necessary conditions for ternary algebras ternary algebras constructed from ternary commutators or as we call them ternutators defined as the alternating sum of products of three operators have been shown to satisfy cubic identities as necessary conditions for their existence here we examine the situation where we permit identities not solely constructed from ternutators or nested ternutators and we find that in general these impose additional restrictions for example the anti commutators or commutators of the operators must obey some linear relations among themselves

perceptual video coding based on ssim inspired divisive normalization we propose a perceptual video coding framework based on the divisive normalization scheme which is found to be an effective approach to model the perceptual sensitivity of biological vision but has not been fully exploited in the context of video coding at the macroblock mb level we derive the normalization factors based on the structural similarity ssim index as an attempt to transform the discrete cosine transform domain frame residuals to a perceptually uniform space we further develop an mb level perceptual mode selection scheme and a frame level global quantization matrix optimization method extensive simulations and subjective tests verify that compared with the h 264 avc video coding standard the proposed method can achieve significant gain in terms of rate ssim performance and provide better visual quality

an envelope for malcev algebras we prove that for every malcev algebra m there exist an algebra u m and a monomorphism m u m of m into the commutator algebra u m such that the image of m lies into the alternative center of u m and u m is a universal object with respect to such homomorphisms the algebra u m in general is not alternative but it has a basis of poincare birkhoff witt type over m and inherits some good properties of universal enveloping algebras of lie algebras in particular the elements of m can be characterized as the primitive elements of the algebra u m with respect to the diagonal homomorphism u m u m u m an extension of ado iwasawa theorem to malcev algebras is also proved

maximum likelihood based estimation of frequency and phase offset in dct ofdm systems under non circular transmissions algorithms analysis and comparisons recently the advantages of the discrete cosine transform dct based orthogonal frequency division multiplexing ofdm have come to the light we thus consider dct ofdm with non circular transmission our results cover circular transmission as well and present two blind joint maximum likelihood frequency offset and phase offset estimators both our theoretical analysis and numerical comparisons reveal new advantages of dct ofdm over the traditional discrete fourier transform dft based ofdm these advantages as well as those already uncovered in the early works on dct ofdm support the belief that dct ofdm is a promising multi carrier modulation scheme

defining relations for automorphism groups of free algebras abstract we describe a set of defining relations for automorphism groups of finitely generated free algebras of nielsen schreier varieties in particular this gives a representation of the automorphism groups of free lie algebras by generators and defining relations

algebras hyperalgebras nonassociative bialgebras and loops abstract sabinin algebras are a broad generalization of lie algebras that include lie malcev and bol algebras as very particular examples we present a construction of a universal enveloping algebra for sabinin algebras and the corresponding poincare birkhoff witt theorem a nonassociative counterpart of hopf algebras is also introduced and a version of the milnor moore theorem is proved loop algebras and universal enveloping algebras of sabinin algebras are natural examples of these nonassociative hopf algebras identities of loops move to identities of nonassociative hopf algebras by a linearizing process in this way nonassociative algebras and hopf algebras interlace smoothly

adaptive image restoration using a generalized gaussian model for unknown noise a model adaptive method is proposed for restoring blurred and noise corrupted images the generalized p gaussian family of probability density functions is used as the approximating parametric noise model distribution shape parameters are estimated from the image and the resulting maximum likelihood optimization problem is solved an iterative algorithm for data directed restoration is presented and analyzed

applications of universal context modeling to lossless compression of gray scale images inspired by theoretical results on universal modeling a general framework for sequential modeling of gray scale images is proposed and applied to lossless compression the model is based on stochastic complexity considerations and is implemented with a tree structure it is efficiently estimated by a modification of the universal algorithm context several variants of the algorithm are described the sequential lossless compression schemes obtained when the context modeler is used with an arithmetic coder are tested with a representative set of gray scale images the compression ratios are compared with those obtained with state of the art algorithms available in the literature with the results of the comparison consistently favoring the proposed approach

regular articlethe structure of the young symmetrizers for spin representations of the symmetric group ii the first paper in this series established that the projective analogue of the young symmetrizer recently introduced by nazarov has a naturalpxq structure comparable with thepq form of the classical symmetrizer this second paper develops the theory on this decomposition further a more efficient construction of the projective symmetrizer is presented for certain classes of partitions this approach yields a compact expression for the intermediate factorx in the projective decomposition

