded from above and the bounds are shown to be resulting from a solution of a set of equations the simulations performed evaluate and exemplify the theoretical derivations

an asymptotic test for the equality of coefficients of variation from k populations the coefficient of variation is often used as a guide of the repeatability of measurements in clinical trials and other medical work when possible one makes repeated measurements on a set of individuals to calculate the relative variability of the test with the understanding that a reliable clinical test should give similar results when repeated on the same patient there are times however when repeated measurements on the same patient are not possible under these circumstances to combine results from different clinical trials or test sites it is necessary to compare the coefficients of variation of several clinical trials using the work of miller we develop a general statistic for testing the hypothesis that the coefficients of variation are the same for k populations with unequal sample sizes this statistic is invariant under the choice of the order of the populations and is asymptotically chi 2 we provide an example using data from yang and hayglass we compare the size and the power of the test to that of bennett doornbos and dijkstra and a statistic based on hedges and olkin

vector quantizer design for memoryless gaussian gamma and laplacian sources locally optimum vector quantizer vq designs are presented for memoryless gaussian gamma and laplacian sources for gaussian sources low 2 6 dimensional vector quantization provides relatively little improvement in mean squared error mse compared to the minimum mean squared error mmse scalar quantizer for laplacian or gamma sources however significant improvement in mse is available with vector quantization the laplacian and gamma 6 bit sixdimensional vector quantizers achieve respectively improvements of 2 and 4 5 db over the corresponding scalar mmse quantizer distortions

on divergences and informations in statistics and information theory the paper deals with the f divergences of csiszar generalizing the discrimination information of kullback the total variation distance the hellinger divergence and the pearson divergence all basic properties of f divergences including relations to the decision errors are proved in a new manner replacing the classical jensen inequality by a new generalized taylor expansion of convex functions some new properties are proved too e g relations to the statistical sufficiency and deficiency the generalized taylor expansion also shows very easily that all f divergences are average statistical informations differences between prior and posterior bayes errors mutually differing only in the weights imposed on various prior distributions the statistical information introduced by de groot and the classical information of shannon are shown to be extremal cases corresponding to alpha 0 and alpha 1 in the class of the so called arimoto alpha informations introduced in this paper for 0 alpha 1 by means of the arimoto alpha entropies some new examples of f divergences are introduced as well namely the shannon divergences and the arimoto alpha divergences leading for alphauarr1 to the shannon divergences square roots of all these divergences are shown to be metrics satisfying the triangle inequality the last section introduces statistical tests and estimators based on the minimal f divergence with the empirical distribution achieved in the families of hypothetic distributions for the kullback divergence this leads to the classical likelihood ratio test and estimator

the complexity of the generalized lloyd max problem corresp a simple combinatorial special case of the generalized lloyd max or quantization problem is shown to be nondeterministic polynomial np complete em a fortiori the general problem of communication theory in its combinatorial forms has at least that complexity

on the covering radius of codes the covering radius r of a code is the maximal distance of any vector from the code this work gives a number of new results concerning t n k the minimal covering radius of any binary code of length n and dimension k for example t n 4 and t n 5 are determined exactly and reasonably tight bounds on t n k are obtained for any k when n is large these results are found by using several new constructions for codes with small covering radius one construction the amalgamated direct sum involves a quantity called the norm of a code codes with norm leq 2 r 1 are called normal and may be combined efficiently the paper concludes with a table giving bounds on t n k for n leq 64

constructions of nonlinear covering codes constructions of nonlinear covering codes are given using any nonlinear starting code of covering radius r spl ges 2 these constructions form an infinite family of codes with the same covering radius a nonlinear code is treated as a union of cosets of a linear code new infinite families of nonlinear covering codes are obtained concepts of r l objects r l partitions and r l length are described for nonlinear codes

a novel block truncation coding of color images using a quaternion moment preserving principle block truncation coding btc is an efficient tool for image compression to compress color pixel blocks a novel color btc algorithm called quaternion moment block truncation coding qmbtc is presented analytical formulas for qmbtc whose computation time is on the order of pixel block size are derived by using quaternion arithmetic and the moment preserving principle the proposed color btc algorithm can adaptively truncate a pixel block into one or two output classes according to the distribution of the color values inside the blocks the experimental results show that the compression ratio is increased as compared with existing color btc algorithms and the picture quality of the reconstructed images is satisfactory in addition a post btc data compression scheme is proposed to further compress the subimage constructed by reproduction colors of truncated pixel blocks using a lookup table to display decoded data this postprocessing scheme can output images acceptable to human eyes

localizing thin metallic cylinders by a 2 5 d linear distributional approach experimental results the problem of detecting and localizing thin metallic scatterers from electromagnetic scattered field measurements is addressed the scatterers are assumed to be infinitely long and a 2 5 dimensional mathematical model is adopted according to the distributional approach the problem is cast as the inversion of a linear integral operator acting on 6 distributions whose supports are representative of the scatterers locations in this paper we present the experimental validation of such an approach to this end we perform the reconstructions by exploiting experimental scattered field data collected in controlled conditions at the electromagnetic diagnostics laboratory of the second university of naples the experiments are conducted in an anechoic chamber where the scatterers are embedded in a homogenous and lossless background medium the multistatic single view multifrequency and the multistatic multiview multifrequency configurations are both considered

