multiple subtraction using statistically estimated inverse wavelets surface related multiple elimination srme typically consists of two steps the first step is prediction and the second step is subtraction in subtraction it is important to effectively attenuate multiple events and preserve primary events when multiples cross with or overlap on primaries least square subtraction usually cannot subtract multiples effectively and may also damage the primaries when multiples overlap with primaries least square subtraction cannot always subtract multiples accurately and often damages the primaries to remedy this problem we propose to statistically estimate the inverse source wavelet correct for errors in the estimate of the inverse wavelet and then use the corrected inverse wavelets for multiple subtraction synthetic tests and real data examples show that the proposed method can effectively attenuate multiples while they also preserve the continuity of reflection events and successfully avoid amplitude distortion the proposed method is characterized by low computational costs and ease of implementation

image analysis by bessel fourier moments in this paper we proposed a new set of moments based on the bessel function of the first kind named bessel fourier moments bfms which are more suitable than orthogonal fourier mellin and zernike moments for image analysis and rotation invariant pattern recognition compared with orthogonal fourier mellin and zernike polynomials of the same degree the new orthogonal radial polynomials have more zeros and these zeros are more evenly distributed the bessel fourier moments can be thought of as generalized orthogonalized complex moments theoretical and experimental results show that the bessel fourier moments perform better than the orthogonal fourier mellin and zernike moments ofmms and zms in terms of image reconstruction capability and invariant recognition accuracy in noise free noisy and smooth distortion conditions

an alternating direction implicit scheme of a fractional order diffusion tensor image registration model abstract in this paper we propose an alternating direction implicit adi scheme of a fractional order diffusion tensor image dti registration model furthermore compatibility stability and convergence of adi scheme are proved moreover five numerical tests are also performed to show the efficiency of this scheme

fixed order stabilising controller design by a mixed randomised deterministic method a novel mixed randomised deterministic method for fixed order controller design is proposed for discrete time single input single output plants it is based on the random generation of schur stable polynomials using reflection coefficients and reflection segments of polynomials stable reflection segments are then projected onto the affine set of closed loop characteristic polynomials and the stable line segments in the controller parameter space are determined a novel approach is proposed for global and local optimisation over reflection segment bunches on the basis of the weighted sum of absolute values of reflection coefficients

error sources and error propagation in the levinson durbin algorithm it is proved that there are two types of numerical error due to finite precision in the levinson durbin algorithms an erratic and a systematic one the erratic one depends on the value the input autocorrelation accidentally takes at an iteration and essentially it affects only the results obtained at this particular recursion on the contrary the systematic numerical error increases with the information the system carries and propagates essentially throughout the algorithm it is shown that for both types of error as well as the overall one there are specific intermediate quantities calculated in the evolution of the algorithm which may serve as precise indicators of the exact number of erroneous digits with which the various quantities are computed including the parcor coefficients and the filter coefficients therefore the generated numerical error can be accurately traced

variational image registration by a total fractional order variation model in this paper a new framework of nonlocal deformation in non rigid image registration is presented it is well known that many non rigid image registration techniques may lead to unsteady deformation e g not one to one if the dissimilarity between the reference and template images is too large we present a novel variational framework of the total fractional order variation to derive the underlying fractional euler lagrange equations and a numerical implementation combining the semi implicit update and conjugate gradients cg solution to solve the nonlinear systems numerical experiments show that the new registration not only produces accurate and smooth solutions but also allows for a large rigid alignment the evaluations of the new model demonstrate substantial improvements in accuracy and robustness over the conventional image registration approaches

a preconditioned numerical solver for stiff nonlinear reaction diffusion equations with fractional laplacians that avoids dense matrices the numerical solution of fractional partial differential equations poses significant computational challenges in regard to efficiency as a result of the spatial nonlocality of the fractional differential operators the dense coefficient matrices that arise from spatial discretisation of these operators mean that even one dimensional problems can be difficult to solve using standard methods on grids comprising thousands of nodes or more in this work we address this issue of efficiency for one dimensional nonlinear space fractional reaction diffusion equations with fractional laplacian operators we apply variable order variable stepsize backward differentiation formulas in a jacobian free newton krylov framework to advance the solution in time a key advantage of this approach is the elimination of any requirement to form the dense matrix representation of the fractional laplacian operator we show how a banded approximation to this matrix which can be formed and factorised efficiently can be used as part of an effective preconditioner that accelerates convergence of the krylov subspace iterative solver our approach also captures the full contribution from the nonlinear reaction term in the preconditioner which is crucial for problems that exhibit stiff reactions numerical examples are presented to illustrate the overall effectiveness of the solver

fast algorithms for generalized displacement structures and lossless systems abstract we derive an efficient recursive procedure for the triangular factorization of strongly regular matrices with generalized displacement structure that includes as special cases a variety of previously studied classes such as toeplitz like and hankel like matrices the derivation is based on combining a simple gaussian elimination procedure with displacement structure and leads to a transmission like interpretation in terms of two cascades of first order sections we further derive state space realizations for each section and for the entire cascades and show that these realizations satisfy a generalized embedding result and a generalized notion of j losslessness the cascades turn out to have intrinsic blocking properties which can be shown to be equivalent to interpolation constrains

galerkin finite element method for two dimensional riesz space fractional diffusion equations abstract in this article a class of two dimensional riesz space fractional diffusion equations is considered some fractional spaces are established and some equivalences between fractional derivative spaces and fractional sobolev space are presented by the galerkin finite element method and backward difference method a fully discrete scheme is obtained according to lax milgram theorem the existence and uniqueness of the solution to the fully discrete scheme are investigated the stability and convergence of the scheme are also derived finally some numerical examples are given for verification of our theoretical analysis

