a genuinely multidimensional convective pressure flux split riemann solver for euler equations a simple inexpensive genuinely multidimensional hll type riemann solver for euler equations of gasdynamics is proposed the genuinely multidimensional formulation is based on the work of balsara 17 in the present approach the missing contact wave in the hll type solver is restored using the hll cps formulation of mandal and panwar 5 a few two dimensional standard test cases are solved to demonstrate the efficacy of the proposed solver a very simple new genuinely multidimensional hll type riemann solver for euler equations is proposed due to the use of closed form expressions for the fluxes the present method is easier to apply the contact discontinuity is restored using the hll cps formulation without the need for independently specifying its direction of evolution numerical test results demonstrate the efficacy of the present method of its ability to capture accurate solutions

gaussian heat kernel upper bounds via the phragmen lindelof theorem we prove that in presence of l gaussian estimates so called davies gaffney estimates on diagonal upper bounds imply precise off diagonal gaussian upper bounds for the kernels of analytic families of operators on metric measure spaces

an improvement to the bit stuffing algorithm the bit stuffing algorithm is a technique for coding constrained sequences by the insertion of bits into an arbitrary data sequence this approach was previously introduced and applied to d k constrained codes results show that the maximum average rate of the bit stuffing code achieves capacity when k d 1 or k spl infin while it is suboptimal for all other d k pairs furthermore this technique was generalized to produce codes with an average rate that achieves capacity for all d k pairs however this extension results in a more complicated scheme this correspondence proposes a modification to the bit stuffing algorithm that maintains its simplicity we show analytically that the proposed algorithm achieves improved average rates over bit stuffing for most d k constraints we further determine all constraints for which this scheme produces codes with an average rate equal to the shannon capacity

on the estimation of optical flow relations between different approaches and some new results abstract a common basis is suggested for the optical flow estimation approaches of nagel 1983 haralick and lee 1983 and tretiak and pastor 1984 based on a discussion of these approaches an exact solution for the system of partial differential equations proposed by horn and schunck 1981 is given at gray value corners and extrema the insight gained by this solution results in a modification of the oriented smoothness approach of nagel 1983 which thereby becomes considerably simpler in addition the optical flow estimation approach of hildreth 1983 1984 can be shown to represent a kind of special case of this modified oriented smoothness approach in a more direct manner than discussed in nagel 1984

fast surface interpolation using hierarchical basis functions an alternative to multigrid relaxation that is much easier to implement and more generally applicable is presented conjugate gradient descent is used in conjunction with a hierarchical multiresolution set of basis functions the resultant algorithm uses a pyramid to smooth the residual vector before the direction is computed simulation results showing the speed of convergence and its dependence on the choice of interpolator the number of smoothing levels and other factors are presented the relationship of this approach to other multiresolution relaxation and representation schemes is also discussed

an efficient coding system for long source sequences the elias source coding scheme is modified to permit a source sequence of practically unlimited length to be coded as a single codeword using arithmetic of only limited precision the result is shown to be a nonblock arithmetic code of the first in first out fifo type source symbols are decoded in the same order as they were encoded codeword lengths which are near optimum for the specified statistical properties of the source can be achieved explicit encoding and decoding algorithms are provided which effectively implement the coding scheme applications to data compression and cryptography are suggested

an analysis of a class of second order accurate godunov type schemes a general analysis including convergence results of second order godunov type schemes is proposed problems related to the entropy condition are discussed numerical experiments show the accuracy and the stability of the schemes

advances in residual vector quantization a review advances in residual vector quantization rvq are surveyed definitions of joint encoder optimality and joint decoder optimality are discussed design techniques for rvqs with large numbers of stages and generally different encoder and decoder codebooks are elaborated and extended fixed rate rvqs and variable rate rvqs that employ entropy coding are examined predictive and finite state rvqs designed and integrated into neural network based source coding structures are revisited successive approximation rvqs that achieve embedded and refinable coding are reviewed a new type of successive approximation rvq that varies the instantaneous block rate by using different numbers of stages on different blocks is introduced and applied to image waveforms and a scalar version of the new residual quantizer is applied to image subbands in an embedded wavelet transform coding system

invariant region preserving dg methods for multi dimensional hyperbolic conservation law systems with an application to compressible euler equations abstract an invariant region preserving irp limiter for multi dimensional hyperbolic conservation law systems is introduced as long as the system admits a global invariant region which is a convex set in the phase space it is shown that the order of approximation accuracy is not destroyed by the irp limiter provided the cell average is away from the boundary of the convex set moreover this limiter is explicit and easy for computer implementation a generic algorithm incorporating the irp limiter is presented for high order finite volume type schemes for arbitrarily high order discontinuous galerkin dg schemes to hyperbolic conservation law systems sufficient conditions are obtained for cell averages to remain in the invariant region provided the projected one dimensional system shares the same invariant region as the full multi dimensional hyperbolic system does the general results are then applied to both one and two dimensional compressible euler equations so to obtain high order irp dg schemes numerical experiments are provided to validate the proven properties of the irp limiter and the performance of irp dg schemes for compressible euler equations

motion compensation via redundant wavelet multihypothesis multihypothesis motion compensation has been widely used in video coding with previous attention focused on techniques employing predictions that are diverse spatially or temporally in this paper the multihypothesis concept is extended into the transform domain by using a redundant wavelet transform to produce multiple predictions that are diverse in transform phase the corresponding multiple phase inverse transform implicitly combines the phase diverse predictions into a single spatial domain prediction for motion compensation the performance advantage of this redundant wavelet multihypothesis approach is investigated analytically invoking the fact that the multiple phase inverse involves a projection that significantly reduces the power of a dense motion residual modeled as additive noise the analysis shows that redundant wavelet multihypothesis is capable of up to a 7 db reduction in prediction residual variance over an equivalent single phase single hypothesis approach experimental results substantiate the performance advantage for a block based implementation

