lossless coding of multichannel signals using optimal vector hierarchical decomposition a methodology is presented for the optimal construction of multichannel reduced pyramids by selecting the interpolation synthesis postfilters so as to minimize the error variance at each level of the pyramid the general optimization methodology is applied for the optimization of pyramids for the compression of electrocardiographic signals and rgb colored images

l stability for linear multiresolution algorithms a new explicit approach part iii the 2 d case abstract this paper is devoted to the stability in the infinity norm for the mallat s multiresolution transform in 2 d explicit error bounds are presented by using some appropriate reformulations of the successive convolutions some contraction properties and some alternative normalizations the two new things in our study is the use of only basic rules and the derivation of explicit bounds in particular it can be understood for a wide part of the scientific community moreover the results should be useful in mathematical medical physical biological and engineering applications

l sub spl infin constrained high fidelity image compression via adaptive context modeling we study high fidelity image compression with a given tight l sub spl infin bound we propose some practical adaptive context modeling techniques to correct prediction biases caused by quantizing prediction residues a problem common to the existing dpcm type predictive near lossless image coders by incorporating the proposed techniques into the near lossless version of calic that is considered by many as the state of the art algorithm we were able to increase its psnr by 1 db or more and or reduce its bit rate by 10 or more more encouragingly at bit rates around 1 25 bpp or higher our method obtained competitive psnr results against the best l sub 2 based wavelet coders while obtaining much smaller l sub spl infin bound

nonlinear image representation for efficient perceptual coding image compression systems commonly operate by transforming the input signal into a new representation whose elements are independently quantized the success of such a system depends on two properties of the representation first the coding rate is minimized only if the elements of the representation are statistically independent second the perceived coding distortion is minimized only if the errors in a reconstructed image arising from quantization of the different elements of the representation are perceptually independent we argue that linear transforms cannot achieve either of these goals and propose instead an adaptive nonlinear image representation in which each coefficient of a linear transform is divided by a weighted sum of coefficient amplitudes in a generalized neighborhood we then show that the divisive operation greatly reduces both the statistical and the perceptual redundancy amongst representation elements we develop an efficient method of inverting this transformation and we demonstrate through simulations that the dual reduction in dependency can greatly improve the visual quality of compressed images

an image multiresolution representation for lossless and lossy compression we propose a new image multiresolution transform that is suited for both lossless reversible and lossy compression the new transformation is similar to the subband decomposition but can be computed with only integer addition and bit shift operations during its calculation the number of bits required to represent the transformed image is kept small through careful scaling and truncations numerical results show that the entropy obtained with the new transform is smaller than that obtained with predictive coding of similar complexity in addition we propose entropy coding methods that exploit the multiresolution structure and can efficiently compress the transformed image for progressive transmission up to exact recovery the lossless compression ratios are among the best in the literature and simultaneously the rate versus distortion performance is comparable to those of the most efficient lossy compression methods

nonlinear wavelet transforms for image coding via lifting we investigate central issues such as invertibility stability synchronization and frequency characteristics for nonlinear wavelet transforms built using the lifting framework the nonlinearity comes from adaptively choosing between a class of linear predictors within the lifting framework we also describe how earlier families of nonlinear filter banks can be extended through the use of prediction functions operating on a causal neighborhood of pixels preliminary compression results for model and real world images demonstrate the promise of our techniques

lossless quantization of hadamard transform coefficients this paper shows that an n spl times 1 integer vector can be exactly recovered from its hadamard transform coefficients even when 0 5n log sub 2 n of the less significant bits of these coefficients are removed the paper introduces a fast lossless dequantization algorithm for this purpose to investigate the usefulness of the procedure in data compression the paper investigates an embedded block image coding technique called the lhad based on the algorithm the results show that lossless compression ratios close to the state of the art can be achieved but that techniques such as calic and s p still perform better

an optimum tapered burg algorithm for linear prediction and spectral analysis several problems associated with the burg algorithm are for the most part alleviated by the use of an appropriate energy taper used in the derivation of the algorithm the tapered burg technique uses a weighted forward backward least squares fit to the parameters of the all pole model subject to levinson s recursion constraint based on a minimum average variance of the estimated frequency of a real sinusoid an optimum taper is derived finally the performance of the optimally tapered burg technique is compared with the least squares yule walker and the usual burg techniques

matrix factorizations for parallel integer transformation integer mapping is critical for lossless source coding and has been used for multicomponent image compression in the new international image compression standard jpeg 2000 in this paper starting from block factorizations for any nonsingular transform matrix we introduce two types of parallel elementary reversible matrix perm factorizations which are helpful for the parallelization of perfectly reversible integer transforms with improved degree of parallelism and parallel performance the cost of multiplications and additions can be respectively reduced to o logn and o log2n for an n by n transform matrix these make perm factorizations an effective means of developing parallel integer transforms for large matrices we also present a scheme to block the matrix and allocate the load of processors for efficient transformation

optimization and implementation of the integer wavelet transform for image coding this paper deals with the design and implementation of an image transform coding algorithm based on the integer wavelet transform iwt first of all criteria are proposed for the selection of optimal factorizations of the wavelet filter polyphase matrix to be employed within the lifting scheme the obtained results lead to the iwt implementations with very satisfactory lossless and lossy compression performance then the effects of finite precision representation of the lifting coefficients on the compression performance are analyzed showing that in most cases a very small number of bits can be employed for the mantissa keeping the performance degradation very limited stemming from these results a vlsi architecture is proposed for the iwt implementation capable of achieving very high frame rates with moderate gate complexity

ell_ 2 optimized predictive image coding with ell_ infty bound in many scientific medical and defense applications of image video compression an l error bound is required however pure l optimized image coding colloquially known as near lossless image coding is prone to structured errors such as contours and speckles if the bit rate is not sufficiently high moreover most of the previous l based image coding methods suffer from poor rate control in contrast the l2 error metric aims for average fidelity and hence preserves the subtlety of smooth waveforms better than the l error metric and it offers fine granularity in rate control but pure l2 based image coding methods e g jpeg 2000 cannot bound individual errors as the l based methods can this paper presents a new compression approach to retain the benefits and circumvent the pitfalls of the two error metrics a common approach of near lossless image coding is to embed into a dpcm prediction loop a uniform scalar quantizer of residual errors the said uniform scalar quantizer is replaced in the proposed new approach by a set of context based l2 optimized quantizers the optimization criterion is to minimize a weighted sum of the l2 distortion and the entropy while maintaining a strict l error bound the resulting method obtains good rate distortion performance in both l2 and l metrics and also increases the rate granularity compared with jpeg 2000 the new method not only guarantees lower l error for all bit rates but also it achieves higher psnr for relatively high bit rates