high capacity data hiding for error diffused block truncation coding block truncation coding btc is an efficient compression technique with extremely low computational complexity however the blocking and false contour effects are two major deficiencies in btc which cause severe perceptual artifacts the former scheme error diffused btc edbtc can significantly improve the above issues through the visual low pass compensation on the bitmap which thus widens its possible application market yet the corresponding security issue may limit its value in this paper a method namely complementary hiding edbtc is developed to cope the above issue this paper is managed by firstly discussing when a single watermark is embedded and then multiple watermarks are employed to test the limitation of the proposed scheme herein an adaptive external bias factor is employed to control the watermark embedding and this factor also affects the image quality and robustness simultaneously experimental results demonstrate that the proposed method only requires an extremely small external bias factor to carry watermarks which enables a high capacity scenario without significantly damaging image quality

a generalized block truncation coding algorithm for image compression block truncation coding is a recently developed approach to image compression whose design is specified by the appropriate moment preserving quantizer in this paper we show how the basic block truncation coding algorithm can be generalized to include a family of moment preserving quantizers with the potential for improved performance we then illustrate by way of example that such improvement is indeed possible from the standpoint of peak signal to noise ratio there is a subclass of this family of moment preserving quantizers for which practical difficulties in implementation exist however we show that frequently we can avoid this subclass and still obtain good performance

use of renyi s divergence to test for the equality of the coefficients of variation a new family of test statistics based on renyi s divergence is introduced for the hypothesis that the coefficients of variation of k normal populations are equal a comparative simulation study is carried out concerning the size and power of these test statistics and earlier ones finally two members of the new family of tests emerge as the best from the simulation study

csisza spl acute r s cutoff rates for the general hypothesis testing problem in csisza spl acute r established the concept of forward spl beta cutoff rate for the error exponent hypothesis testing problem based on independent and identically distributed i i d observations given spl beta 0 spl alpha spl ne 1 similarly for 0 spl beta 1 csisza spl acute r also established the concept of reverse spl beta cutoff rate for the correct exponent hypothesis testing problem in this work we extend csisza spl acute r s results by investigating the forward and reverse spl beta cutoff rates for the hypothesis testing between two arbitrary sources with memory we demonstrate that the lim inf re spl acute nyi spl alpha divergence rate provides the expression for the forward spl beta cutoff rate we also show that if the log likelihood large deviation spectrum admits a limit then the reverse spl beta cutoff rate equals the liminf spl alpha divergence rate where spl alpha 1 1 spl beta and 0 spl beta spl beta sub max where spl beta sub max is the largest spl beta 1 for which the lim inf 1 1 spl beta divergence rate is finite for spl beta sub max spl les spl beta 1 we show that the reverse cutoff rate is in general only upper bounded by the lim inf re spl acute nyi divergence rate unlike in where the alphabet for the source coding cutoff rate problem was assumed to be finite we assume arbitrary countable or continuous source alphabet we also provide several examples to illustrate our forward and reverse spl beta cutoff rates results and the techniques employed to establish them

some properties of renyi entropy and renyi entropy rate in this paper we define the conditional renyi entropy and show that the so called chain rule holds for the renyi entropy then we introduce a relation for the rate of renyi entropy and use it to derive the rate of the renyi entropy for an irreducible aperiodic markov chain we also show that the bound for the renyi entropy rate is simply the shannon entropy rate

on binary linear codes which satisfy the two way chain condition general constructions of binary linear codes satisfying the two way chain condition are found sufficient conditions for their existence are determined some of these codes are proven to be z sub 4 linear an expression for their state complexity profile is also found cases when such codes have covering radius r t n k are shown

noniterative analytical formula for inverse scattering of multiply scattering point targets this paper derives in the exact framework of multiple scattering theory for point targets a noniterative analytical formula for the nonlinear inversion of the target scattering strengths from the scattering or response matrix that can be applied after the target positions have been estimated in a previous step via e g time reversal multiple signal classification or another approach the new formula provides a noniterative analytical alternative to the iterative numerical solution approach for the same problem presented in a recent paper a j devaney e a marengo and f k gruber time reversal based imaging and inverse scattering of multiply scattering point targets j acoust soc am 118 3129 3138 2005 the two methods noniterative versus iterative are comparatively investigated with two numerical examples

lower bounds on t n k from linear inequalities the linear inequality method for covering codes is used to improve the lower bounds of t n k the smallest covering radius of any n k binary linear code to make better use of the strength of this method the relation between the covering radius of a code and the minimum distance of its dual code is studied the authors obtained 65 improved lower bounds for t n k within the range of n

new covering codes from an ads like construction a covering code construction is presented using this construction it is shown that t 52 39 3 t 36 21 4 t 58 32 7 k 32 2 spl les 62 spl middot 2 sup 18 and k 62 5 spl les 31 spl middot 2 sup 37 where t n k is the minimum covering radius among all binary n k codes and k n r is the minimum cardinality of a binary code of length n and covering radius r four new linear codes found by computer search are also given these include a 23 9 5 code a 32 8 10 code a 51 41 2 code and a 45 20 8 code