closed form analytical results for the rejection of narrow band interference in pn spread spectrum systems part ii linear interpolation filters the performance of pn spread spectrum communication systems in the presence of narrow band interference is studied when linear interpolation filters are employed for the estimation and subsequent suppression of the interference closed form analytical expressions for the system s performance are established for a broad class of interference processes the advantages of linear interpolation filters over predictive filters with identical number of taps are examined analytically and some unexpected results are obtained the analytical results are illustrated by examples

efficient inversion of toeplitz block toeplitz matrix an iterative algorithm for the inversion of a toeplitz block toeplitz matrix consisting of m m blocks of size p p is described the algorithm presented exploits the structure of the toeplitz block toeplitz matrix and outperforms akaike s algorithm by a factor of max 2 p m 2 the use of this algorithm for an iterative solution of a toeplitz block toeplitz set of linear equations is also presented

blurred image recognition by legendre moment invariants processing blurred images is a key problem in many image applications existing methods to obtain blur invariants which are invariant with respect to centrally symmetric blur are based on geometric moments or complex moments in this paper we propose a new method to construct a set of blur invariants using the orthogonal legendre moments some important properties of legendre moments for the blurred image are presented and proved the performance of the proposed descriptors is evaluated with various point spread functions and different image noises the comparison of the present approach with previous methods in terms of pattern recognition accuracy is also provided the experimental results show that the proposed descriptors are more robust to noise and have better discriminative power than the methods based on geometric or complex moments

toeplitz properties of the block matrices encountered in the processing of spatiotemporal signals various signal processing applications such as system identification fir finite impulse response wiener filtering linear prediction and spectral estimation are known to lead to the solution of toeplitz systems for the case of one dimensional signals and to toeplitz block toeplitz systems for the case of two dimensional signals the authors investigate such systems for the case of l dimensional signals with l 2 and emphasize their block and persymmetrical nature such important characteristics allow the use of fast algorithms for signals of any dimension the case of three dimensional signals is treated in detail not only because it is of special interest for video applications but also because the reasoning used for this case can be straightforwardly applied to higher dimension signals

levinson type algorithms for polynomial fitting and for cholesky and q factors of hankel and vandermonde matrices this paper presents levinson 1947 type algorithms for i polynomial fitting ii obtaining a q decomposition of vandermonde matrices and a cholesky factorization of hankel matrices iii obtaining the inverse of hankel matrices the algorithm for the least squares solution of hankel systems of equations requires 3n sup 2 9n 3 multiply and divide operation mdo the algorithm for obtaining an orthogonal representation of an m spl times n vandermonde matrix x and computing the cholesky factors f of hankel matrices requires 5mn n sup 2 2n 3m mdo and the algorithm for generating the inverse of hankel matrices requires 3 n sup 2 n 2 2 mdo our algorithms have been tested by means of fitting of polynomials of various orders and fortran versions of all subroutines are provided in the appendix

projection operators and moment invariants to image blurring in this paper we introduce a new theory of blur invariants blur invariants are image features which preserve their values if the image is convolved by a point spread function psf of a certain class we present the invariants to convolution with an arbitrary n fold symmetric psf both in fourier and image domain we introduce a notion of a primordial image as a canonical form of all blur equivalent images it is defined in spectral domain by means of projection operators we prove that the moments of the primordial image are invariant to blur and we derive recursive formulae for their direct computation without actually constructing the primordial image we further prove they form a complete set of invariants and show how to extent their invariance also to translation rotation and scaling we illustrate by simulated and real data experiments their invariance and recognition power potential applications of this method are wherever one wants to recognize objects on blurred images

the deconvolution problem fast algorithms including the preconditioned conjugate gradient to compute a map estimator different aspects of the deconvolution problem are discussed and a solution by the map estimator using the a priori knowledge of smoothness and nonnegativity of the unknown signal is proposed several fast algorithms are examined and the conjugate gradient cg method is show to have several advantages it allows computation of a constrained solution and when used with a preconditioning technique it can be faster than other algorithms for general near to toeplitz systems in particular for toeplitz block toeplitz systems

a fast algorithm for solving a toeplitz system of equations a fast algorithm for the solution of a toeplitz system of equations is presented the algorithm requires order n log n 2 computations where n is the number of equations for banded toeplitz matrices the order of computations is reduced to only n log n m log m 2 where 2m is the maximum number of nonzero principal subdiagonals of the toeplitz matrix the algorithm is in essence a fast implementation of the trench algorithm in reverse thus the algorithm involves imbedding of the given matrix in a cyclic matrix and a fast hd half divisor algorithm to compute the first row of the inverse matrix the desired solution is then obtained directly from the first row by applying fast fourier transform techniques in order n log n computations finally the extension of the algorithm to block toeplitz matrices is also presented

fast algorithms for close to toeplitz plus hankel systems and two sided linear prediction the low displacement rank definition of close to toeplitz ct matrices is extended to close to toeplitz plus hankel ctph matrices fast algorithms for solving ctph systems of equations are presented a matrix is defined as ctph if the sum of a ct matrix and a second ct matrix postmultiplied by an exchange matrix an equivalent definition in terms of uv rank is also given this definition is motivated by the application of the algorithms to two sided linear prediction tsp autocorrelation and covariance forms of tsp analogous to those for one sided linear prediction osp are defined the covariance form of tsp is solved using the ctph fast algorithms just as the covariance form of osp is solved using ct fast algorithms numerical examples show that tsp produces smaller residuals than osp and resolves sharp spectral peaks better than osp and that covariance tsp produces smaller residuals than autocorrelation tsp

pseudo symmetric numerical semigroups with three generators abstract this paper gives a solution to the diophantine frobenius problem for pseudo symmetric numerical semigroups with embedding dimension three we also describe a presentation for this kind of semigroup and a formula to determine whether or not a numerical semigroup with embedding dimension three is pseudo symmetric

