modulated lattice vector quantization how to make quantization index modulation an efficient variable rate source coder the design of a variable rate joint watermarking and compression jwc scheme is examined in this paper the proposed approach called modulated lattice vector quantization mlvq is based on dither modulation quantization index modulation dm qim which allows for embedding information while maintaining good coding performance in the first part we propose a specific indexing method to make mlvq with a multidimensional codebook feasible furthermore a quantization parameter estimation was designed to ensure the invertibility of the embedding the limitations of the compression performance of jwc schemes are studied in the second part we show the existence of a coding rate lower bound which depends mainly on the codebook characteristics and dramatically decreases coding performance to circumvent this drawback two improved mlvq schemes are proposed in the first one called arbitrary mlvq the embedding is performed on part of the signal to ensure a low embedding coding ratio in the second one called deadzone mlvq the coding efficiency is further improved by maintaining the sparsity of the quantized host signal it consists in excluding the sparse signal components from the embedding process then thresholding them these schemes both applying wavelet coding demonstrate their efficiency as variable rate coders

wavelets and filter banks theory and design the wavelet transform is compared with the more classical short time fourier transform approach to signal analysis then the relations between wavelets filter banks and multiresolution signal processing are explored a brief review is given of perfect reconstruction filter banks which can be used both for computing the discrete wavelet transform and for deriving continuous wavelet bases provided that the filters meet a constraint known as regularity given a low pass filter necessary and sufficient conditions for the existence of a complementary high pass filter that will permit perfect reconstruction are derived the perfect reconstruction condition is posed as a bezout identity and it is shown how it is possible to find all higher degree complementary filters based on an analogy with the theory of diophantine equations an alternative approach based on the theory of continued fractions is also given these results are used to design highly regular filter banks which generate biorthogonal continuous wavelet bases with symmetries

new perspectives and improvements on the symmetric extension filter bank for subband wavelet image compression in subband wavelet image coding size limited subband decompositions are ordinarily used to avoid increasing the number of samples that need to be coded to reduce coding distortions that can occur at the borders the symmetric extension filter bank is typically employed this paper introduces some new perspectives and improvements to that decomposition the symmetric extension filter bank is couched in the cyclic frequency domain providing a framework that accommodates fir and iir filters in a natural way all with perfect reconstruction iir filters with both rational and irrational transfer functions can be implemented and in the context of symmetric extension can accommodate iirs that effectively have perfect stopband suppression enhancements to the filter bank at a tree structured system level are also presented and include the application of spectral reversal correction and a transition band normalization approach to designing the constituent filters of the symmetric extension wavelet packet transform

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

optimized wavelet denoising for self similar alpha stable processes we investigate the performance of wavelet shrinkage methods for the denoising of symmetric alpha stable text s alpha text s self similar stochastic processes corrupted by additive white gaussian noise awgn where alpha is tied to the sparsity of the process the wavelet transform is assumed to be orthonormal and the shrinkage function minimizes the mean square approximation error mmse estimator we derive the corresponding formula for the expected value of the averaged estimation error we show that the predicted mmse is a monotone function of a simple criterion that depends on the wavelet and the statistical parameters of the process using the calculus of variations we then optimize this criterion to find the best performing wavelet within the extended family of meyer wavelets which are bandlimited these are compared with the daubechies wavelets which are compactly supported in time we find that the wavelets that are shorter in time in particular the haar basis are better suited to denoise the sparser processes say alpha while the bandlimited ones including the held and shannon wavelets offer the best performance for alpha 1 6 the limit corresponding to the gaussian case fbm with alpha 2

perturbation theory for path integrals of stiff polymers the wormlike chain model of stiff polymers is a nonlinear model in one spacetime dimension in which the ends are fluctuating freely this causes important differences with respect to the presently available theory which exists only for periodic and dirichlet boundary conditions we modify this theory appropriately and show how to perform a systematic large stiffness expansion for all physically interesting quantities in powers of l where l is the length and the persistence length of the polymer this requires special procedures for regularizing highly divergent feynman integrals which we have developed in previous work we show that by adding to the unperturbed action a correction term a corr we can calculate all feynman diagrams with green functions satisfying neumann boundary conditions our expansions yield order by order a properly normalized end to end distribution function in arbitrary dimensionsd its even and odd moments and the two point correlation function