covering radius survey and recent results all known results on covering radius are presented as well as some new results there are a number of upper and lower bounds including asymptotic results a few exact determinations of covering radius some extensive relations with other aspects of coding theory through the reed muller codes and new results on the least covering radius of any linear n k code there is also a recent result on the complexity of computing the covering radius

f divergence inequalities this paper develops systematic approaches to obtain f divergence inequalities dealing with pairs of probability measures defined on arbitrary alphabets functional domination is one such approach where special emphasis is placed on finding the best possible constant upper bounding a ratio of f divergences another approach used for the derivation of bounds among f divergences relies on moment inequalities and the logarithmic convexity property which results in tight bounds on the relative entropy and bhattacharyya distance in terms of chi 2 divergences a rich variety of bounds are shown to hold under boundedness assumptions on the relative information special attention is devoted to the total variation distance and its relation to the relative information and relative entropy including reverse pinsker inequalities as well as on the e gamma divergence which generalizes the total variation distance pinsker s inequality is extended for this type of f divergence a result which leads to an inequality linking the relative entropy and relative information spectrum integral expressions of the renyi divergence in terms of the relative information spectrum are derived leading to bounds on the renyi divergence in terms of either the variational distance or relative entropy

block truncation coding using pattern fitting block truncation coding btc divides an image into blocks having given size and then encodes each block by two representative gray levels and a bit pattern in this work a modified scheme of btc is proposed where the computed representative gray levels are the bias and the contrast in each block secondly instead of determining bit pattern for each block an optimum bit pattern is selected from a pattern book thus the index of the optimum pattern is used to encode in lieu of the explicit pattern thirdly if the contrast is low the block is assumed to be smooth and bit pattern is not required to reconstruct the block this leads to significant reduction in bit rate bpp finally the contrast component and the predictive residual of the bias component are entropy coded to achieve further reduction in bpp performance of the proposed scheme is measured in terms of peak signal to noise ratio and bpp and is compared with other recently reported methods

renyi entropy rate for gaussian processes in this paper we introduce the definition of the conditional renyi entropy for continuous random variables and show that the so called chain rule holds then we use this rule to obtain another relation for getting the rate of renyi entropy using this relation and properties of the renyi entropy we obtain the renyi entropy rate for stationary gaussian processes finally we show that the bound for the renyi entropy rate is simply the shannon entropy rate and that the renyi entropy rate reduces to the shannon entropy rate as a 1

k harmonic means data clustering with simulated annealing heuristic abstract clustering procedures partition a set of objects into clusters such that objects in the same cluster are more similar to each other than objects in different clusters according to some predefined criteria clustering is a popular data analysis and data mining technique since clustering problem have np complete nature the larger the size of the problem the harder to find the optimal solution and furthermore the longer to reach a reasonable results one of the most used techniques for clustering is based on k means such that the data is partitioned into k clusters although k means algorithm is easy to implement and works fast in most situations it suffers from two major drawbacks one is sensitivity to initialization and the other is convergence to local optima it is seen from the studies k harmonic means clustering solves the problem of initialization but since its greedy search nature the second problem convergence to local optima still remains in this paper we develop a new algorithm for solving this problem based on a simulated annealing technique simulated annealing k harmonic means clustering sakhmc the experiment results on the iris and the other well known data illustrate the robustness of the sakhmc clustering algorithm

inferences on the common coefficient of variation the coefficient of variation is often used as a measure of precision and reproducibility of data in medical and biological science this paper considers the problem of making inference about the common population coefficient of variation when it is a priori suspected that several independent samples are from populations with a common coefficient of variation the procedures for confidence interval estimation and hypothesis testing are developed based on the concepts of generalized variables the coverage properties of the proposed confidence intervals and type i errors of the proposed tests are evaluated by simulation the proposed methods are illustrated by a real life example

renyi divergence and kullback leibler divergence renyi divergence is related to renyi entropy much like kullback leibler divergence is related to shannon s entropy and comes up in many settings it was introduced by renyi as a measure of information that satisfies almost the same axioms as kullback leibler divergence and depends on a parameter that is called its order in particular the renyi divergence of order 1 equals the kullback leibler divergence we review and extend the most important properties of renyi divergence and kullback leibler divergence including convexity continuity limits of sigma algebras and the relation of the special order 0 to the gaussian dichotomy and contiguity we also show how to generalize the pythagorean inequality to orders different from 1 and we extend the known equivalence between channel capacity and minimax redundancy to continuous channel inputs for all orders and present several other minimax results

color image compression based on block truncation coding using pattern fitting principle this paper describes a color image compression technique based on block truncation coding using pattern fitting btc pf high degree of correlation between the rgb planes of a color image is reduced by transforming them to o 1o 2o 3 planes each o i plane 1

shape reconstruction from po multifrequency scattered fields via the singular value decomposition approach this paper deals with the problem of determining the shape of unknown perfectly conducting infinitely long cylinders starting from the knowledge of the scattered electric far field under the incidence of plane waves with a fixed angle of incidence and varying frequency the problem is formulated as a nonlinear inverse one by searching for a compact support distribution accounting for the objects contour the nonlinear unknown to data mapping is then linearized by means of the kirchhoff approximation which reduces it into a fourier transform relationship then the fourier transform inversion from incomplete data is dealt with by means of the singular value decomposition svd approach and the features of the reconstructable unknowns are investigated finally numerical results confirm the performed analysis

