the hermite transform applications it is demonstrated how the hermite transform can be used for image coding and analysis hierarchical coding structures based on increasingly specified basic patterns i e general 2 d patterns general 1 d patterns and specific 1 d patterns such as edges and corners are presented in the image coding application the relation with existing pyramid coders is described a new coding scheme based on local one dimensional image approximations is introduced in the image analysis application the relation between the hermite transform and existing line edge detection schemes is described it is shown that by concentrating on more specific patterns the coding efficiency can be increased since fewer coefficients have to be coded meanwhile sufficient descriptive power can be maintained for approximating the most interesting features in natural images

quantization of filter bank frame expansions through moving horizon optimization this paper describes a novel approach to quantization in oversampled filter banks the new technique is based on moving horizon optimization does not rely on an additive white noise quantization model and allows stability to be explicitly enforced in the associated nonlinear feedback loop moreover the quantization structure proposed here includes sigmadelta and linear predictive subband quantizers as a special case and in general outperforms them

approximation of delay systems by fourier laguerre series abstract error estimates are given for the approximation of stable recorded delay systems in the l 2 and h norms using two recently advocated techniques based on laguerre series in addition some theoretical results on l 0 approximation are derived

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

a filter bank for the directional decomposition of images theory and design the authors introduce a directionally oriented 2 d filter bank with the property that the individual channels may be critically sampled without loss of information the passband regions of the component filters are wedge shaped and thus provide directional information it is shown that these filter bank outputs may be maximally decimated to achieve a minimum sample representation in a way that permits the original signal to be exactly reconstructed the authors discuss the theory for directional decomposition and reconstruction in addition implementation issues are addressed where realizations based on both recursive and nonrecursive filters are considered

optimization of linear multiresolution transforms for scene adaptive coding scene adaptive coders are constituted by the cascade of a linear transform scalar quantization entropy coding and a buffer controlled by a feedback loop for bit rate regulation the main contribution of this paper is to derive an analytical criterion evaluating the performances of any perfect reconstruction linear transform in the frame of scene adaptive coding this criterion is thereafter used in order to optimize linear multiresolution transforms the optimization adapts the filters parameters to the codec features and to the statistics of the 2 d sources so the authors call these transforms adapted multiresolution transforms amts the transforms under study are implemented by a cascade of separable perfect reconstruction pr fir two band filter banks that can change at each resolution level two types of filter banks are envisaged the pr orthogonal quadrature mirror filter qmf bank which allows to implement the orthogonal amt and the pr linear phase filter lpf bank which implements the biorthogonal amt they perform the optimization of the filters in their factorized lattice form taking the finite length of the multipliers into account their criterion also allows them to show the performances achieved by these two linear multiresolution transforms compared to other linear multiresolution transforms

perfect reconstruction versus mmse filter banks in source coding classically the filter banks fbs used in source coding schemes have been chosen to possess the perfect reconstruction pr property or to be maximally selective quadrature mirror filters qmfs this paper puts this choice back into question and solves the problem of minimizing the reconstruction distortion which in the most general case is the sum of two terms a first one due to the non pr property of the fb and the other being due to signal quantization in the subbands the resulting filter banks are called minimum mean square error mmse filter banks several quantization noise models are considered first under the classical white noise assumption the optimal positive bit rate allocation in any filter bank possibly nonorthogonal is expressed analytically and an efficient optimization method of the mmse filter banks is derived then it is shown that while in a pr fb the improvement brought by an accurate noise model over the classical white noise one is noticeable it is not the case for the mmse fb the optimization of the synthesis filters is also performed for two measures of the bit rate the classical one which is defined for uniform scalar quantization and the order one entropy measure finally the comparison of rate distortion curves where the distortion is minimized for a given bit rate budget enables us to quantify the snr improvement brought by mmse solutions

two dimensional filter bank design for optimal reconstruction using limited subband information in this correspondence we propose design techniques for analysis and synthesis filters of 2 d perfect reconstruction filter banks prfb s that perform optimal reconstruction when a reduced number of subband signals is used based on the minimization of the squared error between the original signal and some low resolution representation of it the 2 d filters are optimally adjusted to the statistics of the input images so that most of the signal s energy is concentrated in the first few subband components this property makes the optimal prfb s efficient for image compression and pattern representations at lower resolutions for classification purposes by extending recently introduced ideas from frequency domain principal component analysis to two dimensions we present results for general 2 d discrete nonstationary and stationary second order processes showing that the optimal filters are nonseparable particular attention is paid to separable random fields proving that only the first and last filters of the optimal prfb are separable in this case simulation results that illustrate the theoretical achievements are presented

nonseparable multidimensional perfect reconstruction filter banks and wavelet bases for r sup n new results on multidimensional filter banks and their connection to multidimensional nonseparable wavelets are presented among the topics discussed are sampling in multiple dimensions multidimensional perfect reconstruction filter banks the two channel case in multiple dimensions the synthesis of multidimensional filter banks and the design of compactly supported wavelets

technical communique output feedback stabilizing controller for time delay systems this paper considers the problem of output feedback stabilization of unstable linear time delay systems the major features of the approach are 1 the delay system is characterized by a fixed transfer function matrix that contains just the set of unstable or marginally unstable modes plus an h norm for the stable part 2 the controller design is accomplished by dynamic output feedback and 3 sufficient conditions in the form of two algebraic riccati equations and an upper bound explicitly characterize a stabilizing controller the method is restricted to delay systems that satisfy an upper bound on the stable part