rate bounds on ssim index of quantized images in this paper we derive bounds on the structural similarity ssim index as a function of quantization rate for fixed rate uniform quantization of image discrete cosine transform dct coefficients under the high rate assumption the space domain ssim index is first expressed in terms of the dct coefficients of the space domain vectors the transform domain ssim index is then used to derive bounds on the average ssim index as a function of quantization rate for uniform gaussian and laplacian sources as an illustrative example uniform quantization of the dct coefficients of natural images is considered we show that the ssim index between the reference and quantized images fall within the bounds for a large set of natural images further we show using a simple example that the proposed bounds could be very useful for rate allocation problems in practical image and video coding applications

on construction and simulation of autoregressive sources with near laplace marginals in this paper we focus upon the problem of modeling and simulation of stationary non gaussian time series in particular we consider a first order autoregressive process whose marginal distribution is close to the laplace density this model allows us to simulate correlated non gaussian signals typically appearing in speech analysis compression and noise synthesis the monte carlo rejection method is applied to develop efficient algorithms for simulation of the proposed autoregressive process we also extend our theory and algorithms to the related issue of constructing a correlated bivariate time series model with near laplace margins a theoretical analysis of the average complexity of the proposed simulation algorithms is included

free akivis algebras primitive elements and hyperalgebras free akivis algebras and primitive elements in their universal enveloping algebras are investigated it is proved that subalgebras of free akivis algebras are free and that finitely generated subalgebras are finitely residual decidability of the word problem for the variety of akivis algebras is also proved the conjecture of k h hofmann and k strambach problem 6 15 in topological and analytic loops in quasigroups and loops theory and applications series in pure mathematics o chein h o pflugfelder and j d h smith eds vol 8 pp 205 262 heldermann verlag berlin 1990 on the structure of primitive elements is proved to be not valid and a full system of primitive elements in free nonassociative algebra is constructed finally it is proved that every algebra b can be considered as a hyperalgebra that is a system with a series of multilinear operations that plays a role of a tangent algebra for a local analytic loop where the hyperalgebra operations on b are interpreted by certain primitive elements

an mdl framework for sparse coding and dictionary learning the power of sparse signal modeling with learned overcomplete dictionaries has been demonstrated in a variety of applications and fields from signal processing to statistical inference and machine learning however the statistical properties of these models such as underfitting or overfitting given sets of data are still not well characterized in the literature as a result the success of sparse modeling depends on hand tuning critical parameters for each data and application this work aims at addressing this by providing a practical and objective characterization of sparse models by means of the minimum description length mdl principle a well established information theoretic approach to model selection in statistical inference the resulting framework derives a family of efficient sparse coding and dictionary learning algorithms which by virtue of the mdl principle are completely parameter free furthermore such framework allows to incorporate additional prior information to existing models such as markovian dependencies or to define completely new problem formulations including in the matrix analysis area in a natural way these virtues will be demonstrated with parameter free algorithms for the classic image denoising and classification problems and for low rank matrix recovery in video applications however the framework is not limited to this imaging data and can be applied to a wide range of signal and data types and tasks

affine sergeev algebra and q analogues of the young symmetrizers for projective representations of the symmetric group we study a q deformation for the crossed product of the symmetric group s n with the clifford algebra on n anticommuting generators we obtain a q version of the projective analogue for the classical young symmetrizer introduced by the second author our main tool is an analogue of the hecke algebra of complex valued functions on the group mbox gl n over a p adic field relative to the iwahori subgroup

compression artifact reduction by overlapped block transform coefficient estimation with block similarity block transform coded images usually suffer from annoying artifacts at low bit rates caused by the coarse quantization of transform coefficients in this paper we propose a new method to reduce compression artifacts by the overlapped block transform coefficient estimation from non local blocks in the proposed method the discrete cosine transform coefficients of each block are estimated by adaptively fusing two prediction values based on their reliabilities one prediction is the quantized values of coefficients decoded from the compressed bitstream whose reliability is determined by quantization steps the other prediction is the weighted average of the coefficients in nonlocal blocks whose reliability depends on the variance of the coefficients in these blocks the weights are used to distinguish the effectiveness of the coefficients in nonlocal blocks to predict original coefficients and are determined by block similarity in transform domain to solve the optimization problem the overlapped blocks are divided into several subsets each subset contains nonoverlapped blocks covering the whole image and is optimized independently therefore the overall optimization is reduced to a set of sub optimization problems which can be easily solved finally we provide a strategy for parameter selection based on the compression levels experimental results show that the proposed method can remarkably reduce compression artifacts and significantly improve both the subjective and objective qualities of block transform coded images