the block processing ftf adaptive algorithm a new block type adaptive filtering algorithm is presented this new block adaptive filter differs from the frequency domain block adaptive filters of ferrara 1980 and of clark mitra and parker 1980 in that the new method applies a deterministic time domain least squares criteria within each of the data blocks information is carried from block to block via a weighted initial condition this new block fast transversal filters bftf algorithm is a numerically stable algorithm and can also be used to perform efficient least squares system identification on any one data block in which case it shows a moderate computational advantage over the previous most efficient single data block algorithms of morf et al 1977 of marple 1981 and of kalouptsidis manolakis and carayannis 1984 1985 mechanisms for tracking and varying block length from block to block are also presented and evaluated finally we indicate how the new algorithm could be pipelined for maximum throughput with delay proportional to the number of parameters after computation of the sample correlation lags

finite difference finite element method for two dimensional space and time fractional bloch torrey equations in this paper a class of two dimensional space and time fractional bloch torrey equations 2d stfbtes are considered some definitions and properties of fractional derivative spaces are presented by finite difference method and galerkin finite element method a semi discrete variational formulation for 2d stfbtes is obtained the stability and convergence of the semi discrete form are discussed then a fully discrete scheme of 2d stfbtes is derived and the convergence is investigated finally some numerical examples based on linear piecewise polynomials and quadratic piecewise polynomials are given to prove the correctness of our theoretical analysis

a generalization of the levinson algorithm for hermitian toeplitz matrices with any rank profile the paper describes a recursive algorithm for solving hermitian toeplitz systems of linear equations without any restriction on the ranks of their nested toeplitz subsystems such a general algorithm is needed e g to obtain the eigenfilters for signal processing applications or to compute the inverse of a nondefinite toeplitz matrix the regular portion of the algorithm is made of the classical levinson recursion the singular portion requires solving some well defined systems of linear equations with gradient structure the dimension of each of these sytems equals the amplitude of the corresponding singularity

boundary element solution for periodic acoustic problems abstract this work shows when using the boundary element method to solve 3d acoustic scattering problems from periodic structures the coefficient matrix can be represented as a block toeplitz matrix by exploiting the toeplitz structure the computational time and storage requirements to construct the coefficient matrix are significantly reduced to solve the linear system of equations the original matrix is embedded into a larger and more structured matrix called the block circulant matrix discrete fourier transform is then employed in an iterative algorithm to solve the block toeplitz system to demonstrate the effectiveness of the formulation for periodic acoustic problems two exterior acoustic case studies are considered the first case study examines a continuous structure to predict the noise generated by a sharp edged flat plate under quadrupole excitation directivity plots obtained using the periodic boundary element method technique are compared with numerical results obtained using a conventional boundary element model the second case study examines a discrete periodic structure to predict the acoustic performance of a sonic crystal noise barrier results for the barrier insertion loss are compared with both finite element results and available data in the literature

adaptive tracking of multiple sinusoids whose power levels are widely separated the behavior of the gradient transversal filter lms the gradient lattice gl and the least squares lattice lsl when used to track multiple sinusoidal or narrow band components whose power levels are widely separated is investigated these approaches to the realization of the pth order one step linear predictor of the time series are recursive in time the lags of the instantaneous frequency estimates from their actual underlying values are of particular interest the frequency tracking characteristics of the lms gl and lsl algorithms are illustrated in several situations included are simulations of dual sinusoids undergoing a variety of frequency versus time dynamics and a formant tracking example of real speech

finite difference approximations for fractional advection dispersion flow equations fractional advection dispersion equations are used in groundwater hydrology to model the transport of passive tracers carried by fluid flow in a porous medium in this paper we develop practical numerical methods to solve one dimensional fractional advection dispersion equations with variable coefficients on a finite domain the practical application of these results is illustrated by modeling a radial flow problem use of the fractional derivative allows the model equations to capture the early arrival of tracer observed at a field site

szego polynomials applied to frequency analysis abstract this paper is concerned with the problem of determining unknown frequencies 1 i using an observed discrete time signal xn xn m arising from a continuous waveform that is the superposition of a finite number of sinusoidal waves with well defined frequencies j periods p j 2 n j n z j 1 i we investigate the wiener levinson method formulated here in terms of szeg polynomials n n z orthogonal on the unit circle with respect to a distribution function n defined by the n observed values of the signal we prove that if n0 denotes the number of critical points eiwj then for every n n0 and n 1 the zeros z j n n of n n z can be arranged so that limn z j n n eiwj for each of the frequencies wj this result confirms one of the main parts of the conjecture given by jones njastad and saff this journal 1990 on the convergence of zeros of the szeg polynomials a related result on the convergence of corresponding two point pade approximants is also given

fir filters and recursive forms for continuous time invariant state space models an fir finite impulse response filter and an fir smoother are introduced for continuous time invariant state space models it is shown in this note that finite impulse responses of the fir filter and smoother can be easily determined by solving a simple riccati type matrix differential equation on a finite interval especially for systems with stationary processes finite impulse responses of the fir filter and smoother become time invariant and can be computed from simpler equations for fast computational purposes recursive forms of the fir filter and smoother are derived by using adjoint variables in this case all gains for recursive forms are shown to be constant

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

degraded image analysis an invariant approach analysis and interpretation of an image which was acquired by a nonideal imaging system is the key problem in many application areas the observed image is usually corrupted by blurring spatial degradations and random noise classical methods like blind deconvolution try to estimate the blur parameters and to restore the image we propose an alternative approach we derive the features for image representation which are invariant with respect to blur regardless of the degradation psf provided that it is centrally symmetric as we prove in the paper there exist two classes of such features the first one in the spatial domain and the second one in the frequency domain we also derive so called combined invariants which are invariant to composite geometric and blur degradations knowing these features we can recognize objects in the degraded scene without any restoration

fast alternating direction finite difference methods for three dimensional space fractional diffusion equations fractional diffusion equations model phenomena exhibiting anomalous diffusion that cannot be modeled accurately by second order diffusion equations because of the nonlocal property of fractional differential operators numerical methods for space fractional diffusion equations generate dense or even full coefficient matrices with complicated structures traditionally these methods were solved via gaussian elimination which requires computational work of o n 3 per time step and o n 2 of memory to store where n is the number of spatial grid points in the discretization the significant computational work and memory requirement of these methods makes a numerical simulation of three dimensional space fractional diffusion equations computationally prohibitively expensive we present an alternating direction implicit adi finite difference formulation for space fractional diffusion equations in three space dimensions and prove its unconditional stability and convergence rate provided that the fractional partial difference operators along x y z directions commute we base on the adi formulation to develop a fast iterative adi finite difference method which has a computational work count of o n log n per iteration at each time step and a memory requirement of o n we also develop a fast multistep adi finite difference method which has a computational work count of o n log 2 n per time step and a memory requirement of o n log n numerical experiments of a three dimensional space fractional diffusion equation show that these both fast methods retain the same accuracy as the regular three dimensional implicit finite difference method but have significantly improved computational cost and memory requirement these numerical experiments show the utility of the fast method

on symmetric numerical semigroups a numerical semigroup is a subset s of n such that is closed under sums contains the zero and generates z as a group from this definition w x one obtains see for example 2 that s has a conductor c i e the maximum among all the natural numbers not belonging to s a numerical semigroup s is called symmetric if for every integer z f s c y z g s the study of the subsemigroups of n is a classical problem which is equivalent to study of the sets of natural solutions of linear equations with w x coefficients in n from 1970 and after the works 5 6 and others the study of the subsemigroups of n is also motivated by its applications to algebraic geometry an example arises when we consider an analytically irreducible one dimensional noetherian local domain r the integral closure v of r in the quotient field of r is a discrete valuation ring if we assume that r and v have the same residue class field and we denote by the valuation attached to v then s s r is a numerical semigroup r then properties on the semigroup s imply properties of the ring r for r w x w x example 6 proves that r is gorenstein see 1 if and only if s is r symmetric the close relation between numerical semigroups and monomial curves has produced the usage of algebraic geometry terminology in the field of numerical semigroups for example the smallest integer m greater than zero in s is usually called the multiplicity of s the cardinal e of a minimal system of generators for s is called the embedding dimension of s and a finite presentation for s is called a relation for s

on the family of ml spectral estimates for mixed spectrum identification a recently developed point spectrum identification procedure based on a family of ar and ml spectral estimates is exploited to arrive at a mixed spectrum identification procedure to this end a variety of properties of the ar and ml estimates as a function of model order are described these properties relate to amplitude convergence resolution and a characterization of the ar spectral artifact which is used to arrive at improved continuous spectral estimates a variety of examples are presented

linearizing integral transform for the multicomponent lattice kp abstract we present a generalization of the direct linearization method for the kadomtsev petviashvili kp equation and its lattice analogues such as the two dimensional toda equation the generalization consists of a riemann hilbert type of integral transform which relates solutions of the associated spectral problem to any given solution of the spectral problem by dimensional reduction we obtain the integral transform for the korteweg de vries kdv equation and its lattice analogues the integral transform is well suited for the investigation of the finite matrix generalizations of the above mentioned equations such finite matrix generalizations may be of use in connection with partial difference equations for spin correlation functions in the two dimensional ising model

euclid algorithm orthogonal polynomials and generalized routh hurwitz algorithm this paper is concerned with the relations between the euclid algorithm the theory of orthogonal polynomials and the problem of locating the zeros of a complex polynomial with respect to the imaginary axis in particular a simple generalized routh hurwitz algorithm is proposed which allows one to determine in any situation the numbers of zeros of an arbitrary complex polynomial in the right half plane on the imaginary axis and hence in the left half plane moreover it turns out that this algorithm yields as a side result a well defined factorization of the considered polynomial furthermore as a straightforward consequence of the adopted approach two presumably original algorithms are put into light which involve linear arithmetic operations only a polynomial nonnegativity test on the real axis and a characterization of positive real functions

order selection for and design of iir filters the design of infinite impulse response digital filters can be viewed as a spectral factorization problem when one knows what the numerator and denominator orders are this design problem is greatly simplified selection of the appropriate orders has long been a significant problem in recursive filter design recent work by gray et al suggests a general method by which the orders may be selected prior to design in this paper infinite impulse response digital filters are designed from finite impulse response prototypes using the gray technique to first select the order once the order has been determined the recursive filter coefficients are determined directly from the finite impulse filter because of the wealth of knowledge available concerning order lengths for nonrecursive filters the procedures used here permit direct comparison between the two filter methods

superfast tikhonov regularization of toeplitz systems toeplitz structured linear systems arise often in practical engineering problems correspondingly a number of algorithms have been developed that exploit toeplitz structure to gain computational efficiency when solving these systems the earliest fast algorithms for toeplitz systems required o n 2 operations while more recent superfast algorithms reduce the cost to o n log n 2 or below in this work we present a superfast algorithm for tikhonov regularization of toeplitz systems using an extension and transformation technique our algorithm translates a tikhonov regularized toeplitz system into a type of specialized polynomial problem known as tangential interpolation under this formulation we can compute the solution in only o n log n 2 operations we use numerical simulations to demonstrate our algorithm s complexity and verify that it returns stable solutions