a new approach to the design of critically sampled m channel uniform band perfect reconstruction linear phase fir filter banks a new approach is presented for the design of uniform band m channel perfect reconstruction pr fir filter banks employing linear phase analysis and synthesis filters the technique designs on the impulse responses of the analysis filters directly the design problem is formulated as an optimization program the filter bank s pr feature can either be implicitly enforced through a set of mathematical relationships among the analysis filters coefficients or through a set of constraints in the optimization program the former approach results in a filter bank whose pr feature s dependency on hardware and software is eliminated or at least minimized the synthesis filters are then obtained by a set of relationships that describe each synthesis filter as a function of the analysis filters the criterion for optimality is least squares where the square of the difference between the ideal and actual frequency responses is integrated over the appropriate frequency bands for all m analysis filters and minimized

hybrid picture coding with wavelet transform and overlapped motion compensated interframe prediction coding a novel video coding scheme using an orthonormal wavelet transform is proposed the wavelet transform is used in a motion compensated interframe coder in which a blockless motion compensation technique is employed to increase efficiency of wavelet transform coding a new scanning method for wavelet coefficients is also proposed which is rather different from subband coding simulation work is carried out to evaluate the proposed coding method significant improvement in subjective quality is obtained over that obtained with conventional hybrid coding methods that use blockwise motion compensation and dct some improvement has also been realized in the signal to noise ratio although wavelet coding is still in its early stages of development it appears to hold great promise for motion picture coding

scalar quantization error analysis for image subband coding using qmfs the authors analyze the coding errors due to quantization by explicitly incorporating a mathematical model for a lloyd max quantizer into a quadrature mirror filter qmf splitting and reconstruction scheme p h westerink et al 1988 this approach explicitly incorporates quantization errors into a qmf system by means of a quantizer model this makes it possible to discriminate between different types of coding errors such as the aliasing error other errors that can be distinguished are a qmf design error a signal error and a random error which is uncorrelated with the original image both a mean squared error calculation and a subjective judgment of the coding errors show that the aliasing errors can be neglected for filter lengths of 12 taps or more the signal error determines the sharpness of the reconstructed image while the random error is most visible in the flat areas

genetic algorithm based technique for solving chance constrained problems management and measurement of risk is an important issue in almost all areas that require decisions to be made under uncertain information chance constrained programming ccp have been used for modelling and analysis of risks in a number of application domains however the resulting mathematical problems are non trivial to represent using algebraic modelling languages and pose significant computational challenges due to their non linear non convex and the stochastic nature we develop and implement c classes to represent such ccp problems we propose a framework consisting of genetic algorithm and monte carlo simulation in order to process the problems the non linear and non convex nature of the ccp problems are processed using genetic algorithm whereas the stochastic nature is addressed through simulation the computational investigations have shown that the framework can efficiently represent and obtain good solutions for seven test problems

all optimal hankel norm approximations of linear multivariable systems and their l error bounds the problem of approximating a multivariable transfer function g s of mcmillan degree n by s of mcmillan degree k is considered a complete characterization of all approximations that minimize the hankel norm is derived the solution involves a characterization of all rational functions s f s that minimize where s has mcmillan degree k and f s is anticavisal the solution to the latter problem is via results on balanced realizations all pass functions and the inertia of matrices all in terms of the solutions to lyapunov equations it is then shown that where k 1 g s is the k l st hankel singular value of g s and for one class of optimal hankel norm approximations the method is not computationally demanding and is applied to a 12 state model

discrete fourier transform and h sub infinity approximation it is shown that uniform rational approximation of nonrational transfer functions can always be obtained by means of the discrete fourier transform dft as long as such approximants exist based on this fact it is permissible to apply the fast fourier transform fft algorithm in carrying out rational approximations without being apprehensive of convergence the dft is used to obtain traditional approximations for transfer functions of infinite dimensional systems justification is provided for using the dft in such approximations it is established that whenever a stable transfer function can be approximated uniformly on the right half plane by a rational function its approximants can always be recognized by means of a dft

subband coding of images using asymmetrical filter banks we address the problem of the choice of subband filters in the context of image coding the ringing effects that occur in subband based compression schemes are the major unpleasant distortions a new set of two band filter banks suitable for image coding applications is presented the basic properties of these filters are linear phase perfect reconstruction asymmetric length and maximum regularity the better overall performances compared to the classical qmf subband filters are explained the asymmetry of the filter lengths results in a better compaction of the energy especially in the highpass subbands moreover the quantization error is reduced due to the short lowpass synthesis filter the undesirable ringing effect is considerably reduced due to the good step response of the synthesis lowpass filter the proposed design takes into account the statistics of natural images and the effect of quantization errors in the reconstructed images which explains the better coding performance

subband coding systems incorporating quantizer models a new method for dealing with the effects of quantization in a subband system is proposed it uses the gain plus additive noise linear model for the lloyd max quantizer based on this it is demonstrated how by an appropriate choice of synthesis filters one can cancel all signal dependent errors at the output of the system the only remaining error is random in nature and not correlated with the input signal we therefore have a tradeoff between the error being only random or having signal dependent components as well since the error variances in both cases are comparable as a result of having only a random error it is possible to reduce this error using for example a noise removal technique the result is then extended to the case where the input is a multidimensional signal and arbitrary sampling lattices are used as well as to the qmf alias cancellation case to demonstrate the validity of the proposed approach two types of experiments on images are carried out in a toy example it is shown that using noise removal could be beneficial for a more realistic coding scheme however it is demonstrated that even in the case when the model is no longer valid when some of the subbands are discarded the output error is still much less correlated with the input signal as opposed to the commonly used subband system while visually the reconstructed images look very similar