embedded image coding using zerotrees of wavelet coefficients the embedded zerotree wavelet algorithm ezw is a simple yet remarkably effective image compression algorithm having the property that the bits in the bit stream are generated in order of importance yielding a fully embedded code the embedded code represents a sequence of binary decisions that distinguish an image from the null image using an embedded coding algorithm an encoder can terminate the encoding at any point thereby allowing a target rate or target distortion metric to be met exactly also given a bit stream the decoder can cease decoding at any point in the bit stream and still produce exactly the same image that would have been encoded at the bit rate corresponding to the truncated bit stream in addition to producing a fully embedded bit stream the ezw consistently produces compression results that are competitive with virtually all known compression algorithms on standard test images yet this performance is achieved with a technique that requires absolutely no training no pre stored tables or codebooks and requires no prior knowledge of the image source the ezw algorithm is based on four key concepts 1 a discrete wavelet transform or hierarchical subband decomposition 2 prediction of the absence of significant information across scales by exploiting the self similarity inherent in images 3 entropy coded successive approximation quantization and 4 universal lossless data compression which is achieved via adaptive arithmetic coding

optimal biorthogonal wavelet bases for signal decomposition the selection of scaling functions for optimal signal representation by general multidimensional biorthogonal wavelet bases is investigated criterion for optimality is the minimization of the mean square approximation error at each level of the decomposition conditions are given under which the approximation error of the decomposition approaches zero as the level increases given arbitrary synthesis filters the optimal corresponding analysis filters are determined globally optimal families of filters are also found and suboptimal linear and nonlinear phase filters for the realization of the optimal scaling functions are explicitly determined

families of biorthogonal wavelets several families of biorthogonal wavelet bases are constructed with various properties in particular for a given filter fn of finite length 2n 1 a parametric family of dual filters fvn of length 2n 1 is constructed the parametric nature of the dual filters makes it possible to design the optimum dual filter fv0n corresponding to a fixed filter fn

adaptive transforms for image coding using spatially varying wavelet packets we introduce a novel adaptive image representation using spatially varying wavelet packets wps our adaptive representation uses the fast double tree algorithm introduced previously herley et al 1993 to optimize an operational rate distortion r d cost function as is appropriate for the lossy image compression framework this involves jointly determining which filter bank tree wp frequency decomposition to use and when to change the filter bank tree spatial segmentation for optimality the spatial and frequency segmentations must be done jointly not sequentially due to computational complexity constraints we consider quadtree spatial segmentations and binary wp frequency decompositions corresponding to two channel filter banks for application to image coding we present results verifying the usefulness and versatility of this adaptive representation for image coding using both a first order entropy rate measure based coder as well as a powerful space frequency quantization based spq based wavelet coder introduced by xiong et al 1993

biorthogonal bases of compactly supported wavelets orthonormal bases of compactly supported wavelet bases correspond to subband coding schemes with exact reconstruction in which the analysis and synthesis filters coincide we show here that under fairly general conditions exact reconstruction schemes with synthesis filters different from the analysis filters give rise to two dual riesz bases of compactly supported wavelets we give necessary and sufficient conditions for biorthogonality of the corresponding scaling functions and we present a sufficient condition for the decay of their fourier transforms we study the regularity of these biorthogonal bases we provide several families of examples all symmetric corresponding to linear phase filters in particular we can construct symmetric biorthogonal wavelet bases with arbitrarily high preassigned regularity we also show how to construct symmetric biorthogonal wavelet bases close to a nonsymmetric orthonormal basis

