on factorization of m channel paraunitary filterbanks we systematically investigate the factorization of causal finite impulse response fir paraunitary filterbanks with given filter length based on the singular value decomposition of the coefficient matrices of the polyphase representation a fundamental order one factorization form is first proposed for general paraunitary systems then we develop a new structure for the design and implementation of paraunitary system based on the decomposition of hermitian unitary matrices within this framework the linear phase filterbank and pairwise mirror image symmetry filterbank are revisited their structures are special cases of the proposed general structures compared with the existing structures more efficient ones that only use approximately half the number of free parameters are derived the proposed structures are complete and minimal although the factorization theory with or without constraints is discussed in the framework of m channel filterbanks the results can be applied to wavelets and multiwavelet systems and could serve as a general theory for paraunitary systems

maximally decimated paraunitary linear phase fir filter bank design via iterative svd approach a necessary and sufficient condition for m channel maximally decimated paraunitary fir filter banks is derived when the lengths of all the filters are the same and they are integer multiples of m based on the derived condition a family of this kind of filter banks is defined these results are also applied to the corresponding linear phase filter banks then the design of this type of filter banks with the linear phase property is formulated as two orthogonal procrustes optimization problems the analytical solution of each optimization problem is derived based on a singular value decomposition approach since no numerical optimization computer aided design tool is required for finding the analytical solution of each optimization problem the computational power required for our proposed method is much lower than that for existing methods computer numerical simulation results show that our proposed method can obtain a design instantaneously

the capacity region of the gaussian multiple input multiple output broadcast channel the gaussian multiple input multiple output mimo broadcast channel bc is considered the dirty paper coding dpc rate region is shown to coincide with the capacity region to that end a new notion of an enhanced broadcast channel is introduced and is used jointly with the entropy power inequality to show that a superposition of gaussian codes is optimal for the degraded vector broadcast channel and that dpc is optimal for the nondegraded case furthermore the capacity region is characterized under a wide range of input constraints accounting as special cases for the total power and the per antenna power constraints

lapped unimodular transforms lifting factorization and structural regularity in this paper the lifting factorization and structural regularity of the lapped unimodular transforms luts are studied the proposed m channel lifting factorization is complete is minimal in the mcmillan sense and has diagonal entries of unity in addition to allowing for integer to integer mapping and guaranteeing perfect reconstruction even under finite precision the proposed lifting factorization structurally ensures unimodularity for regular lut design structural conditions that impose 1 1 1 2 and 2 1 regularity onto the filter banks fbs are presented consequently the optimal filter coefficients can be obtained through unconstrained optimizations a special lifting based lattice structure is used for parameterizing nonsingular matrices which not only helps impose regularity but also has rational coefficient unimodular fbs as a by product the regular luts can be transformed to the lifting domain with the proposed factorization for faster and multiplierless implementations the lifting factorization and the regularity conditions are derived for two different type i and type ii factorizations of the first order unimodular fbs design examples are presented to confirm the proposed theory

on m channel linear phase fir filter banks and application in image compression this paper investigates the theory and structure of a large subclass of m channel linear phase perfect reconstruction fir filter banks systems with analysis and synthesis filters of length l sub i k sub i m spl beta where spl beta is an arbitrary integer 0 spl les spl beta m and k sub i is any positive integer for this subclass of systems we first investigate the necessary conditions for the existence of linear phase perfect reconstruction filter banks lpprfbs next we develop a complete and minimal factorization for all even channel linear phase paraunitary systems the most general lapped orthogonal transforms to date finally several design examples as well as comparisons with previous generalized lapped orthogonal transforms genlots in image compression are presented to confirm the validity of the theory

fast global oscillations in networks of integrate and fire neurons with low firing rates we study analytically the dynamics of a network of sparsely connected inhibitory integrate and fire neurons in a regime where individual neurons emit spikes irregularly and at a low rate in the limit when the number of neurons n 1 the network exhibits a sharp transition between a stationary and an oscillatory global activity regime where neurons are weakly synchronized the activity becomes oscillatory when the inhibitory feedback is strong enough the period of the global oscillation is found to be mainly controlled by synaptic times but depends also on the characteristics of the external input in large but finite networks the analysis shows that global oscillations of finite coherence time generically exist both above and below the critical inhibition threshold their characteristics are determined as functions of systems parameters in these two different regimes the results are found to be in good agreement with numerical simulations