a hermitian toeplitz matrix is unitarily similar to a real toeplitz plus hankel matrix two unitary matrices are presented that transform a hermitian toeplitz matrix into a real toeplitz plus hankel matrix and vice versa additional properties and consequences of these unitary transformations are also presented for a certain class of n dimensional toeplitz plus hankel systems of equations an efficient method of solution is presented an example is given to illustrate the similarity transforms toeplitz plus hankel systems arise in a wide variety of applications such as linear filtering theory discrete inverse scattering and discretization of certain integral equations arising in mathematical physics

the density of occupied nearest neighbor pairs on a rectangular 2 n lattice space utilizing a 15 term recursion that describes exactly the composite nearest neighbor degeneracy for simple indistinguishable particles distributed on a 2 n lattice space 11 the expectation of the normalized number of occupied nearest neighbor pairs is calculated as a function of coverage and the reduced interaction potential

transverse nearest neighbor degeneracies on a 2 n lattice an exact 15 term recursion relation and the associated generating function are derived for the number of arrangements of q particles on a 2 n lattice such that s occupied nearest neighbor pairs v of which are transverse and t unoccupied nearest neighbor pairs are formed

least squares adaptive lattice and transversal filters a unified geometric theory a unified theory is presented to characterize least squares adaptive filters in either lattice or transversal filter form for nonstationary processes the derivations are based upon a geometric formulation of least squares estimation and on the concept of displacement rank a few basic geometric relations are shown to underlie the various algorithms insights into the fundamental concepts that unify lattice and transversal filter approaches to least squares adaptive filters are also given the general results are illustrated by applications to the so called pre windowed and growing memory covariance formulations of the deterministic least squares problem

fast inversion of triangular toeplitz matrices an algorithm requiring 0 n log n operations is proposed for the inversion of triangular toeplitz matrices this algorithm is faster than existing techniques even for relatively small values of n and can easily be written in fortran

a look ahead levinson algorithm for general toeplitz systems the authors present an extension of levinson s algorithm that is guaranteed to be weakly stable for a large class of general toeplitz matrices namely those that do not have many consecutive ill conditioned leading principal submatrices the new algorithm adapts itself to the given toeplitz matrix by skipping over all the ill conditioned leading principal submatrices encountered during the solution process this is done by a look ahead strategy that monitors the condition of the leading principal submatrices and if necessary switches to a block step of suitable size the overhead of the look ahead algorithm is typically small compared to the classical levinson algorithm and in addition a reliable condition number estimate is produced

best stable and invertible approximations for arma systems a method is proposed for finding the best stable and invertible approximations for an autoregressive moving average arma system relative to a general quadratic metric in the coefficient space mathematically the problem is equivalent to projecting the regression and moving average vectors of the system onto the set s of coefficients of monic schur polynomials the geometry of s is too complex to allow the problem to be approached directly in the arma coefficient space a solution is obtained by constrained steepest descent in the hypercube of reflection coefficients which is homomorphic to s

combined blur and affine moment invariants and their use in pattern recognition abstract the paper is devoted to the recognition of objects and patterns deformed by imaging geometry as well as by unknown blurring we introduce a new class of features invariant simultaneously to blurring with a centrosymmetric psf and to affine transformation as we prove in the paper they can be constructed by combining affine moment invariants and blur invariants derived earlier combined invariants allow to recognize objects in the degraded scene without any restoration

the weak and strong stability of algorithms in numerical linear algebra the stability of algorithms in numerical linear algebra is discussed the concept of stability is extended to notions of weak stability and strong stability justifications are given for these extensions and the implications of error analyses in terms of these definitions are discussed the concept of weak stability helps to clarify some of the controversy which has arisen concerning the stability of algorithms for toeplitz systems

identification and restoration of noisy blurred images using the expectation maximization algorithm a maximum likelihood approach to the blur identification problem is presented the expectation maximization algorithm is proposed to optimize the nonlinear likelihood function in an efficient way in order to improve the performance of the identification algorithm low order parametric image and blur models are incorporated into the identification method the resulting iterative technique simultaneously identifies and restores noisy blurred images

efficient recursive in order least squares fir filtering and prediction this paper is concerned with the efficient determination of the optimum in the least squares sense fir filter on the basis of data samples of the input and desired response signals by procedures recursive in the filter order this situation typically arises when no a priori statistics are available and the system order is not known the general multiinput multioutput multichannel case is considered here and a fast algorithm is presented requiring for single channel signals approximately 2s 15m multiplications mps per order m s being the number of samples in the special case of linear prediction it calls for about s 12m mps hence it offers a computational reduction of 5m and 2m mps in comparison to the methods of marple 1 and morf et al 2 respectively additionally the proposed scheme is inherently symmetric and is suited very well to initialization of fast sequential algorithms as well as algorithms searching for the optimum lag filter

comparing ls fir filtering and l step ahead linear prediction this comparative study of the l step ahead linear prediction and least squares finite impulse response ls fir filtering problems emphasizes the numerical behavior of the resulting toeplitz systems it is shown that although these systems are similar the restraints on the autocorrelation coefficients fundamentally differentiate them in the process of doing so a new algorithmic scheme for the computation of the lagged lattice coefficients is developed which exhibits fundamentally improved numerical behavior moreover explicit formulas for the supremums of the absolute values of both the lagged lattice and filter coefficients are found theoretically and are experimentally confirmed by using the proposed algorithm finally the bounds of the ls fir filter coefficients are treated in comparison with the supremums of the lagged quantities

a new algorithm for computing orthogonal polynomials the aim of this paper is to present an algorithm for computing orthogonal polynomials the fast fourier transform completes the connection given by draux between the three term recurrence relationship and the euclidian algorithm applications to hankel systems and numerical examples illustrate our purpose