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

joint space frequency segmentation using balanced wavelet packet trees for least cost image representation we examine the question of how to choose a space varying filterbank tree representation that minimizes some additive cost function for an image the idea is that for a particular cost function e g energy compaction or quantization distortion some tree structures perform better than others while the wavelet tree represents a good choice for many signals it is generally outperformed by the best tree from the library of wavelet packet frequency selective trees the double tree library of bases performs better still by allowing different wavelet packet trees over all binary spatial segments of the image we build on this foundation and present efficient new pruning algorithms for both one and two dimensional 1 d and 2 d trees that will find the best basis from a library that is many times larger than the library of the single tree or double tree algorithms the augmentation of the library of bases overcomes the constrained nature of the spatial variation in the double tree bases and is a significant enhancement in practice use of these algorithms to select the least cost expansion for images with a rate distortion cost function gives a very effective signal adaptive compression scheme this scheme is universal in the sense that without assuming a model for the signal or making use of training data it performs very well over a large class of signal types in experiments it achieves compression rates that are competitive with the best training based schemes

adaptive prediction trees for image compression this paper presents a complete general purpose method for still image compression called adaptive prediction trees efficient lossy and lossless compression of photographs graphics textual and mixed images is achieved by ordering the data in a multicomponent binary pyramid applying an empirically optimized nonlinear predictor exploiting structural redundancies between color components then coding with hex trees and adaptive runlength huffman coders color palettization and order statistics prefiltering are applied adaptively as appropriate over a diverse image test set the method outperforms standard lossless and lossy alternatives the competing lossy alternatives use block transforms and wavelets in well studied configurations a major result of this paper is that predictive coding is a viable and sometimes preferable alternative to these methods

matrix factorizations for reversible integer mapping reversible integer mapping is essential for lossless source coding by transformation a general matrix factorization theory for reversible integer mapping of invertible linear transforms is developed concepts of the integer factor and the elementary reversible matrix erm for integer mapping are introduced and two forms of erm triangular erm term and single row erm serm are studied we prove that there exist some approaches to factorize a matrix into terms or serms if the transform is invertible and in a finite dimensional space the advantages of the integer implementations of an invertible linear transform are i mapping integers to integers ii perfect reconstruction and iii in place calculation we find that besides a possible permutation matrix the term factorization of an n by n nonsingular matrix has at most three terms and its serm factorization has at most n 1 serms the elementary structure of erm transforms is the ladder structure an executable factorization algorithm is also presented then the computational complexity is compared and some optimization approaches are proposed the error bounds of the integer implementations are estimated as well finally three erm factorization examples of dft dct and dwt are given

generalized block lifting factorization of m channel biorthogonal filter banks for lossy to lossless image coding generalized block lifting factorization of m channel m 2 biorthogonal filter banks bofbs for lossy to lossless image coding is presented in this paper since the proposed block lifting structure is more general than the conventional lifting factorizations and does not require many restrictions such as paraunitary number of channels and mcmillan degree in each building block unlike the conventional lifting factorizations its coding gain is higher than that of the previous methods several proposed bofbs are designed and applied to image coding comparing the results with conventional lossy to lossless image coding structures including the 5 3 and 9 7 tap discrete wavelet transforms in jpeg 2000 and a 4 8 hierarchical lapped biorthogonal transform in jpeg xr the proposed bofbs achieve better result in both objective measure and perceptual visual quality for the images with a lot of high frequency components

reversible integer to integer wavelet transforms for image compression performance evaluation and analysis in the context of image coding a number of reversible integer to integer wavelet transforms are compared on the basis of their lossy compression performance lossless compression performance and computational complexity of the transforms considered several were found to perform particularly well with the best choice for a given application depending on the relative importance of the preceding criteria reversible integer to integer versions of numerous transforms are also compared to their conventional i e nonreversible real to real counterparts for lossy compression at low bit rates reversible integer to integer and conventional versions of transforms were found to often yield results of comparable quality factors affecting the compression performance of reversible integer to integer wavelet transforms are also presented supported by both experimental data and theoretical arguments

symmetric extension compatible reversible integer to integer wavelet transforms symmetric extension is explored as a means for constructing nonexpansive reversible integer to integer iti wavelet transforms for finite length signals two families of reversible iti wavelet transforms are introduced and their constituent transforms are shown to be compatible with symmetric extension one of these families is then studied in detail and several interesting results concerning its member transforms are presented in addition some new reversible iti structures are derived that are useful in conjunction with techniques like symmetric extension last the relationship between symmetric extension and per lifting step extension is explored and some new results are obtained in this regard

reversible intraframe compression of medical images the performance of several reversible intraframe compression methods is compared by applying them to angiographic and magnetic resonance mr images reversible data compression involves two consecutive steps decorrelation and coding the result of the decorrelation step is presented in terms of entropy because huffman coding generally approximates these entropy measures within a few percent coding has not been investigated separately it appears that a hierarchical decorrelation method based on interpolation hint outperforms all other methods considered the compression ratio is around 3 for angiographic images of 8 9 b pixel but is considerably less for mr images whose noise level is substantially higher

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

generalized s transform the generalized s transform gst a family of reversible integer to integer transforms inspired by the s transform is proposed this family of transforms is then studied in detail by considering topics such as gst parameter calculation the effects of using different rounding operators in the gst and the relationship between the gst and the lifting scheme some examples of specific transforms in the gst family are also given in particular a new transform in this family is introduced and its practical utility is demonstrated

an algorithm for finite element analysis of partly wrinkled membranes a generalization and numerical implementation is presented of the stein hedgepeth 1961 continuum theory for the analysis of partly wrinkled membranes such as the tensioned membrane surfaces which are found in spacecraft structural components the approach has its basis in experimental observations showing that when wrinkles develop in a membrane parallel to the x direction the associated overall contraction in the y direction exceeds that predicted by the poisson s ratio effect

numerical study of the wrinkling of a stretched thin sheet a thin sheet clamped at opposite ends and stretched develops wrinkles parallel to the direction of the applied tensile strain due to the hindered poisson lateral contraction at the clamps to study this phenomenon a variational model recently proposed by puntel deseri and fried is adopted the relevant energy functional includes bending and membranal contributions and is minimized subject to a constraint on the area of the mid surface of the sheet a fourth order partial differential equation is henceforth obtained and numerically implemented using b splines predictions are obtained concerning the number of wrinkles critical applied stretches and scaling relationships for wrinkle amplitude and wavelength both a linearized version of the boundary value problem based on the small slope approximation and a fully nonlinear one are considered their results are found to be in good agreement for the whole range of applied stretches taken into account comparisons with previous analytical results by puntel deseri and fried who used different boundary conditions and an ansatz on the deflection function are also provided the numerical results substantially confirm the validity of the analytical predictions the present work provides then an alternative numerical method for the study of wrinkling in thin sheets and supports the use of analytical and semi analytical solutions as viable options for specific geometries though further investigation particularly experimental is still needed extensive comparisons of the results with other studies available in the literature provide confirmation for the scaling laws and signal that predicted values of the critical stretches may only be accurate for higher length to width aspect ratios

a unifying framework for lossless and progressive image coding progressive coding is a desirable feature for image database telebrowsing or image transmissions over low bandwidth channels furthermore for some applications exact image reconstruction is required in this paper we show that most of the lossless and progressive coders can be described by a common nonlinear subband decomposition scheme this unifying framework provides useful guidelines for the analysis and improvement of the considered decomposition methods finally we compare the respective performances of these methods in terms of shannon entropy for several images and also evaluate their compression ability when combined with a hierarchical coding technique

reversible integer color transform in this correspondence we introduce a systematic algorithm that can convert any 3 times 3 color transform into a reversible integer to integer transform we also discuss the ways to improve accuracy and reduce implementation complexity we derive the integer rgb to kla iv1v2 ycbcr dct yuv and yiq transforms that are optimal in accuracy

avoidance of singular point in integer orthonormal transform for lossless coding in this correspondence the singular point sp problem peculiar to an integer orthonormal transform is discussed and compatibility of the integer transform with the corresponding real valued transform is improved to avoid the sp problem we introduce two point permutations of order and sign of signals since it satisfies the commutative law it becomes possible to reduce computational cost to find the best combination of the permutations which minimizes errors due to rounding of signals inside the integer transform

customizable triangular factorizations of matrices abstract customizable triangular factorizations of matrices find their applications in computer graphics and lossless transform coding in this paper we prove that any n n nonsingular matrix a can be factorized into 3 triangular matrices a plus where p is a permutation matrix l is a unit lower triangular matrix u is an upper triangular matrix of which the diagonal entries are customizable and can be given by all means as long as its determinant is equal to that of a up to a possible sign adjustment and s is a unit lower triangular matrix of which all but n 1 off diagonal elements are set zeros and the positions of those n 1 elements are also flexibly customizable such as a single row a single column a bidiagonal matrix or other specially patterned matrices a pseudo permutation matrix which is a simple unit upper triangular matrix with off diagonal elements being 0 1 or 1 can take the role of the permutation matrix p as well in some cases p may be the identity matrix besides plus a customizable factorization also has other alternatives lusp psul or sulp for lower s and puls ulsp pslu slup for upper s

optimization of integer wavelet transforms based on difference correlation structures in this paper a novel lifting integer wavelet transform based on difference correlation structure dccs liwt is proposed first we establish a relationship between the performance of a linear predictor and the difference correlations of an image the obtained results provide a theoretical foundation for the following construction of the optimal lifting filters then the optimal prediction lifting coefficients in the sense of least square prediction error are derived dccs liwt puts heavy emphasis on image inherent dependence a distinct feature of this method is the use of the variance normalized autocorrelation function of the difference image to construct a linear predictor and adapt the predictor to varying image sources the proposed scheme also allows respective calculations of the lifting filters for the horizontal and vertical orientations experimental evaluation shows that the proposed method produces better results than the other well known integer transforms for the lossless image compression

object tracking from image sequences using adaptive models in fuzzy particle filter this paper describes a vision based system for tracking objects from image sequences the proposed system has the standard architecture with a particle filter which is a popular algorithm to track objects in real time many tracking algorithms have a great difficulty in tracking objects robustly by reason of complex background and rapid changes under a real complex environment such as a traffic road to make a robust algorithm for object tracking we propose the method that uses the adaptive autoregressive model as a state transition model and the adaptive appearance mixture model as an observation model but in case of changing the state of a tracked object suddenly the adaptive models may not make the optimal parameters for accurate states at current time because the noise variance of the adaptive models in this case is larger than that in normal case it has an effect on the accuracy of an object tracking algorithm thus we propose a fuzzy particle filter to overcome problems from the occurrence of the unexpected improper variances due to several causes in this paper as the process noises and the observation noises in a fuzzy particle filter are considered as fuzzy variables by using the possibility theory a fuzzy particle filter with fuzzy noises is used to manage uncertainty in various noise models also we make possibility measure as using the fuzzy relation equation which is defined by these fuzzy variables and then the states are estimated by using a fuzzy expected value operator also because the proposed algorithm applies several functions to improve the accuracy of tracking an object the performance of tracking speed deteriorates to resolve this problem to some extent we consider the fact that a fuzzy particle filter has a little bit of an effect on the number of particles consequently we propose the method which can adjust the number of particles by using the result from a measurement step in order to improve the speed for an object tracking in the proposed algorithm the experiments of this paper show that the proposed method is efficient and has many advantages for an object tracking in real environments

image interpolation by adaptive 2 d autoregressive modeling and soft decision estimation the challenge of image interpolation is to preserve spatial details we propose a soft decision interpolation technique that estimates missing pixels in groups rather than one at a time the new technique learns and adapts to varying scene structures using a 2 d piecewise autoregressive model the model parameters are estimated in a moving window in the input low resolution image the pixel structure dictated by the learnt model is enforced by the soft decision estimation process onto a block of pixels including both observed and estimated the result is equivalent to that of a high order adaptive nonseparable 2 d interpolation filter this new image interpolation approach preserves spatial coherence of interpolated images better than the existing methods and it produces the best results so far over a wide range of scenes in both psnr measure and subjective visual quality edges and textures are well preserved and common interpolation artifacts blurring ringing jaggies zippering etc are greatly reduced

adaptive predictor based on maximally flat halfband filter in lifting scheme for complex short time varying signals a high order predictor does not always yield good performance for this we investigate the use of a short order adaptive predictor since the maximally flat filters are the optimal predictors for polynomial signal prediction the adaptation is based on the combination of a set of maximally flat filters for compression efficiency the dynamic ranges of the weighting variables are specially considered for this based on the bernstein filters another form to represent the weighting variables is used these two sets of weighting coefficients can be transformed into each other with a simple linear transform thus the adaptation can be made in both the time domain and the frequency domain for block based image coding the least square criterion is used to derive the weighting coefficients experimental results show that the adaptive predictor performs better than the s p transform the median edge detector med and the gradient adjusted predictor gap

lossless and near lossless image compression based on multiresolution analysis there are applications in data compression where quality control is of utmost importance certain features in the decoded signal must be exactly or very accurately recovered yet one would like to be as economical as possible with respect to storage and speed of computation in this paper we present a multi scale data compression algorithm within harten s interpolatory framework for multiresolution that gives a specific estimate of the precise error between the original and the decoded signal when measured in the l and in the l p p 1 2 discrete norms the proposed algorithm does not rely on a tensor product strategy to compress two dimensional signals and it provides a priori bounds of the peak absolute error pae the root mean square error rmse and the peak signal to noise ratio psnr of the decoded image that depend on the quantization parameters in addition after data compression by applying this non separable multi scale transformation the user has an the exact value of the pae rmse and psnr before the decoding process takes place we show how this technique can be used to obtain lossless and near lossless image compression algorithms

improved spectrum performance via a data adaptive weighted burg technique a new method for generating autoregressive ar parameters for spectral estimation is introduced and shown to be a data adaptive weighted burg dab technique the respective ar coefficient estimates minimize a weighted measure of the squared forward and backward linear predictive errors with weights that are proportional to the common energy of the forward and backward process realizations and result in a stable filter representation spectra are computed comparing the new method to other weighted burg techniques e g rectangular hamming and optimum parabolic weighting and demonstrate performance improvements in frequency bias and resolution no evidence of a line splitting tendency is exhibited however somewhat greater spectral variability is exhibited by the dab method in processing nonsinusoidal signals the provision of asymptotically unbiased ar parameter estimates is presented

performance analysis of reversible image compression techniques for high resolution digital teleradiology the performances of a number of block based reversible compression algorithms suitable for compression of very large format images 4096 4096 pixels or more are compared to that of a novel two dimensional linear predictive coder developed by extending the multichannel version of the burg algorithm to two dimensions the compression schemes implemented are huffman coding lempel ziv coding arithmetic coding two dimensional linear predictive coding in addition to the aforementioned one transform coding using discrete fourier discrete cosine and discrete walsh transforms linear interpolative coding and combinations thereof the performances of these coding techniques for a few mammograms and chest radiographs digitized to sizes up to 4096 4096 10 b pixels are discussed compression from 10 b to 2 5 3 0 b pixel on these images has been achieved without any loss of information the modified multichannel linear predictor outperforms the other methods while offering certain advantages in implementation

integer mdct with enhanced approximation of the dct iv integer transform plays an important role in lossless signal compression in order to achieve high accuracy to its corresponding theoretical transform the rounding number should be as low as possible at the same time the matrix factorization for reversible integer mapping should be handled with care especially when the processing block length is high n 16 in this correspondence a new method for realizing reversible integer discrete cosine transform type iv dct iv is proposed that is a key component used in audio compression the proposed method exhibits low rounding number 2 5n and low complexity o nlog sub 2 n as well as well as accurately represents its counterpart floating point dct iv transformation

an exact recursion for the composite nearest neighbor degeneracy for a 2 n lattice space a set theoretic argument is utilized to develop a recursion relation that yields exactly the composite nearest neighbor degeneracy for simple indistinguishable particles distributed on a 2 n lattice space the associated generating functions as well as the expectation of the resulting statistics are also treated

orientation sensitive interpolative pyramids for lossless and progressive image coding this paper presents a modified jpeg coder that is applied to the compression of mixed documents containing text natural images and graphics for printing purposes the modified jpeg coder proposed in this paper takes advantage of the distinct perceptually significant regions in these documents to achieve higher perceptual quality than the standard jpeg coder the region adaptivity is performed via classified thresholding being totally compliant with the baseline standard a computationally efficient classification algorithm is presented and the improved performance of the classified jpeg coder is verified

two dimensional ar spectral estimation using a two dimensional minimum free energy method we present a 2 d extension of the minimum free energy mfe autoregressive parameter and spectral estimation technique mfe can outperform the multidimensional levinson algorithm producing superior spectral estimation of 2 d sinusoids in white gaussian noise mfe spectral estimates are found to be comparable to modified covariance method estimates mfe also outperforms the conventional fourier method for closely spaced sinusoids at low signal to noise ratio and low data set size

modifying jpeg binary arithmetic codec for exploiting inter intra block and dct coefficient sign redundancies this article presents four modifications to the jpeg arithmetic coding jac algorithm a topic not studied well before it then compares the compression performance of the modified jpeg with jpeg xr the latest block based image coding standard we first show that the bulk of inter intra block redundancy caused due to the use of the block based approach by jpeg can be captured by applying efficient prediction coding we propose the following modifications to jac to take advantages of our prediction approach 1 we code a totally different dc difference 2 jac tests a dct coefficient by considering its bits in the increasing order of significance for coding the most significant bit position it causes plenty of redundancy because jac always begins with the zeroth bit we modify this coding order and propose alternations to the jpeg coding procedures 3 we predict the sign of significant dct coefficients a problem is not addressed from the perspective of the jpeg decoder before 4 we reduce the number of binary tests that jac codes to mark end of block we provide experimental results for two sets of eight bit gray images the first set consists of nine classical test images mostly of size 512 ntn512 pixels the second set consists of 13 images of size 2000ntn3000 pixels or more our modifications to jac obtain extra ordinary amount of code reduction without adding any kind of losses more specifically when we quantize the images using the default quantizers our modifications reduce the total jac code size of the images of these two sets by about 8 9 and 10 6 and the jpeg huffman code size by about 16 3 and 23 4 respectively on the average gains are even higher for coarsely quantized images finally we compare the modified jac with two settings of jpeg xr one with no block overlapping and the other with the default transform we denote them by jxr0 and jxr1 respectively our results show that for the finest quality rate image coding the modified jac compresses the large set images by about 5 8 more than jxr1 and by 6 7 more than jxr0 on the average we provide some rate distortion plots on lossy coding which show that the modified jac distinctly outperforms jxr0 but jxr1 beats us by about a similar margin

lossless subband coding system based on rounding transform we propose a new rounding transform called the overlapping rounding transform ort it is defined as a two port input two port output fir filtering system with a pair of rounding operations the ort is applied to develop lossless subband coding systems the ort approach has both a simpler representation and more possibilities for lossless subband implementation than the lifting scheme

minlab minimum noise structure for ladder based biorthogonal filter banks we introduce a minimum noise structure for ladder based biorthogonal minlab filter bank the minimum noise structure ensures that the quantization error has a unity noise gain even though the filter bank is biorthogonal the coder has a very low design and implementation cost the perfect reconstruction property is structurally preserved optimal bit allocation and coding gain formulas are derived we show that the coding gain of the optimal minlab coder is always greater than or equal to unity for both ar 1 process and ma 1 process the minlab coder with two taps has a higher coding gain than the optimal orthonormal coder with an infinite number of taps in addition to its superior decorrelation ability it has many other desired features that make it a potentially valuable and attractive alternative to the orthonormal coder especially for a high fidelity compression

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

infinity norm rotation transforms a new general paradigm of dynamic range preserving one to one mapping infinity norm rotations analogous to the general 2 norm rotations are proposed in this paper analogous to the well known discrete cosine transforms the linear 2 norm rotation transforms which preserve the 2 norm of the rotated vectors the proposed infinity norm rotation transforms are piecewise linear transforms which preserve the infinity norm of vectors besides the advantages of perfect reversibility in place calculation and dynamic range preservation the infinity norm rotation transforms also have good energy compact ability which is suitable for signal compression and analysis it can be implemented by shear transforms based on the 2 d rotation factorization of similar orthogonal transform matrices such as dct matrices the performance of the new transforms is illustrated with 2 d patterns and histograms its good performance in lossy and lossless image compression compared with other integer reversible transforms is demonstrated in the experiments

on the necessity and sufficiency of plus factorizations plus factorizations or customizable triangular factorizations of nonsingular matrices have found applications in source coding and computer graphics however there are still some open problems in this paper we present a new necessary condition and a sufficient condition for the existence of generic plus factorizations

a c0 discontinuous galerkin method for the stationary quasi geostrophic equations of the ocean abstract this work concerns the development of a finite element algorithm for the stationary quasi geostrophic equations to treat the large scale wind driven ocean circulation the algorithm is developed based on the streamfunction formulation involving fourth order gradients of the streamfunction here we examine the adaptation of a relatively inexpensive nonconforming method based on c 0 basis functions we develop the variational form of the method and establish consistency the method weakly enforces continuity of the normal flux across interelement boundaries and stabilization is achieved via nitsche s method explicit expression for the choice of the stabilization parameter is derived moreover the theoretical error estimate for the linear stommel munk model is performed numerical results from several benchmark problems on rectangular and curved domains are provided to demonstrate the accuracy and robustness of the method we also provide the mediterranean sea example to demonstrate the capability of the approach to the wind driven ocean circulation simulation

design of iir orthogonal wavelet filter banks using lifting scheme the lifting scheme is well known to be an efficient tool for constructing second generation wavelets and is often used to design a class of biorthogonal wavelet filter banks for its efficiency the lifting implementation has been adopted in the international standard jpeg2000 it is known that the orthogonality of wavelets is an important property for many applications this paper presents how to implement a class of infinite impulse response iir orthogonal wavelet filter banks by using the lifting scheme with two lifting steps it is shown that a class of iir orthogonal wavelet filter banks can be realized by using allpass filters in the lifting steps then the design of the proposed iir orthogonal wavelet filter banks is discussed the designed iir orthogonal wavelet filter banks have approximately linear phase responses finally the proposed iir orthogonal wavelet filter banks are applied to the image compression and then the coding performance of the proposed iir filter banks is evaluated and compared with the conventional wavelet transforms

recursive autoregressive spectral estimation by minimization of the free energy a digital signal processing technique applicable to power spectrum estimation designated as the minimum free energy method is described with no a priori model assumption and no attempt to extract special features such as sinusoids one can obtain high resolution even with high noise contamination of the measured signal the technique is demonstrated by modification of the burg recursive method of spectral analysis a recursive minimum free energy method in which the reflection coefficient is chosen at each step is proposed for minimizing the free energy the burg energy measure minus the product of a temperature and an information entropy the method produces a spectral estimator more impervious to high noise contamination than the burg method and diminishes the burg tendency to produce spurious peaks

regularization operators for natural images based on nonlinear perception models image restoration requires some a priori knowledge of the solution some of the conventional regularization techniques are based on the estimation of the power spectrum density simple statistical models for spectral estimation just take into account second order relations between the pixels of the image however natural images exhibit additional features such as particular relationships between local fourier or wavelet transform coefficients biological visual systems have evolved to capture these relations we propose the use of this biological behavior to build regularization operators as an alternative to simple statistical models the results suggest that if the penalty operator takes these additional features in natural images into account it will be more robust and the choice of the regularization parameter is less critical

modulo transforms an alternative to lifting this paper introduces a new paradigm for the construction of reversible transforms that map integers to integers transform matrices with integer entries are first considered and the modular arithmetic properties of transform coefficients are studied it is shown that these transform coefficients are redundant in modular arithmetic further this redundancy can be exploited by quantizing transform coefficients critically so as to produce an effective scaled transformation with unit determinant this forms the basis of a class of transforms referred to as modulo transforms that are reversible and unit determinant conditions necessary for applications such as lossless compression and reversible image rotation the theory of modulo transforms is examined in depth analysis based on modular arithmetic shows that two dimensional rotations can be critically quantized albeit with nonequal bin widths along axes a construction procedure is derived for realizing a reversible transform with small or unit scaling factors and a theorem is stated wherein certain pythagorean triples can be scalar quantized to produce a reversible normalized scalefree transform matrix modulo transforms and lifting are compared and contrasted in theory and in experiments the computational aspects of modulo transforms are also discussed in this paper