unwarping of unidirectionally distorted epi images echo planar imaging epi is a fast nuclear magnetic resonance imaging mri method unfortunately local magnetic field inhomogeneities induced mainly by the subject s presence cause significant geometrical distortion predominantly along the phase encoding direction which must be undone to allow for meaningful further processing so far this aspect has been too often neglected in this paper the authors suggest a new approach using an algorithm specifically developed for the automatic registration of distorted epi images with corresponding anatomically correct mri images they model the deformation field with splines which gives us a great deal of flexibility while comprising the affine transform as a special case the registration criterion is least squares interestingly the complexity of its evaluation does not depend on the resolution of the control grid the spline model gives the authors good accuracy thanks to its high approximation order the short support of splines leads to a fast algorithm a multiresolution approach yields robustness and additional speedup the algorithm was tested on real as well as synthetic data and the results were compared with a manual method a wavelet based sobolev type random deformation generator was developed for testing purposes a blind test indicates that the proposed automatic method is faster more reliable and more precise than the manual one

a cartesian grid embedded boundary method for hyperbolic conservation laws we present a second order godunov algorithm to solve time dependent hyperbolic systems of conservation laws on irregular domains our approach is based on a formally consistent discretization of the conservation laws on a finite volume grid obtained from intersecting the domain with a cartesian grid we address the small cell stability problem associated with such methods by hybridizing our conservative discretization with a stable nonconservative discretization at irregular control volumes and redistributing the difference in the mass increments to nearby cells in a way that preserves stability and local conservation the resulting method is second order accurate in l 1 for smooth problems and is robust in the presence of large amplitude discontinuities intersecting the irregular boundary

adaptive grid refinement procedures for efficient optical flow computation two approaches are described that improve the efficiency of optical flow computation without incurring loss of accuracy the first approach segments images into regions of moving objects the method is based on a previously defined galerkin finite element method on a triangular mesh combined with a multiresolution segmentation approach for object flow computation images are automatically segmented into subdomains of moving objects by an algorithm that employs a hierarchy of mesh coarseness for the flow computation and these subdomains are reconstructed over a finer mesh on which to recompute flow more accurately the second approach uses an adaptive mesh in which the resolution increases where motion is found to occur optical flow is computed over a reasonably coarse mesh and this is used to construct an optimal adaptive mesh in a way that is different from the gradient methods reported in the literature the finite element mesh facilitates a reduction in computational effort by enabling processing to focus on particular objects of interest in a scene i e those areas where motion is detected the proposed methods were tested on real and synthetic image sequences and promising results are reported

contact in a multi material eulerian finite element formulation in a multi material eulerian formulation for problems in solid mechanics the default interaction between the surfaces of adjacent materials is perfect bonding in contrast for the lagrangian formulation the surfaces don t interact and may pass through each other freely unless a contact algorithm is introduced to enforce the contact inequality constraints sophisticated contact algorithms have been developed for lagrangian calculations and are routinely used in large deformation applications such as automobile crashworthiness in comparison the eulerian finite element method lags far behind the lagrangian finite element method in modeling contact a natural application for the eulerian formulation is machining which includes large deformations material failure and contact of a tool with a workpiece making its simulation a challenging problem the simulation of the isolated chips involving material failure due to shear bands is used as a test problem to investigate the strength and weakness of the different approaches to implementing contact in multi material eulerian calculations

generalized sampling a variational approach i theory we consider the problem of reconstructing a multidimensional vector function f sub in spl ropf sup m spl rarr spl ropf sup n from a finite set of linear measures these can be irregularly sampled responses of several linear filters traditional approaches reconstruct in an a priori given space e g the space of bandlimited functions instead we have chosen to specify a reconstruction that is optimal in the sense of a quadratic plausibility criterion j first we present the solution of the generalized interpolation problem later we also consider the approximation problem and we show that both lead to the same class of solutions imposing generally desirable properties on the reconstruction largely limits the choice of the criterion j linearity leads to a quadratic criterion based on bilinear forms specifically we show that the requirements of translation rotation and scale invariance restrict the form of the criterion to essentially a one parameter family we show that the solution can be obtained as a linear combination of generating functions we provide analytical techniques to find these functions and the solution itself

adaptive entropy coded subband coding of images the authors describe a design approach called 2 d entropy constrained subband coding ecsbc based upon recently developed 2 d entropy constrained vector quantization ecvq schemes the output indexes of the embedded quantizers are further compressed by use of noiseless entropy coding schemes such as huffman or arithmetic codes resulting in variable rate outputs depending upon the specific configurations of the ecvq and the ecpvq over the subbands many different types of sbc schemes can be derived within the generic 2 d ecsbc framework among these the authors concentrate on three representative types of 2 d ecsbc schemes and provide relative performance evaluations they also describe an adaptive buffer instrumented version of 2 d ecsbc called 2 d ecsbc aec for use with fixed rate channels which completely eliminates buffer overflow underflow problems this adaptive scheme achieves performance quite close to the corresponding ideal 2 d ecsbc system

multidimensional upwind methods for hyperbolic conservation laws abstract we present a class of second order conservative finite difference algorithms for solving numerically time dependent problems for hyperbolic conservation laws in several space variables these methods are upwind and multidimensional in that the numerical fluxes are obtained by solving the characteristic form of the full multidimensional equations at the zone edge and that all fluxes are evaluated and differenced at the same time in particular operator splitting is not used correct behavior at discontinuities is obtained by the use of solutions to the riemann problem and by limiting some of the second order terms numerical results are presented which show that the methods described here yield the same high resolution as the corresponding operator split methods

on the accuracy and stability of explicit schemes for multidimensional linear homogeneous advection equations in 1 roe provided in a simple form conditions which determine the accuracy of a numerical scheme for the solution of the one dimensional linear advection equation u sub 1 au sub x 0 where a is a constant wavespeed by considering a general scheme for 1 in the form u sub i sup n 1 sigma a sub a u sub i a sup n a where u sub i sup n u i delta chi n delta t a sub a is a finite set of constant nonzero coefficients delta chi is the constant mesh spacing and delta t is the timestep define the courant number as nu a delta t delta chi roe proved the following two theorems theorem 1 if u sub i sup n is a polynomial of degree p in i scheme 2 will give the exact solution to 1 if and only if sigma a sup 1 a sub a nu sup q a for all integers q such that 0 le q le p theorem 2 if scheme 2 meets the conditions of theorem 1 the leading term in its pointwise error is a delta chi sup p nu p 1 nu sup p 1 sigma a sup p 1 aa partial derivative sup p 1 partial derivative chi sup p 1 u these two theorems enabled the following definition definition 1 any scheme of the form 2 for the one dimensionalmore linear advection equation 1 that satisfies the conditions in theorem 1 is called p sup th order accurate in space and time the aim of this paper is to extend roe s result to two and three dimensions methods of finding stability restrictions on multidimensional schemes are also discussed 5 refs less