sending a laplacian source using hybrid digital analog codes in this paper we study transmission of a memoryless laplacian source over three types of channels additive white laplacian noise awln additive white gaussian noise awgn and slow flat fading rayleigh channels under both bandwidth compression and bandwidth expansion for this purpose we analyze two well known hybrid digital analog hda joint source channel coding schemes for bandwidth compression and one for bandwidth expansion then we obtain achievable absolute error distortion regions of the hda schemes for the matched signal to noise ratio snr case as well as the mismatched snr scenario using numerical examples it is shown that these schemes can achieve a distortion very close to the provided lower bound for the awln channel and to the optimum performance theoretically attainable bound for awgn and rayleigh fading channels on mean absolute error distortion under matched snr conditions in addition a non linear analog coding scheme is analyzed and its performance is compared to the hda schemes for bandwidth compression under both matched and mismatched snr scenarios the results show that the hda schemes outperform the non linear analog coding over the whole csnr region

model selection and the principle of minimum description length this article reviews the principle of minimum description length mdl for problems of model selection by viewing statistical modeling as a means of generating descriptions of observed data the mdl framework discriminates between competing models based on the complexity of each description this approach began with kolmogorov s theory of algorithmic complexity matured in the literature on information theory and has recently received renewed attention within the statistics community here we review both the practical and the theoretical aspects of mdl as a tool for model selection emphasizing the rich connections between information theory and statistics at the boundary between these two disciplines we find many interesting interpretations of popular frequentist and bayesian procedures as we show mdl provides an objective umbrella under which rather disparate approaches to statistical modeling can coexist and be compared we illustrate the mdl principle by considering problems in regression nonpar

distributions of the two dimensional dct coefficients for images for a two dimensional discrete cosine transform dct image coding system there have been different assumptions concerning the distributions of the transform coefficients this paper presents results of distribution tests that indicate that for many images the statistics of the coefficients are best approximated by a gaussian distribution for the dc coefficient and a laplacian distribution for the other coefficients furthermore from a simulation of the dct coding system it is shown that the assumption that the coefficients are laplacian yields a higher actual output signal to noise ratio and a much better agreement between theory and simulation than the gaussian assumption

free braided nonassociative hopf algebras and sabinin τ algebras abstract let v be a linear space over a field k with a braiding v v v v we prove that the braiding has a unique extension on the free nonassociative algebra k v freely generated by v so that k v is a braided algebra moreover we prove that the free braided algebra k v has a natural structure of a braided nonassociative hopf algebra such that every element of the space of generators v is primitive in the case of involutive braidings 2 id we describe braided analogues of shestakov umirbaev operations and prove that these operations are primitive operations we introduce a braided version of sabinin algebras and prove that the set of all primitive elements of a nonassociative algebra is a sabinin algebra

lie s correspondence for commutative automorphic formal loops abstract we develop lie s correspondence for commutative automorphic formal loops which are natural candidates for non associative abelian groups to show how linearization techniques based on hopf algebras can be applied to study non linear structures over fields of characteristic zero we prove that the category of commutative automorphic formal loops is equivalent to certain category of lie triple systems an explicit baker campbell hausdorff formula for these loops is also obtained with the help of formal power series with coefficients in the algebra of 3 by 3 matrices our formula is strongly related to the function e 2 s e 2 t s t 2 e 2 s t 1

universal coding information prediction and estimation a connection between universal codes and the problems of prediction and statistical estimation is established a known lower bound for the mean length of universal codes is sharpened and generalized and optimum universal codes constructed the bound is defined to give the information in strings relative to the considered class of processes the earlier derived minimum description length criterion for estimation of parameters including their number is given a fundamental information theoretic justification by showing that its estimators achieve the information in the strings it is also shown that one cannot do prediction in gaussian autoregressive moving average arma processes below a bound which is determined by the information in the data