achieving the bayes error rate in synchronization and block models by sdp robustly we study the statistical performance of semidefinite programming sdp relaxations for clustering under random graph models under the mathbb z 2 synchronization model censored block model cbm and stochastic block model sbm we show that sdp achieves an error rate of the form exp 1 o 1 bar n i here bar n is an appropriate multiple of the number of nodes and i is an information theoretic measure of the signal to noise ratio we provide matching lower bounds on the bayes error for each model and therefore demonstrate that the sdp approach is bayes optimal as a corollary our results imply that sdp achieves the optimal exact recovery threshold under each model furthermore we show that sdp is robust the above bound remains valid under semirandom versions of the models in which the observed graph is modified by a monotone adversary our proof is based on a novel primal dual analysis of sdp under a unified framework for all three models and the analysis shows that sdp tightly approximates a joint majority voting procedure

new lower bounds for binary covering codes g d chen et al ibid vol it 32 p 680 94 1986 presented two new lower bounds for k n r where k n r denotes the minimum cardinality of a binary code of length n and covering radius r the author shows that a slight modification gives further improvements and some examples are given to confirm the argument codes that have a certain partitioning property are considered

beyond physical optics svd shape reconstruction of metallic cylinders we consider the problem of reconstructing the shape of perfectly conducting cylinders under the physical optics approximation for direct scattering physical optics provides small model errors when the scatterers are convex smooth have large radii of curvature as compared to the impinging wavelength and are noninteracting in this paper we investigate whether these hypotheses can be relaxed for the inverse problem in particular we consider three classes of scatterers circular cylinder with radius smaller than the wavelength multiple cylinders and a concave cylinder and we show that for them the model error is provided by a multiplicative almost frequency independent factor since this factor can be incorporated within the unknown distribution representing the scatterers illuminated boundaries then we are able to show that successful reconstructions also beyond the physical optics limits can be obtained

block truncation coding with entropy coding block truncation coding btc is a simple and fast image compression algorithm which achieves a constant bit rate of 2 0 bits per pixel the method is however suboptimal we propose a modification of btc in which the compression ratio is improved by coding the quantization data and the bit plane by arithmetic coding with an adaptive modelling scheme the results compare favorable with other btc variants the bit rate for test image lena is 1 53 bits per pixel with a mean square error of 16 51

interpolative btc image coding with vector quantization the authors suggest two interpolative block truncation coding btc image coding schemes with vector quantization and median filters as the interpolator the first scheme is based on quincunx subsampling and the second one on every other row and every other column subsampling it is shown that the schemes yield a significant reduction in bit rate at only a small performance degradation and in general better channel error resisting capabilities as compared to the absolute moment btc the methods are further demonstrated to outperform the corresponding btc schemes with pure vector quantization at the same bit rate and require minimal computations for the interpolation

probabilistic distance measures of the dirichlet and beta distributions we give the analytical definitions of the chernoff bhattacharyya and jeffreys matusita probabilistic distances between two dirichlet distributions and two beta distributions as its special case for all other known probabilistic distances we show their inappropriateness in the analytical case we discuss the parameter learning of the dirichlet distribution from a finite sample set and present an application for split and merge image segmentation

a 55 16 19 binary goppa code and related codes having large minimum distance a 55 16 19 binary goppa code is used to construct 57 17 17 58 17 18 59 17 19 and 60 17 20 codes the first two codes have smaller redundancy than previously known codes linear or nonlinear of the same length and minimum distance the last two codes have parameters previously attained only by nonlinear codes

do most binary linear codes achieve the goblick bound on the covering radius corresp the following two problems are dealt with p1 finding the smallest rate r of a binary code of length n admitting a prescribed covering radius rho n p2 discovering whether a majority of codes with any rate larger than r admits the given covering radius for the class of unrestricted nonlinear codes a solution to both problems is obtained by an elementary averaging argument the solution to p1 is r 1 h rho o n 1 log n and the answer to p2 is positive as for the more interesting class of linear codes goblick s extension method shows that the solution to p1 is the same as in the unrestricted case in contrast p2 seems to remain an open question a simple derivation of goblick s result is presented and a discussion is made of the positive conjecture concerning p2 for linear codes

optimal binary vector quantization via enumeration of covering codes binary vector quantization bvq refers to block coding of binary vectors under a fidelity measure covering codes were studied as a means of lattice bvq but a further source coding problem hidden in the equivalence of covering codes has seemingly eluded attention given a d dimensional hypercube code space equivalent covering codes of the same covering radius but of different codewords have different expected bvq distortions for a general probability mass function thus one can minimize within the code equivalence the expected distortion over all different covering codes this leads a two stage optimization scheme for bvq design first we use an optimal covering code to minimize the maximum per vector distortion at a given rate then under the minmax constraint we minimize the expected quantization distortion this minmax constrained bvq method mcbvq controls both the maximum and average distortions and hence improves subjective quality of compressed binary images mcbvq also avoids poor local minima that may trap the generalized lloyd method the 7 4 hamming code and 8 4 extended hamming code are found to be particularly suitable for mcbvq on binary images an efficient and simple algorithm is introduced to enumerate all distinct 7 4 hamming 8 4 extended hamming codes and compute the corresponding expected distortions in optimal mcbvq design furthermore mcbvq using linear covering codes has a compact codebook and a fast syndrome encoding algorithm