a geometrical characterization of banach spaces in which martingale difference sequences are unconditional we study banach space valued martingale transforms and in particular characterize those banach spaces for which the classical theorems of the real valued case carry over for example if b is a banach space and 1 0 and zeta x y leq x y text if x leq 1 leq y

vertical versus conical square functions we study the difference between vertical and conical square functions in the abstract and also in the specific case where the square functions come from an elliptic operator trans amer math soc 364 2012 no 10 5469 5489

low bit rate video coding using dense motion field and uncovered background prediction it is well known that accurate dense motion field can improve the video coding efficiency this paper presents a novel markov random field mrf model that estimates both the dense motion and uncovered background fields in image sequences and the application of these estimates in h 263 based video coding framework

arithmetic coding for finite state noiseless channels the authors analyze the expected delay for infinite precision arithmetic codes and suggest a practical implementation that closely approximates the idealized infinite precision model

general procedure for riemann solver to eliminate carbuncle and shock instability a novel procedure for the riemann solver flux calculation is proposed in this paper with this simple normal velocity reconstruction procedure all of the commonly used flux solvers such as goduno

motion compensating prediction with fractional pel accuracy the effect of fractional pel accuracy on the efficiency of motion compensating predictors is studied using various spatial prediction interpolation filters in model calculations the power spectral density of the prediction error is related to the probability density function of the displacement error prediction can be improved both by higher accuracy of motion compensation and by spatial wiener filtering in the predictor beyond a critical accuracy the possibility of further improving prediction by more accurate motion compensation is small experiments with videophone signals and with broadcast tv signals confirm these model calculations sinc interpolation bilinear interpolation and wiener filtering are compared at integer pel 1 2 pel 1 4 pel and 1 8 pel accuracies a three state technique for reliable displacement estimation with fractional pel accuracy is introduced it is based on phase correlation for motion compensation with block size of 16 pels 16 pels 1 4 pel accuracy appears to be sufficient for broadcast tv signals whereas for videophone signals 1 2 pel accuracy is desirable

efficient solution algorithms for the riemann problem for real gases a procedure for constructing solutions to the riemann problem for gas dynamics with a general convex equation of state is given approximate procedures involving a local parametrization of the equation of state are introduced in order to calculate numerical fluxes in conservative finite difference schemes this leads to difference schemes which are as accurate and almost as fast as the analogous schemes for polytropic gases numerical results in one and two space variables are presented

bmo spaces related to schrodinger operators with potentials satisfying a reverse holder inequality we identify the dual space of the hardy type space related to the time independent schrodinger operator v with v a potential satisfying a reverse holder inequality as a bmo type space we prove the boundedness in this space of the versions of some classical operators associated to hardy littlewood semigroup and poisson maximal functions square function fractional integral operator we also get a characterization of in terms of carlesson measures

application of the grp scheme to open channel flow equations the grp generalized riemann problem scheme originally conceived for gasdynamics is reformulated for the numerical integration of the shallow water equations in channels of rectangular cross section variable width and bed profile including a friction model for the fluid channel shear stress this scheme is a second order analytic extension of the first order godunov scheme based on time derivatives of flow variables at cell interfaces resulting from piecewise linear data reconstruction in cells the second order time integration is based on solutions to generalized riemann problems at cell interfaces thus accounting for the full governing equations including source terms the source term due to variable bed elevation is treated in a well balanced way so that quiescent flow is exactly replicated this is done by adopting the surface gradient method sgm several problems of steady or unsteady open channel flow are considered including the terms corresponding to variable channel width and bed elevation as well as to shear stress at the fluid channel interface using the manning friction model in all these examples remarkable agreement is obtained between the numerical integration and the exact or accurate solutions

a hierarchical optical flow estimation algorithm based on the interlevel motion smoothness constraint abstract an optical flow estimation algorithm is proposed based on the multiresolution representation of the image i e the image pyramid since the image pyramid consists of several low pass filtered versions of the image sequence the motion vector at each pyramid level is also the low pass filtered versions of the motion vector at the finest level thus the interlevel motion smoothness constraint is introduced in the motion estimation by defining the operators to establish an appropriate relationship between two adjacent pyramid levels the employment of the image pyramid allows us to estimate the large flow vectors and to adopt easily the multigrid technique to improve the convergence speed of the proposed algorithm the simulation results reveal that the proposed algorithm provides more accurate motion estimation compared to the methods using the smoothness constraints such as horn and schunck s algorithm in addition the theoretical analysis of the convergence behavior of the proposed algorithm is also provided in this paper

semi implicit second order schemes for numerical solution of level set advection equation on cartesian grids abstract a new parametric class of semi implicit numerical schemes for a level set advection equation on cartesian grids is derived and analyzed an accuracy and a stability study is provided for a linear advection equation with a variable velocity using partial lax wendroff procedure and numerical von neumann stability analysis the obtained semi implicit scheme is 2nd order accurate in space and time in any dimensional case when using a dimension by dimension extension of the one dimensional scheme that is not the case for analogous fully explicit or fully implicit schemes a further improvement is obtained by using so called corner transport upwind extension in two dimensional case the extended semi implicit scheme with a specific velocity dependent value of is 3rd order accurate in space and time for a constant advection velocity and it is unconditional stable according to the numerical von neumann stability analysis for the linear advection equation in general

uniformly convex and smooth banach spaces and lp boundedness properties of littlewood paley and area functions associated with semigroups abstract in this paper we obtain new characterizations of the uniformly convex and smooth banach spaces these characterizations are established by using l p boundedness properties of littlewood paley functions and area integrals associated with heat semigroups and involving fractional derivatives our results apply for instance by considering the heat semigroups defined by hermite and laguerre operators that do not satisfy the markovian property

application of the godunov method and its second order extension to cascade flow modeling the godunov method and a new second order accurate extension of the method are used for the solution of two dimensional euler equations both numerical schemes are described in detail their performances in the subsonic transonic and supersonic flow regimes are first tested on the problem of flow in a channel with a circular arc bump the niethods are then applied to calculate the transonic flow through a supercritical com pressor cascade designed by j sanzo for this case the solution with the second order extension of the godunov method gives verygood agreement with the design distribution of parameters given by sanzo

