the dynamics of three phase triple junction and contact points we use the method of matched asymptotic expansions to study the sharp interface limit of the three phase system modeled by the cahn hilliard equations with the relaxation boundary condition the dynamic laws for the interfaces the triple junction and the contact points are derived at different time scales in particular we show at o t time scale the dynamic of the triple junction is determined by the balance of the chemical potential gradient along the three interfaces meeting at the triple junction at faster time scale o epsilon t the motion of the triple junction is controlled by the contact point motions and geometric constraints

existence results for the flow of viscoelastic fluids with a differential constitutive law where 2 is the symmetric extra stress tensor the total stress is given by g pl i where p is the hydrodynamic pressure 4 is the rate of deformation tensor g u vu vu u being the velocity field a is the relaxation time a2 the retardation time 0 i a a1 and q is the fluid viscosity the symbol a d t denotes an objective frame indifferent derivative i 181 more precisely

on the relation between the standard phase field model and a thermodynamically consistent phase field model abstract a further comparison is made between the standard phase field equations t 2 1 2 g u u t 2 u 1 2 l t and the relevant thermodynamically consistent model of phase transitions proposed by the authors physica d 43 1990 44 62 here we concentrate on the usual case where g 3 and for comparison purposes retain this expression for the analogous nonlinear functions in the latter model it is brought out among other things that the standard model is thermodynamically consistent in the sense of being derivable from a free energy functional however this free energy functional is of a somewhat unusual kind it implies that at constant temperature the energy density varies linearly with the order parameter and the entropy density is a non concave function of the example of a hard sphere system indicates that such behaviour is not impossible but in most other models the energy density and the entropy are both strictly concave in

on the large time galerkin approximation of the navier stokes equations in this article we are interested in the difficult problem of relating the large time behaviour of the navier stokes equations to the large time behaviour of their galerkin approximation we restrict ourselves to the simplest situation dealing with stationary solutions and the question is the following one if the computed approximation of the time dependent equations seems to converge to some limit as t to infty is the same true for the exact problem and are the limits related we give here some sufficient conditions reasonably easy to verify which guarantee a positive answer to this question

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

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

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

thin interface asymptotics for an energy entropy approach to phase field models with unequal conductivities karma and rappel phys rev e 57 1998 4342 recently developed a new sharp interface asymptotic analysis of the phase field equations that is especially appropriate for modeling dendritic growth at low undercoolings their approach relieves a stringent restriction on the interface thickness that applies in the conventional asymptotic analysis and has the added advantage that interfacial kinetic effects can also be eliminated however their analysis focussed on the case of equal thermal conductivities in the solid and liquid phases when applied to a standard phase field model with unequal conductivities anomalous terms arise in the limiting forms of the boundary conditions for the interfacial temperature that are not present in conventional sharp interface solidification models as discussed further by almgren siam j appl math 59 1999 2086 in this paper we apply their asymptotic methodology to a generalized phase field model which is derived using a thermodynamically consistent approach that is based on independent entropy and internal energy gradient functionals that include double wells in both the entropy and internal energy densities the additional degrees of freedom associated with the generalized phase field equations can be used to eliminate the anomalous terms that arise for unequal conductivities

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

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

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

the conserved penrose fife system with temperature dependent memory abstract a nonlinear parabolic system of penrose fife type with a singular evolution term arising from modelling dynamic phenomena of the nonisothermal diffusive phase separation is studied here we consider the evolution of a material in which the heat flux is a superposition of two different contributions one part is proportional to the spacial gradient of the inverse of the absolute temperature while the other agrees with the gurtin pipkin law introduced in the theory of materials with thermal memory the phase transition here is described through the evolution of the conserved order parameter which may represent the density or concentration of some substance it is shown that an initial boundary value problem for the resulting state equations has a unique solution