it formulae for gamma target mutual information and relative entropy in this paper we introduce new stein identities for gamma target distribution as well as a new non linear channel specifically designed for gamma inputs from these two ingredients we derive an explicit and simple formula for the derivative of the input output mutual information of this non linear channel with respect to the channel quality parameter this relation is reminiscent of the well known link between the derivative of the input output mutual information of additive gaussian noise channel with respect to the signal to noise ratio and the minimum mean square error the proof relies on a rescaled version of de bruijn identity for gamma target distribution together with a stochastic representation for the gamma specific fisher information finally we are able to derive precise bounds and asymptotics for the input output mutual information of the non linear channel with gamma inputs

dynamic instabilities in scalar neural field equations with space dependent delays in this paper we consider a class of scalar integral equations with a form of space dependent delay these non local models arise naturally when modelling neural tissue with active axons and passive dendrites such systems are known to support a dynamic oscillatory turing instability of the homogeneous steady state in this paper we develop a weakly nonlinear analysis of the travelling and standing waves that form beyond the point of instability the appropriate amplitude equations are found to be the coupled mean field ginzburg landau equations describing a turing hopf bifurcation with modulation group velocity of o 1 importantly we are able to obtain the coefficients of terms in the amplitude equations in terms of integral transforms of the spatio temporal kernels defining the neural field equation of interest indeed our results cover not only models with axonal or dendritic delays but those which are described by a more general distribution of delayed spatio temporal interactions we illustrate the predictive power of this form of analysis with comparison against direct numerical simulations paying particular attention to the competition between standing and travelling waves and the onset of benjamin feir instabilities

theory of regular m band wavelet bases orthonormal m band wavelet bases have been constructed and applied by several authors this paper makes three main contributions first it generalizes the minimal length k regular 2 band wavelets of daubechies 1988 to the m band case by deriving explicit formulas for k regular m band scaling filters several equivalent characterizations of k regularity are given and their significance explained second two approaches to the construction of the m 1 wavelet filters and associated wavelet bases are described one relies on a state space characterization with a novel technique to obtain the unitary wavelet filters the other uses a factorization approach third this paper gives a set of necessary and sufficient condition on the m band scaling filter for it to generate an orthonormal wavelet basis the conditions are very similar to those obtained by cohen 1990 and lawton 1990 for 2 band wavelets

multiple bumps in a neuronal model of working memory we study a partial integro differential equation defined on a spatially extended domain that arises from the modeling of working or short term memory in a neuronal network the equation is capable of supporting spatially localized regions of high activity which can be switched on and off by transient external stimuli we analyze the effects of coupling between units in the network showing that if the connection strengths decay monotonically with distance then no more thanon e regionof high activity canpersist whereas if they decay inanoscillatory fashion then multiple regions can persist

natural exponential families with quadratic variance functions statistical theory the normal poisson gamma binomial negative binomial and nefghs distributions are the six univariate natural exponential families nef with quadratic variance functions qvf this sequel to morris 1982 treats certain statistical topics that can be handled within this unified nef qvf formulation including unbiased estimation bhattacharyya and cramer rao lower bounds conditional distributions and moments quadratic regression conjugate prior distributions moments of conjugate priors and posterior distributions empirical bayes and g 2 minimax marginal distributions and their moments parametric empirical bayes and characterizations

orthonormal fbs with rational sampling factors and oversampled dft modulated fbs a connection and filter design methods widely used to design filters for uniformly sampled filter banks fbs are not applicable for fbs with rational sampling factors and oversampled discrete fourier transform dft modulated fbs in this paper we show that the filter design problem with regularity factors vanishing moments for these two types of fbs is the same following this we propose two finite impulse response fir filter design methods for these fbs the first method describes a parameterization of fbs with a single regularity factor vanishing moment the second method which can be used to design fbs with an arbitrary number of regularity factors vanishing moments uses results from frame theory we also describe how to modify this method so as to obtain linear phase filters finally we discuss and provide a motivation for iterated dft modulated fbs

a new entropy power inequality a strengthened version of shannon s entropy power inequality for the case where one of the random vectors involved is gaussian is proved in particular it is shown that if independent gaussian noise is added to an arbitrary multivariate random variable the entropy power of the resulting random variable is a concave function of the variance power of the added noise the strengthened inequality is shown to hold for the class of stable distributions