capacity achieving code constructions for two classes of d k constraints this correspondence presents two variable rate encoding algorithms that achieve capacity for the d k constraint when k 2d 1 or when k d 1 is not prime the first algorithm symbol sliding is a generalized version of the bit flipping algorithm introduced by aviran in addition to achieving capacity for d 2d 1 constraints it comes close to capacity in other cases the second algorithm is based on interleaving and is a generalized version of the bit stuffing algorithm introduced by bender and wolf this method uses fewer than k d biased bit streams to achieve capacity for d k constraints with k d 1 not prime in particular the encoder for d d 2 sup m 1 constraints 2 spl les m spl infin requires only m biased bit streams

a fast nonrigid image registration with constraints on the jacobian using large scale constrained optimization this paper presents a new nonrigid monomodality image registration algorithm based on b splines the deformation is described by a cubic b spline field and found by minimizing the energy between a reference image and a deformed version of a floating image to penalize noninvertible transformation we propose two different constraints on the jacobian of the transformation and its derivatives the problem is modeled by an inequality constrained optimization problem which is efficiently solved by a combination of the multipliers method and the l bfgs algorithm to handle the large number of variables and constraints of the registration of 3 d images numerical experiments are presented on magnetic resonance images using synthetic deformations and atlas based segmentation

adaptive entropy coded subband coding of image sequences a new approach to image sequence coding based on variable rate entropy constrained subband coding ecsbc is described the corresponding practical implementation of the ecsbc scheme for fixed rate channels is developed by extending recent adaptive entropy coded aec quantization techniques although the entropy constrained design of subband coding systems provides improve coding efficiency compared to level constrained design approaches the resulting coding system generates variable rate outputs which must be buffered before fixed rate transmissions in this case the finite buffer however large that interfaces the encoder and the channel will eventually overflow or underflow resulting in a catastrophic loss of encoder decoder synchronism with an associated large amount of distortion a buffer adaptive arithmetic coded implementation of the ecsbc scheme called adaptive entropy coded subband coding ecsbc aec is described to completely eliminate the associated encoder buffer overflow underflow problems even with a very small encoder buffer

motion based object segmentation and estimation using the mdl principle there are increasing demands for ultralow bit rate video image transmission we present a new formulation of moving object segmentation and motion estimation to quantify the potential gain in using object oriented motion compensation in image sequence coding motivated by real valued parameter estimation required in object oriented motion compensated video source coding a framework motivated by rissanen s 1983 minimum description length mdl principle is proposed to more tightly couple motion estimation and object segmentation algorithms to the overall objective of minimizing source bit rate a new objective function is constructed and a suboptimal procedure to segment and estimate moving objects in a scene is proposed each object is represented by chain coded block boundaries affine motion parameters and motion compensated prediction error a number of experimental comparisons between block and object oriented coding schemes suggests a significant potential coding gain using object oriented motion compensated coding

image analysis using multigrid relaxation methods image analysis problems posed mathematically as variational principles or as partial differential equations are amenable to numerical solution by relaxation algorithms that are local iterative and often parallel although they are well suited structurally for implementation on massively parallel locally interconnected computational architectures such distributed algorithms are seriously handi capped by an inherent inefficiency at propagating constraints between widely separated processing elements hence they converge extremely slowly when confronted by the large representations of early vision application of multigrid methods can overcome this drawback as we showed in previous work on 3 d surface reconstruction in this paper we develop multiresolution iterative algorithms for computing lightness shape from shading and optical flow and we examine the efficiency of these algorithms using synthetic image inputs the multigrid methodology that we describe is broadly applicable in early vision notably it is an appealing strategy to use in conjunction with regularization analysis for the efficient solution of a wide range of ill posed image analysis problems

runlength codes from source codes a class of binary runlength codes also known as d k codes is analyzed these codes are developed by constructing a lossless source code that maps runlengths into unconstrained binary sequences the source code is constructed for the maxentropic distribution on runlengths the inverse of the source code which outputs runlengths guided toward the ideal maxentropic distribution is the d k code four types of source codes are investigated for this purpose huffman enumerative variable length to block and elias or arithmetic the rates of the codes are each proven to converge to the capacity with increasing complexity the codes are not state dependent and are variable rate except for the fixed rate enumerative code a combined source d k code is presented that is based on the arithmetic code

a multispeed discrete boltzmann model for transcritical 2d shallow water flows in this work a discrete boltzmann model for the solution of transcritical 2d shallow water flows is presented and validated in order to provide the model with transcritical capabilities a particular multispeed velocity set has been employed for the discretization of the boltzmann equation it is shown that this particular set naturally yields a simple and closed procedure to determine higher order equilibrium distribution functions needed to simulate transcritical flow the model is validated through several classical benchmarks and is proven to correctly and accurately simulate both 1d and 2d transitions between the two flow regimes

a filter based bit allocation scheme for subband compression of hdtv the authors compare the subband compression capabilities of eight filter sets consisting of linear phase quadrature mirror filters qmfs perfect reconstruction filters and nonlinear phase wavelets at different bit rates using a filter based bit allocation procedure using dpcm and pcm in hdtv subband coding it is found that qmfs have an edge over the rest

reprint of atmospheric models used for practical climate simulation must be capable handling the transport of hundreds of tracers for computational efficiency conservative multi tracer semi lagrangian type transport schemes are appropriate global models based on high order galerkin approach employ highly non uniform spectral element grids and semi lagrangian transport is a challenge on those grids a conservative semi lagrangian scheme spelt spectral element lagrangian transport employing a multi moment compact reconstruction procedure is developed for non uniform quadrilateral grids the scheme is based on a characteristic semi lagrangian method that avoids complex and expensive upstream area computations the spelt scheme has been implemented in the high order method modeling environment homme which is based on a cubed sphere grid with spectral element spatial discretization additionally we show the strong scalability and multi tracer efficiency using several benchmark tests the spelt solution can be made monotonic positivity preserving by combining the flux corrected transport algorithm which is demonstrated on a uniform resolution grid in particular spelt can be efficiently used for non uniform grids and provides accurate and stable results for high resolution meshes

subband finite state scalar quantization a new image coding algorithm that exploits the relationship between various subbands of an image is presented in this correspondence using local variance for state selection and uniform threshold quantizers on subbands we have achieved a reduction in quantization noise compared to other published techniques for lena at various bit rates

