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

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

positive 2 1 dimensional exact shock waves solutions to the broadwell model the exact solutions for the discrete boltzmann models are sums of similarity shock waves at least three for the 2 1 dimensional solutions two spatial coordinates here for the three dimensional six velocities broadwell model shock waves solutions are also constructed the difficult problem is the determination of solutions with positive density it is proven that in the arbitrary parameters space from which the solutions are constructed there exists a domain leading to positivity as an illustration a numerical example is discussed in the spatial coordinate plane both shock waves along one axis and bumps along the other are observed the movement of these structures with time is discussed

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

oriented texture completion by am fm reaction diffusion we provide an automated method to repair broken occluded oriented image textures our approach is based on partial differential equations pdes and am fm image modeling reconstruction of the texture occurs via simultaneous pde generated diffusion and reaction in the diffusion process the image is adaptively smoothed preserving important boundaries and features the reaction process produces the reconstructed textural information in the occluded image regions gabor 1946 filters are designed and used in the reaction process using an am fm dominant component analysis an am fm model of the texture image is constructed making it possible to localize the reaction filters spatio spectrally in contrast to previous disocclusion techniques that depend on interpolation on continuity of the connected components within the image level sets or on texture estimation the reaction diffusion process proposed here yields a seamless transition between the recreated region and the unoccluded image regions using am fm dominant component analysis we avoid the ad hoc parameter selection typified with other reaction diffusion approaches as a useful example we focus on the repair of broken occluded fingerprints we also treat several exemplary natural textures to demonstrate the technique s generality

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

am fm energy detection and separation in noise using multiband energy operators this paper develops a multiband or wavelet approach for capturing the am fm components of modulated signals immersed in noise the technique utilizes the recently popularized nonlinear energy operator psi s s sup 2 ss to isolate the am fm energy and an energy separation algorithm esa to extract the instantaneous amplitudes and frequencies it is demonstrated that the performance of the energy operator esa approach is vastly improved if the signal is first filtered through a bank of bandpass filters and at each instant analyzed via psi and the esa using the dominant local channel response moreover it is found that uniform worst case performance across the frequency spectrum is attained by using a constant q or multiscale wavelet like filter bank the elementary stochastic properties of psi and of the esa are developed first the performance of psi and the esa when applied to bandpass filtered versions of an am fm signal plus noise combination is then analyzed the predicted performance is greatly improved by filtering if the local signal frequencies occur in band these observations motivate the multiband energy operator and esa approach ensuring the in band analysis of local am pm energy in particular the multi bands must have the constant q or wavelet scaling property to ensure uniform performance across bands the theoretical predictions and the simulation results indicate that improved practical strategies are feasible for tracking and identifying am fm components in signals possessing pattern coherencies manifested as local concentrations of frequencies

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

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

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

analyzing image structure by multidimensional frequency modulation we develop a mathematical framework for quantifying and understanding multidimensional frequency modulations in digital images we begin with the widely accepted definition of the instantaneous frequency vector if as the gradient of the phase and define the instantaneous frequency gradient tensor ifgt as the tensor of component derivatives of the if vector frequency modulation bounds are derived and interpreted in terms of the eigendecomposition of the ifgt using the ifgt we derive the ordinary differential equations odes that describe image flowlines we study the diagonalization of the odes of multidimensional frequency modulation on the ifgt eigenvector coordinate system and suggest that separable transforms can be computed along these coordinates we illustrate these new methods of image pattern analysis on textured and fingerprint images we envision that this work will find value in applications involving the analysis of image textures that are nonstationary yet exhibit local regularity examples of such textures abound in nature

2d and 3d exact shock wave solutions with specular reflection to the discrete boltzmann models the authors construct exact solutions which are 2d two spatial coordinates for the four velocity planar model 3d for the cubic broadwell models and p dimensional for the p dimensional hypercubic discrete boltzmann model these solutions are shock waves which satisfy a specular reflection boundary condition at a wall

localized measurement of emergent image frequencies by gabor wavelets the authors derive implement and demonstrate a computational approach for the measurement of emergent image frequencies measuring emergent signal frequencies requires spectral measurements accurate in both frequency and time or space conflicting requirements that are shown to be balanced by a generalized uncertainty relationship such spectral measurements can be obtained from the responses of multiple wavelet like channel filters that sample the signal spectrum and that yield a locus of possible solutions for each locally emergent frequency it is shown analytically that this locus of solutions is maximally localized in both space and frequency if the channel filters used are gabor wavelets a constrained solution is obtained by imposing a stabilizing term that develops naturally from the assumptions on the signal the measurement of frequencies is then cast as an ill posed extremum problem regularized by the stabilizing term leading to an iterative constraint propagation algorithm the technique is demonstrated by application to a variety of 2 d textured images