the binomial qmf wavelet transform for multiresolution signal decomposition perfect reconstruction quadrature mirror filters pr qmf s have been proposed as structures suitable for hierarchical subband coding ll 4 and also for multiresolution signal decomposition as might be used in image pyramid coding 5 more recently multiresolution signal decomposition methods are being examined from the standpoint of the discrete wavelet transform for continuous time signals 6 8 in this paper we describe a class of orthogonal binomial filters that provide basis functions for a perfect reconstruction bank of finite impulse response qmf s the orthonormal wavelet filters derived by daubechies 171 from a discrete wavelet transform approach are shown to be the same as the solutions inherent in the binomial based filters the energy compaction performance of the binomial qmf decomposition is computed and shown to be better than the dct for the markov source models as well as real world images considered the proposed binomial structure is efficient simple to implement on vlsi and suitable for multiresolution signal decomposition and coding applications

near perfect reconstruction pseudo qmf banks a novel approach to the design of m channel pseudo quadrature mirror filter qmf banks is presented in this approach the prototype filter is constrained to be a linear phase spectral factor of a 2mth band filter as a result the overall transfer function of the analysis synthesis system is a delay moreover the aliasing cancellation ac constraint is derived such that all the significant aliasing terms are canceled consequently the aliasing level at the output is comparable to the stopband attenuation of the prototype filter in other words the only error at the output of the analysis synthesis system is the aliasing error which is at the level of stopband attenuation using this approach it is possible to design a pseudo qmf bank where the stopband attenuation of the analysis and thus synthesis filters is on the order of spl minus 100 db moreover the resulting reconstruction error is also on the order of spl minus 100 db several examples are included

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

a linear approximation method for solving a special class of the chance constrained programming problem abstract this article presents a technique which seeks the optimum or near optimum solution of a nonlinear problem by searching through the set of nondominated solutions of the bicriterion linear programming blp problem an approximation formula for constructing two linear objective functions based on the nonlinear objective function of the equivalent deterministic form edf of the stochastic programming model is presented it is proved that a finite number of nondominated solutions need to be investigated before the algorithm converges to the optimum solution point each nondominated solution point is the optimum solution of a linear problem over the feasible region of the nonlinear problem along with an added compromise constraint this compromise constraint is a hyperplane passing through the ideal solution point of the blp problem the most attractive feature of this new practical technique is its ability to search for the optimal solution without examining the whole set of feasible solutions

subband coded image reconstruction for lossy packet networks transmission of digital subband coded images over lossy packet networks presents a reconstruction problem at the decoder this paper presents two techniques for reconstruction of lost subband coefficients one for low frequency coefficients and one for high frequency coefficients the low frequency reconstruction algorithm is based on inherent properties of the hierarchical subband decomposition to maintain smoothness and exploit the high intraband correlation a cubic interpolative surface is fit to known coefficients to interpolate lost coefficients accurate edge placement crucial for visual quality is achieved by adapting the interpolation grid in both the horizontal and vertical directions as determined by the edges present an edge model is used to characterize the adaptation and a quantitative analysis of this model demonstrates that edges can be identified by simply examining the high frequency bands without requiring any additional processing of the low frequency band high frequency reconstruction is performed using linear interpolation which provides good visual performance as well as maintains properties required for edge placement in the low frequency reconstruction algorithm the complete algorithm performs well on loss of single coefficients vectors and small blocks and is therefore applicable to a variety of source coding techniques

modeling analysis and optimum design of quantized m band filter banks this paper provides a rigorous modeling and analysis of quantization effects in m band subband codecs followed by optimal filter bank design and compensation the codec is represented by a polyphase decomposition of the analysis synthesis filter banks and an embedded nonlinear gain plus additive noise model for the pdf optimized scalar quantizers we construct an equivalent time invariant but nonlinear structure operating at the slow clock rate that allows us to compute the exact expression for the mean square quantization error in the reconstructed output this error is shown to consist of two components a distortion component and a dominant random noise component uncorrelated with the input signal we determine the optimal paraunitary and biorthogonal fir filter coefficients compensators and integer bit allocation to minimize this mse subject to the constraints of filter length average bit rate and perfect reconstruction pr in the absence of quantizers the biorthogonal filter bank results in a smaller mse but the filter coefficients are very sensitive to signal statistics and to average bit constraints by comparison the paraunitary structure is much more robust we also show that the null compensated design that eliminates the distortion component is more robust than the optimally compensated case that minimizes the total mse but only at nominal conditions both modeling and optimal design are validated by simulation in the two channel case

the design and use of steerable filters the authors present an efficient architecture to synthesize filters of arbitrary orientations from linear combinations of basis filters allowing one to adaptively steer a filter to any orientation and to determine analytically the filter output as a function of orientation steerable filters may be designed in quadrature pairs to allow adaptive control over phase as well as orientation the authors show how to design and steer the filters and present examples of their use in the analysis of orientation and phase angularly adaptive filtering edge detection and shape from shading one can also build a self similar steerable pyramid representation the same concepts can be generalized to the design of 3 d steerable filters

a new approximation method for time delay systems we develop a rational approximant b sub n sup spl alpha of e sup ds and make a detailed analysis on the approximant b sub n sup spl alpha g of e sup ds g where g spl isin rl sup 2 we prove l sup p 2 spl infin error convergence and provide corresponding error bounds explicitly comparative study with other approximants is performed in order to make clear the properties of b sub n sup spl alpha making full use of its recursive structure b sub n sup spl alpha is shown to be a suitable approximant for a class of h sup spl infin problems involving time delay

probabilistic programming for nitrate pollution control comparing different probabilistic constraint approximations abstract agricultural nitrate emissions within a river catchment are due to rainfall and other sources of natural variation uncertain a regulator aiming to reduce nitrate emissions into surface and groundwater faces a trade off between reliability in achieving emission standards and the cost of compliance to agriculture this paper explores this trade off by comparing different assumptions about the probability distribution of nitrate emissions and thus the probabilistic constraint included in the catchment model three categories of probabilistic constraints are considered 1 non parametric 2 normal and 3 lognormal the results indicate that the restrictiveness of the non parametric assumption could lead to a significant reduction in profit relative to the normal and lognormal the lognormal assumption although it is theoretically correct cannot be generalised to the case of correlated emissions however ignoring the dependence between different sources of nitrate emissions introduces more bias than mis specifying their distribution therefore a probabilistic constraint based on a correlated normal distribution of emissions gives the best approximation for nitrate emissions in this study