dynamic contrast based quantization for lossy wavelet image compression this paper presents a contrast based quantization strategy for use in lossy wavelet image compression that attempts to preserve visual quality at any bit rate based on the results of recent psychophysical experiments using near threshold and suprathreshold wavelet subband quantization distortions presented against natural image backgrounds subbands are quantized such that the distortions in the reconstructed image exhibit root mean squared contrasts selected based on image subband and display characteristics and on a measure of total visual distortion so as to preserve the visual system s ability to integrate edge structure across scale space within a single unified framework the proposed contrast based strategy yields images which are competitive in visual quality with results from current visually lossless approaches at high bit rates and which demonstrate improved visual quality over current visually lossy approaches at low bit rates this strategy operates in the context of both nonembedded and embedded quantization the latter of which yields a highly scalable codestream which attempts to maintain visual quality at all bit rates a specific application of the proposed algorithm to jpeg 2000 is presented

image coding using wavelet transform a scheme for image compression that takes into account psychovisual features both in the space and frequency domains is proposed this method involves two steps first a wavelet transform used in order to obtain a set of biorthogonal subclasses of images the original image is decomposed at different scales using a pyramidal algorithm architecture the decomposition is along the vertical and horizontal directions and maintains constant the number of pixels required to describe the image second according to shannon s rate distortion theory the wavelet coefficients are vector quantized using a multiresolution codebook to encode the wavelet coefficients a noise shaping bit allocation procedure which assumes that details at high resolution are less visible to the human eye is proposed in order to allow the receiver to recognize a picture as quickly as possible at minimum cost a progressive transmission scheme is presented it is shown that the wavelet transform is particularly well adapted to progressive transmission

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

shearlet based total variation diffusion for denoising we propose a shearlet formulation of the total variation tv method for denoising images shearlets have been mathematically proven to represent distributed discontinuities such as edges better than traditional wavelets and are a suitable tool for edge characterization common approaches in combining wavelet like representations such as curvelets with tv or diffusion methods aim at reducing gibbs type artifacts after obtaining a nearly optimal estimate we show that it is possible to obtain much better estimates from a shearlet representation by constraining the residual coefficients using a projected adaptive total variation scheme in the shearlet domain we also analyze the performance of a shearlet based diffusion method numerical examples demonstrate that these schemes are highly effective at denoising complex images and outperform a related method based on the use of the curvelet transform furthermore the shearlet tv scheme requires far fewer iterations than similar competitors

spectrum decomposition for image signal coding in conventional subband wavelet image coding the subband decomposition is performed on the spatial domain image here we introduce a novel decomposition where the subband decomposition is performed on the global dct spectrum of the image that is the two dimensional spectrum rather than the image is represented by a sum of basis functions each weighted by the transform coefficients the distinct features of this decomposition are analyzed from a transform perspective this spectral subband decomposition is then used as the basis for a new image coder building on the condensed wavelet packet cwp algorithm ironically this new method is shown to have lower arithmetic complexity than conventional subband wavelet coders that directly decompose a time or spatial domain signal comparisons of the new method against conventional subband wavelet coders that use the popular 9 7 dyadic decomposition condensed wavelet packets and generalized lapped orthogonal transforms show that the new method has lower complexity and higher compression performance

image coding with an l sup spl infin norm and confidence interval criteria a new image coding technique based on an l sup spl infin norm criterion and exploiting statistical properties of the reconstruction error is investigated the original image is preprocessed quantized encoded and reconstructed within a given confidence interval two important classes of preprocessing namely linear prediction and iterated filterbanks are used the approach is also shown to be compatible with previous techniques the approach allows a great flexibility in that it can perform lossless coding as well as a controlled lossy one specifications are typically that only p the reconstructed pixels are different from the original ones