a region based selective optical flow back projection for genuine motion vector estimation motion vector plays one significant feature in moving object segmentation however the motion vector in this application is required to represent the actual motion displacement rather than regions of visually significant similarity in this paper region based selective optical flow back projection rsofb which back projects optical flows in a region to restore the region s motion vector from gradient based optical flows is proposed to obtain genuine motion displacement the back projection is performed based on minimizing the projection mean square errors of the motion vector on gradient directions as optical flows of various magnitudes and directions provide various degrees of reliability in the genuine motion restoration the optical flows to be used in the rsofb are optimally selected based on their sensitivity to noises and their tendency in causing motion estimation errors in this paper a deterministic solution is also derived for performing the minimization and obtaining the genuine motion magnitude and motion direction

aon waf type schemes for multidimensional hyperbolic conservation laws we explore how the weighted average flux approach can be used to generate first and second order accurate finite volume schemes for the linear advection equatons in one two and three space dimensions the derived schemes have multidimensional upwinding aspects and good stability properties from the two dimensional methods we construct a scheme for nonlinear systems of hyperbolic conservation laws that is second order accurate in smooth flow spurious oscillations are controlled by making use of one dimensional tvd limiter functions numerical results are presented for the shallow water equations in two space dimensions the equivalent schemes are derived for nonlinear systems in three space dimensions

the use of contextual information in the reversible compression of medical images the authors investigate the use of conditioning events or contexts in improving the performances of known compression methods by building a source model with multiple contexts to code the decorrelated pixels three methods for reversible compression namely dpcm differential pulse code modulation wht walsh hadamard transform and hint hierarchical interpolation employing respectively predictive decorrelation transform decorrelation and multiresolution decorrelation are considered it is shown that the performance of these methods can be enhanced significantly sometimes even up to 40 by using contexts the enhanced dpcm method is found to perform the best for mr and ut ultrasound medical images the enhanced wht method is found to be the best for x ray images the source models used in the enhanced models employ several hundred contexts

fast parametric elastic image registration we present an algorithm for fast elastic multidimensional intensity based image registration with a parametric model of the deformation it is fully automatic in its default mode of operation in the case of hard real world problems it is capable of accepting expert hints in the form of soft landmark constraints much fewer landmarks are needed and the results are far superior compared to pure landmark registration particular attention has been paid to the factors influencing the speed of this algorithm the b spline deformation model is shown to be computationally more efficient than other alternatives the algorithm has been successfully used for several two dimensional 2 d and three dimensional 3 d registration tasks in the medical domain involving mri spect ct and ultrasound image modalities we also present experiments in a controlled environment permitting an exact evaluation of the registration accuracy test deformations are generated automatically using a random hierarchical fractional wavelet based generator

cellwise conservative unsplit advection for the volume of fluid method we present a cellwise conservative unsplit ccu advection scheme for the volume of fluid method vof in 2d contrary to other schemes based on explicit calculations of the flux balances the ccu advection adopts a cellwise approach where the pre images of the control volumes are traced backwards through the flow map the donating regions of the fluxes are calculated via the streaklines of the grid intersections represented as polygonal chains whose vertices are determined by backward tracing of particles injected in the flow at different times high order accuracy is obtained from the fourth order runge kutta method where intermediate velocities along pathlines are determined with quadratic temporal and bicubic spatial interpolations the volumes of the donating regions are corrected in order to fulfill the discrete continuity of incompressible flows consequently the calculation produces non overlapping donating regions and pre images with conforming edges to their neighbors resulting in the conservativeness and the boundedness liquid volume fraction inside the interval 0 1 of the ccu advection scheme finally the update of the liquid volume fractions is computed from the intersections of the pre image polygons with the reconstructed interfaces the ccu scheme is tested on several benchmark tests for the vof advection together with the standard piecewise linear interface calculation plic the geometrical errors of the ccu compare favorably with other unsplit vof plic schemes finally potential improvements of the vof method with the use of more precise interface representation techniques and the future extension of the ccu scheme to 3d are discussed cellwise vof update through backward tracing of the cell s pre image accuracy enhanced via bicubic spatial interpolation and polygonal chain streakline the ccu advection scheme is fully conservative and bounded no limitation on the courant number geometrical errors dominated by plic interface representation errors

vector valued littlewood paley stein theory for semigroups abstract we develop a generalized littlewood paley theory for semigroups acting on l p spaces of functions with values in uniformly convex or smooth banach spaces we characterize in the vector valued setting the validity of the one sided inequalities concerning the generalized littlewood paley stein g function associated with a subordinated poisson symmetric diffusion semigroup by the martingale cotype and type properties of the underlying banach space we show that in the case of the usual poisson semigroup and the poisson semigroup subordinated to the ornstein uhlenbeck semigroup on r n this general theory becomes more satisfactory and easier to be handled in virtue of the theory of vector valued calderon zygmund singular integral operators

a cell centered adaptive projection method for the incompressible euler equations we present an algorithm to compute adaptive solutions for incompressible flows using block structured local refinement in both space and time this method uses a projection formulation based on a cell centered approximate projection which allows the use of a single set of cell centered solvers because of refinement in time additional steps are taken to accurately discretize the advection and projection operators at grid refinement boundaries using composite operators which span the coarse and refined grids this ensures that the method is approximately freestream preserving and satisfies an appropriate form of the divergence constraint

universal modeling and coding the problems arising in the modeling and coding of strings for compression purposes are discussed the notion of an information source that simplifies and sharpens the traditional one is axiomatized and adaptive and nonadaptive models are defined with a measure of complexity assigned to the models a fundamental theorem is proved which states that models that use any kind of alphabet extension are inferior to the best models using no alphabet extensions at all a general class of so called first in first out fifo arithmetic codes is described which require no alphabet extension devices and which therefore can be used in conjunction with the best models because the coding parameters are the probabilities that define the model their design is easy and the application of the code is straightforward even with adaptively changing source models