random walk graph laplacian based smoothness prior for soft decoding of jpeg images given the prevalence of joint photographic experts group jpeg compressed images optimizing image reconstruction from the compressed format remains an important problem instead of simply reconstructing a pixel block from the centers of indexed discrete cosine transform dct coefficient quantization bins hard decoding soft decoding reconstructs a block by selecting appropriate coefficient values within the indexed bins with the help of signal priors the challenge thus lies in how to define suitable priors and apply them effectively in this paper we combine three image priors laplacian prior for dct coefficients sparsity prior and graph signal smoothness prior for image patches to construct an efficient jpeg soft decoding algorithm specifically we first use the laplacian prior to compute a minimum mean square error initial solution for each code block next we show that while the sparsity prior can reduce block artifacts limiting the size of the overcomplete dictionary to lower computation would lead to poor recovery of high dct frequencies to alleviate this problem we design a new graph signal smoothness prior desired signal has mainly low graph frequencies based on the left eigenvectors of the random walk graph laplacian matrix lerag compared with the previous graph signal smoothness priors lerag has desirable image filtering properties with low computation overhead we demonstrate how lerag can facilitate recovery of high dct frequencies of a piecewise smooth signal via an interpretation of low graph frequency components as relaxed solutions to normalized cut in spectral clustering finally we construct a soft decoding algorithm using the three signal priors with appropriate prior weights experimental results show that our proposal outperforms the state of the art soft decoding algorithms in both objective and subjective evaluations noticeably

the projective representations of the hyperoctahedral group the hyperoctahedral group the weyl group of the root system bn has seven distinct nonsplit double covers for n 4 and hence seven families of projective representations we give constructions of all the irreducible representations of these seven double covers in terms of symmetric group representations and determine the associated character tables as a corollary we also obtain the irreducible projective representations and characters of the weyl group of the root system dn

globally convergent algorithms for estimating generalized gamma distributions in fast signal and image processing many applications in real time signal image and video processing require automatic algorithms for rapid characterizations of signals and images through fast estimation of their underlying statistical distributions we present fast and globally convergent algorithms for estimating the three parameter generalized gamma distribution g gamma d the proposed method is based on novel scale independent shape estimation sise equations we show that the sise equations have a unique global root in their semi infinite domains and the probability that the sample sise equations have a unique global root tends to one the consistency of the global root its scale and index shape estimators is obtained furthermore we establish that with probability tending to one newton raphson nr algorithms for solving the sample sise equations converge globally to the unique root from any initial value in its given domain in contrast to existing methods another remarkable novelty is that the sample sise equations are completely independent of gamma and polygamma functions and involve only elementary mathematical operations making the algorithms well suited for real time both hardware and software implementations the sise estimators also allow the maximum likelihood ml ratio procedure to be carried out for testing the generalized gaussian distribution ggd versus the g gamma d finally the fast global convergence and accuracy of our algorithms for finite samples are demonstrated by both simulation studies and real image analysis

operational rate distortion modeling for wavelet video coders based on our statistical investigation of a typical three dimensional 3 d wavelet codec we present a unified mathematical model to describe its operational rate distortion rd behavior the quantization distortion of the reconstructed video frames is assessed by tracking the quantization noise along the 3 d wavelet decomposition trees the coding bit rate is estimated for a class of embedded video coders experimental results show that the model captures sequence characteristics accurately and reveals the relationship between wavelet decomposition levels and the overall rd performance after being trained with offline rd data the model enables accurate prediction of real rd performance of video codecs and therefore can enable optimal rd adaptation of the encoding parameters according to various network conditions

noise level estimation for natural images based on scale invariant kurtosis and piecewise stationarity noise level estimation is crucial in many image processing applications such as blind image denoising in this paper we propose a novel noise level estimation approach for natural images by jointly exploiting the piecewise stationarity and a regular property of the kurtosis in bandpass domains we design a k means based algorithm to adaptively partition an image into a series of non overlapping regions each of whose clean versions is assumed to be associated with a constant but unknown kurtosis throughout scales the noise level estimation is then cast into a problem to optimally fit this new kurtosis model in addition we develop a rectification scheme to further reduce the estimation bias through noise injection mechanism extensive experimental results show that our method can reliably estimate the noise level for a variety of noise types and outperforms some state of the art techniques especially for non gaussian noises

hybrid no reference natural image quality assessment of noisy blurry jpeg2000 and jpeg images in this paper we propose a new image quality assessment method based on a hybrid of curvelet wavelet and cosine transforms called hybrid no reference hnr model from the properties of natural scene statistics the peak coordinates of the transformed coefficient histogram of filtered natural images occupy well defined clusters in peak coordinate space which makes nr possible compared to other methods hnr has three benefits 1 it is an nr method applicable to arbitrary images without compromising the prediction accuracy of full reference methods 2 as far as we know it is the only general nr method well suited for four types of filters noise blur jpeg2000 and jpeg compression and 3 it can classify the filter types of the image and predict filter levels even when the image is results from the application of two different filters we tested hnr on very intensive video image database our image library and laboratory for image video engineering a public library results are compared to the state of the art methods including peak snr structural similarity visual information fidelity and so on