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

wavelet domain image restoration with adaptive edge preserving regularization in this paper we consider a wavelet based edge preserving regularization scheme for use in linear image restoration problems our efforts build on a collection of mathematical results indicating that wavelets are especially useful for representing functions that contain discontinuities i e edges in two dimensions or jumps in one dimension we interpret the resulting theory in a statistical signal processing framework and obtain a highly flexible framework for adapting the degree of regularization to the local structure of the underlying image in particular we are able to adapt quite easily to scale varying and orientation varying features in the image while simultaneously retaining the edge preservation properties of the regularizer we demonstrate a half quadratic algorithm for obtaining the restorations from observed data

fast adaptive wavelet packet image compression wavelets are ill suited to represent oscillatory patterns rapid variations of intensity can only be described by the small scale wavelet coefficients which are often quantized to zero even at high bit rates our goal is to provide a fast numerical implementation of the best wavelet packet algorithm in order to demonstrate that an advantage can be gained by constructing a basis adapted to a target image emphasis is placed on developing algorithms that are computationally efficient we developed a new fast two dimensional 2 d convolution decimation algorithm with factorized nonseparable 2 d filters the algorithm is four times faster than a standard convolution decimation an extensive evaluation of the algorithm was performed on a large class of textured images because of its ability to reproduce textures so well the wavelet packet coder significantly out performs one of the best wavelet coder on images such as barbara and fingerprints both visually and in term of psnr

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

an improved image compression algorithm using binary space partition scheme and geometric wavelets geometric wavelet is a recent development in the field of multivariate nonlinear piecewise polynomials approximation the present study improves the geometric wavelet gw image coding method by using the slope intercept representation of the straight line in the binary space partition scheme the performance of the proposed algorithm is compared with the wavelet transform based compression methods such as the embedded zerotree wavelet ezw the set partitioning in hierarchical trees spiht and the embedded block coding with optimized truncation ebcot and other recently developed sparse geometric representation based compression algorithms the proposed image compression algorithm outperforms the ezw the bandelets and the gw algorithm the presented algorithm reports a gain of 0 22 db over the gw method at the compression ratio of 64 for the cameraman test image

fast wavelet transforms and numerical algorithms i a class of algorithms is introduced for the rapid numerical application of a class of linear operators to arbitrary vectors previously published schemes of this type utilize detailed analytical information about the operators being applied and are specific to extremely narrow classes of matrices in contrast the methods presented here are based on the recently developed theory of wavelets and are applicable to all calderon zygmund and pseudo differential operators the algorithms of this paper require order o n or o n log n operations to apply an n n matrix to a vector depending on the particular operator and the version of the algorithm being used and our numerical experiments indicate that many previously intractable problems become manageable with the techniques presented here

perfect reconstruction iir digital filter banks supporting nonexpansive linear signal extensions in this paper perfect reconstruction polyphase infinite impulse response iir filter banks involving causal and anticausal inverses are examined for finite length signals first a novel and efficient nonexpansive perfect reconstruction algorithm based on the state space implementation is presented then the proposed method is extended to support linear signal extensions at the boundaries in a nonexpansive manner the powerfulness of the proposed algorithm is demonstrated with the image compression results

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

distortion rate models for entropy coded lattice vector quantization the increasing demand for real time applications requires the use of variable rate quantizers having good performance in the low bit rate domain in order to minimize the complexity of quantization as well as maintaining a reasonably high psnr ratio we propose to use an entropy coded lattice vector quantizer eclvq these quantizers have proven to outperform the well known ezw algorithm s performance in terms of rate distortion tradeoff we focus our attention on the modeling of the mean squared error mse distortion and the prefix code rate for eclvq first we generalize the distortion model of jeong and gibson 1993 on fixed rate cubic quantizers to lattices under a high rate assumption second we derive new rate models for eclvq efficient at low bit rates without any high rate assumptions simulation results prove the precision of our models

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

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

stationary probability model for bitplane image coding through local average of wavelet coefficients this paper introduces a probability model for symbols emitted by bitplane image coding engines which is conceived from a precise characterization of the signal produced by a wavelet transform main insights behind the proposed model are the estimation of the magnitude of wavelet coefficients as the arithmetic mean of its neighbors magnitude the so called local average and the assumption that emitted bits are under complete representations of the underlying signal the local average based probability model is introduced in the framework of jpeg2000 while the resulting system is not jpeg2000 compatible it preserves all features of the standard practical benefits of our model are enhanced coding efficiency more opportunities for parallelism and improved spatial scalability