lattice structure for regular paraunitary linear phase filterbanks and m band orthogonal symmetric wavelets parauninary linear phase pulp m channel uniform filterbanks which are also known as the generalized lapped orthogonal transforms genlots can be designed and implemented using lattice structures this paper discusses how to impose regularity constraints onto the lattice structure of pulp filterbanks these conditions are expressed in term of the rotation angles of the lattice components by which the resulting filterbanks are guaranteed to have one or two degrees of regularity iterating these new regular filterbanks on the lowpass subband generates a large family of symmetric m band orthonormal wavelets design procedures with many design examples are presented smooth interpolation using regular pulp filterbanks is illustrated through image coding experiments where the novel m band wavelets consistently yield smoother reconstructed images and better perceptual quality

optimization of integer wavelet transforms based on difference correlation structures in this paper a novel lifting integer wavelet transform based on difference correlation structure dccs liwt is proposed first we establish a relationship between the performance of a linear predictor and the difference correlations of an image the obtained results provide a theoretical foundation for the following construction of the optimal lifting filters then the optimal prediction lifting coefficients in the sense of least square prediction error are derived dccs liwt puts heavy emphasis on image inherent dependence a distinct feature of this method is the use of the variance normalized autocorrelation function of the difference image to construct a linear predictor and adapt the predictor to varying image sources the proposed scheme also allows respective calculations of the lifting filters for the horizontal and vertical orientations experimental evaluation shows that the proposed method produces better results than the other well known integer transforms for the lossless image compression

representation of mutual information via input estimates a relationship between information theory and estimation theory was recently shown for the gaussian channel relating the derivative of mutual information with the minimum mean square error this paper generalizes the link between information theory and estimation theory to arbitrary channels giving representations of the derivative of mutual information as a function of the conditional marginal input distributions given the outputs we illustrate the use of this representation in the efficient numerical computation of the mutual information achieved by inputs such as specific codes or natural language

generalized sure for exponential families applications to regularization stein s unbiased risk estimate sure was proposed by stein for the independent identically distributed i i d gaussian model in order to derive estimates that dominate least squares ls recently the sure criterion has been employed in a variety of denoising problems for choosing regularization parameters that minimize an estimate of the mean squared error mse however its use has been limited to the i i d case which precludes many important applications in this paper we begin by deriving a sure counterpart for general not necessarily i i d distributions from the exponential family this enables extending the sure design technique to a much broader class of problems based on this generalization we suggest a new method for choosing regularization parameters in penalized ls estimators we then demonstrate its superior performance over the conventional generalized cross validation and discrepancy approaches in the context of image deblurring and deconvolution the sure technique can also be used to design estimates without predefining their structure however allowing for too many free parameters impairs the estimate s performance to address this inherent tradeoff we propose a regularized sure objective and demonstrate its use in the context of wavelet denoising

mean field equations for stochastic firing rate neural fields with delays derivation and noise induced transitions abstract in this manuscript we analyze the collective behavior of mean field limits of large scale spatially extended stochastic neuronal networks with delays rigorously the asymptotic regime of such systems is characterized by a very intricate stochastic delayed integro differential mckean vlasov equation that remain impenetrable leaving the stochastic collective dynamics of such networks poorly understood in order to study these macroscopic dynamics we analyze networks of firing rate neurons i e with linear intrinsic dynamics and sigmoidal interactions in that case we prove that the solution of the mean field equation is gaussian hence characterized by its two first moments and that these two quantities satisfy a set of coupled delayed integro differential equations these equations are similar to usual neural field equations and incorporate noise levels as a parameter allowing analysis of noise induced transitions we identify through bifurcation analysis several qualitative transitions due to noise in the mean field limit in particular stabilization of spatially homogeneous solutions synchronized oscillations bumps chaotic dynamics wave or bump splitting are exhibited and arise from static or dynamic turing hopf bifurcations these surprising phenomena allow further exploring the role of noise in the nervous system

the genlot generalized linear phase lapped orthogonal transform the general factorization of a linear phase paraunitary filter bank lppufb is revisited from this new perspective a class of lapped orthogonal transforms with extended overlap generalized linear phase lapped orthogonal transforms genlots is developed as a subclass of the general class of lppufb in this formulation the discrete cosine transform dct is the order 1 genlot the lapped orthogonal transform is the order 2 genlot and so on for any filter length that is an integer multiple of the block size the genlots are based on the dct and have fast implementation algorithms the implementation of genlots is explained including the method to process finite length signals the degrees of freedom in the design of genlots are described and design examples are presented along with image compression tests