image compression with variable block size segmentation high quality variable rate image compression is achieved by segmenting an image into regions of different sizes classifying each region into one of several perceptually distinct categories and using a distinct coding procedure for each category segmentation is performed with a quadtree data structure by isolating the perceptually more important areas of the image into small regions and separately identifying larger random texture blocks since the important regions have been isolated the remaining parts of the image can be coded at a lower rate than would be otherwise possible high quality coding results are achieved at rates between 0 35 and 0 7 b p depending on the nature of the original image and satisfactory results have been obtained at 0 25 b p

prioritized dct for compression and progressive transmission of images an approach is based on the block discrete cosine transform dct the novelty of this approach is that the transform coefficients of all image blocks are coded and transmitted in absolute magnitude order the resulting ordered by magnitude transmission is accomplished without sacrificing coding efficiency by using partition priority coding coding and transmission are adaptive to the characteristics of each individual image and therefore very efficient another advantage of this approach is its high progression effectiveness since the largest transform coefficients that capture the most important characteristics of images are coded and transmitted first this method is well suited for progressive image transmission further compression of the image data is achieved by multiple distribution entropy coding a technique based on arithmetic coding experiments show that the approach compares favorably with previously reported dct and subband image codecs

estimating the distribution of a sum of independent lognormal random variables four methods that can be used to approximate the distribution function df of a sum of independent lognormal random variables rvs are compared the aim is to determine the best method to compute the df considering both accuracy and computational effort the investigation focuses on values of the db spread valid for practical problems in wireless transmission where is between 6 db and 12 db contrary to some previous reports our results show that the simpler wilkinson s approach gives a more accurate estimate in some cases of interest than schwartz and yeh s 1982 approach

space frequency quantization for wavelet image coding a new class of image coding algorithms coupling standard scalar quantization of frequency coefficients with tree structured quantization related to spatial structures has attracted wide attention because its good performance appears to confirm the promised efficiencies of hierarchical representation this paper addresses the problem of how spatial quantization modes and standard scalar quantization can be applied in a jointly optimal fashion in an image coder we consider zerotree quantization zeroing out tree structured sets of wavelet coefficients and the simplest form of scalar quantization a single common uniform scalar quantizer applied to all nonzeroed coefficients and we formalize the problem of optimizing their joint application we develop an image coding algorithm for solving the resulting optimization problem despite the basic form of the two quantizers considered the resulting algorithm demonstrates coding performance that is competitive often outperforming the very best coding algorithms in the literature

controller design for distributed systems based on hankel norm approximations a procedure for obtaining a finite dimensional reduced order model for a class of distributed systems is developed it is based on a combination of a modal approximation and an optimal hankel norm approximation and the approximation error can be accurately predicted the reduced order model can be used to design a precompensator for the original system as its performance and robust stability characteristics can be deduced from the reduced order model and finitely many modal parameters the procedure is applied to a parabolic system

estimated stochastic programs with chance constraints we will consider a non parametric estimation procedure for chance constrained stochastic programs where the random parameters appear on the right hand side of linear constraints for the decision variable the assumed independence of the components of the random right hand side data results in stochastic programs with a separability structure in the constraints we estimate the unknown probability distribution of the random right hand side data via isotonic regression estimates of increasing hazard rates our choice of the estimates was motivated by the relationship between logarithmic concave measures and increasing hazard rate distributions we establish large deviation results for optimal values and optimal solution sets of the estimated programs finally we discuss the numerical treatment of the estimated chance constrained programs and report on a test run

an asymptotic modal observer for linear autonomous time lag systems a full state vector observer is derived for a class of linear autonomous time lag systems represented by differential equations the major features of the approach are 1 an observer is constructed just for the set of unstable or poorly damped modes of the delayed system once they have been determined and 2 the design is accomplished by using a partial fraction expansion separating the unstable part from the system and then applying well known finite dimensional state vector techniques a procedure for the construction is given along with some numerical results to illustrate the simplicity of the observer

transform trellis coding of images at low bit rates a transform trellis coding scheme is used to encode images at rates below 1 b pel resulting in high snr values and very good subjective performance a discrete cosine transform dct is used to decorrelate the data samples and a trellis encoder is used to encode the transformed coefficients to overcome image nonstationarity a clustering algorithm is used to segment the transformed image into distinct regions and a separate trellis diagram is then constructed for each cluster to further improve the image quality particularly to reduce the blocking effect a scalar quantizer is used to quantize large magnitude coefficients of the error image in the transform domain the performance of the proposed scheme is found to be better than that of other recently reported schemes

cyclostationary modeling analysis and optimal compensation of quantization errors in subband codecs the paper is concerned with the analysis and modeling of the effects of quantization of subband signals in subband codecs using cyclostationary representations the authors derive equations for the autocorrelation and power spectral density psd of the reconstructed signal y n in terms of the analysis synthesis filters the psd of the input and the pdf optimized quantizer model formulas for the mean square error mse and for compaction gain are obtained in terms of these parameters the authors constrain the filter bank to be perfect reconstruction pr but not necessarily paraunitary in the absence of quantization and transmission errors these formulas set the stage for filter optimization maximization of compaction gain and minimization of mse subject to pr and bit constraints optimal filters are designed optimal compensation is performed and the theoretical results are confirmed with simulations the floating point quantizer wherein only the mantissa is uniformly quantized is also analyzed and compared with the fixed point pdf optimized filter bank for high bit rates their performance is comparable