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

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

orthonormal bases of compactly supported wavelets we construct orthonormal bases of compactly supported wavelets with arbitrarily high regularity the order of regularity increases linearly with the support width we start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction the construction then follows from a synthesis of these different approaches

a block spin construction of ondelettes part i lemarie functions using block spin assignments we construct anl2 orthonormal basis consisting of dyadic scalings and translates of just a finite number of functions these functions have exponential localization and for even values of a construction parameterm one can make them classcm 1 with vanishing moments up to orderm inclusive such a basis has an important application to phase cell cluster expansions in quantum field theory

tomographic reconstruction using nonseparable wavelets in this paper the use of nonseparable wavelets for tomographic reconstruction is investigated local tomography is also presented the algorithm computes both the quincunx approximation and detail coefficients of a function from its projections simulation results showed that nonseparable wavelets provide a reconstruction improvement versus separable wavelets

subband coding of images using vector quantization a novel two dimensional subband coding technique is presented that can be applied to images as well as speech a frequency band decomposition of the image is carried out by means of 2d separable quadrature mirror filters which split the image spectrum into 16 equal rate subbands these 16 parallel subband signals are regarded as a 16 dimensional vector source and coded as such using vector quantization in the asymptotic case of high bit rates a theoretical analysis yields that a lower bound to the gain is attainable by choosing this approach over scalar quantization of each subband with an optimal bit allocation it is shown that vector quantization in this scheme has several advantages over coding the subbands separately experimental results are given and it is shown the scheme has a performance that is comparable to that of more complex coding techniques

adaptive wavelet thresholding for image denoising and compression the first part of this paper proposes an adaptive data driven threshold for image denoising via wavelet soft thresholding the threshold is derived in a bayesian framework and the prior used on the wavelet coefficients is the generalized gaussian distribution ggd widely used in image processing applications the proposed threshold is simple and closed form and it is adaptive to each subband because it depends on data driven estimates of the parameters experimental results show that the proposed method called bayesshrink is typically within 5 of the mse of the best soft thresholding benchmark with the image assumed known it also outperforms sureshrink donoho and johnstone 1994 1995 donoho 1995 most of the time the second part of the paper attempts to further validate claims that lossy compression can be used for denoising the bayesshrink threshold can aid in the parameter selection of a coder designed with the intention of denoising and thus achieving simultaneous denoising and compression specifically the zero zone in the quantization step of compression is analogous to the threshold value in the thresholding function the remaining coder design parameters are chosen based on a criterion derived from rissanen s minimum description length mdl principle experiments show that this compression method does indeed remove noise significantly especially for large noise power however it introduces quantization noise and should be used only if bitrate were an additional concern to denoising

a lower bound on the average error of vector quantizers corresp a lower bound is proposed for the mean squared error of an n dimensional vector quantizer with a large number of output points

image coding using vector quantization a review a review of vector quantization techniques used for encoding digital images is presented first the concept of vector quantization is introduced then its application to digital images is explained spatial predictive transform hybrid binary and subband vector quantizers are reviewed the emphasis is on the usefulness of the vector quantization when it is combined with conventional image coding techniques or when it is used in different domains

the wavelet transform time frequency localization and signal analysis two different procedures for effecting a frequency analysis of a time dependent signal locally in time are studied the first procedure is the short time or windowed fourier transform the second is the wavelet transform in which high frequency components are studied with sharper time resolution than low frequency components the similarities and the differences between these two methods are discussed for both schemes a detailed study is made of the reconstruction method and its stability as a function of the chosen time frequency density finally the notion of time frequency localization is made precise within this framework by two localization theorems