reversible resampling of integer signals except some extremely special cases signal resampling was generally considered to be irreversible because of strong attenuation of high frequencies after interpolation in this paper we prove that signal resampling based on polynomial interpolation can be reversible even for integer signals i e the original signal can be reconstructed losslessly from the resampled data by using matrix factorization we also propose a reversible method for uniform shifted resampling and uniform scaled and shifted resampling the new factorization yields three elementary integer reversible matrices the method is actually a new way to compute linear transforms and a lossless integer implementation of linear transforms with the factor matrices it can be applied to integer signals by in place integer reversible computation which needs no auxiliary memory to keep the original sample data for the transformation during the process or for ldquoundordquo recovery after the process some examples of low order resampling solutions are also presented in this paper and our experiments show that the resampling error relative to the original signal is comparable to that of the traditional irreversible resampling

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

scalable image coding using reversible integer wavelet transforms reversible integer wavelet transforms allow both lossless and lossy decoding using a single bitstream we present a new fully scalable image coder and investigate the lossless and lossy performance of these transforms in the proposed coder the lossless compression performance of the presented method is comparable to jpeg ls the lossy performance is quite competitive with other efficient lossy compression methods

image interpolation for progressive transmission by using radial basis function networks investigates the application of a radial basis function network rbfn to hierarchical image coding for progressive transmission the rbfn is then used to generate an interpolated image from the subsampled version an efficient method of computing the network parameters is developed for reduction in computational and memory requirements the coding method does not suffer from problems of blocking effect and can produce the coarsest image quickly quantization error effects introduced at one stage are considered in decoding images at the following stages thus allowing lossless progressive transmission

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

nonlinear multiresolution signal decomposition schemes ii morphological wavelets interest in multiresolution techniques for signal processing and analysis is increasing steadily an important instance of such a technique is the so called pyramid decomposition scheme this paper presents a general theory for constructing linear as well as nonlinear pyramid decomposition schemes for signal analysis and synthesis the proposed theory is based on the following ingredients 1 the pyramid consists of a finite or infinite number of levels such that the information content decreases toward higher levels and 2 each step toward a higher level is implemented by an information reducing analysis operator whereas each step toward a lower level is implemented by an information preserving synthesis operator one basic assumption is necessary synthesis followed by analysis yields the identity operator meaning that no information is lost by these two consecutive steps several examples of pyramid decomposition schemes are shown to be instances of the proposed theory a particular class of linear pyramids morphological skeleton decompositions the morphological haar pyramid median pyramids etc furthermore the paper makes a distinction between single scale and multiscale decomposition schemes i e schemes without or with sample reduction finally the proposed theory provides the foundation of a general approach to constructing nonlinear wavelet decomposition schemes and filter banks

spline based finite element method for the stationary quasi geostrophic equations on arbitrary shaped coastal boundaries abstract this work concerns a b spline based finite element algorithm for the stationary quasi geostrophic equations to treat the large scale wind driven ocean circulation on arbitrary shaped domains the algorithm models arbitrary shaped coastal boundaries on intra element or embedded boundaries dirichlet boundary conditions on the embedded boundaries are weakly imposed and stabilization is achieved via nitsche s method we employ a hierarchical local refinement approach to improve the geometrical representation of curved boundaries results from several benchmark problems on rectangular and curved domains are provided to demonstrate the accuracy and robustness of the method we also provide the mediterranean sea example that illustrates the effectiveness of the approach in the wind driven ocean circulation simulation

a wavelet based two stage near lossless coder in this paper we present a two stage near lossless compression scheme it belongs to the class of lossy plus residual coding and consists of a wavelet based lossy layer followed by arithmetic coding of the quantized residual to guarantee a given linfin error bound in the pixel domain we focus on the selection of the optimum bit rate for the lossy layer to achieve the minimum total bit rate unlike other similar lossy plus lossless approaches using a wavelet based lossy layer the proposed method does not require iteration of decoding and inverse discrete wavelet transform in succession to locate the optimum bit rate we propose a simple method to estimate the optimal bit rate with a theoretical justification based on the critical rate argument from the rate distortion theory and the independence of the residual error

prediction based lower triangular transform a new nonunitary transform called the prediction based lower triangular transform plt is introduced for signal compression the new transform has the same decorrelation property as the kahurnen loeve transform klt but its implementational cost is less than one half of klt compared with the klt the design cost of an m spl times m plt is much lower and is only of the order of o m sup 2 moreover the plt can be factorized into simple building blocks using two different factorizations we introduce two minimum noise structures that have roughly the same complexity as the direct implementation of plt these minimum noise structures have the following properties 1 its noise gain is unity even though the transform is nonunitary 2 perfect reconstruction is structurally guaranteed 3 it can be used for both lossy lossless compression we show that the coding gain of plt implemented using the minimum noise structure is the same as that of klt furthermore universal transform coders using plt are derived for ar 1 process the m spl times m plt has a closed form and needs only m 1 multiplications and additions

joint source channel coding for deep space image transmission using rateless codes a new coding scheme for image transmission over noisy channel is proposed similar to standard image compression the scheme includes a linear transform followed by successive refinement scalar quantization unlike conventional schemes though in the proposed system the quantized transform coefficients are linearly mapped into channel symbols using systematic linear encoders this fixed to fixed length linear index coding approach avoids the use of an explicit entropy coding stage e g arithmetic or huffman coding which is typically fragile to channel post decoding residual errors we use linear codes over gf 4 which are particularly suited for this application since they are matched to the dead zone quantizer symbol alphabet and to the qpsk modulation used on the deep space communication channel we optimize the proposed system where the linear codes are systematic raptor codes over gf 4 the rateless property of raptor encoders allows to implement a continuum of coding rates in order to accurately match the channel coding rate to the transmission channel capacity and to the quantized source entropy rate for each transform subband and refinement level comparisons are provided with respect to the concatenation of state of the art image coding and channel coding schemes used by jet propulsion laboratories jpl for the mars exploration rover mer mission