experimental subwavelength localization of scatterers by decomposition of the time reversal operator interpreted as a covariance matrix the d o r t method french acronym for decomposition of the time reversal operator is an active remote sensing technique using arrays of antennas for the detection and localization of scatterers prada et al j acoust soc am 99 2067 2076 1996 the analogy between the time reversal operator and the covariance matrix used for classical sources separation in passive remote sensing bienvenu et al ieee trans assp 31 1235 1247 1983 is established then an experiment of subwavelength detection and localization of point like scatterers with a linear array of transducers is presented using classical estimators in reception like maximum likelihood and multiple signal characterization music two point like scatterers separated by 3 and placed at 100 from the array of transducers are resolved in these experiments the role of multiple scattering and the existence of additional eigenvectors associated with dipolar and monopolar radiation of each scatterer is discussed

time reversal imaging with multiple signal classification considering multiple scattering between the targets the time reversal imaging with multiple signal classification method for the location of point targets developed within the framework of the born approximation in lehman and devaney transmission mode time reversal super resolution imaging j acoust soc am 113 2742 2753 2003 is generalized to incorporate multiple scattering between the targets it is shown how the same method can be used in the location of point targets even if there is multiple scattering between them on the other hand both the conventional images and the calculated values of the target scattering amplitudes are scattering model dependent

linear distribution imaging of thin metallic cylinders under mutual scattering in this paper we address the problem of imaging thin metallic cylinders from the knowledge of the electric far field scattered under the incidence of plane waves a scattering model based on a multipole expansion accounting for the mutual scattering is introduced and then simplified under the single and second order scattering hypotheses the locations of the unknown cylinders for the inverse problem are described in terms of support of spl delta functions the performances of a truncated singular value decomposition based linear inversion algorithm in the presence of model errors due to mutual scattering is investigated by both analytical and numerical arguments in three different measurement configurations single frequency multiview multifrequency single view and multifrequency multiview the different effects of the angular and frequency diversities are pointed out

application of honey bee mating optimization algorithm on clustering cluster analysis is one of attractive data mining technique that use in many fields one popular class of data clustering algorithms is the center based clustering algorithm k means used as a popular clustering method due to its simplicity and high speed in clustering large datasets however k means has two shortcomings dependency on the initial state and convergence to local optima and global solutions of large problems cannot found with reasonable amount of computation effort in order to overcome local optima problem lots of studies done in clustering over the last decade modeling the behavior of social insects such as ants and bees for the purpose of search and problem solving has been the context of the emerging area of swarm intelligence honey bees are among the most closely studied social insects honey bee mating may also be considered as a typical swarm based approach to optimization in which the search algorithm is inspired by the process of marriage in real honey bee honey bee has been used to model agent based systems in this paper we proposed application of honeybee mating optimization in clustering hbmk means we compared hbmk means with other heuristics algorithm in clustering such as ga sa ts and aco by implementing them on several well known datasets our finding shows that the proposed algorithm works than the best one

a survey of the theory of source coding with a fidelity criterion the purpose of this paper is threefold 1 to acquaint the reader with the types of problems that have been considered in the area of source coding with a fidelity criterion 2 to survey results that have been obtained on these problems and 3 to outline future research trends in the area

moment preserving quantization signal processing the general solution to the moment preserving mp quantizer problem is presented it is shown that the moment preserving quantizer is related to the gauss jacobi mechanical quadrature the output levels of the n level mp quantizer are the n zeros of an nth degree orthogonal polynomial associated with the input probability distribution function and the n 1 thresholds of the mp quantizer are related to the christoffel numbers through the chebyshev markov stieltjes separation theorem the statistical convergence of the mp quantizer is investigated mp quantizer tables are presented for the uniform gaussian and laplacian density functions the moment preserving quantizer is shown to be related to block truncation coding

robust hypothesis testing with a relative entropy tolerance this paper considers the design of a minimax test for two hypotheses where the actual probability densities of the observations are located in neighborhoods obtained by placing a bound on the relative entropy between actual and nominal densities the minimax problem admits a saddle point which is characterized the robust test applies a nonlinear transformation which flattens the nominal likelihood ratio in the vicinity of one results are illustrated by considering the transmission of binary data in the presence of additive noise

btc image coding using median filter roots in this paper we source encode the truncated block used in block truncation coding it is shown that the truncated block is well approximated by wide sense markoff statistics a signal having these characteristics has a high probability of belonging to the root signal set of median filters because the root signal space is much smaller than the binary space it takes fewer bits to specify the truncated block in the root signal space obtaining in this manner rate compression using two dimensional filtering we can reduce the standard btc rate of 1 63 bits pel to 1 31 bits pel using one dimensional filtering along with a trellis encoder rates close to 1 1 bits pel are obtained with this fixed length coding method

btc vq dct hybrid coding of digital images a hybrid btc vq dct block truncation coding vector quantization and discrete cosine transform image coding algorithm is presented the algorithm combines the simple computation and edge preservation properties of btc and the high fidelity and high compression ratio of adaptive dct with the high compression ratio and good subjective performance of vq and can be implemented with significantly lower coding delays than either vq or dct alone the bit map generated by btc is decomposed into a set of vectors which are vector quantized since the space of the btc bit map is much smaller than that of the original 8 b image a lookup table based vq encoder has been designed to fast encode the bit map adaptive dct coding using residual error feedback is implemented to encode the high mean and low mean subimages the overall computational complexity of btc vq dct coding is much less than either dct and vq while the fidelity performance is competitive the algorithm has strong edge preserving ability because of the implementation of btc as a precompress decimation the total compression ratio is about 10 1

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

modified bounds for covering codes the covering radius of binary codes is studied bounds on k n r the minimum cardinality of any binary code of length n and covering radius r are found modifications of the van wee lower bounds are proved for k n r the minimal number of codewords in any binary code of length n and covering radius r the first of the two van wee bounds is based on studying the hamming spheres of radius 1 centered at the points which have distance r to the code c the points covered by more than one codeword are divided into several classes and better estimates for some of these classes are obtained using a suitable averaging process the lower bound for k n r when r or 2 is improved the second van wee bound studies spheres of radius 2 centered at the points which have distance r 1 or r to the code c these points are divided essentially into two classes the points that are covered by only one codeword of c and the points that are covered by more than one codeword

computing automorphism groups of error correcting codes an algorithm is described for computing the automorphism group of an error correcting code the algorithm determines the order of the automorphism group and produces a set of monomial permutations which generate the group it has been implemented on a computer and has been used successfully on a great number of codes of moderate length

the iterative time reversal process analysis of the convergence the efficiency of a time reversal acoustic mirror to focus on a reflective target through an inhomogeneous media has been demonstrated in a multitarget media the ability of such a mirror to work in an iterative mode in order to focus selectively on the strongest target was shown c prada f wu and m fink j acoust soc am 90 1119 1991 the theory of how the iterative time reversal process is built is based on a matrix formalism and treats the array of l transducers in a given medium as a linear system of l inputs l outputs the system is characterized at each frequency by its transfer matrix k and the time reversal iterative process is then described by a time reversal operator k k because of the reciprocity principle this operator is hermitian the following result is shown if the scattering medium is a set of well resolved targets of different reflectivities then each eigenvector of the operator k k with nonzero eigenvalue corresponds to one of the targets in the set and provides the opt

subcodes and covering radius corresp a sharp lower bound on the covering radius of a linear binary code is given in terms of the covering radius of any subcode of index two an upper bound on the norm of a code is then derived these results hold for all linear codes over gf 2

further results on the covering radius of codes a number of upper and lower bounds are obtained for k n r the minimal number of codewords in any binary code of length n and covering radius r several new constructions are used to derive the upper bounds including an amalgamated direct sum construction for nonlinear codes this construction works best when applied to normal codes and we give some new and stronger conditions which imply that a linear code is normal an upper bound is given for the density of a covering code over any alphabet and it is shown that k n 2 r 1 leq k n r holds for sufficiently large n

inequalities for covering codes any code c with covering radius r must satisfy a set of linear inequalities that involve the lloyd polynomial l sub r x these generalize the sphere bound syndrome graphs associated with a linear code c are introduced to help keep track of low weight vectors in the same coset of c if there are too many such vectors c cannot exist illustrations show that t 17 10 3 and t 23 15 3 where t n k is the smallest covering radius of any n k code

complexity constrained trellis quantizers a reasonable measure of quantizer complexity is the expected number of quanta per input sample for which distortion is computed given this measure a rate distortion complexity theory is obtained by extending earlier work in alphabet constrained rate distortion theory numerical results show that operation on the alphabet constrained rate distortion bound can be obtained with a complexity of two furthermore lloyd max conditions are shown to describe the minimum of a slightly constrained version of the rate distortion complexity problem complexity constrained design methods are applied first to trellis coded quantizers where they are shown to reduce arithmetic operations by at least 25 they are then used to develop model based trellis quantizers the trellises of which are derived from a markov model of the source simulation results confirm that excellent performance can be obtained with modest complexity

a robust noniterative method for obtaining scattering strengths of multiply scattering point targets a noniterative method based on the least squares technique is presented in this letter to obtain the scattering strengths of multiply scattering point targets benefiting from the least squares optimization property this new method achieves a good estimation of the scattering strengths compared with the noniterative method proposed in a recent paper e a marengo and f k gruber noniterative analytical formula for inverse scattering of multiply scattering point targets j acoust soc am 120 3782 3788 2006 the new method produces more accurate results in the presence of noise

on exact and renyi common informations recently two extensions of wyner s common information exact and renyi common informations were introduced respectively by kumar li and el gamal kle and the present authors the class of common information problems involves determining the minimum rate of the common input to two independent processors needed to exactly or approximately generate a target joint distribution for the exact common information problem exact generation of the target distribution is required while for wyner s and alpha renyi common informations the relative entropy and renyi divergence with order alpha were respectively used to quantify the discrepancy between the synthesized and target distributions the exact common information is larger than or equal to wyner s common information however it was hitherto unknown whether the former is strictly larger than the latter for some joint distributions in this paper we first establish the equivalence between the exact and infty renyi common informations and then provide single letter upper and lower bounds for these two quantities for doubly symmetric binary sources we show that the upper and lower bounds coincide which implies that for such sources the exact and infty renyi common informations are completely characterized interestingly we observe that for such sources these two common informations are strictly larger than wyner s this answers an open problem posed by kle furthermore we extend wyner s infty renyi and exact common informations to sources with countably infinite or continuous alphabets including gaussian sources