lattice codebook enumeration for generalized gaussian source the goal of this correspondence is to propose a low complexity enumeration algorithm for lattice vectors based on a geometrical interpretation and valid for different source distributions i e for different l sub p norms in the range 0 p spl les 2 as a particular case we obtain the laplacian enumeration formula of fischer this point of view offers various advantages and particularly it enables one to make the link with the generalized theta series and to reduce the algorithm to the calculation of a few convolutional products in the special cases p 1 and p 2 using a dedicated digital signal processing dsp architecture convolutional products are easy to implement and require few arithmetic operations our algorithm developed for the z sup n lattice can be generalized to other lattices like the d sub n

asymptotic quantization error of continuous signals and the quantization dimension extensions of the limiting qnanfizafion error formula of bennet are proved these are of the form d s k n f n beta b where n is the number of output levels d s k n f is the s th moment of the metric distance between quantizer input and output beta b 0 k s beta is the signal space dimension and f is the signal distribution if a suitably well behaved k dimensional signal density f x exists b b s k int f rho x dx 1 rho rho k s k and b s k does not depend on f for k 1 s 2 this reduces to bennett s formula if f is the cantor distribution on 0 1 0 and this k equals the fractal dimension of the cantor set 12 13 random quantization optimal quantization in the presence of an output information constraint and quantization noise in high dimensional spaces are also investigated

on bounds of shift variance in two channel multirate filter banks critically sampled multirate fir filter banks exhibit periodically shift variant behavior caused by nonideal antialiasing filtering in the decimation stage we assess their shift variance quantitatively by analysing changes in the output signal when the filter bank operator and shift operator are interchanged we express these changes by a so called commutator we then derive a sharp upper bound for shift variance via the operator norm of the commutator which is independent of the input signal its core is an eigensystem analysis carried out within a frequency domain formulation of the commutator leading to a matrix norm which depends on frequency this bound can be regarded as a worst case instance holding for all input signals for two channel fir filter banks with perfect reconstruction pr we show that the bound is predominantly determined by the structure of the filter bank rather than by the type of filters used moreover the framework allows to identify the signals for which the upper bound is almost reached as so called near maximizers of the frequency dependent matrix norm for unitary pr filter banks these near maximizers are shown to be narrow band signals to complement this worst case bound we derive an additional bound on shift variance for input signals with given amplitude spectra where we use wide band model spectra instead of narrow band signals like the operator norm this additional bound is based on the above frequency dependent matrix norm we provide results for various critically sampled two channel filter banks such as quadrature mirror filters pr conjugated quadrature filters wavelets and biorthogonal filters banks

nonparametric estimation of jump diffusion models abstract this paper develops the asymptotics for nonparametric kernel estimators of local time drift and volatilities and levy measure in jump diffusion models our asymptotics are developed in a very general set up allowing the sample span to increase as the sampling interval decreases and without assuming stationarity for drift and volatilities we analyze both local constant and local linear estimators we consider not only estimators for instantaneous conditional second moment but also threshold estimators to disentangle diffusive and jump volatilities the optimal bandwidths are provided for all these estimators

eigen image based compression for the image based relighting with cascade recursive least squared networks this paper presents a principal component analysis pca based data compression method for the image base relighting ibl technology which needs tremendous reference images to produce high quality rendering the method contains two main steps eigen image based representation and eigen image compression we extract eigen images by the cascade recursive least squared crls networks based pca due to the large data dimension by keeping only a few important eigen images which are enough to describe the ibl data set the data size can be drastically reduced to further reduce the data size we use the embedded zero wavelet ezw approach to compress those retained eigen images and use uniform quantization plus arithmetic coding to compress the representing coefficients simulation results demonstrate that our approach is superior to that of compressing reference images separately with jpeg or ezw

painless nonorthogonal expansions in a hilbert space h discrete families of vectors hj with the property that f j hj f hj for every f in h are considered this expansion formula is obviously true if the family is an orthonormal basis of h but also can hold in situations where the hj are not mutually orthogonal and are overcomplete the two classes of examples studied here are i appropriate sets of weyl heisenberg coherent states based on certain non gaussian fiducial vectors and ii analogous families of affine coherent states it is believed that such quasiorthogonal expansions will be a useful tool in many areas of theoretical physics and applied mathematics

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed