understanding optimising and extending data compression with anisotropic diffusion galic et al journal of mathematical imaging and vision 31 255 269 2008 have shown that compression based on edge enhancing anisotropic diffusion eed can outperform the quality of jpeg for medium to high compression ratios when the interpolation points are chosen as vertices of an adaptive triangulation however the reasons for the good performance of eed remained unclear and they could not outperform the more advanced jpeg 2000 the goals of the present paper are threefold firstly we investigate the compression qualities of various partial differential equations this sheds light on the favourable properties of eed in the context of image compression secondly we demonstrate that it is even possible to beat the quality of jpeg 2000 with eed if one uses specific subdivisions on rectangles and several important optimisations these amendments include improved entropy coding brightness and diffusivity optimisation and interpolation swapping thirdly we demonstrate how to extend our approach to 3 d and shape data experiments on classical test images and 3 d medical data illustrate the high potential of our approach

still image coding based on vector quantization and fractal approximation in this paper we propose a coding algorithm for still images using vector quantization vq and fractal approximation in which low frequency components of an input image are approximated by vq and its residual is coded by fractal mapping the conventional fractal coding algorithms indirectly used the gray patterns of an original image with contraction mapping whereas the proposed fractal coding method employs an approximated and then decimated image as a domain pool and uses its gray patterns thus the proposed algorithm utilizes fractal approximation without the constraint of contraction mapping for approximation of an original image we employ the discrete cosine transform dct rather than conventional polynomial based transforms in addition for variable blocksize segmentation we use the fractal dimension of a block that represents the roughness of the gray surface of a region computer simulations with several test images show that the proposed method shows better performance than the conventional fractal coding methods for encoding still pictures

the fast hartley transform algorithm the fast hartley transform fht is similar to the cooley tukey fast fourier transform fft but performs much faster because it requires only real arithmetic computations compared to the complex arithmetic computations required by the fft through use of the fht discrete cosine transforms dct and discrete fourier transforms dft can be obtained the recursive nature of the fht algorithm derived in this paper enables us to generate the next higher order fht from two identical lower order fht s in practice this recursive relationship offers flexibility in programming different sizes of transforms while the orderly structure of its signal flow graphs indicates an ease of implementation in vlsi

the algebraic approach to the discrete cosine and sine transforms and their fast algorithms it is known that the discrete fourier transform dft used in digital signal processing can be characterized in the framework of the representation theory of algebras namely as the decomposition matrix for the regular module mathbb c z n mathbb c x x n 1 this characterization provides deep insight into the dft and can be used to derive and understand the structure of its fast algorithms in this paper we present an algebraic characterization of the important class of discrete cosine and sine transforms as decomposition matrices of certain regular modules associated with four series of chebyshev polynomials then we derive most of their known algorithms by pure algebraic means we identify the mathematical principle behind each algorithm and give insight into its structure our results show that the connection between algebra and digital signal processing is stronger than previously understood

efficient quadtree coding of images and video the quadtree data structure is commonly used in image coding to decompose an image into separate spatial regions to adaptively identify the type of quantizer used in various regions of an image the authors describe the theory needed to construct quadtree data structures that optimally allocate rate given a set of quantizers a lagrange multiplier method finds these optimal rate allocations with no monotonicity restrictions they use the theory to derive a new quadtree construction method that uses a stepwise search to find the overall optimal quadtree structure the search can be driven with either actual measured quantizer performance or ensemble average predicted performance they apply this theory to the design of a motion compensated interframe video coding system using a quadtree with vector quantization

synchronization of linear dynamical networks on time scales this paper studies the synchronization problem of complex dynamical networks cdns on time scales a pinning impulsive control scheme that takes into account of time delay effects is designed to achieve synchronization of cdns on time scales with the state of an isolated node based on the theory of time scales and the direct lyapunov method a synchronization criterion is established for linear cdns on general time scales our result shows that by impulsive control a small portion of nodes the consensus of cdns on time scales can be achieved according to our pinning impulsive control scheme different numbers of nodes will be selected at each impulsive instant and time delay is considered in the pinning impulses the modeling framework developed in this paper is a unification and generalization of many existing continuous time and discrete time cdn models while the pinning impulsive control scheme is an extension of the existing control scheme for synchronization of continuous time cdns moreover the idea of studying dynamical systems on time scales provide a unified approach to investigate continuous time system and its discrete time counterpart simultaneously numerical simulations are given to illustrate the effectiveness of the theoretical analysis

recursive block coding a new approach to transform coding the concept of fast kl transform coding introduced earlier 7 8 for first order markov processes and certain random fields has been extended to higher order autoregressive ar sequences and practical images yielding what we call recursive block coding rbc algorithms in general the rate distortion performance for these algorithms is significantly superior to that of the conventional block kl transform algorithm moreover these algorithms permit the use of small size transforms thereby removing the need for fast transforms and making the hardware implementation of such coders more appealing this improved performance has been verified for practical image data and results in suppression of the block boundary effect commonly observed in traditional transform coding techniques this is illustrated by comparing rbc with cosine transform coding using both one and twodimensional algorithms examples of rbc encoded images at various rates are given

a two dimensional fast cosine transform a two dimensional fast cosine transform algorithm 2 d fct is developed for 2m 2ndata points this algorithm is an extended version of the 1 d fct algorithm introduced in a recent paper but with significantly reduced computations for a 2 d field the rationale for this 2 d fct is a 2 d decomposition of data sequences into 2 d subblocks with reduced dimension halves rather than serial one dimensional separable treatment for the columns and rows of the data sets computer simulation for the 2 d fct algorithms using a smaller block of data and finite word precision proves to be excellent in comparison with the direct 2 d discrete cosine transform 2 d dct an example of a 4 4 2 d inverse fast cosine transform 2 d ifct algorithm development is presented in this paper together with a signal flow graph

a fast recursive algorithm for computing the discrete cosine transform the discrete cosine transform dct is widely applied in various fields including image data compression because it operates like the karhunen loeve transform for stationary random data this paper presents a recursive algorithm for dct with a structure that allows the generation of the next higher order dct from two identical lower order dct s as a result the method for implementing this recursive dct requires fewer multipliers and adders than other dct algorithms

a normalizing isospectral flow on complex hessenberg matrices abstract we study an isospectral flow lax flow that provides an explicit deformation from upper hessenberg complex matrices to normal matrices extending to the complex case and to the case of normal matrices the results of 2 the lax flow is given by d a d t a a d u a where brackets indicate the usual matrix commutator a b a b b a a is the conjugate transpose of a and the matrix a a d u is the matrix equal to a a along diagonal and upper triangular entries and zero below diagonal we prove that if the initial condition a 0 is an upper hessenberg matrix with simple spectrum then lim t a t exists and it is a normal upper hessenberg matrix isospectral to a 0 and if the spectrum of a 0 is contained in a line in the complex plane then the limit set is actually a tridiagonal normal matrix furthermore we show that this flow is also the solution of an infinite time horizon optimal control problem and we prove that it can be used to construct even dimensional real skew symmetric tridiagonal matrices with given simple spectrum and with given signs pattern for the codiagonal elements

least squares quantization in pcm it has long been realized that in pulse code modulation pcm with a given ensemble of signals to handle the quantum values should be spaced more closely in the voltage regions where the signal amplitude is more likely to fall it has been shown by panter and dite that in the limit as the number of quanta becomes infinite the asymptotic fractional density of quanta per unit voltage should vary as the one third power of the probability density per unit voltage of signal amplitudes in this paper the corresponding result for any finite number of quanta is derived that is necessary conditions are found that the quanta and associated quantization intervals of an optimum finite quantization scheme must satisfy the optimization criterion used is that the average quantization noise power be a minimum it is shown that the result obtained here goes over into the panter and dite result as the number of quanta become large the optimum quautization schemes for 2 b quanta b 1 2 cdots 7 are given numerically for gaussian and for laplacian distribution of signal amplitudes

restructured recursive dct and dst algorithms the discrete cosine transform dct and the discrete sine transform dst have found wide applications in speech and image processing as well as telecommunication signal processing for the purpose of data compression feature extraction image reconstruction and filtering in this paper we present new recursive algorithms for the dct and the dst the proposed method is based on certain recursive properties of the dct coefficient matrix and can be generalized to design recursive algorithms for the 2 d dct and the 2 d dst these new structured recursive algorithms are able to decompose the dct and the dst into two balanced lower order subproblems in comparison to previous research works therefore when converting our algorithms into hardware implementations we require fewer hardware components than other recursive algorithms finally we propose two parallel algorithms for accelerating the computation

synchronization control for nonlinear stochastic dynamical networks pinning impulsive strategy in this paper a new control strategy is proposed for the synchronization of stochastic dynamical networks with nonlinear coupling pinning state feedback controllers have been proved to be effective for synchronization control of state coupled dynamical networks we will show that pinning impulsive controllers are also effective for synchronization control of the above mentioned dynamical networks some generic mean square stability criteria are derived in terms of algebraic conditions which guarantee that the whole state coupled dynamical network can be forced to some desired trajectory by placing impulsive controllers on a small fraction of nodes an effective method is given to select the nodes which should be controlled at each impulsive constants the proportion of the controlled nodes guaranteeing the stability is explicitly obtained and the synchronization region is also derived and clearly plotted numerical simulations are exploited to demonstrate the effectiveness of the pinning impulsive strategy proposed in this paper

scene adaptive coder an efficient single pass adaptive bandwidth compression technique using the discrete cosine transform is described the coding process involves a simple thresholding and normalization operation on the transform coefficients adaptivity is achieved by using a rate buffer for channel rate equalization the buffer status and input rate are monitored to generate a feedback normalization factor excellent results are demonstrated for coding of color images at 0 4 bits pixel corresponding to real time color television transmission over a 1 5 mbit s channel

a fast 4 4 dct algorithm for the recursive 2 d dct the authors present an efficient algorithm for the computation of the 4 4 discrete cosine transform dct the algorithm is based on the decomposition of the 4 4 dct into four 4 point 1 d dcts thus only 1 d transformations and some additions are required it is shown that the proposed algorithm requires only 16 multiplications which is half the number needed for the conventional row column method since the 2 sup m 2 sup m dct can be computed using the 4 4 dct recursively for any m the proposed algorithm leads to a fast algorithm for the computation of the 2 d dct

low complexity multidimensional dct approximations for high order tensor data decorrelation in this paper we introduce low complexity multidimensional discrete cosine transform dct approximations 3d dct approximations are formalized in terms of high order tensor theory the formulation is extended to higher dimensions with arbitrary lengths several multiplierless 8 times 8 times 8 approximate methods are proposed and the computational complexity is discussed for the general multidimensional case the proposed methods complexity cost was assessed presenting considerably lower arithmetic operations when compared with the exact 3d dct the proposed approximations were embedded into 3d dct based video coding scheme and a modified quantization step was introduced the simulation results showed that the approximate 3d dct coding methods offer almost identical output visual quality when compared with exact 3d dct scheme the proposed 3d approximations were also employed as a tool for visual tracking the approximate 3d dct based proposed system performs similarly to the original exact 3d dct based method in general the suggested methods showed competitive performance at a considerably lower computational cost

pinning control of scale free dynamical networks abstract recently it has been demonstrated that many large complex networks display a scale free feature that is their connectivity distributions have the power law form in the present work control of a scale free dynamical network by applying local feedback injections to a fraction of network nodes is investigated the specifically and randomly pinning schemes are considered the specifically pinning of the most highly connected nodes is shown to require a significantly smaller number of local controllers as compared to the randomly pinning scheme the method is applied to an array of chua s oscillators as an example

fast algorithms for the dft and other sinusoidal transforms a new matrix factorization is proposed for dct iv which is the basis of fast algorithms for many sinusoidal transforms the new fast algorithm for dft based on the new factorization requires the same number of multiplications and far fewer additions than the preuss algorithm

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

isospectral flows on a class of finite dimensional jacobi matrices abstract we present a new matrix valued isospectral ordinary differential equation that asymptotically block diagonalizes n n zero diagonal jacobi matrices employed as its initial condition this o d e features a right hand side with a nested commutator of matrices and structurally resembles the double bracket o d e studied by r w brockett in 1991 we prove that its solutions converge asymptotically that the limit is block diagonal and above all that the limit matrix is defined uniquely as follows for n even a block diagonal matrix containing 2 2 blocks such that the super diagonal entries are sorted by strictly increasing absolute value furthermore the off diagonal entries in these 2 2 blocks have the same sign as the respective entries in the matrix employed as the initial condition for n odd there is one additional 1 1 block containing a zero that is the top left entry of the limit matrix the results presented here extend some early work of kac and van moerbeke

fast algorithms for multidimensional dct to dct computation between a block and its associated subblocks in this paper we first propose an efficient algorithm for computing one dimensional 1 d discrete cosine transform dct for a signal block given its two adjacent subblocks in the dct domain and then introduce several algorithms for the fast computation of multidimensional m d dct with size n sub 1 spl times n sub 2 spl times spl times n sub m given 2 sup m subblocks of dct coefficients with size n sub 1 2 spl times n sub 2 2 spl times spl times n sub m 2 where n sub i i 1 2 m are powers of 2 obviously the row column method which employs the most efficient algorithms along each dimension reduces the computational complexity considerably compared with the traditional method which employs only the one dimensional 1 d fast dct and inverse dct idct algorithms however when m spl ges 2 the traditional method which employs the most efficient multidimensional dct idct algorithms has lower computational complexity than the row column method besides we propose a direct method by dividing the data into 2 sup m parts for independent fast computation in which only two steps of r dimensional r 1 2 m idct and additional multiplications and additions are required if all the dimensional sizes are the same the number of multiplications required for the direct method is only 2 sup m 1 m2 sup m 1 times of that required for the row column method and if n spl ges 2 sup 2m 1 the computational efficiency of the direct method is surely superior to that of the traditional method which employs the most efficient multidimensional dct idct algorithms

synchronization of coupled reaction diffusion neural networks with time varying delays via pinning impulsive controller in this paper global exponential synchronization stability in an array of linearly diffusively coupled reaction diffusion neural networks with time varying delays is investigated by adding impulsive controller to a small fraction of nodes pinning impulsive controller in order to overcome the difficulty resulting from the fact that the impulsive controller affects only the dynamical behaviors of the controlled nodes a new analysis method is developed by using the developed method two known lemmas on stability of delayed functional differential equation with and without impulses and lyapunov stability theory several novel and easily verified synchronization criteria guaranteeing the whole network will be pinned to a homogenous solution are derived moreover the effects of the pinning impulsive controller and the dynamics of the uncontrolled nodes and the diffusive couplings on the synchronization process are explicitly expressed in the obtained criteria our results also show that we can always de

stereo image coding a projection approach due to advances in display technology three dimensional 3 d imaging systems are becoming increasingly popular one way of stimulating 3 d perception is to use stereo pairs a pair of images of the same scene acquired from different perspectives since there is an inherent redundancy between the images of a stereo pair data compression algorithms should be employed to represent stereo pairs efficiently this paper focuses on the stereo image coding problem we begin with a description of the problem and a survey of current stereo coding techniques a new stereo image coding algorithm that is based on disparity compensation and subspace projection is described this algorithm the subspace projection technique spt is a transform domain approach with a space varying transformation matrix and may be interpreted as a spatial transform domain representation of the stereo data the advantage of the proposed approach is that it can locally adapt to the changes in the cross correlation characteristics of the stereo pairs several design issues and implementations of the algorithm are discussed finally we present empirical results suggesting that the spt approach outperforms current stereo coding techniques

on algebras related to the discrete cosine transform abstract an algebraic theory for the discrete cosine transform dct is developed which is analogous to the well known theory of the discrete fourier transform dft whereas the latter diagonalizes a convolution algebra which is a polynomial algebra modulo a product of various cyclotomic polynomials the former diagonalizes a polynomial algebra modulo a product of various polynomials related to the chebyshev types when the dimension of the algebra is a power of 2 the dct diagonalizes a polynomial algebra modulo a product of chebyshev polynomials of the first type in both dft and dct cases the chinese remainder theorem plays a key role in the design of fast algorithms

analysis of pruning in fast cosine transform the discrete cosine transform dct is now the established technique for image and video coding in most image coding set schemes a large number of high frequency transform coefficients can be neglected and need not be calculated therefore significant savings in computation can be obtained by applying pruning in the fast algorithms we analyze pruning in chan and ho s 1990 fast dct algorithm and evaluate the saving of operations

periodicity of scalar dynamic equations and applications to population models easily verifiable sufficient criteria are established for the existence of periodic solutions of a class of nonautonomous scalar dynamic equations on time scales which incorporate as special cases many single species models governed by ordinary differential and difference equations when the time scale is the set of all real and all integer numbers respectively

a new algorithm to compute the discrete cosine transform a new algorithm is introduced for the 2m point discrete cosine transform this algorithm reduces the number of multiplications to about half of those required by the existing efficient algorithms and it makes the system simpler

quadtree structured recursive plane decomposition coding of images the approximation of two dimensional highly correlated grey value functions can be performed using a linear model of the type f x y a bx cy the set of plane parameters pps a b c can be determined in the least squares sense for a block of size n n pixels for example starting with a block size of 2 2 pixels it is shown that the pps obey a recursive law such that the pps of a 2n 2n block can be computed recursively when only the pps of the four adjacent subblocks of size n n in the lower decomposition level are known this concept of recursive plane decomposition rpd is embedded in a quadtree data structure to obtain a new variable block size image coding algorithm that offers a high performance at a low computational cost extensive comparisons to other state of the art image coding algorithms are reported

space frequency quantization for image compression with directionlets the standard separable 2 d wavelet transform wt has recently achieved a great success in image processing because it provides a sparse representation of smooth images however it fails to efficiently capture 1 d discontinuities like edges or contours these features being elongated and characterized by geometrical regularity along different directions intersect and generate many large magnitude wavelet coefficients since contours are very important elements in the visual perception of images to provide a good visual quality of compressed images it is fundamental to preserve good reconstruction of these directional features in our previous work we proposed a construction of critically sampled perfect reconstruction transforms with directional vanishing moments imposed in the corresponding basis functions along different directions called directionlets in this paper we show how to design and implement a novel efficient space frequency quantization sfq compression algorithm using directionlets our new compression method outperforms the standard sfq in a rate distortion sense both in terms of mean square error and visual quality especially in the low rate compression regime we also show that our compression method does not increase the order of computational complexity as compared to the standard sfq algorithm

finite time stability and settling time estimation of nonlinear impulsive systems abstract this paper studies the problem of finite time stability fts for nonlinear impulsive systems based on impulsive control theory several lyapunov based fts theorems involving stabilizing impulses and destabilizing impulses are established respectively our proposed results provide sufficient conditions for estimating the settling time with respect to suitable classes of impulse time sequences it is shown that the settling time of nonlinear impulsive systems depends not only on the initial state but also on the impulse effect as compared with the case without using stabilizing impulses a smaller bound of setting time can be derived when a fts system is subject to stabilizing impulses conversely a larger bound of settling time can be derived when the fts system is subject to destabilizing impulses as compared with the case without using destabilizing impulses as a special case we extend the ideas to nonlinear impulsive delay systems and derive some delay independent fts results examples and their simulations are given to demonstrate the applicability of the proposed results

brief paper exponential stability of nonlinear time delay systems with delayed impulse effects the problem of exponential stability for nonlinear time delay systems with delayed impulses is addressed in this paper lyapunov based sufficient conditions for exponential stability are derived respectively for two kinds of delayed impulses i e destabilizing delayed impulses and stabilizing delayed impulses it is shown that if a nonlinear impulsive time delay system without impulse input delays is exponentially stable then under some conditions its stability is robust with respect to small impulse input delays moreover it is also shown that for a stable nonlinear impulsive time delay system if the magnitude of the delayed impulses is sufficiently small then under some conditions the delayed impulses do not destroy the stability irrespective of the sizes of the impulse input delays the efficiency of the proposed results is illustrated by three numerical examples

matrix factorizations and integrable systems on montre que les algorithmes qr lij et de cholesky pour calculer les valeurs propres de matrices reelles sont les evaluations a temps entier de flots hamiltoniens completement integrables