how effective delays shape oscillatory dynamics in neuronal networks abstract synaptic dendritic and single cell kinetics generate significant time delays that shape the dynamics of large networks of spiking neurons previous work has shown that such effective delays can be taken into account with a rate model through the addition of an explicit fixed delay roxin et al 2005 2006 29 30 here we extend this work to account for arbitrary symmetric patterns of synaptic connectivity and generic nonlinear transfer functions specifically we conduct a weakly nonlinear analysis of the dynamical states arising via primary instabilities of the asynchronous state in this way we determine analytically how the nature and stability of these states depend on the choice of transfer function and connectivity we arrive at two general observations of physiological relevance that could not be explained in previous work these are 1 fast oscillations are always supercritical for realistic transfer functions and 2 traveling waves are preferred over standing waves given plausible patterns of local connectivity we finally demonstrate that these results show good agreement with those obtained performing numerical simulations of a network of hodgkin huxley neurons

field theoretic approach to fluctuation effects in neural networks a well defined stochastic theory for neural activity which permits the calculation of arbitrary statistical moments and equations governing them is a potentially valuable tool for theoretical neuroscience we produce such a theory by analyzing the dynamics of neural activity using field theoretic methods for nonequilibrium statistical processes assuming that neural network activity is markovian we construct the effective spike model which describes both neural fluctuations and response this analysis leads to a systematic expansion of corrections to mean field theory which for the effective spike model is a simple version of the wilson cowan equation we argue that neural activity governed by this model exhibits a dynamical phase transition which is in the universality class of directed percolation more general models which may incorporate refractoriness can exhibit other universality classes such as dynamic isotropic percolation because of the extremely high connectivity in typical networks it is expected that higher order terms in the systematic expansion are small for experimentally accessible measurements and thus consistent with measurements in neocortical slice preparations we expect mean field exponents for the transition we provide a quantitative criterion for the relative magnitude of each term in the systematic expansion analogous to the ginsburg criterion experimental identification of dynamic universality classes in vivo is an outstanding and important question for neuroscience

a master equation formalism for macroscopic modeling of asynchronous irregular activity states many efforts have been devoted to modeling asynchronous irregular ai activity states which resemble the complex activity states seen in the cerebral cortex of awake animals most of models have considered balanced networks of excitatory and inhibitory spiking neurons in which ai states are sustained through recurrent sparse connectivity with or without external input in this letter we propose a mesoscopic description of such ai states using master equation formalism we derive a second order mean field set of ordinary differential equations describing the temporal evolution of randomly connected balanced networks this formalism takes into account finite size effects and is applicable to any neuron model as long as its transfer function can be characterized we compare the predictions of this approach with numerical simulations for different network configurations and parameter spaces considering the randomly connected network as a unit this approach could be used to build large scale networks of such connected units with an aim to model activity states constrained by macroscopic measurements such as voltage sensitive dye imaging

integer dct based on direct lifting of dct idct for lossless to lossy image coding a discrete cosine transform dct can be easily implemented in software and hardware for the jpeg and mpeg formats however even though some integer dcts intdcts for lossless to lossy image coding have been proposed such transform requires redesigned devices this paper proposes a hardware friendly intdct that can be applied to both lossless and lossy coding our intdct is implemented by direct lifting of dct and inverse dct idct consequently any existing dct device can be directly applied to every lifting block although our method requires a small side information block sib it is validated by its application to lossless to lossy image coding

theory and factorization for a class of structurally regular biorthogonal filter banks regularity is a fundamental and desirable property of wavelets and perfect reconstruction filter banks prfbs among others it dictates the smoothness of the wavelet basis and the rate of decay of the wavelet coefficients this paper considers how regularity of a desired degree can be structurally imposed onto biorthogonal filter banks bofbs so that they can be designed with exact regularity and fast convergence via unconstrained optimization the considered design space is a useful class of m channel causal finite impulse response fir bofbs having anticausal fir inverses that are characterized by the dyadic based structure w z i uv sup spl dagger z sup 1 uv sup spl dagger for which u and v are m spl times spl gamma parameter matrices satisfying v sup spl dagger u i sub spl gamma 1 spl les spl gamma spl les m for any m spl ges 2 structural conditions for regularity are derived where the householder transform is found convenient as a special case a class of regular linear phase bofbs is considered by further imposing linear phase lp on the dyadic based structure in this way an alternative and simplified parameterization of the biorthogonal linear phase filter banks glbts is obtained and the general theory of structural regularity is shown to simplify significantly regular bofbs are designed according to the proposed theory and are evaluated using a transform based image codec they are found to provide better objective performance and improved perceptual quality of the decompressed images specifically the blocking artifacts are reduced and texture details are better preserved for fingerprint images the proposed biorthogonal transform codec outperforms the fbi scheme by 1 1 6 db in psnr