lagrange multiplier approaches to the design of two channel perfect reconstruction linear phase fir filter banks the authors present two approaches to the design of two channel perfect reconstruction linear phase finite impulse response fir filter banks both approaches analyze and design the impulse responses of the analysis filter bank directly the synthesis filter bank is then obtained by simply changing the signs of odd order coefficients in the analysis filter bank the approach deals with unequal length filter banks by designing the lower length filters first one can take advantage of the fact that the number of variables for designing the higher length filters is more than the number of perfect reconstruction constraint equations the second approach generalizes the first and covers the design for all parts of linear phase perfect reconstruction constraint equations

image coding using wavelet transforms and entropy constrained trellis coded quantization the discrete wavelet transform has recently emerged as a powerful technique for decomposing images into various multi resolution approximations multi resolution decomposition schemes have proven to be very effective for high quality low bit rate image coding in this work we investigate the use of entropy constrained trellis coded quantization ectcq for encoding the wavelet coefficients of both monochrome and color images ectcq is known as an effective scheme for quantizing memoryless sources with low to moderate complexity the ectcq approach to data compression has led to some of the most effective source codes found to date for memoryless sources performance comparisons are made using the classical quadrature mirror filter bank of johnston and nine tap spline filters that were built from biorthogonal wavelet bases we conclude that the encoded images obtained from the system employing nine tap spline filters are marginally superior although at the expense of additional computational burden excellent peak signal to noise ratios are obtained for encoding monochrome and color versions of the 512 spl times 512 lenna image comparisons with other results from the literature reveal that the proposed wavelet coder is quite competitive

optimal filter banks for signal reconstruction from noisy subband components conventional design techniques for analysis and synthesis filters in subband processing applications guarantee perfect reconstruction of the original signal from its subband components the resulting filters however lose their optimality when additive noise due for example to signal quantization disturbs the subband sequences we propose filter design techniques that minimize the reconstruction mean squared error mse taking into account the second order statistics of signals and noise in the case of either stochastic or deterministic signals a novel recursive pseudo adaptive algorithm is proposed for efficient design of these filters analysis and derivations are extended to 2 d signals and filters using powerful kronecker product notation a prototype application of the proposed ideas in subband coding is presented simulations illustrate the superior performance of the proposed filter banks versus conventional perfect reconstruction filters in the presence of additive subband noise

theory and design of dyadic subband tree structures with embedded pdf optimized quantizers we develop a methodology for the analysis of signal quantization effects in critically sampled dyadic subband tree structures using a nonlinear gain plus additive noise model for the probability density function pdf optimized quantizer we constrain the two band nonquantized and uncompensated structure at each level to be perfect reconstruction pr we develop an equivalent uniform filter bank followed by its polyphase structure described by primitive submatrices and compute a rigorously correct mean squared error mse in the frequency domain using cyclostationary concepts in terms of 1 the allocated quantizer bits 2 the filter coefficients 3 an embedded compensation parameter vector this mse is then minimized over all three items above our optimization method is applied to the specific case of a four channel dyadic tree with average bit rate constraint this tree is represented by an eight channel polyphase equivalent whose interchannel signals are correlated we show how to represent rigorously the correlation of random noise between channels due to the embedded quantizers our design of paraunitary and biorthogonal structures with identical and nonidentical stages is performed compared and validated by computer simulation under the assumption of uncorrelated cross band noise the nonidentical stage biorthogonal filter bank turned out to have the best performance in mse sense but the most robust structure is the nonidentical stage paraunitary filter bank

optimal pyramidal decomposition for progressive multidimensional signal coding using optimal quantizers optimal hierarchical coding is sought for progressive or scalable multidimensional signal transmission by minimizing the variance of the error difference between the original image and its lower resolution renditions the optimal according to the above criterion pyramidal coders are determined for images quantized using the optimal vector lloyd max quantizers a rigorous general statistical model of a vector lloyd max quantizer is used consisting of a linear time invariant filter followed by additive noise uncorrelated with the input given arbitrary analysis filters the optimal synthesis filters are found the optimal analysis filters are subsequently determined leading to formulas for globally optimal structures for pyramidal multidimensional signal decompositions these structures produce replicas of the original image which at lower resolutions retain as much similarity to the original as possible this is highly useful for the progressive coding of two or three dimensional 2 d or 3 d images needed in applications such as fast browsing through image databases furthermore the minimization of the variance of the error image leads to minimization of the variance of the quantization noise for this image and hence to its optimally efficient compression experimental results illustrate the implementation and performance of the optimal pyramids in application for the coding of still 2 d images

integer wavelet transform for embedded lossy to lossless image compression the use of the discrete wavelet transform dwt for embedded lossy image compression is now well established one of the possible implementations of the dwt is the lifting scheme ls because perfect reconstruction is granted by the structure of the ls nonlinear transforms can be used allowing efficient lossless compression as well the integer wavelet transform iwt is one of them this is an interesting alternative to the dwt because its rate distortion performance is similar and the differences can be predicted this topic is investigated in a theoretical framework a model of the degradations caused by the use of the iwt instead of the dwt for lossy compression is presented the rounding operations are modeled as additive noise the noise are then propagated through the ls structure to measure their impact on the reconstructed pixels this methodology is verified using simulations with random noise as input it predicts accurately the results obtained using images compressed by the well known ezw algorithm experiment are also performed to measure the difference in terms of bit rate and visual quality this allows to a better understanding of the impact of the iwt when applied to lossy image compression