on error exponents in hypothesis testing the classical result of blahut which characterizes achievable error exponents in binary hypothesis testing is generalized in two different directions first in m ary hypothesis testing the tradeoff of all m m 1 types of error exponents and corresponding optimal decision schemes are explored then motivated by a power constrained distributed detection scenario binary hypothesis testing is revisited and the tradeoff of power consumption versus error exponents is fully characterized in the latter scenario sensors are allowed to make random decisions as to whether they should remain silent and save power or transmit and improve detection quality it is then shown by an example that optimal sensor decisions may indeed be random

interpretations of renyi entropies and divergences abstract in this paper a new operational definition of renyi divergence and renyi entropy is presented other operational definitions are mentioned

shape reconstruction by the spectral data of the far field operator analysis and performances the second version of the linear sampling method is considered with reference to perfectly conducting cylinders and its performances analyzed it is pointed out that for nonconvex objects the shape of the object under test is not retrieved whereas in its place the convex hull is recovered we also point out that in the case of aspect limited data neither the convex hull of the object is reconstructed

explicit codes with low covering radius a series of explicit low rate binary linear codes that have relatively low covering radius and can be rapidly decoded is exhibited these codes can be derived from higher dimensional analogs of the gale berlekamp switching game conjectures of independent interest involving hadamard matrices are given that could yield semiexplicit covering codes of very low density

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

an improved sphere covering bound for the codes with n 3r 2 let c be a binary code not necessarily linear with covering radius r and length n 3r 2 the sphere covering bound on the cardinality of c is improved considerably provided c has minimal distance d 2 some new results on the function t n k the smallest covering radius of any binary linear code with length n and dimension k t 38 6 or 13 t 47 7 or 16 t 59 8 or 20 are given

minimax robust hypothesis testing minimax robust hypothesis testing is studied for the cases where the collected data samples are corrupted by outliers and are mismodeled due to modeling errors for the former case huber s clipped likelihood ratio test is introduced and analyzed for the latter case first a robust hypothesis testing scheme based on the kullback leibler divergence is designed this approach generalizes a previous work by levy second dabak and johnson s asymptotically robust test is introduced and other possible designs based on f divergences are investigated all proposed and analyzed robust tests are extended to fixed sample size and sequential probability ratio tests simulations are provided to exemplify and evaluate the theoretical derivations

decomposition of the time reversal operator detection and selective focusing on two scatterers the decomposition of the time reversal operator dort method is a selective detection and focusing technique using an array of transmit receive transducers it relies on the theory of iterative time reversal mirrors which was presented by prada et al c prada j l thomas and m fink j acoust soc am 97 62 71 1995 the time reversal operator was defined as k k where is the frequency means complex conjugate and k is the transfer matrix of the array of l transducers insonifying a time invariant scattering medium it was shown that this time reversal operator can be diagonalized and that for ideally resolved scatterers of different reflectivities each of its eigenvectors of nonzero eigenvalue provides the phase law to be applied to the transducers in order to focus on one of the scatterers the dort method consists in determining these eigenvectors and using them for the selective focusing this paper presents a complete analysis of this method in the case of two scatterers the

centroidal voronoi tessellations applications and algorithms a centroidal voronoi tessellation is a voronoi tessellation whose generating points are the centroids centers of mass of the corresponding voronoi regions we give some applications of such tessellations to problems in image compression quadrature finite difference methods distribution of resources cellular biology statistics and the territorial behavior of animals we discuss methods for computing these tessellations provide some analyses concerning both the tessellations and the methods for their determination and finally present the results of some numerical experiments

renyi divergence measures for commonly used univariate continuous distributions abstract probabilistic distances also called divergences which in some sense assess how close two probability distributions are from one another have been widely employed in probability statistics information theory and related fields of particular importance due to their generality and applicability are the renyi divergence measures this paper presents closed form expressions for the renyi and kullback leibler divergences for nineteen commonly used univariate continuous distributions as well as those for multivariate gaussian and dirichlet distributions in addition a table summarizing four of the most important information measure rates for zero mean stationary gaussian processes namely renyi entropy differential shannon entropy renyi divergence and kullback leibler divergence is presented lastly a connection between the renyi divergence and the variance of the log likelihood ratio of two distributions is established thereby extending a previous result by song j stat plan infer 93 2001 on the relation between renyi entropy and the log likelihood function a table with the corresponding variance expressions for the univariate distributions considered here is also included

counterexamples in distributed detection specific counterexamples violating three very plausible conjectures about optimal design of distributed detection and decision systems are reported the numerical magnitude of the violation is small in each case

the covering radius of the 2 15 16 reed muller code is at least 16276 two interesting cosets of the first order reed muller code of block length 2 15 are described they provide counterexamples to a conjecture on the covering radius