maximally robust 2 d channel estimation for ofdm systems two dimensional minimum mean square error mmse channel estimation for orthogonal frequency division multiplexing ofdm systems is known to perform better than the least squares as well as the conventional 1 d mmse estimation owing to its ability of exploiting both the time and the frequency correlations among the channel frequency response cfr coefficients its superior performance comes however at the price of increased requirements the knowledge of observation noise power and that of the channel frequency as well as time correlation functions in practical transmission scenarios where channel correlation functions are not known or cannot be easily estimated it is desirable to have an estimator that is robust to mismatches between the assumed and the actual channel correlation function while such a robust estimator for the case of an infinite number of observations is well known for various uncertainty classes not much attention has been paid to the practical case of a finite number of observations we derive in this paper the maximally robust mr 2 d channel estimator for the case of a finite number of pilot observations under some realistic constraints on the uncertainty class to which the 2 d channel correlation sequence belongs we demonstrate that the correlation sequence associated with the mr estimator can be obtained by a simple semi definite optimization procedure and is interestingly different from the well known heuristic proposals simulation results establish the superiority of the proposed mr estimator over commonly employed heuristic robust estimator by as much as 3 db in terms of the worst case estimation mse and around 1 db in terms of the average ber performance under different practical transmission scenarios of interest

recognition of images degraded by gaussian blur in this paper we propose a new theory of invariants to gaussian blur we introduce a notion of a primordial image as a canonical form of all gaussian blur equivalent images the primordial image is defined in spectral domain by means of projection operators we prove that the moments of the primordial image are invariant to gaussian blur and we derive recursive formulas for their direct computation without actually constructing the primordial image itself we show how to extend their invariance also to image rotation the application of these invariants is in blur invariant image comparison and recognition in the experimental part we perform an exhaustive comparison with two main competitors 1 the zhang distance and 2 the local phase quantization

lattice boltzmann method for the fractional advection diffusion equation mass transport such as movement of phosphorus in soils and solutes in rivers is a natural phenomenon and its study plays an important role in science and engineering it is found that there are numerous practical diffusion phenomena that do not obey the classical advection diffusion equation ade such diffusion is called abnormal or superdiffusion and it is well described using a fractional advection diffusion equation fade the fade finds a wide range of applications in various areas with great potential for studying complex mass transport in real hydrological systems however solution to the fade is difficult and the existing numerical methods are complicated and inefficient in this study a fresh lattice boltzmann method is developed for solving the fractional advection diffusion equation labfade the fade is transformed into an equation similar to an advection diffusion equation and solved using the lattice boltzmann method the labfade has all the advantages of the conventional lattice boltzmann method and avoids a complex solution procedure unlike other existing numerical methods the method has been validated through simulations of several benchmark tests a point source diffusion a boundary value problem of steady diffusion and an initial boundary value problem of unsteady diffusion with the coexistence of source and sink terms in addition by including the effects of the skewness the fractional order and the single relaxation time the accuracy and convergence of the method have been assessed the numerical predictions are compared with the analytical solutions and they indicate that the method is second order accurate the method presented will allow the fade to be more widely applied to complex mass transport problems in science and engineering

efficient construction of canonical ladder forms for vector autoregressive processes the paper treats the problem of constructing canonical ladder realizations for vector autoregressive ar processes specified by their characteristic matrix polynomials the difficulty of this problem is rooted in the fact that the backward matrix polynomial corresponding to a given vector ar process is a nontrivial function of the forward matrix polynomial the construction calls for solving a discrete lyapunov equation in block controller form two efficient procedures for solving this equation are presented both requiring a number of operations that is proportional to at most the square of the model order applications of the new procedures to stability tests simulation of ar processes and model reduction are described

generalized chandrasekhar recursions from the generalized schur algorithm presents a new approach to the chandrasekhar recursions and some generalizations thereof the derivation uses the generalized schur recursions which are o n sup 2 recursions for the triangular factorization of n spl times n matrices having a certain toeplitz like displacement structure it is shown that when the extra structure provided by an underlying state space model is properly incorporated into the generalized schur algorithm it reduces to the chandrasekhar recursions which are o nn sup 2 recursions for estimating the n dimensional state of a time invariant or constant parameter system from n measured outputs it is further noted that the generalized schur algorithm factors more general structured matrices and this fact is readily used to extend the chandrasekhar recursions to a class of time variant state space models special cases of which often arise in adaptive filtering

complements to cost equivalent realizations abstract skelton 1981 and skelton and yousuff 1983 use component cost analysis to obtain a reduced order model that is coat equivalent to a full order stochastic system this paper presents a more direct and numerically efficient method to obtain the same reduced order model which is shown to be a first order autoregressive model

direct multichannel predictive deconvolution the levinson principle generally can be used to compute recursively the solution of linear equations it can also be used to update the error terms directly this is used to do single channel deconvolution directly on seismic data without computing or applying a digital filter multichannel predictive deconvolution is used for seismic multiple attenuation in a standard procedure the prediction error filter matrices are computed with a levinson recursive algorithm using a covariance matrix of the input data the filtered output is the prediction errors or the nonpredictable part of the data starting with the classical levinson recursion wehave derived new algorithms for direct recursive calculationof the prediction errors without computing the data covariance matrix or computing the prediction error filters one algorithm generates recursively the one step forward and backward predic tion errors and the l step forward prediction error computing only the filter matrices with the highest index a numeri

combined blur translation scale and rotation invariant image recognition by radon and pseudo fourier mellin transforms the idea of scale and rotation invariant image recognition based on radon and fourier mellin transforms has been presented recently in this paper we extend the previous work and propose a new method to construct a set of combined blur translation scale and rotation invariants using radon and pseudo fourier mellin transforms named radon and pseudo fourier mellin invariants rpfmi the proposed method is robust to additive white noise as a result of summing pixel values to generate projections in the radon transform step we also present a mathematical framework of obtaining the radon and pseudo fourier mellin transforms of blurred images and a framework of deriving the combined blur scale and rotation invariants theoretical and experimental results show the superiority of the proposed method and its robustness to additive white noise in comparison with some recent methods