arithmetic coding with dual symbol sets and its performance analysis we propose a novel adaptive arithmetic coding method that uses dual symbol sets a primary symbol set that contains all the symbols that are likely to occur in the near future and a secondary symbol set that contains all other symbols the simplest implementation of our method assumes that symbols that have appeared in the previously are highly likely to appear in the near future it therefore fills the primary set with symbols that have occurred in the previously symbols move dynamically between the two symbol sets to adapt to the local statistics of the symbol source the proposed method works well for sources such as images that are characterized by large alphabets and alphabet distributions that are skewed and highly nonstationary we analyze the performance of the proposed method and compare it to other arithmetic coding methods both theoretically and experimentally we show experimentally that in certain contexts e g with a wavelet based image coding scheme that has appeared in the literature the compression performance of the proposed method is better than that of the conventional arithmetic coding method and the zero frequency escape arithmetic coding method

a computational framework and an algorithm for the measurement of visual the robust measurement of visual motion from digitized image sequences has been an important but difficult problem in computer vision this paper describes a hierarchical computational framework for the determination of dense displacement fields from a pair of images and an algorithm consist ent with that framework our framework is based on the separation of the image intensity information as well as the process of measuring motion according to scale the large scale intensity information is first used to obtain rough estimates of image motion which are then refined by using intensity information at smaller scales the estimates are in the form of displacement or velocity vectors for pixels and are accompanied by a direction dependent confidence measure a smoothness constraint is employed to propagate the measurements with high confidence to their neigboring areas where the confidences are low at all levels the computations are pixel parallel uniform across the image and based on information from a small neighborhood of a pixel for our algorithm the local displacement vectors are determind by mini mizing the sum of squared differences ssd of intensities the confidence measures are derived from the shape of the ssd surface and the smoothness constraint is cast in the form of energy minimization results of applying our algorithm to pairs of real images are included in addition to our own

layered video coding based on displaced frame difference prediction and multiresolution block matching this paper presents a new video coding technique based on displaced frame difference dfd prediction and multiresolution block matching for layered transmission starting from the base layer the algorithm encodes one layer at a time until the design of the top layer is completed for the encoding of each layer the dfd prediction and multistage motion vector quantization msmvq techniques are employed so that the results of dfd encoding and block matching at previous layers can be used to enhance the coding efficiency at that layer numerical results show that the algorithm is effective for the applications where high rate distortion performance and low computational complexity for layered video transmission are required

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

robust hllc riemann solver with weighted average flux scheme for strong shock many researchers have reported failures of the approximate riemann solvers in the presence of strong shock this is believed to be due to perturbation transfer in the transverse direction of shock waves we propose a simple and clear method to prevent such problems for the harten lax van leer contact hllc scheme by defining a sensing function in the transverse direction of strong shock the hllc flux is switched to the harten lax van leer hll flux in that direction locally and the magnitude of the additional dissipation is automatically determined using the hll scheme we combine the hllc and hll schemes in a single framework using a switching function high order accuracy is achieved using a weighted average flux waf scheme and a method for v shear treatment is presented the modified hllc scheme is named hllc hll it is tested against a steady normal shock instability problem and quirk s test problems and spurious solutions in the strong shock regions are successfully controlled

a three dimensional unsplit godunov method for scalar conservation laws linear advection of a scalar quantity by a specified velocity field arises in a number of different applications of particular interest here is the transport of species and energy in low mach number models for combustion atmospheric flows and astrophysics as well as contaminant transport in darcy models of saturated subsurface flow an important characteristic of these problems is that the velocity field is not known analytically instead an auxiliary equation is solved to compute averages of the velocities over faces in a finite volume discretization in this paper we present a customized three dimensional finite volume advection scheme for this class of problems that provides accurate resolution for smooth problems while avoiding undershoot and overshoot for nonsmooth profiles the method is an extension of an algorithm by bell dawson and shubin bds which was developed for a class of scalar conservation laws arising in porous media flows in two dimensions the original bds algorithm is a variant of unsplit higher order godunov methods based on construction of a limited bilinear profile within each computational cell here we present a three dimensional extension of the original bds algorithm that is based on a limited trilinear profile within each cell we compare this new method to several other unsplit approaches including piecewise linear methods piecewise parabolic methods and wave propagation schemes

fast optimization based conservative remap of scalar fields through aggregate mass transfer abstract we develop a fast efficient and accurate optimization based algorithm for the high order conservative and local bound preserving remap constrained interpolation of a scalar conserved quantity between two close meshes with the same connectivity the new formulation is as robust and accurate as the flux variable flux target optimization based remap fvft obr 1 2 yet has the computational efficiency of an explicit remapper the coupled system of linear inequality constraints resulting from the flux form of remap is the main efficiency bottleneck in fvft obr while advection based remappers use the flux form to directly enforce mass conservation the optimization setting allows us to treat mass conservation as one of the constraints to take advantage of this fact we consider an alternative mass variable mass target mvmt obr formulation in which the optimization variables are the net mass updates per cell and a single linear constraint enforces the conservation of mass in so doing we change the structure of the obr problem from a global linear inequality constrained qp to a singly linearly constrained qp with simple bounds using the structure of the mvmt obr problem and the fact that in remap the old and new grids are close we are able to develop a simple efficient and easily parallelizable optimization algorithm for the primal mvmt obr qp numerical studies on a variety of affine and non affine grids confirm that mvmt obr is as accurate and robust as fvft obr but has the same computational cost as the explicit state of the art fcr

linear time adaptive arithmetic coding the issue of how arithmetic coding should be implemented is addressed a data structure is described and shown to support adaptive arithmetic coding on an arbitrary sized alphabet in time linear in the size of the inputs and outputs experimental results that show the method to be useful even on relatively small alphabets are given

efficient multiplication free arithmetic codes arithmetic coding is a powerful lossless data compression technique that has attracted much attention it provides more flexibility and better efficiency than huffman coding does however the multiplications needed in its encoding and decoding algorithms are very undesirable rissanen and mohiuddin 1989 have proposed a simple scheme to avoid the multiplications the present authors found that the performance of their proposed scheme might degrade significantly in some cases they propose a multiplication free multialphabet arithmetic code which can be shown to have minor performance degradation in all cases in the proposed scheme each multiplication is replaced by a single shift and add the authors prove by both theoretical analysis and simulation results that the degradation of the proposed multiplication free scheme is always several times 2 7 times in the present experiments smaller than that of the rissanen mohiuddin s scheme

a comparison of enumerative and adaptive codes the problem of noiselessly encoding a message when prior statistics are known is considered the close relationship of arithmetic and enumerative coding for this problem is shown by computing explicit arithmetic coding probabilities for various enumerative coding examples this enables a comparison to be made of the coding efficiency of markov models and enumerative codes as well as a new coding scheme intermediate between the two these codes are then extended to messages whose statistics are not known em a priori two adaptive codes are described for this problem whose coding efficiency is upper bounded by the extended enumerative codes on some practical examples the adaptive codes perform significantly better than the nonadaptive ones

multiscale modeling and estimation of motion fields for video coding we present a systematic approach to forward motion compensated predictive video coding the first step is the definition of a flexible model that compactly represents motion fields the inhomogeneity and spatial coherence properties of motion fields are captured using linear multiscale models one possible design is based on linear finite elements and yields a multiscale extension of the triangle motion compensation tmc method the second step is the choice of a computational technique that identifies the coefficients of the linear model we study a modified optical flow technique and minimize a cost function closely related to horn and schunck s 1981 criterion the cost function balances accuracy and complexity of the motion compensated predictor and is viewed as a measure of goodness of the motion field it determines not only the coefficients of the model but also the quantization method we formulate the estimation and quantization problems jointly as a discrete optimization problem and solve it using a fast multiscale relaxation algorithm a hierarchical extension of the algorithm allows proper handling of large displacements simulations on a variety of video sequences have produced improvements over tmc and over the half pel accuracy full search block matching algorithm in excess of 0 5 db in average the results are visually superior as well in particular the reconstructed video is entirely free of blocking artifacts

some new function spaces and their applications to harmonic analysis abstract in this paper a family of spaces is introduced which seems well adapted for the study of a variety of questions related to harmonic analysis and its applications these spaces are the tent spaces they provide the natural setting for the study of such things as maximal functions the relevant space here is t p and also square functions where the space t2p is relevant as such these spaces lead to unifications and simplifications of some basic techniques in harmonic analysis thus they are closely related to lp and hardy spaces important parts of whose theory become corollaries of the description of tent spaces also as proc conf harmonic analysis cortona lect notes in math vol 992 springer verlag berlin new york 1983 already indicated where these spaces first appeared explicitly the tent spaces can be used to simplify some of the results related to the cauchy integral on lipschitz curves and multilinear analysis in retrospect one can recognize that various ideas important for tent spaces had been used if only implicitly for quite some time here one should mention carleson s inequality its simplifications and extensions the theory of hardy spaces and atomic decompositions

rate distortion optimization for h 264 interframe coding a general framework and algorithms rate distortion rd optimization for h 264 interframe coding with complete baseline decoding compatibility is investigated on a frame basis using soft decision quantization sdq rather than the standard hard decision quantization we first establish a general framework in which motion estimation quantization and entropy coding in h 264 for the current frame can be jointly designed to minimize a true rd cost given previously coded reference frames we then propose three rd optimization algorithms a graph based algorithm for near optimal sdq in h 264 baseline encoding given motion estimation and quantization step sizes an algorithm for near optimal residual coding in h 264 baseline encoding given motion estimation and an iterative overall algorithm to optimize h 264 baseline encoding for each individual frame given previously coded reference frames with them embedded in the indicated order the graph based algorithm for near optimal sdq is the core given motion estimation and quantization step sizes it is guaranteed to perform optimal sdq if the weak adjacent block dependency utilized in the context adaptive variable length coding of h 264 is ignored for optimization the proposed algorithms have been implemented based on the reference encoder jm82 of h 264 with complete compatibility to the baseline profile experiments show that for a set of typical video testing sequences the graph based algorithm for near optimal sdq the algorithm for near optimal residual coding and the overall algorithm achieve on average 6 8 and 12 respectively rate reduction at the same psnr ranging from 30 to 38 db when compared with the rd optimization method implemented in the h 264 reference software

motion vector quantization for video coding a new algorithm is developed for the vector quantization of motion vectors this algorithm called motion vector quantization mvq simultaneously estimates and vector quantizes the motion vectors by reinterpreting the block matching algorithm as a type of vector quantization an iterative design algorithm based on this concept is developed in addition to reducing rate for fixed length encoding the algorithm also reduces the computation considerably we include coding simulation results on the flower garden sequence

a conservative adaptive projection method for the variable density incompressible navier stokes equations in this paper we present a method for solving the equations governing time dependent variable density incompressible flow in two or three dimensions on an adaptive hierarchy of grids the method is based on a projection formulation in which we first solve advection diffusion equations to predict intermediate velocities and then project these velocities onto a space of approximately divergence free vector fields our treatment of the first step uses a specialized second order upwind method for differencing the nonlinear convection terms that provides a robust treatment of these terms suitable for inviscid and high reynolds number flow density and other scalars are advected in such a way as to maintain conservation if appropriate and free stream preservation our approach to adaptive refinement uses a nested hierarchy of logically rectangular girds with simultaneous refinement of the girds in both space and time the integration algorithm on the grid hierarchy is a recursive procedure in which coarse grids are advanced in time fine grids are advanced multiple steps to reach the same time as the coarse grids and the data at different levels are then synchronized the single grid algorithm is described briefly but the emphasis here is on the time stepping procedure for the adaptive hierarchy numerical examples are presented to demonstrate the algorithms s accuracy and convergence properties and illustrate the behavior of the method an additional example demonstrates the performance of the method on a more realistic problem namely a three dimensional variable density shear layer

an implicit explicit hybrid method for lagrangian hydrodynamics abstract we describe a new implicit explicit hybrid method for solving the equations of hydrodynamics the scheme is an extension of the explicit second order piecewise parabolic method ppm which is unconditionally stable the scheme is thus of the godunov type it is conservative accurate to second order in both space and time and makes use of a nonlinear riemann solver to obtain fluxes of the conserved quantities the hybrid character of the method provides increased accuracy and computational efficiency switching between implicit and explicit formulations occurs smoothly and in a natural way and is performed separately for each characteristic family of waves the method provides high resolution with shocks spread over only one zone and can produce accurate answers to most reasonable problems without the use of an artificial viscosity 1986 academic press inc

conservative multi implicit spectral deferred correction methods for reacting gas dynamics in most models of reacting gas dynamics the characteristic time scales of chemical reactions are much shorter than the hydrodynamic and diffusive time scales rendering the reaction part of the model equations stiff moreover non linear forcings may introduce into the solutions sharp gradients or shocks the robust behavior and correct propagation of which require the use of specialized spatial discretization procedures this study presents high order conservative methods for the temporal integration of model equations of reacting flows by means of a method of lines discretization on the flux difference form of the equations these methods compute approximations to the cell averaged or finite volume solution the temporal discretization is based on a multi implicit generalization of spectral deferred correction methods the advection term is integrated explicitly and the diffusion and reaction terms are treated implicitly but independently with the splitting errors reduced via the spectral deferred correction procedure to reduce computational cost different time steps may be used to integrate processes with widely differing time scales numerical results show that the conservative nature of the methods allows a robust representation of discontinuities and sharp gradients the results also demonstrate the expected convergence rates for the methods of orders three four and five for smooth problems

adaptive progressive motion vector resolution selection based on rate distortion optimization in the state of the art h 265 hevc video coding standard the motion vector mv resolution is fixed to be 1 4 pel for the entire video sequence while the inherent video characteristics e g texture complexities and motion activities have been largely ignored obviously such strategy may not suffice the demand of high accuracy motion compensation in this paper we propose a specially designed rate distortion model in terms of the mv resolution by taking the video characteristics into consideration in particular the mv resolution selection is formulated as a rate distortion optimization problem by analyzing the rate distortion cost of each mv resolution candidate to further improve the coding performance the progressive mv resolution strategy is employed where the optimal progressive mv resolution is determined by decision trees constructed with the rate distortion model in this manner a novel adaptive progressive motion vector resolution selection scheme can be realized and the mv resolution can be adaptively adjusted based on the properties of local content extensive experiments and comparisons show that the proposed algorithm significantly improves the coding performance and 1 8 bd rate gain on average has been achieved without introducing any noticeable computational complexity

an implicit explicit eulerian godunov scheme for compressible flow a hybrid implicit explicit scheme is developed for eulerian hydrodynamics the hybridization is a continuous switch and operates on each characteristic field separately the explicit scheme is a version of the second order godunov scheme the implicit method is only first order accurate in time but leads to a block tridiagonal matrix inversion for efficiency and is unconditionally stable for the case of linear advection the methodology is described for the cases of linear advection for nonlinear scalar problems and for gas dynamics an important element of our work is the use of a modified engquist osher flux function in place of the godunov flux several numerical results are presented to demonstrate the properties of the method especially stable numerical shocks at very high cfl numbers and second order accurate steady states

generalized sampling a variational approach ii applications for pt i see ibid vol 50 no 8 p 1965 76 2000 the variational reconstruction theory from a companion paper finds a solution consistent with some linear constraints and minimizing a quadratic plausibility criterion it is suitable for treating vector and multidimensional signals here we apply the theory to a generalized sampling system consisting of a multichannel filterbank followed by a nonuniform sampling we provide ready made formulas which should permit application of the technique directly to problems at hand we comment on the practical aspects of the method such as numerical stability and speed we show the reconstruction formula and apply it to several practical examples including new variational formulation of derivative sampling landmark warping and tomographic reconstruction

on the reservoir technique convergence for nonlinear hyperbolic conservation laws part i abstract this paper is devoted to the analysis of flux schemes coupled with the reservoir technique for approximating hyperbolic equations and linear hyperbolic systems of conservation laws f alouges f de vuyst g le coq e lorin the reservoir scheme for systems of conservation laws in finite volumes for complex applications iii porquerolles 2002 lab anal topol probab cnrs marseille 2002 pp 247 254 electronic f alouges f de vuyst g le coq e lorin un procede de reduction de la diffusion numerique des schemas a difference de flux d ordre un pour les systemes hyperboliques non lineaires c r math acad sci paris 335 7 2002 627 632 f alouges f de vuyst g le coq e lorin the reservoir technique a way to make godunov type schemes zero or very low diffusive application to colella glaz eur j mech b fluids 27 6 2008 we prove the long time convergence of the reservoir technique and its tvd property for some specific but still general configurations proofs are based on a precise study of the treatment by the reservoir technique of shock and rarefaction waves

high order multi implicit spectral deferred correction methods for problems of reactive flow models for reacting flow are typically based on advection diffusion reaction a d r partial differential equations many practical cases correspond to situations where the relevant time scales associated with each of the three sub processes can be widely different leading to disparate time step requirements for robust and accurate time integration in particular interesting regimes in combustion correspond to systems in which diffusion and reaction are much faster processes than advection the numerical strategy introduced in this paper is a general procedure to account for this time scale disparity the proposed methods are high order multi implicit generalizations of spectral deferred correction methods misdc methods constructed for the temporal integration of a d r equations spectral deferred correction methods compute a high order approximation to the solution of a differential equation by using a simple low order numerical method to solve a series of correction equations each of which increases the order of accuracy of the approximation the key feature of misdc methods is their flexibility in handling several sub processes implicitly but independently while avoiding the splitting errors present in traditional operator splitting methods and also allowing for different time steps for each process the stability accuracy and efficiency of misdc methods are first analyzed using a linear model problem and the results are compared to semi implicit spectral deferred correction methods furthermore numerical tests on simplified reacting flows demonstrate the expected convergence rates for misdc methods of orders three four and five the gain in efficiency by independently controlling the sub process time steps is illustrated for nonlinear problems where reaction and diffusion are much stiffer than advection although the paper focuses on this specific time scales ordering the generalization to any ordering combination is straightforward

a multiscale relaxation algorithm for snr maximization in nonorthogonal subband coding develops a technique for improving the applicability of complete nonorthogonal multiresolution transforms to image coding as is well known the l sup 2 norm of the quantization errors is not preserved by nonorthogonal transforms so the l sup 2 reconstruction error may be unacceptably large however given the quantizers and synthesis filters the authors show that this artifact can be eliminated by formulating the coding problem as that of minimizing the l sup 2 reconstruction error over the set of possible encoded images with this new formulation the coding problem becomes a high dimensional discrete optimization problem and features a coupling between the redundancy removing and quantization operations a practical solution to the optimization problem is presented in the form of a multiscale relaxation algorithm using inter and intrascale quantization noise feedback filters bounds on the coding gain over the standard coding technique are derived a simple extension of the algorithm allows for the use of a weighted l sup 2 error criterion and deadband non mmse quantizers experiments using biorthogonal spline filter banks demonstrate appreciable snr gains over the standard coding technique and comparable visual improvements