gradient of mutual information in linear vector gaussian channels this paper considers a general linear vector gaussian channel with arbitrary signaling and pursues two closely related goals i closed form expressions for the gradient of the mutual information with respect to arbitrary parameters of the system and ii fundamental connections between information theory and estimation theory generalizing the fundamental relationship recently unveiled by guo shamai and verdu spl acute we show that the gradient of the mutual information with respect to the channel matrix is equal to the product of the channel matrix and the error covariance matrix of the best estimate of the input given the output gradients and derivatives with respect to other parameters are then found via the differentiation chain rule

stochastic neural field theory and the system size expansion we analyze a master equation formulation of stochastic neurodynamics for a network of synaptically coupled homogeneous neuronal populations each consisting of n identical neurons the state of the network is specified by the fraction of active or spiking neurons in each population and transition rates are chosen so that in the thermodynamic or deterministic limit n rightarrow infty we recover standard activity based or voltage based rate models we derive the lowest order corrections to these rate equations for large but finite n using two different approximation schemes one based on the van kampen system size expansion and the other based on path integral methods both methods yield the same series expansion of the moment equations which at mathcal o 1 n can be truncated to form a closed system of equations for the first and second order moments taking a continuum limit of the moment equations while keeping the system size n fixed generates a system of integrodifferential equations for the

hessian and concavity of mutual information differential entropy and entropy power in linear vector gaussian channels within the framework of linear vector gaussian channels with arbitrary signaling the jacobian of the minimum mean square error and fisher information matrices with respect to arbitrary parameters of the system are calculated in this paper capitalizing on prior research where the minimum mean square error and fisher information matrices were linked to information theoretic quantities through differentiation the hessian of the mutual information and the entropy are derived these expressions are then used to assess the concavity properties of mutual information and entropy under different channel conditions and also to derive a multivariate version of an entropy power inequality due to costa

stability bifurcation and multistability in a system of two coupled neurons with multiple time delays a system of delay differential equations representing a model for a pair of neurons with time delayed connections between the neurons and time delayed feedback from each neuron to itself is studied conditions for the linear stability of the trivial solution of this system are represented in a parameter space consisting of the sum of the time delays between the elements and the product of the strengths of the connections between the elements it is shown that the trivial fixed point may lose stability via a pitchfork bifurcation a hopf bifurcation or one of three types of codimension two bifurcations multistability near these latter bifurcations is predicted using center manifold analysis and confirmed using numerical simulations

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

dyadic based factorizations for regular paraunitary filterbanks and m band orthogonal wavelets with structural vanishing moments paraunitary filterbanks pufbs can be designed and implemented using either degree one or order one dyadic based factorization this work discusses how regularity of a desired degree is structurally imposed on such factorizations for any number of channels m spl ges 2 without necessarily constraining the phase responses the regular linear phase pufbs become a special case under the proposed framework we show that the regularity conditions are conveniently expressed in terms of recently reported m channel lifting structures which allow for fast reversible and possibly multiplierless implementations in addition to improved design efficiency as suggested by numerical experience m band orthonormal wavelets with structural vanishing moments are obtained by iterating the resulting regular pufbs on the lowpass channel design examples are presented and evaluated using a transform based image coder and they are found to outperform previously reported designs

a progressive transmission image coder using linear phase uniform filterbanks as block transforms this paper presents a novel image coding scheme using m channel linear phase perfect reconstruction filterbanks lpprfbs in the embedded zerotree wavelet ezw framework introduced by shapiro 1993 the innovation here is to replace the ezws dyadic wavelet transform by m channel uniform band maximally decimated lpprfbs which offer finer frequency spectrum partitioning and higher energy compaction the transform stage can now be implemented as a block transform which supports parallel processing and facilitates region of interest coding decoding for hardware implementation the transform boasts efficient lattice structures which employ a minimal number of delay elements and are robust under the quantization of lattice coefficients the resulting compression algorithm also retains all the attractive properties of the ezw coder and its variations such as progressive image transmission embedded quantization exact bit rate control and idempotency despite its simplicity our new coder outperforms some of the best image coders published previously in the literature for almost all test images especially natural hard to code ones at almost all bit rates

an extremal inequality motivated by multiterminal information theoretic problems we prove a new extremal inequality motivated by the vector gaussian broadcast channel and the distributed source coding with a single quadratic distortion constraint problems as a corollary this inequality yields a generalization of the classical entropy power inequality epi as another corollary this inequality sheds insight into maximizing the differential entropy of the sum of two dependent random variables

improved technique for design of perfect reconstruction fir qmf banks with lossless polyphase matrices a technique is developed for the design of analysis filters in an m channel maximally decimated perfect reconstruction finite impulse response quadrature mirror filter fir qmf bank that has a lossless polyphase component matrix e z the aim is to optimize the parameters characterizing e z until the sum of the stopband energies of the analysis filters is minimized there are four novel elements in the procedure reported here the first is a technique for efficient initialization of one of the m analysis filters as a spectral factor of an mth band filter the factorization itself is done in an efficient manner using the eigenfilters approach without the need for root finding techniques the second element is the initialization of the internal parameters which characterize e z based on the above spectral factor the third element is a modified characterization mostly free from rotation angles of the fir e z the fourth is the incorporation of symmetry among the analysis filters so as to minimize the number of unknown parameters being optimized the resulting design procedure always gives better filter responses than earlier ones for a given filter length and converges much faster

james stein state filtering algorithms in 1961 james and stein discovered a remarkable estimator that dominates the maximum likelihood estimate of the mean of a p variate normal distribution provided the dimension p is greater than two this paper extends the james stein estimator and highlights the benefits of applying these extensions to adaptive signal processing problems the main contribution of this paper is the derivation of the james stein state filter jssf which is a robust version of the kalman filter the jssf is designed for situations where the parameters of the state space evolution model are not known with any certainty in deriving the jssf we derive several other results we first derive a james stein estimator for estimating the regression parameter in a linear regression a recursive implementation which we call the james stein recursive least squares js rls algorithm is derived the resulting estimate although biased has a smaller mean square error than the traditional rls algorithm finally several heuristic algorithms are presented including a james stein version of the yule walker equations for ar parameter estimation

on the equivalence between stein and de bruijn identities this paper focuses on illustrating 1 the equivalence between stein s identity and de bruijn s identity and 2 two extensions of de bruijn s identity first it is shown that stein s identity is equivalent to de bruijn s identity under additive noise channels with specific conditions second for arbitrary but fixed input and noise distributions under additive noise channels the first derivative of the differential entropy is expressed by a function of the posterior mean and the second derivative of the differential entropy is expressed in terms of a function of fisher information several applications over a number of fields such as signal processing and information theory are presented to support the usefulness of the developed results in this paper

fast multiplierless approximations of the dct with the lifting scheme we present the design implementation and application of several families of fast multiplierless approximations of the discrete cosine transform dct with the lifting scheme called the bindct these bindct families are derived from chen s 1977 and loeffler s 1989 plane rotation based factorizations of the dct matrix respectively and the design approach can also be applied to a dct of arbitrary size two design approaches are presented in the first method an optimization program is defined and the multiplierless transform is obtained by approximating its solution with dyadic values in the second method a general lifting based scaled dct structure is obtained and the analytical values of all lifting parameters are derived enabling dyadic approximations with different accuracies therefore the bindct can be tuned to cover the gap between the walsh hadamard transform and the dct the corresponding two dimensional 2 d bindct allows a 16 bit implementation enables lossless compression and maintains satisfactory compatibility with the floating point dct the performance of the bindct in jpeg h 263 and lossless compression is also demonstrated

integer fast fourier transform a concept of integer fast fourier transform intfft for approximating the discrete fourier transform is introduced unlike the fixed point fast fourier transform fxpfft the new transform has the properties that it is an integer to integer mapping is power adaptable and is reversible the lifting scheme is used to approximate complex multiplications appearing in the fft lattice structures where the dynamic range of the lifting coefficients can be controlled by proper choices of lifting factorizations split radix fft is used to illustrate the approach for the case of 2 sup n point fft in which case an upper bound of the minimal dynamic range of the internal nodes which is required by the reversibility of the transform is presented and confirmed by a simulation the transform can be implemented by using only bit shifts and additions but no multiplication a method for minimizing the number of additions required is presented while preserving the reversibility the intfft is shown experimentally to yield the same accuracy as the fxpfft when their coefficients are quantized to a certain number of bits complexity of the intfft is shown to be much lower than that of the fxpfft in terms of the numbers of additions and shifts finally they are applied to noise reduction applications where the intfft provides significantly improvement over the fxpfft at low power and maintains similar results at high power

complete factorization for poly phase matrix with linear phase based on semi rank orthogonal projection matrix abstract this paper puts forward a new factorization named the semi rank factorization for para unitary poly phase matrix with linear phase and reveals the equivalent relationship between the orthogonal projection matrix and the linear phase and characterizes the orthogonal projection matrix the semi rank factorization has the completeness property no matter for even or odd number of channels in addition a decomposition technique for the starting block matrix is developed using the reflection matrix the semi rank factorization provides an efficient and compact representation for multi band filter banks with linear phase in particular the complete representation for multi band symmetry filter banks with odd number of channels is brand new as a result the programmable algorithms are obtained for designs of optimal filter banks based on the complete representation the optimal examples are presented to illustrate the excellent performance on image compression

symmetric delay factorization generalized framework for paraunitary filter banks the symmetric delay factorization sdf was introduced to synthesize linear phase paraunitary filter banks lppufbs with uniform order i e filter length equal to nm for arbitrary n and real valued coefficients the sdf presents the advantage of decomposing the polyphase transfer matrix ptm into only orthogonal matrices even at the boundary of finite duration signals simplifying significantly the design of time bounded filter banks tbfbs or of time varying filter banks tvfbs however the symmetric delay factorization applies only to lppufbs on the other hand lattice structures as well as finite size lattice structures are proposed for classes of nonlinear phase paraunitary filter banks as the modulated lapped transform mlt and the extended tapped transform elt this paper describes a new minimal and complete symmetric delay factorization valid for a larger class of paraunitary filter banks encompassing paraunitary cosine modulated filter banks with nonlinear phase basis functions as well as for a set of lppufbs including the linear phase lapped orthogonal transforms lots and the generalized tapped orthogonal transforms genlots the derivations for filter banks with even and odd numbers of channels are formulated in a unified form this approach opens new perspectives in the design of time varying filter banks used for image and video compression especially in the framework of region or object based coding

entropy and the fourth moment phenomenon we develop a new method for bounding the relative entropy of a random vector in terms of its stein factors our approach is based on a novel representation for the score function of smoothly perturbed random variables as well as on the de bruijn s identity of information theory when applied to sequences of functionals of a general gaussian field our results can be combined with the carbery wright inequality in order to yield multidimensional entropic rates of convergence that coincide up to a logarithmic factor with those achievable in smooth distances such as the 1 wasserstein distance in particular our findings settle the open problem of proving a quantitative version of the multidimensional fourth moment theorem for random vectors having chaotic components with explicit rates of convergence in total variation that are independent of the order of the associated wiener chaoses the results proved in the present paper are outside the scope of other existing techniques such as for instance the multidimensional stein s method for normal approximations

information theoretic proofs of entropy power inequalities while most useful information theoretic inequalities can be deduced from the basic properties of entropy or mutual information up to now shannon s entropy power inequality epi is an exception existing information theoretic proofs of the epi hinge on representations of differential entropy using either fisher information or minimum mean square error mmse which are derived from de bruijn s identity in this paper we first present an unified view of these proofs showing that they share two essential ingredients 1 a data processing argument applied to a covariance preserving linear transformation 2 an integration over a path of a continuous gaussian perturbation using these ingredients we develop a new and brief proof of the epi through a mutual information inequality which replaces stam and blachman s fisher information inequality fii and an inequality for mmse by guo shamai and verdu used in earlier proofs the result has the advantage of being very simple in that it relies only on the basic properties of mutual information these ideas are then generalized to various extended versions of the epi zamir and feder s generalized epi for linear transformations of the random variables takano and johnson s epi for dependent variables liu and viswanath s covariance constrained epi and costa s concavity inequality for the entropy power

rank reduction and james stein estimation this correspondence addresses the problem of estimating the signal in a signal plus gaussian noise model when it is known that the signal lies in a given subspace an alternative to rank reduction is presented the new estimator has the remarkable property of having a smaller mean square error than that of the maximum likelihood also least squares estimator for all parameter values