the structure of the young symmetrizers for spin representations of the symmetric group i abstract this paper is the first in a series of three papers on the young symmetrizers for the spin representations of the symmetric group in this opening paper it is shown that the projective analogue of the young symmetrizer recently introduced by nazarov has a structure resembling thep q form exhibited by the classical symmetrizer in contrast to the classical case our decomposition of the projective symmetrizer requires an additional intermediate factorx this factor will be studied in greater detail in the later papers

hybrid laplace distribution based low complexity rate distortion optimized quantization rate distortion optimized quantization rdoq is an efficient encoder optimization method that plays an important role in improving the rate distortion rd performance of the high efficiency video coding hevc codecs however the superior performance of rdoq is achieved at the expense of high computational complexity cost in two stages rd minimization including the determination of optimal quantized level among available candidates for each transformed coefficient and the determination of best quantized coefficients for transform units with the minimum total cost to softly optimize the quantized coefficients to reduce the computational cost of the rdoq algorithm in hevc we propose a low complexity rdoq scheme by modeling the statistics of the transform coefficients with hybrid laplace distribution in this manner specifically designed block level rate and distortion models are established based on the coefficient distribution therefore the optimal quantization levels can be directly determined by optimizing the rd performance of the whole block while the complicated rd cost calculations can be eventually avoided extensive experimental results show that with about 0 3 0 4 rd performance degradation the proposed low complexity rdoq algorithm is able to reduce around 70 quantization time with up to 17 total encoding time reduction compared with the original rdoq implementation in hevc on average

probability distribution estimation for autoregressive pixel predictive image coding pixelwise linear prediction using backward adaptive least squares or weighted least squares estimation of prediction coefficients is currently among the state of the art methods for lossless image compression while current research is focused on mean intensity prediction of the pixel to be transmitted best compression requires occurrence probability estimates for all possible intensity values apart from common heuristic approaches we show how prediction error variance estimates can be derived from the weighted least squares training region and how a complete probability distribution can be built based on an autoregressive image model the analysis of image stationarity properties further allows deriving a novel formula for weight computation in weighted least squares proofing and generalizing ad hoc equations from the literature for sparse intensity distributions in non natural images a modified image model is presented evaluations were done in the newly developed c framework volumetric artificial and natural image lossless coder vanilc which can compress a wide range of images including 16 bit medical 3d volumes or multichannel data a comparison with several of the best available lossless image codecs proofs that the method can achieve very competitive compression ratios in terms of reproducible research the source code of vanilc has been made public

dct regularized extreme visual recovery here we study the extreme visual recovery problem in which over 90 of pixel values in a given image are missing existing low rank based algorithms are only effective for recovering data with at most 90 missing values thus we exploit visual data s smoothness property to help solve this challenging extreme visual recovery problem based on the discrete cosine transform dct we propose a novel dct regularizer that involves all pixels and produces smooth estimations in any view our theoretical analysis shows that the total variation regularizer which only achieves local smoothness is a special case of the proposed dct regularizer we also develop a new visual recovery algorithm by minimizing the dct regularizer and nuclear norm to achieve a more visually pleasing estimation experimental results on a benchmark image data set demonstrate that the proposed approach is superior to the state of the art methods in terms of peak signal to noise ratio and structural similarity

loop of formal diffeomorphisms and faa di bruno coloop bialgebra abstract we consider a generalization of pro algebraic loops defined on general categories of algebras and the dual notion of a coloop bialgebra suitable to represent them as functors we prove that the natural loop of formal diffeomorphisms with associative coefficients is proalgebraic and we give the closed formulas of the codivisions on its coloop bialgebra this result provides a generalization of the lagrange inversion formula to series with non commutative coefficients and a loop theoretic explanation to the existence of the non commutative faa di bruno hopf algebra