differential equation for the amplitude of wrinkles introduction t he renewed interest in the phenomenonof wrinkling of membranes fueled by applications to the aerospace industry has spurred considerable activity on both the theoretical and computational aspectsof the subject althoughthe wrinklingphenomenonis known to be a case of shell buckling it seems unwise to utilize this knowledge in actual computations because treating the membrane as a shell with a vanishinglysmall thickness leads to the frustrating effects of numerical instability there exist on the other hand techniques based on themembrane theory alone that permit us to obtain with relative ease and numerical robustness not only the extent of thewrinkledzones but also the eldof directionsof thewrinkles 1i4 all that is needed therefore is a means for calculating the amplitude and wavelength of the wrinkles in an already known wrinkled domain in this note we derive an ordinary differential equation whose solution delivers such information for clarity of the presentation the equation is obtained under a number of simplifying assumptions mostly involving the smallness of the deformations however the method is straightforwardlyextendable to the general case our guiding principle has been to keep only those aspects of the model that are clearly determinant of the result while leaving all other aspects for future re nement we believe that this philosophy will serve to highlight the essential features rather than the technicalities of the proposedequation note that even under a geometrically andmaterially linear regime the resultingdifferentialequation is highly nonlinear the physical reason for this nonlinearityis to be foundin that becausewrinklingentailsno stress in thedirectionperpendicular to the wrinkles there exists a severe constraint between the wavelength and amplitude of the wrinkles this can be phrased intuitively as follows for a given amount of wrinkling strain the larger the number of wrinkles the smaller their amplitude to the best of our knowledge the only attempt in a direction similar to the one proposed herein is due to wong and pellegrino in their work these authors present a model basedmainly on the particular case of shearing of a rectangular panel their results are very valuable and will be used here as a benchmark for validation purposes

worst case error analysis of lifting based fast dct algorithms integer dcts have a wide range of applications in lossless coding especially in image compression an integer to integer dct of radix 2 length n is a nonlinear left invertible mapping which acts on spl zopf sup n and approximates the classical discrete cosine transform dct of length n all known integer to integer dct algorithms of length 8 are based on factorizations of the cosine matrix c sub 8 sup ii into a product of sparse matrices and work with lifting steps and rounding off for fast implementation one replaces floating point numbers by appropriate dyadic rationals both rounding and approximation leads to truncation errors in this paper we consider an integer to integer transform for 2 spl times 2 rotation matrices and give estimates of the truncation errors for arbitrary approximating dyadic rationals further using two known integer to integer dct algorithms we show examplarily how to estimate the worst case truncation error of lifting based integer to integer algorithms in fixed point arithmetic whose factorizations are based on 2 spl times 2 rotation matrices

error estimates of b spline based finite element methods for the stationary quasi geostrophic equations of the ocean abstract this paper presents theoretical error estimates of b spline based finite element methods for the streamfunction formulation of the stationary quasi geostrophic equations which describe the large scale wind driven ocean circulation we introduce variational formulations of the streamfunction formulation inspired by the interior penalty discontinuous galerkin method dirichlet boundary conditions are weakly enforced in the formulations and stabilizations are achieved via nitsche s method existence and uniqueness of the approximation are proved and optimal error estimates in the energy norm are demonstrated under a small data assumption numerical experiments are performed to verify the theoretical error estimates on rectangular and l shape geometries

fuzzy logic based matching pursuits for lossless predictive coding of still images this paper presents an application of fuzzy logic techniques to the reversible compression of grayscale images with reference to a spatial differential pulse code modulation dpcm scheme prediction may be accomplished in a space varying fashion either as adaptive i e with predictors recalculated at each pixel or as classified in which image blocks or pixels are labeled in a number of classes for which fitting predictors are calculated here an original tradeoff is proposed a space varying linear regression prediction is obtained through fuzzy logic techniques as a problem of matching pursuit in which a predictor different for every pixel is obtained as an expansion in series of a finite number of prototype nonorthogonal predictors that are calculated in a fuzzy fashion as well to enhance entropy coding the spatial prediction is followed by context based statistical modeling of prediction errors a thorough comparison with the most advanced methods in the literature as well as an investigation of performance trends and computing times to work parameters highlight the advantages of the proposed fuzzy approach to data compression

rounding transform and its application for lossless pyramid structured coding a new transform called the rounding transform rt is introduced in this paper this transform maps an integer vector onto another integer vector by using weighted average and difference filters followed by a rounding operation the rt can be applied to lossless pyramid structured coding with various elementary block sizes and filters in addition it generalizes other mean based lossless pyramid structured coding schemes

r d optimized tree structured compression algorithms with discrete directional wavelet transform a new image coding method based on discrete directional wavelet transform s wt and quad tree decomposition is proposed here the s wt is a kind of transform proposed in v velisavljevic b beferull lozano m vetterli p l dragotti directionlets anisotropic multidirectional representation with separable filtering ieee trans image process 15 7 2006 which is based on lattice theory and with the difference with the standard wavelet transform is that the former allows more transform directions because the directional property in a small region is more regular than in a big block generally in order to sufficiently make use of the multidirectionality and directional vanishing moment dvm of s wt the input image is divided into many small regions by means of the popular quad tree segmentation and the splitting criterion is on the rate distortion sense after the optimal quad tree is obtained by means of the embedded property of speck a resource bit allocation algorithm is fast implemented utilizing the model proposed in m rajpoot model based optimal bit allocation in ieee data compression conference 2004 proceedings dcc 2004 19 experiment results indicate that our algorithms perform better compared to some state of the art image coders