on low complexity approximation of matrices the operation multiplication of a vector by a matrix can be represented by a computational scheme or model that acts on the entries of the vector sequentially the number of intermediate quantities states that are needed in the computations is a measure of the complexity of the model if that complexity is low then not only multiplication but also other operations such as inversion can be carried out efficiently using the model rather than the original matrix in the introductory sections we describe an algorithm to derive a computational model of minimal complexity that gives an exact representation of an arbitrary upper triangular matrix the main result of the paper is an algorithm for computing an approximating matrix with a model of much lower complexity than the original as low as possible for a given tolerance on the approximation error as measure for the tolerance we will use a strong norm which we will call the hankel norm it is a generalization of the hankel norm which is used in the classical model approximation theory for complex analytical functions

scaling and rotation invariant analysis approach to object recognition based on radon and fourier mellin transforms various types of orthogonal moments have been widely used for object recognition and classification however these moments do not natively possess scaling invariance essential image normalization and binarization prior to moments extraction will lead to error of resampling and requantifying this paper describes a new scaling and rotation invariant analysis method for object recognition in the proposed method the radon transform is utilized to project the image onto projection space to convert the rotation of the original image to a translation of the projection in the angle variable and the scaling of the original image to a scaling of the projection in the spatial variable together with an amplitude scaling of the projection and then the fourier mellin transform is applied to the result to convert the translation in the angle variable and the scaling in the spatial variable as well as the amplitude scaling of the projection to a phase shift and an amplitude scaling respectively in order to achieve a set of completely invariant descriptors a rotation and scaling invariant function is constructed a k nearest neighbors classifier is employed to implement classification theoretical and experimental results show the high classification accuracy of this approach as a result of using the rotation and scaling invariant function instead of image binarization and normalization it is also shown that this method is relatively robust in the presence of white noise

maximum entropy and spectral estimation a review the method of maximum entropy is reviewed with emphasis on its relationship to entropy rate wiener filters autoregressive processes extrapolation the levinson algorithm lattice all pole and all pass filters and stability

the fractional order governing equation of levy motion a governing equation of stable random walks is developed in one dimension this fokker planck equation is similar to and contains as a subset the second order advection dispersion equation ade except that the order a of the highest derivative is fractional e g the 1 65th derivative fundamental solutions are levy s a stable densities that resemble the gaussian except that they spread proportional to time 1 a have heavier tails and incorporate any degree of skewness the measured variance of a plume undergoing levy motion would grow faster than fickian plume at a rate of time 2 a where 0 a 2 the equation is parsimonious since the parameters are not functions of time or distance the scaling behavior of plumes that undergo levy motion is accounted for by the fractional derivatives which are appropriate measures of fractal functions in real space the fractional derivatives are integrodifferential operators so the fractional ade describes a spatially nonlocal process that is ergodic and has analytic solutions for all time and space

blur identification using the bispectrum the authors propose inspecting the zero crossings in the central slice of the bispectrum of the observed image for blur identification this method is an extension of the classical methods for blur identification in which the power spectrum or the power cepstrum of the blurred image is applied to the bispectrum domain the proposed bispectrum based approach utilizes the ability of the bispectrum to suppress additive signal independent gaussian observation noise simulation results indicate that the method performs significantly better than the classical power spectrum based approach at low signal to noise ratios

olriv a new fast adaptive algorithm for rectangular block toeplitz systems in this paper we propose a new algorithm for solving overdetermined systems when they are rectangular block toeplitz the blocks can have more rows than columns it is based on the expression of the matrix of the system to solve as the intercorrelation between two vectorial processes namely the original and the instrumental processes the instrumental process has generally more components than the original one therefore it takes the overdetermined character of the system into consideration the proposed algorithm known as the overdetermined lattice recursive instrumental variable olriv belongs to the fast rls family and lies on a double lattice structure where one lattice performs the prediction of the original process and the other one the prediction of the instrumental process the geometric complete derivation of the proposed algorithm is given in the paper afterwards we show how olriv can be applied to perform blind adaptive identification of ar channels using high order statistics where the systems to solve are often overdetermined to ensure identifiability both the scalar and the vectorial cases are investigated simulation results are finally given to show the performances of olriv

a fast but unstable orthogonal triangularization technique for toeplitz matrices abstract d sweet s clever qr decomposition algorithm for toeplitz matrices is considered it requires only o n 2 flops to factor an n n matrix we analyze the algorithm to point out its deficiencies and compare it against two other toeplitz solvers

fast inversion of the simplicial bernstein mass matrix we consider the mass matrix arising from bernstein polynomials as finite element shape functions in particular we give an explicit formula for its eigenvalues and exact characterization of the eigenspaces in terms of the bernstein representation of orthogonal polynomials we then derive a fast algorithm for solving linear systems involving the element mass matrix after establishing these results we describe the application of bernstein techniques to the discontinuous galerkin finite element method for hyperbolic conservation laws obtaining optimal complexity algorithms finally we present numerical results investigating the accuracy of the mass inversion algorithms and the scaling of total run time for the function evaluation needed in dg time stepping