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

discrete velocity models of the boltzmann equation a survey on the mathematical aspects of the theory discrete velocity models of the boltzmann equation are of considerable conceptual interest in the kinetic theory of gases and at the same time a fascinating mathematical subject the last decade has seen a lot of work on this subject which is reviewed here we put an emphasis on mathematical aspects in particular the global existence question qualitative properties of solutions explicit solutions and the fluid dynamical limit the mechanical background is discussed more concisely in part i numerous contributions concerning other questions are outlined we try to give a complete reference list up to and including 1985

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

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

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

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 comparison of the squared energy and teager kaiser operators for short term energy estimation in additive noise time frequency distributions that evaluate the signal s energy content both in the time and frequency domains are indispensable signal processing tools especially for nonstationary signals various short time energy computation schemes are used in practice including the mean squared amplitude and teager kaiser energy approaches herein we focus primarily on the short and medium term properties of these two energy estimation schemes as well as on their performance in the presence of additive noise to facilitate this analysis and generalize the approach we use a harmonic noise model to approximate the noise component the error analysis is conducted both in the continuous and discrete time domains deriving similar conclusions the estimation errors are measured in terms of normalized deviations from the expected signal energy and are shown to greatly depend on both the signals spectral content and the analysis window length when medium and long term analysis windows are employed the teager kaiser energy operator is proven superior to the common squared energy operator provided that the spectral content of the noise is more lowpass than the corresponding signal content and vice versa however for shorter window lengths the teager kaiser operator always outperforms the squared energy operator the theoretical results are experimentally verified for synthetic signals finally the performance of the proposed energy operators is evaluated for short term analysis of noisy speech signals and the implications for speech processing applications are outlined

multidimensional quasi eigenfunction approximations and multicomponent am fm models we develop multicomponent am fm models for multidimensional signals the analysis is cast in a general n dimensional framework where the component modulating functions are assumed to lie in certain sobolev spaces for both continuous and discrete linear shift invariant lsi systems with am fm inputs powerful new approximations are introduced that provide closed form expressions for the responses in terms of the input modulations the approximation errors are bounded by generalized energy variances quantifying the localization of the filter impulse response and by sobolev norms quantifying the smoothness of the modulations the approximations are then used to develop novel spatially localized demodulation algorithms that estimate the am and fm functions for multiple signal components simultaneously from the channel responses of a multiband linear filterbank used to isolate components two discrete computational paradigms are presented dominant component analysis estimates the locally dominant modulations in a signal which are useful in a variety of machine vision applications while channelized components analysis delivers a true multidimensional multicomponent signal representation we demonstrate the techniques on several images of general interest in practical applications and obtain reconstructions that establish the validity of characterizing images of this type as sums of locally narrowband modulated components

on amplitude and frequency demodulation using energy operators it is shown that the nonlinear energy tracking signal operator psi x dx dt sup 2 xd sup 2 x dt sup 2 and its discrete time counterpart can estimate the am and fm modulating signals specifically psi can approximately estimate the amplitude envelope of am signals and the instantaneous frequency of fm signals bounds are derived for the approximation errors which are negligible under general realistic conditions these results coupled with the simplicity of psi establish the usefulness of the energy operator for am and fm signal demodulation these ideas are then extended to a more general class of signals that are sine waves with a time varying amplitude and frequency and thus contain both an am and an fm component for such signals it is shown that psi can approximately track the product of their amplitude envelope and their instantaneous frequency the theoretical analysis is done for both continuous and discrete time signals

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

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

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

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

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

a boundary value problem for the two dimensional broadwell model it is shown that a certain boundary value problem for the steady two dimensional broadwell model on a rectangle has a solution the boundary conditions specify the ingoing particle densities on each side of the rectangle