nearest neighbor clustering a baseline method for consistent clustering with arbitrary objective functions clustering is often formulated as a discrete optimization problem the objective is to find among all partitions of the data set the best one according to some quality measure however in the statistical setting where we assume that the finite data set has been sampled from some underlying space the goal is not to find the best partition of the given sample but to approximate the true partition of the underlying space we argue that the discrete optimization approach usually does not achieve this goal and instead can lead to inconsistency we construct examples which provably have this behavior as in the case of supervised learning the cure is to restrict the size of the function classes under consideration for appropriate small function classes we can prove very general consistency theorems for clustering optimization schemes as one particular algorithm for clustering with a restricted function space we introduce nearest neighbor clustering similar to the k nearest neighbor classifier in supervised learning this algorithm can be seen as a general baseline algorithm to minimize arbitrary clustering objective functions we prove that it is statistically consistent for all commonly used clustering objective functions

quantization of prior probabilities for hypothesis testing in this paper bayesian hypothesis testing is investigated when the prior probabilities of the hypotheses taken as a random vector are quantized nearest neighbor and centroid conditions are derived using mean bayes risk error mbre as a distortion measure for quantization a high resolution approximation to the distortion rate function is also obtained human decision making in segregated populations is studied assuming bayesian hypothesis testing with quantized priors

put absolute moment block truncation coding in perspective the purpose of this letter is to point out that the udpikar and raina 1987 modified block truncation coding btc has been misleading researchers as a different btc scheme in multiple publications for years in fact their algorithm is exactly identical to the second version of the lema and mitchell 1984 absolute moment block truncation coding ambtc mathematical proof is provided

formulas for renyi information and related measures for univariate distributions in a recent paper song j stat plan infer 93 2001 51 considered renyi information of order and established its connection to the loglikelihood from this relation an intrinsic distribution measure was proposed and analytic expressions of this measure and renyi information were derived for some standard continuous distributions in this paper we derive analytical formulas for renyi and shannon entropies as well as for song s measure for 26 flexible families of univariate continuous distributions we believe that the results presented here will serve as an important reference for scientists and engineers in many areas

single bit map block truncation coding of color images using a hopfield neural network abstract this paper describes a new single bit map block truncation coding sbbtc scheme that works with a hopfield neural network hnn for the coding of color images an incoming color block is encoded using three block truncation coding btc encoders with a common bit map for each of the three primary color planes an hnn is used to generate a good single bit map in the sbbtc by clustering the color vectors in the block into two classes the considering block is then encoded by the generated bit map and the two reconstruction colors each associated to one of the two classes in comparison with other existing methods the proposed color btc gives the best mean square error mse performance at the same bit rate

constructions for perfect mixed codes and other covering codes a construction for an infinite family of perfect mixed codes with covering radius 2 is presented these are the first known nontrivial perfect mixed codes with covering radius greater than 1 based on mixed codes constructions for binary covering codes that lead to a considerable improvement of upper bounds on the sizes of covering codes are presented these codes and some other codes can be obtained by the blockwise direct sum construction two infinite families of codes are of special interest they are quasi perfect nonlinear union of their disjoint translates covers the space and their density as covering codes is remarkably low

on the string consensus problem and the manhattan sequence consensus problem abstract we study the manhattan sequence consensus problem msc problem in which we are given k integer sequences each of length l and we are to find an integer sequence x of length l called a consensus sequence such that the maximum manhattan distance of x from each of the input sequences is minimized a related problem with hamming distance instead of manhattan distance is called hamming string consensus hsc also known under the names of string center problem or closest string problem for binary sequences manhattan distance coincides with hamming distance hence in this case hsc is a special case of msc we design a practically efficient o l time algorithm solving msc for k 5 sequences it improves upon the quadratic algorithm by amir et al 2012 1 for hsc for k 5 binary strings similarly as in the algorithm of amir et al we use a column based framework we replace the implied general integer linear programming by its easy special cases due to combinatorial properties of msc for k 5 practicality of our algorithms has been verified experimentally we also show that for a general parameter k any instance can be reduced in linear time to a kernel of size k so the problem is fixed parameter tractable nevertheless for k 4 this is still too large for any naive solution to be feasible in practice this is a full version of an article published at spire 2014 15

misspecified and asymptotically minimax robust quickest change detection we investigate the quickest detection of an unknown change in the distribution of a stochastic process generating independent and identically distributed observations we develop new bounds on the performance of misspecified cumulative sum cusum rules and pose minimax robust versions of the popular lorden and pollak criteria with polynomial or higher order moment detection delay penalties by exploiting our results for misspecified cusum rules we identify solutions to our robust quickest change detection problems in the asymptotic regime of few false alarms in contrast to previous robust quickest change detection treatments our asymptotic results hold under relaxed conditions on the uncertainty sets of possible prechange and postchange distributions we illustrate our results in simulations and apply them to the problem of detecting target manoeuvres in low signal to noise ratio settings i e dim target manoeuvre detection

a method of block truncation coding for color image compression a basic color block truncation coding cbtc algorithm for color image compression is described a modification of the algorithm that reduces truncation errors is also described the block statistics related to cbtc methods are investigated some experimental results are given for a 256 256 pixel color image with 24 b pixel

on the optimal linear receiving filter for digital transmission over nonlinear channels a recent paper by e biglieri et al see ibid vol 35 p 620 5 may 1989 shows that the matched filter tapped delay line structure is optimum not only for linear pulse modulated signals and linear channel distortion but also for nonlinear finite alphabet pulse modulation and some nonlinear channel distortion this has important practical applications therefore its connection with other work reported in the literature is presented