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

two fast architectures for the direct 2 d discrete wavelet transform we propose two architectures for the direct two dimensional 2 d discrete wavelet transform dwt the first one is based on a modified recursive pyramid algorithm mrpa and performs a nonstandard decomposition i e mallat s 1989 tree of an n spl times n image in approximately 2n sup 2 3 clock cycles ccs this result consistently speeds up other known architectures that commonly need approximately n sup 2 ccs furthermore the proposed architecture is simpler than others in terms of hardware complexity subsequently we show how symmetric anti symmetric properties of linear phase wavelet filter bases can be exploited in order to further reduce the vlsi area this is used to design a second architecture that provides one processing unit for each level of decomposition pipelined approach and performs a decomposition in approximately n sup 2 2 ccs in many practical cases even this architecture is simpler than general mrpa based devices having only one processing unit

a generalized parametric pr qmf design technique based on bernstein polynomial approximation a generalized parametric perfect reconstruction quadrature mirror filter pr qmf design technique based on bernstein polynomial approximation in the magnitude square domain is presented the parametric nature of this solution provides useful insights to the pr qmf problem several well known orthonormal wavelet filters pr qmfs are shown to be the special cases of the proposed technique energy compaction performances of a few popular signal decomposition techniques are presented for ar 1 signal sources it is observed that the hierarchical qmf filter banks considered outperform the block transforms as expected

optimal construction of subband coders using lloyd max quantizers a new method is presented for the analysis of the effects of lloyd max quantization in subband filterbanks and for the optimal design of such filterbanks a rigorous statistical model of a vector lloyd max quantizer is established first consisting of a linear time invariant filter followed by additive noise uncorrelated with the input on the basis of this model an expression for this variance of the error of a subband coder using lloyd max quantizers is explicitly determined given analysis filters that statistically separate the subbands it is shown that this variance is minimized if the synthesis filters are chosen which mould achieve perfect reconstruction in lossless coding the globally optimum of such a filterbank minimizing the coder error variance is further obtained by proper choice of its analysis filters an alternative design method is also evaluated and optimized in this the errors correlated with the signal are set to zero leaving a random error residue uncorrelated with the signal this design method is optimized by choosing the analysis filters so as to minimize the random error variance the results are evaluated experimentally in the realistic setting of a logarithmically split subband image coding scheme

a provisioning problem with stochastic payments abstract we consider the problem of determining the minimal requirement one must establish in order to meet a series of future random payments it is shown in a very general setting that this problem can be recast as a chance constrained model and how the technique of sample average approximation can be employed to find solutions we also use comonotonic theory to analyze analytical approximations in a restricted gaussian setting our numerical illustrations demonstrate that the sample average approximation is a viable and efficient way to solve the stated problem generally and outperforms the analytical approximations in passing we present a result that is related to stein s famous lemma stein 1981 and is of interest in itself

coding gain in paraunitary analysis synthesis systems a formal proof that bit allocation results hold for the entire class of paraunitary subband coders is presented the problem of finding an optimal paraunitary subband coder so as to maximize the coding gain of the system is discussed the bit allocation problem is analyzed for the case of the paraunitary tree structured filter banks such as those used for generating orthonormal wavelets the even more general case of nonuniform filter banks is also considered in all cases it is shown that under optimal bit allocation the variances of the errors introduced by each of the quantizers have to be equal expressions for coding gains for these systems are derived

minimax design of two channel nonuniform division filterbanks using iir allpass filters the design of two channel linear phase nonuniform division filter ndf banks constructed by infinite impulse response iir digital allpass filters dafs in the sense of l sub spl infin error criteria is considered first the theory of two channel ndf bank structures using two iir dafs is developed then the design problem is appropriately formulated to result in a simple optimization problem utilizing a variant of karmarkar s algorithm we can efficiently solve the optimization problem through a frequency sampling and iterative approximation method to find the coefficients for the iir dafs the resulting two channel ndf banks can possess approximately linear phase response without magnitude distortion the effectiveness of the proposed technique is achieved by forming an appropriate chebyshev approximation of a desired phase response and then to find its solution from a linear subspace in a few iterations several simulation examples are presented for illustration and comparison

significance linked connected component analysis for wavelet image coding the success in wavelet image coding is mainly attributed to a recognition of the importance of data organization and representation there have been several very competitive wavelet coders developed namely shapiro s 1993 embedded zerotree wavelets ezw servetto et al s 1995 morphological representation of wavelet data mrwd and said and pearlman s see ieee trans circuits syst video technol vol 6 p 245 50 1996 set partitioning in hierarchical trees spiht we develop a novel wavelet image coder called significance linked connected component analysis slcca of wavelet coefficients that extends mrwd by exploiting both within subband clustering of significant coefficients and cross subband dependency in significant fields extensive computer experiments on both natural and texture images show convincingly that the proposed slcca outperforms ezw mrwd and spiht for example for the barbara image at 0 25 b pixel slcca outperforms ezw mrwd and spiht by 1 41 db 0 32 db and 0 60 db in psnr respectively it is also observed that slcca works extremely well for images with a large portion of texture for eight typical 256 spl times 256 grayscale texture images compressed at 0 40 b pixel slcca outperforms spiht by 0 16 db 0 63 db in psnr this performance is achieved without using any optimal bit allocation procedure thus both the encoding and decoding procedures are fast

region adaptive subband image coding we present a region adaptive subband image coding scheme using the statistical properties of image subbands for various subband decompositions motivated by analytical results obtained when the input signal to the subband decomposition is a unit step function we analyze the energy packing properties toward the lower frequency subbands edges and the dependency of energy distribution on the orientation of the edges in subband decomposed images based on these investigations and ideal analysis synthesis filtering done in the frequency domain the region adaptive subband image coding scheme extracts suitably shaped regions in each subband and then uses adaptive entropy constrained quantizers for different regions under the assumption of a generalized gaussian distribution for the image subbands we also address the problem of determining an optimal subband decomposition among all possible decompositions experimental results show that visual degradations in the reconstructed image are negligible at a bit rate of 1 0 b pel and reasonable quality images are obtainable at rates as low as 0 25 b pel

visibility of wavelet quantization noise the discrete wavelet transform dwt decomposes an image into bands that vary in spatial frequency and orientation it is widely used for image compression measures of the visibility of dwt quantization errors are required to achieve optimal compression uniform quantization of a single band of coefficients results in an artifact that we call dwt uniform quantization noise it is the sum of a lattice of random amplitude basis functions of the corresponding dwt synthesis filter we measured visual detection thresholds for samples of dwt uniform quantization noise in y cb and cr color channels the spatial frequency of a wavelet is r2 sup spl lambda where r is the display visual resolution in pixels degree and spl lambda is the wavelet level thresholds increase rapidly with wavelet spatial frequency thresholds also increase from y to cr to cb and with orientation from lowpass to horizontal vertical to diagonal we construct a mathematical model for dwt noise detection thresholds that is a function of level orientation and display visual resolution this allows calculation of a perceptually lossless quantization matrix for which all errors are in theory below the visual threshold the model may also be used as the basis for adaptive quantization schemes

l approximation and nuclearity of delay systems abstract the l convergence of partial fraction decompositions of single input single output delay systems is studied conditions for the nuclearity of such systems are derived and examples given

l approximation of a parabolic system regarded as a delay system abstract we present an approach to the problem of finding an l approximant of the infinite dimensional system describing the diffusion of heat in a wall we show that this system can be regarded as a delay system with laplace variable s we are able to get results established in zwart et al 1988 about partial fraction expansion for delay systems achieved by some adjustment to the specificities of our particular case the determination of an l approximant is realised in two steps using the optimal hankel norm approximation

construction of optimal subband coders using optimized and optimal quantizers a method is presented for the optimization of arbitrary quantizers by use of a compensating postfilter it is shown that the resulting optimized quantizers fit the model of a linear time invariant filter followed by additive noise uncorrelated with the input which also characterizes the optimal lloyd max quantizers on the basis of this model an expression for the variance of the error of a subband coder using optimized quantizers is explicitly determined given analysis filters which statistically separate the subbands it is shown that this variance is minimized if these synthesis filters are chosen which would achieve perfect reconstruction in lossless coding the globally optimum filter bank minimizing the coder error variance is further obtained by proper choice of its analysis filters a novel method for the determination of optimal bit allocation to subbands of the filter banks with optimized quantizers is also developed the results are evaluated experimentally by comparison of the optimum uniformly split subband image coding scheme to classical logarithmically split filter bank wavelet coding methods

approximation of unstable infinite dimensional systems using coprime factors abstract the effectiveness of comprime factor techniques in l 2 and l model reduction of unstable linear systems is analysed asymptotic estimates are given of the achievable error in the stable and unstable parts of the approximate system measured in a number of different norms some involving the associated hankel operators the chordal metric is introduced as a measure of approximation and is shown to yield the graph topology finally it is deduced that asymptotically optimal l 2 and l convergence rates can be obtained for a large class of unstable systems

optimal transforms for multispectral and multilayer image coding multispectral images are composed of a series of images at differing optical wavelengths since these images can be quite large they invite efficient source coding schemes for reducing storage and transmission requirements because multispectral images include a third spectral dimension with nonstationary behavior these multilayer data sets require specialized coding techniques the authors develop both a theory and specific methods for performing optimal transform coding of multispectral images the theory is based on the assumption that a multispectral image may be modeled as a set of jointly stationary gaussian random processes therefore the methods may be applied to any multilayer data set which meets this assumption although the authors do not assume the autocorrelation has a separable form they show that the optimal transform for coding has a partially separable structure in particular they prove that a coding scheme consisting of a frequency transform within each layer followed by a separate kl transform across the layers at each spatial frequency is asymptotically optimal as the block size becomes large two simplifications of this method are also shown to be asymptotically optimal if the data can be assumed to satisfy additional constraints the proposed coding techniques are then implemented using subband filtering methods and the various algorithms are tested on multispectral images to determine their relative performance characteristics

image filtering using multiresolution representations it is shown how multiresolution representations can be used for filter design and implementation these representations provide a coarse frequency decomposition of the image which forms the basis for two filtering techniques the first method based on image pyramids is used for approximating the convolution of an image with a given mask in this technique a filter is designed using a least squares procedure based on filters synthesized from the basic pyramid equivalent filters the second method is an adaptive noise reduction algorithm an optimally filtered image is synthesized from the multiresolution levels which in this case are maintained at the original sampling density individual pixels of the image representation are linearly combined under a minimum mean square error criterion this uses a local signal to noise ratio estimate to provide the best compromise between noise removal and resolution loss

the laplacian pyramid as a compact image code we describe a technique for image encoding in which local operators of many scales but identical shape serve as the basis functions the representation differs from established techniques in that the code elements are localized in spatial frequency as well as in space pixel to pixel correlations are first removed by subtracting a lowpass filtered copy of the image from the image itself the result is a net data compression since the difference or error image has low variance and entropy and the low pass filtered image may represented at reduced sample density further data compression is achieved by quantizing the difference image these steps are then repeated to compress the low pass image iteration of the process at appropriately expanded scales generates a pyramid data structure the encoding process is equivalent to sampling the image with laplacian operators of many scales thus the code tends to enhance salient image features a further advantage of the present code is that it is well suited for many image analysis tasks as well as for image compression fast algorithms are described for coding and decoding

robust detection in nominally laplace noise the authors consider the robust detection of a known constant signal in additive mutually independent and identically distributed noise which is nominally laplace employing the classical saddlepoint methodology of huber 1951 they specify the form of the robust detector and obtain closed form results which allow for the analysis of the performance of the robust detector they show via examples that the robustness can entail a considerable cost in detector performance in addition they compare the performance of the robust detector to that of the neyman pearson detector for examples where the noise is laplace and also where the noise is least favorable for the given detector

three dimensional subband coding of video we describe and show the results of video coding based on a three dimensional 3 d spatio temporal subband decomposition the results include a 1 mbps coder based on a new adaptive differential pulse code modulation scheme adpcm and adaptive bit allocation this rate is useful for video storage on cd rom coding results are also shown for a 384 kbps rate that are based on adpcm for the lowest frequency band and a new form of vector quantization geometric vector quantization gvq for the data in the higher frequency bands gvq takes advantage of the inherent structure and sparseness of the data in the higher bands results are also shown for a 128 kbps coder that is based on an unbalanced tree structured vector quantizer utsvq for the lowest frequency band and gvq for the higher frequency bands the results are competitive with traditional video coding techniques and provide the motivation for investigating the 3 d subband framework for different coding schemes and various applications

image subband coding using context based classification and adaptive quantization adaptive compression methods have been a key component of many proposed subband or wavelet image coding techniques this paper deals with a particular type of adaptive subband image coding where we focus on the image coder s ability to adjust itself on the fly to the spatially varying statistical nature of image contents this backward adaptation is distinguished from more frequently used forward adaptation in that forward adaptation selects the best operating parameters from a predesigned set and thus uses considerable amount of side information in order for the encoder and the decoder to operate with the same parameters specifically we present backward adaptive quantization using a new context based classification technique which classifies each subband coefficient based on the surrounding quantized coefficients we couple this classification with online parametric adaptation of the quantizer applied to each class a simple uniform threshold quantizer is employed as the baseline quantizer for which adaptation is achieved our subband image coder based on the proposed adaptive classification quantization idea exhibits excellent rate distortion performance in particular at very low rates for popular test images it is comparable or superior to most of the state of the art coders in the literature

the standard h sub spl infin problem in systems with a single input delay the standard h sub spl infin problem is solved for lti systems with a single pure input lag the solution is based on state space analysis mixing a finite dimensional and an abstract evolution model utilizing the relatively simple structure of these distributed systems the associated operator riccati equations are reduced to a combination of two algebraic riccati equations and one differential riccati equation over the delay interval the results easily extend to finite time and time varying problems where the algebraic riccati equations are substituted by differential riccati equations over the process time duration

image compression via joint statistical characterization in the wavelet domain we develop a probability model for natural images based on empirical observation of their statistics in the wavelet transform domain pairs of wavelet coefficients corresponding to basis functions at adjacent spatial locations orientations and scales are found to be non gaussian in both their marginal and joint statistical properties specifically their marginals are heavy tailed and although they are typically decorrelated their magnitudes are highly correlated we propose a markov model that explains these dependencies using a linear predictor for magnitude coupled with both multiplicative and additive uncertainties and show that it accounts for the statistics of a wide variety of images including photographic images graphical images and medical images in order to directly demonstrate the power of the model we construct an image coder called epwic embedded predictive wavelet image coder in which subband coefficients are encoded one bitplane at a time using a nonadaptive arithmetic encoder that utilizes conditional probabilities calculated from the model bitplanes are ordered using a greedy algorithm that considers the mse reduction per encoded bit the decoder uses the statistical model to predict coefficient values based on the bits it has received despite the simplicity of the model the rate distortion performance of the coder is roughly comparable to the best image coders in the literature

second order statistical characterization of the filter bank and its elements this correspondence proposes an alternative scheme for characterizing the wide sense cyclostationary wscs processes and applies it for the analysis of the filter banks whose output is wscs for wide sense stationary and wscs inputs the proposed representation clearly illustrates the kind of transformation taking place in multiscale stochastic systems these relationships are extended to the filter bank to make clear the effect of the various stages of the filter bank on wscs processes

an optimal design procedure for intraband vector quantized subband coding subband coding with vector quantization is addressed in this paper forming the data vectors from both between and within the subbands is considered the former of these two schemes is referred to as interband coding and the latter as intraband coding interband coder design is relatively straightforward since the design of the single codebook involved follows readily from a representative set of interband data vectors intraband coder design is more complicated since it entails the selection of a vector dimension and a bit rate for each subband the main contribution of this work is an optimal methodology for intraband subband vector quantizer design the problem formulation includes constraints on the bit rate and the encoding complexity and is solved with nonlinear programming methods subband vector quantization image coding in conjunction with a human visual system model is thoroughly investigated results of a large number of experiments indicate that the optimal intraband coder yields superior results from quantitative as well as subjective points of view than the interband coder for comparable bit rates this improvement becomes more pronounced as the computational complexity of the intraband encoder is allowed to increase

on the rate distortion efficiency of subband coding it is shown that for the realizable subband coding of a wide sense stationary gaussian source with the implied separate encoding of the subband signals the encoding performance is generally inferior to the rate distortion function of the source it is established that for small encoding distortion except for special cases the subband coding is generally suboptimum

on the study of four parallelogram filter banks the most commonly used 2 d filter banks are separable filter banks which can be obtained by cascading two 1 d filter banks in the form of a tree the supports of the analysis and synthesis filters in the separable systems are unions of four rectangles the natural nonseparable generalization of such supports are those that are unions of four parallelograms we study four parallelogram filter banks which is the class of 2 d filter banks in which the supports of the analysis and synthesis filters consist of four parallelograms for a given a decimation matrix there could be more than one possible configuration the collection of passbands of the analysis filters various types of configuration are constructed for four parallelogram filter banks conditions on the configurations are derived such that good design of analysis and synthesis filters are possible we see that there is only one category of these filter banks the configurations of four parallelogram filter banks in this category can always be achieved by designing filter banks of low design cost

partial fraction expansions for delay systems abstract partial fraction decompositions for single input single output delay systems are studied the results have application in rational l approximations which play an important role in robust compensator design for delay systems