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

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

nonlinear aspects of the cahn hilliard equation abstract this paper treats phase separation within the context of the phenomenological cahn hilliard equation c t m c f c k 2 c where c is the concentration m c is the mobility and f c is homogeneou s free energy which is assumed here to be a fourth degree polynomial natural boundary conditions are introduced the full set of equilibrium solutions is specified a comparison theorem for stability criteria which was postulated by langer is proved here within the framework of the natural boundary conditions energy methods are used to define and estimate the limit of monotonic global stability it is pointed out that within the parameter region where the uniform homogeneous state is the only equilibrium solution there may still exist some internal excitable region in which the homogeneous solution possesses growing fluctuations furthermore a periodic instability is shown to exist in the metastable region in addition to the well known nucleation instability

thermodynamically consistent models of phase field type for the kinetics of phase transitions abstract a general framework is given for the phenomenological kinetics of phase transitions in which not only the order parameter but also the temperature may vary in time and space instead of a ginzburg landau free energy functional as used in formulating the cahn hilliard equation we use the analogous entropy functional model entropy functionals and the kinetic equations resulting from them are constructed for various cases phase transitions with and without a critical point and in the former case with or without a latent heat the class considered is general enough to include the entropy functionals for the ising model in mean field approximation the van der waals fluid and a simplified version of the density functional theory of freezing a case without critical point for which the energy is conserved but the order parameter is not provides a thermodynamically consistent derivation of the phase field equations studied by caginalp fix and others and also leads in a natural way to the lyapunov functional given by langer for these equations but the treatment also suggests that a modified version of the phase field equations might provide a more realistic model of freezing

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

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

on a nonlocal phase separation model abstract an alternative to the cahn hilliard model of phase separation for two phase systems in a simplified isothermal case is given the model is derived from a free energy with a nonlocal interacting term and allows reasonable bounds for the concentrations using the free energy as lyapunov functional the asymptotic state of the system is investigated and characterized by a variational principle

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

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

a mathematical model of dynamics of non isothermal phase separation abstract a mathematical model of thermally activated phase separation in binary systems is proposed the construction is based on the landau ginzburg theory of phase transitions and non equilibrium thermodynamics the proposed system of differential equations represents an extension of the cahn hilliard model to the non isothermal situation the model is shown to be consistent with the first principles of thermodynamics the stability solutions is considered and for the one dimensional case numerical results are presented

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

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

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

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

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

nonlinear stability of flows of jeffreys fluids at low weissenberg numbers we consider the stability of steady flows of viscoelastic fluids of jeffreys type for sufficiently small weissenberg numbers but arbitrary reynolds numbers it is proved that the flow is stable to small disturbances if the spectrum of the linearized operator is in the left half plane

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

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

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

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

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

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

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

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

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

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

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

existence of slow steady flows of viscoelastic fluids of white metzner type abstract this work is concerned with the study of steady flows of viscoelastic fluids for which the extra stress is given by a differential constitutive equation of white metzner type

hyperbolicity and change of type in the flow of viscoelastic fluids the equations governing the flow of viscoelastic liquids are classified according to the symbol of their differential operators propagation of singularities is discussed and conditions for a change of type are investigated the vorticity equation for steady flow can change type when a critical condition involving speed and stresses is satisfied this leads to a partitioning of the field of flow into subcritical and supercritical regions as in the problem of transonic flow

on anisotropic order parameter models for multi phase system and their sharp interface limits abstract for a general class of diffuse anisotropic multi phase order parameter or phase field models we use formally matched asymptotic expansions to determine the asymptotic limit when a small parameter related to the thickness of the interface tends to zero in the case of anisotropic allen cahn systems we obtain in the limit that the interface moves by anisotropic mean curvature flow at triple junctions a force balance holds which in the anisotropic case includes shear forces herring torque terms acting normal to the interface we further identify the singular limit of anisotropic cahn hilliard systems

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

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

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

a diffuse interface model for alloys with multiple components and phases a nonisothermal phase field model for alloys with multiple phases and components is derived the model allows for arbitrary phase diagrams we relate the model to classical sharp interface models by formally matched asymptotic expansions in addition we discuss several examples and relate our model to the ones already existing

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

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