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

lossless compression of color mosaic images lossless compression of color mosaic images poses a unique and interesting problem of spectral decorrelation of spatially interleaved r g b samples we investigate reversible lossless spectral spatial transforms that can remove statistical redundancies in both spectral and spatial domains and discover that a particular wavelet decomposition scheme called mallat wavelet packet transform is ideally suited to the task of decorrelating color mosaic data we also propose a low complexity adaptive context based golomb rice coding technique to compress the coefficients of mallat wavelet packet transform the lossless compression performance of the proposed method on color mosaic images is apparently the best so far among the existing lossless image codecs

tension field theory a general theory of the tension field is developed for application to the analysis of wrinkling in isotropic elastic membranes undergoing finite deformations the principal contribution is a partial differential equation describing a geometrical property of tension trajectories this is one of a system of two equations which describes the state of stress independently of the deformation this system is strongly elliptic at any stable solution whereas the deformation is described by a system of parabolic type controllable solutions i e those states that can be maintained in any isotropic elastic material by application of edge tractions and lateral pressure alone are obtained the general axisymmetric problem is solved implicitly and the theory is applied to the solution of two representative examples existing small strain theories are shown to correspond to a singular limit of the general theory at which the underlying system changes from elliptic to parabolic type

b spline based finite element method for the stationary quasi geostrophic equations of the ocean abstract we present a b spline based conforming finite element method of the streamfunction formulation of the stationary one layer quasi geostrophic equations for the study of the large scale wind driven ocean circulation the method encompasses standard simplifications of these equations in particular the linear stommel and stommel munk models a variational form of the method is developed and its consistency is established in this formulation dirichlet boundary conditions are enforced only weakly and stabilization is achieved via nitsche s method stability parameters are evaluated by solving a local generalized eigenvalue problem on the dirichlet boundary and by monitoring the condition number of the resulting linear systems comparisons of the results from our simulations with previously published results and convergence studies lead us to conclude that our finite element discretization is accurate

lossy to lossless compression of medical volumetric data using three dimensional integer wavelet transforms we study lossy to lossless compression of medical volumetric data using three dimensional 3 d integer wavelet transforms to achieve good lossy coding performance it is important to have transforms that are unitary in addition to the lifting approach we first introduce a general 3 d integer wavelet packet transform structure that allows implicit bit shifting of wavelet coefficients to approximate a 3 d unitary transformation we then focus on context modeling for efficient arithmetic coding of wavelet coefficients two state of the art 3 d wavelet video coding techniques namely 3 d set partitioning in hierarchical trees kim et al 2000 and 3 d embedded subband coding with optimal truncation xu et al 2001 are modified and applied to compression of medical volumetric data achieving the best performance published so far in the literature both in terms of lossy and lossless compression

adaptive ar modeling in white gaussian noise autoregressive ar modeling is widely used in signal processing the coefficients of an ar model can be easily obtained with a least mean square lms prediction error filter however it is known that this filter gives a biased solution when the input signal is corrupted by white gaussian noise treichler 1979 suggested the spl gamma lms algorithm to remedy this problem and proved that the mean weight vector can converge to the wiener solution in this paper we develop a new algorithm that extends works of vijayan et al 1990 for adaptive ar modeling in the presence of white gaussian noise by theoretical analysis we show that the performance of the new algorithm is superior to the spl gamma lms filter simulations are also provided to support our theoretical results

imposing dirichlet boundary conditions with nitsche s method and spline based finite elements a key challenge while employing non interpolatory basis functions in finite element methods is the robust imposition of dirichlet boundary conditions the current work studies the weak enforcement of such conditions for b spline basis functions with application to both second and fourth order problems this is achieved using concepts borrowed from nitsche s method which is a stabilized method for imposing constraints on surfaces conditions for the stability of the system of equations are derived for each class of problem stability parameters in the nitsche weak form are then evaluated by solving a local generalized eigenvalue problem at the dirichlet boundary the approach is designed to work equally well when the grid used to build the splines conforms to the physical boundary of interest as well as to the more general case when it does not through several numerical examples the approach is shown to yield optimal rates of convergence copyright 2010 john wiley sons ltd

lossless image compression with projection based and adaptive reversible integer wavelet transforms reversible integer wavelet transforms are increasingly popular in lossless image compression as evidenced by their use in the recently developed jpeg2000 image coding standard in this paper a projection based technique is presented for decreasing the first order entropy of transform coefficients and improving the lossless compression performance of reversible integer wavelet transforms the projection technique is developed and used to predict a wavelet transform coefficient as a linear combination of other wavelet transform coefficients it yields optimal fixed prediction steps for lifting based wavelet transforms and unifies many wavelet based lossless image compression results found in the literature additionally the projection technique is used in an adaptive prediction scheme that varies the final prediction step of the lifting based transform based on a modeling context compared to current fixed and adaptive lifting based transforms the projection technique produces improved reversible integer wavelet transforms with superior lossless compression performance it also provides a generalized framework that explains and unifies many previous results in wavelet based lossless image compression

reversible symmetric nonexpansive convolution an effective image boundary processing for mbi m channel lifting based linear phase filter banks we present an effective image boundary processing for m channel m in bbn m geq 2 lifting based linear phase filter banks that are applied to unified lossy and lossless image compression coding i e lossy to lossless image coding the reversible symmetric extension we propose is achieved by manipulating building blocks on the image boundary and reawakening the symmetry of each building block that has been lost due to rounding error on each lifting step in addition complexity is reduced by extending nonexpansive convolution called reversible symmetric nonexpansive convolution because the number of input signals does not even temporarily increase our method not only achieves reversible boundary processing but also is comparable with irreversible symmetric extension in lossy image coding and outperformed periodic extension in lossy to lossless image coding

morse description and geometric encoding of digital elevation maps two complementary geometric structures for the topographic representation of an image are developed in this work the first one computes a description of the morse topological structure of the image while the second one computes a simplified version of its drainage structure the topographic significance of the morse and drainage structures of digital elevation maps dems suggests that they can been used as the basis of an efficient encoding scheme as an application we combine this geometric representation with an interpolation algorithm and lossless data compression schemes to develop a compression scheme for dems this algorithm achieves high compression while controlling the maximum error in the decoded elevation map a property that is necessary for the majority of applications dealing with dems we present the underlying theory and compression results for standard dem data

lossless image compression based on optimal prediction adaptive lifting and conditional arithmetic coding the optimal predictors of a lifting scheme in the general n dimensional case are obtained and applied for the lossless compression of still images using first quincunx sampling and then simple row column sampling in each case the efficiency of the linear predictors is enhanced nonlinearly directional postprocessing is used in the quincunx case and adaptive length postprocessing in the row column case both methods are seen to perform well the resulting nonlinear interpolation schemes achieve extremely efficient image decorrelation we further investigate context modeling and adaptive arithmetic coding of wavelet coefficients in a lossless compression framework special attention is given to the modeling contexts and the adaptation of the arithmetic coder to the actual data experimental evaluation shows that the best of the resulting coders produces better results than other known algorithms for multiresolution based lossless image coding