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

a mathematical analysis of the dct coefficient distributions for images over the past two decades there have been various studies on the distributions of the dct coefficients for images however they have concentrated only on fitting the empirical data from some standard pictures with a variety of well known statistical distributions and then comparing their goodness of fit the laplacian distribution is the dominant choice balancing simplicity of the model and fidelity to the empirical data yet to the best of our knowledge there has been no mathematical justification as to what gives rise to this distribution we offer a rigorous mathematical analysis using a doubly stochastic model of the images which not only provides the theoretical explanations necessary but also leads to insights about various other observations from the literature this model also allows us to investigate how certain changes in the image statistics could affect the dct coefficient distributions

adaptive sequential prediction of multidimensional signals with applications to lossless image coding we investigate the problem of designing adaptive sequential linear predictors for the class of piecewise autoregressive multidimensional signals and adopt an approach of minimum description length mdl to determine the order of the predictor and the support on which the predictor operates the design objective is to strike a balance between the bias and variance of the prediction errors in the mdl criterion the predictor design problem is particularly interesting and challenging for multidimensional signals e g images and videos because of the increased degree of freedom in choosing the predictor support our main result is a new technique of sequentializing a multidimensional signal into a sequence of nested contexts of increasing order to facilitate the mdl search for the order and the support shape of the predictor and the sequentialization is made adaptive on a sample by sample basis the proposed mdl based adaptive predictor is applied to lossless image coding and its performance is empirically established to be the best among all the results that have been published till present

lossless compression of color map images by context tree modeling significant lossless compression results of color map images have been obtained by dividing the color maps into layers and by compressing the binary layers separately using an optimized context tree model that exploits interlayer dependencies even though the use of a binary alphabet simplifies the context tree construction and exploits spatial dependencies efficiently it is expected that an equivalent or better result would be obtained by operating directly on the color image without layer separation in this paper we extend the previous context tree based method to operate on color values instead of binary layers we first generate an n ary context tree by constructing a complete tree up to a predefined depth and then prune out nodes that do not provide compression improvements experiments show that the proposed method outperforms existing methods for a large set of different color map images

translation invariant directional framelet transform combined with gabor filters for image denoising this paper is devoted to the study of a directional lifting transform for wavelet frames a nonsubsampled lifting structure is developed to maintain the translation invariance as it is an important property in image denoising then the directionality of the lifting based tight frame is explicitly discussed followed by a specific translation invariant directional framelet transform tidft the tidft has two framelets 1 2 with vanishing moments of order two and one respectively which are able to detect singularities in a given direction set it provides an efficient and sparse representation for images containing rich textures along with properties of fast implementation and perfect reconstruction in addition an adaptive block wise orientation estimation method based on gabor filters is presented instead of the conventional minimization of residuals furthermore the tidft is utilized to exploit the capability of image denoising incorporating the map estimator for multivariate exponential distribution consequently the tidft is able to eliminate the noise effectively while preserving the textures simultaneously experimental results show that the tidft outperforms some other frame based denoising methods such as contourlet and shearlet and is competitive to the state of the art denoising approaches

recompression of jpeg images by requantization we report a novel heuristic for requantizing jpeg images the resulting images are generally smaller and often have improved perceptual image quality over a blind requantization approach that is one that does not consider the properties of the quantization matrices the heuristic is supported by a detailed mathematical treatment which incorporates the well known laplacian distribution of the ac discrete cosine transform dct coefficients with an analysis of the error introduced by requantization we note that the technique is applicable to any image compression method which employs discrete cosine transforms and quantization

local adaptivity to variable smoothness for exemplar based image regularization and representation a novel adaptive and exemplar based approach is proposed for image restoration denoising and representation the method is based on a pointwise selection of similar image patches of fixed size in the variable neighborhood of each pixel the main idea is to associate with each pixel the weighted sum of data points within an adaptive neighborhood we use small image patches e g 7 7 or 9 9 patches to compute these weights since they are able to capture local geometric patterns and texels seen in images in this paper we mainly focus on the problem of adaptive neighborhood selection in a manner that balances the accuracy of approximation and the stochastic error at each spatial position the proposed pointwise estimator is then iterative and automatically adapts to the degree of underlying smoothness with minimal a priori assumptions on the function to be recovered the method is applied to artificially corrupted real images and the performance is very close and in some cases even surpasses to that of the already published denoising methods the proposed algorithm is demonstrated on real images corrupted by non gaussian noise and is used for applications in bio imaging

on hopf algebra structures over free operads the operad lie can be constructed as the operad of primitives primas from the operad as of associative algebras this is reflected by the theorems of friedrichs poincare birkhoff witt and cartier milnor moore we replace the operad as by families of free operads p which include the operad mag freely generated by a non commutative non associative binary operation and the operad of stasheff polytopes we obtain poincare birkhoff witt type theorems and collect information about the operads primp e g in terms of characteristic functions