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

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

analysis of multichannel narrow band filters for image texture segmentation a model for texture analysis and segmentation using multiple oriented channel filters is analyzed in the general framework several different arguments are applied leading to the conclusion that the two dimensional gabor filters possess strong optimality properties for this task properties of the multiple channel segmentation approach are analyzed in particular perturbations of textures from an ideal model are found to have important effects on the segmentation that can usually be ameliorated by simply preceding the segmentation process by a logarithmic operation and using a low pass postfilter prior to making region assignments the difficult problems of space variant textures and multiple component textures are also considered local spatial frequency estimation approaches are suggested that use the responses as constraints in estimating the locally emergent texture frequencies complex texture aggregates containing multiple shared frequency components can be analyzed if the textures are distinct and few in number

conditions for positivity of an energy operator the authors present necessary and sufficient conditions such that the output from the teager kaiser 1989 energy operator spl lsqb s spl dot t ds t dt spl rsqb spl psi sub c spl lsqb s t spl rsqb s spl dot sup 2 t spl minus s t s spl uml t for continuous time signals s t and the output from the corresponding discrete time energy operator spl psi sub d spl lsqb s n spl rsqb s sup 2 n spl minus s n 1 s n spl minus 1 be non negative everywhere these operators have been shown to be effective for am and fm demodulation in several useful classes of signals such as speech and image signals

limits on discrete modulated signals we develop theorems of a general nature that apply to the analysis of am fm signals of the form a m exp j spl phi m or a m cos spl phi m and to their behavior both in linear systems and in simple nonlinear systems comprised of products of linear elements such product systems include interesting nonlinear demodulation operators such as the teager kaiser 1990 operator expressions for the approximate system responses to am fm signals are derived by making an analogy to the eigenfunction interpretation of sinusoids in linear systems for the case of sinusoidal signals the approximations are exact these expressions are collectively called quasieigenfunction approximations qeas for nonsinusoidal am fm signals the approximations have errors that are tightly bounded by functionals that express the smoothness of the am and fm information signals and the durations of the involved system impulse responses the bounds are independent of the bandwidths of the am and fm functions two general applications are considered first the approximations are found to be useful for analyzing discrete time nonlinear energy operators including the teager kaiser operator next the approximation theorems lead to the selection of an optimal class of bandpass filters for use in a discrete multiband am fm demodulation system the filter class selected is optimal in the sense of achieving the lower bound of a novel discrete uncertainty principle

exact 2 1 dimensional solutions for two discrete velocity boltzmann models with four independent densities for the square discrete velocity boltzmann model the authors obtain exact 2 1 dimensional space x y time t solutions these are rational solutions with three exponential variables relaxing towards non uniform maxwellian equilibrium states with two exponential variables these are also solutions of another model with four independent densities and eight velocities oriented towards the eight corners of a cube the positivity problem for the densities is non trivial

construction of positive exact 2 1 dimensional shock wave solutions for two discrete boltzmann models it is proved that 2 1 dimensional spacex y timet positive exact shock wave solutions of two discrete boltzmann models exist for each densityni these solutions are linear combinations of three similarity shock waves n i n0i j n ji 1 d j exp j y y j x j t j 1 2 3 two models with four independent densities are investigated the square discrete velocity boltzmann model and the model with eight velocities oriented toward the eight corners of a cube the positivity problem for the densities is nontrivial two classes of solutions are considered for which the two first similarity shock wave components depend on only one spatial dimension j const j j 1 2 for the positivity if 1 2 0 it is sufficient to prove that the 16 asymptotic shock limitsn0i n0i n3i j 0 2 n ji j 0 3 n ji are positive the density solutions are built up with five arbitrary parameters and we prove that there exist subdomains of the arbitrary parameter space in which the 16 shock limits are positive we study numerically two explicit shock wave solutions we are interested in the movement of the shock front when the time is growing and in the possible appearance of bumps in the space at intermediate times these bumps represent populations of particles which are larger than at initial time or at equilibrium time

statistical am fm models extended kalman filter demodulation cramer rao bounds and speech analysis a stochastic dynamical system model for describing time signals that are jointly amplitude am and frequency fm modulated is presented the signal is assumed to be bandpass perhaps originating from a filter bank applied to a broadband signal and includes the constraint that the magnitude of the complex baseband signal is positive motivated by speech processing and the desire for narrowband modulating signals time is divided into frames and the modulating signals are smoothly interpolated across each frame the model allows a detailed characterization of the bandwidth of the modulating signals and the statistical character of the measurement noise an adaptive estimation algorithm based on extended kalman filtering ideas for extracting the modulating signals from the measured signal is described and demonstrated on both voiced and unvoiced speech signals the cramer rao bound on the performance of any estimator is computed