context based lossless interband compression extending calic this paper proposes an interband version of calic context based adaptive lossless image codec which represents one of the best performing practical and general purpose lossless image coding techniques known today interband coding techniques are needed for effective compression of multispectral images like color images and remotely sensed images it is demonstrated that calic s techniques of context modeling of dpcm errors lend themselves easily to modeling of higher order interband correlations that cannot be exploited by simple interband linear predictors alone the proposed interband calic exploits both interband and intraband statistical redundancies and obtains significant compression gains over its intrahand counterpart on some types of multispectral images interband calic can lead to a reduction in bit rate of more than 20 as compared to intraband calic interband calic only incurs a modest increase in computational cost as compared to intraband calic

statistical model of quantized dct coefficients application in the steganalysis of jsteg algorithm the goal of this paper is to propose a statistical model of quantized discrete cosine transform dct coefficients it relies on a mathematical framework of studying the image processing pipeline of a typical digital camera instead of fitting empirical data with a variety of popular models proposed in this paper to highlight the accuracy of the proposed model this paper exploits it for the detection of hidden information in jpeg images by formulating the hidden data detection as a hypothesis testing this paper studies the most powerful likelihood ratio test for the steganalysis of jsteg algorithm and establishes theoretically its statistical performance based on the proposed model of dct coefficients a maximum likelihood estimator for embedding rate is also designed numerical results on simulated and real images emphasize the accuracy of the proposed model and the performance of the proposed test

transparent composite model for dct coefficients design and analysis the distributions of discrete cosine transform dct coefficients of images are revisited on a per image base to better handle the heavy tail phenomenon commonly seen in the dct coefficients a new model dubbed a transparent composite model tcm is proposed and justified for both modeling accuracy and an additional data reduction capability given a sequence of the dct coefficients a tcm first separates the tail from the main body of the sequence then a uniform distribution is used to model the dct coefficients in the heavy tail whereas a different parametric distribution is used to model data in the main body the separate boundary and other parameters of the tcm can be estimated via maximum likelihood estimation efficient online algorithms are proposed for parameter estimation and their convergence is also proved experimental results based on kullback leibler divergence and 2 test show that for real valued continuous ac coefficients the tcm based on truncated laplacian offers the best tradeoff between modeling accuracy and complexity for discrete or integer dct coefficients the discrete tcm based on truncated geometric distributions gmtcm models the ac coefficients more accurately than pure laplacian models and generalized gaussian models in majority cases while having simplicity and practicality similar to those of pure laplacian models in addition it is demonstrated that the gmtcm also exhibits a good capability of data reduction or feature extraction the dct coefficients in the heavy tail identified by the gmtcm are truly outliers and these outliers represent an outlier image revealing some unique global features of the image overall the modeling performance and the data reduction feature of the gmtcm make it a desirable choice for modeling discrete or integer dct coefficients in the real world image or video applications as summarized in a few of our further studies on quantization design entropy coding design and image understanding and management

ell_ 2 restoration of ell_ infty decoded images via soft decision estimation the l constrained image coding is a technique to achieve substantially lower bit rate than strictly mathematically lossless image coding while still imposing a tight error bound at each pixel however this technique becomes inferior in the l2 distortion metric if the bit rate decreases further in this paper we propose a new soft decoding approach to reduce the l2 distortion of l decoded images and retain the advantages of both minmax and least square approximations the soft decoding is performed in a framework of image restoration that exploits the tight error bounds afforded by the l constrained coding and employs a context modeler of quantization errors experimental results demonstrate that the l constrained hard decoded images can be restored to gain more than 2 db in peak signal to noise ratio psnr while still retaining tight error bounds on every single pixel the new soft decoding technique can even outperform jpeg 2000 a state of the art encoder optimized image codec for bit rates higher than 1 bpp a critical rate region for applications of near lossless image compression all the coding gains are made without increasing the encoder complexity as the heavy computations to gain coding efficiency are delegated to the decoder

an analysis of some common scanning techniques for lossless image coding though most image coding techniques use a raster scan to order pixels prior to coding hilbert and other scans have been proposed as having better performance due to their superior locality preserving properties however a general understanding of the merits of various scans has been lacking this paper develops an approach for quantitatively analyzing the effect of pixel scan order for context based predictive lossless image compression and uses it to compare raster hilbert random and hierarchical scans specifically for a quantized gaussian image model and a given scan order it shows how the encoding rate can be estimated from the frequencies with which various pixel configurations are available as previously scanned contexts and from the corresponding conditional differential entropies formulas are derived for such context frequencies and entropies assuming an isotropic image model and contexts consisting of previously scanned adjacent pixels it is found that the raster scan is better than the hilbert scan which is often used in compression applications due to its locality preserving properties the hierarchical scan is better still though it is based on nonadjacent contexts the random scan is the worst of the four considered extensions and implications of the results to lossy coding are also discussed

a universal data compression system a universal data compression algorithm is described which is capable of compressing long strings generated by a finitely generated source with a near optimum per symbol length without prior knowledge of the source this class of sources may be viewed as a generalization of markov sources to random fields moreover the algorithm does not require a working storage much larger than that needed to describe the source generating parameters

low rank decomposition based restoration of compressed images via adaptive noise estimation images coded at low bit rates in real world applications usually suffer from significant compression noise which significantly degrades the visual quality traditional denoising methods are not suitable for the content dependent compression noise which usually assume that noise is independent and with identical distribution in this paper we propose a unified framework of content adaptive estimation and reduction for compression noise via low rank decomposition of similar image patches we first formulate the framework of compression noise reduction based upon low rank decomposition compression noises are removed by soft thresholding the singular values in singular value decomposition of every group of similar image patches for each group of similar patches the thresholds are adaptively determined according to compression noise levels and singular values we analyze the relationship of image statistical characteristics in spatial and transform domains and estimate compression noise level for every group of similar patches from statistics in both domains jointly with quantization steps finally quantization constraint is applied to estimated images to avoid over smoothing extensive experimental results show that the proposed method not only improves the quality of compressed images obviously for post processing but are also helpful for computer vision tasks as a pre processing method

statistical model of jpeg noises and its application in quantization step estimation in this paper we present a statistical analysis of jpeg noises including the quantization noise and the rounding noise during a jpeg compression cycle the jpeg noises in the first compression cycle have been well studied however so far less attention has been paid on the statistical model of jpeg noises in higher compression cycles our analysis reveals that the noise distributions in higher compression cycles are different from those in the first compression cycle and they are dependent on the quantization parameters used between two successive cycles to demonstrate the benefits from the analysis we apply the statistical model in jpeg quantization step estimation we construct a sufficient statistic by exploiting the derived noise distributions and justify that the statistic has several special properties to reveal the ground truth quantization step experimental results demonstrate that the proposed estimator can uncover jpeg compression history with a satisfactory performance

edge directed prediction for lossless compression of natural images this paper sheds light on the least square ls based adaptive prediction schemes for lossless compression of natural images our analysis shows that the superiority of the ls based adaptation is due to its edge directed property which enables the predictor to adapt reasonably well from smooth regions to edge areas recognizing that ls based adaptation improves the prediction mainly around the edge areas we propose a novel approach to reduce its computational complexity with negligible performance sacrifice the lossless image coder built upon the new prediction scheme has achieved noticeably better performance than the state of the art coder calic with moderately increased computational complexity

shifted tableaux and the projective representations of symmetric groups les groupes de representation de s n classes de conjugaison algebres de clifford et la representation spin de base produits induits pour des representations spin une application caracteristique pour des caracteres de spin tableaux decales et q fonctions de schur les caracteres de spin irreductibles de s n et a n une analogue decalee de la regle lr produits tensoriels interieurs

nilpotent sabinin algebras abstract in this paper we establish several basic properties of nilpotent sabinin algebras namely we show that nilpotent sabinin algebras 1 can be integrated to produce nilpotent loops 2 satisfy an analogue of the ado theorem 3 have nilpotent lie envelopes we also give a new set of axioms for sabinin algebras these axioms reflect the fact that a complementary subspace to a lie subalgebra in a lie algebra is a sabinin algebra finally we note that the non associative version of the jennings theorem produces a version of the ado theorem for loops whose commutator associator filtration is of finite length

dependence correlation and gaussianity in independent component analysis independent component analysis ica is the decomposition of a random vector in linear components which are as independent as possible here independence should be understood in its strong statistical sense it goes beyond second order decorrelation and thus involves the non gaussianity of the data the ideal measure of independence is the mutual information and is known to be related to the entropy of the components when the search for components is restricted to uncorrelated components this paper explores the connections between mutual information entropy and non gaussianity in a larger framework without resorting to a somewhat arbitrary decorrelation constraint a key result is that the mutual information can be decomposed under linear transforms as the sum of two terms one term expressing the decorrelation of the components and one expressing their non gaussianity our results extend the previous understanding of these connections and explain them in the light of information geometry we also describe the local geometry of ica by re expressing all our results via a gram charlier expansion by which all quantities of interest are obtained in terms of cumulants

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