causal compensation for erasures in frame representations in a variety of signal processing and communications contexts erasures occur inadvertently or can be intentionally introduced as part of a data reduction strategy this paper discusses causal compensation for erasures in frame representations of signals the approach described assumes linear synthesis of the signal using a prespecified frame but no specific generation mechanism for the coefficients under this assumption it is demonstrated that erasures can be compensated for using low complexity causal systems if the transmitter is aware of the occurrence of the erasure an optimal compensation is to project the erasure error to the remaining coefficients it is demonstrated that the same compensation can be executed using a transmitter receiver combination in which the transmitter is not aware of the erasure occurrence the transmitter precompensates using projections as if assuming erasures will occur the receiver undoes the compensation for the coefficients that have not been erased thus maintaining the compensation only of the erased coefficients the stability of the resulting systems is explored and stability conditions are derived it is shown that stability for any erasure pattern can be enforced by optimizing a constrained quadratic program at the system design stage the paper concludes with examples and simulations that verify the theoretical results and illustrate key issues in the algorithms

simultaneous image fusion and denoising by using fractional order gradient information abstract image fusion and denoising are significant in image processing because of the availability of multi sensor and the presence of the noise the first order and second order gradient information have been effectively applied to deal with fusing the noise free source images in this paper we utilize the fractional order derivatives to represent image features and propose two new convex variational models for fusing noisy source images furthermore we apply an alternating direction method of multiplier admm to solve the minimization problems in the proposed models numerical experiments show that the proposed methods outperform the conventional total variation methods for simultaneously fusing and denoising

similarity transformation parameters recovery based on radon transform application in image registration and object recognition the radon transform since its introduction in the beginning of the last century has been studied deeply and applied by researchers in a great number of applications especially in the biomedical imaging fields by using the radon transform properties the issue is to recover the transformation parameters regarding the rotation scaling and translation by handling only the image projections assuming no access to the spatial domain of the image this paper proposes an algorithm using an extended version of the radon transform to recover such parameters relating to two unknown images directly from their projection data especially our approach deals with the problem of the estimation accuracy of the rotation angle and its finding in one step instead of two steps as it is reported in the literature this method may be applied in image registration as well in object recognition the results are for the first time exploited in object recognition where comparison with powerful descriptors shows the outstanding performance of the proposed paradigm moreover the influence of additive noise on registration and recognition experiments is discussed and shows the efficiency of the method to reduce the effect of the noise highlightswe define 2 based radon transform rt and motivate its use we propose an algorithm to recover rst transforms using only rt the algorithm is tested on images in real world application e g ct mri etc this rst parameter recovery method is newly applied in object recognition a new confusion matrix is designed to identify also a mislabeled class element

fast solution methods for space fractional diffusion equations we develop fast solution methods for a shifted grunwald finite difference method for steady state and time dependent space fractional diffusion equations these methods reduce the memory requirement of the finite difference scheme from o n 2 to o n and the computational complexity from o n 3 to o n log 2 n preliminary numerical example runs show the utility of these methods over the traditional direct solvers of the finite difference methods in terms of computational cost and memory requirements

arma spectral estimation of narrow band processes via model reduction the problem of estimating autoregressive moving average arma models for narrowband processes is considered the following approach is proposed estimate a high order autoregressive ar approximation of the process by model reduction based on a truncated internally balanced realization or optimal hankel norm model reduction reduce the order of this high order ar estimate to find a lower order arma model this algorithm gives arma spectral estimates with excellent resolution properties without using iterative numerical minimization methods as for the maximum likelihood method how to take the narrowband assumption into account in the model reduction step is discussed in detail

genus of numerical semigroups generated by three elements abstract let h a b c be a numerical semigroup generated by three elements and let r k h be its semigroup ring over a field k we assume that h is not symmetric and assume that the defining ideal of r is defined by maximal minors of the matrix x y z y z x then we will show that the genus of h is determined by the frobenius number f h and or in particular we show that h is pseudo symmetric if and only if 1 or 1 also we will give a simple algorithm to get all the pseudo symmetric numerical semigroups h a b c with given frobenius number

the statistics of interacting dumbbells on a 2 n lattice space a set theoretic argument is utilizied to determine a 31 term recursion that describes exactly the composite nearest neighbor degeneracy for indistinguishable dumbbell particles distributed on a rectangular 2 n lattice space the associated generating functions the expectation of the lattice coverage and the density of occupied nearest neighbor pairs are also determined

fast algorithms for linear prediction and system identification filters with linear phase a general finite impulse response fir filter can be used as a linear prediction filter if given only an input sample sequence or as a system identification model if given the input and output sequences from an unknown system with known correlation the coefficients of the fir filter that minimize the mean square error in both applications are found by solution of a set of normal equations with toeplitz structure using only data samples the coefficients that yield the least squared error in both applications are found by solution of a set of normal equations with near to toeplitz structure computationally efficient fast algorithms have been published to solve for the coefficients from both types of normal equation structures if the fir filter is constrained to have a linear phase then the impulse response must be symmetric this then leads to normal equations with toeplitz plus hankel or near to toeplitz plus hankel structure fast algorithms for solving these normal equations for the filter coefficients are developed in this paper they have computational complexity proportional to m2and parameter storage proportional to m where m is the filter order an application of one of these algorithms for spectral estimation concludes the paper

fast subsampled updating stabilized fast transversal filter fsu sftf rls algorithm for adaptive filtering we present a new doubly fast algorithm for recursive least squares rls adaptive filtering that uses displacement structure and subsampled updating the fast subsampled updating stabilized fast transversal filter fsu sftf algorithm is mathematically equivalent to the classical fast transversal filter ftf algorithm the ftf algorithm exploits the shift invariance that is present in the rls adaptation of an fir filter the ftf algorithm is in essence the application of a rotation matrix to a set of filters and in that respect resembles the levinson 1947 algorithm in the subsampled updating approach we accumulate the rotation matrices over some time interval before applying them to the filters it turns out that the successive rotation matrices themselves can be obtained from a schur type algorithm that once properly initialized does not require inner products the various convolutions that appear in the algorithm are done using the fast fourier transform fft the resulting algorithm is doubly fast since it exploits ftf and ffts the roundoff error propagation in the fsu sftf algorithm is identical to that in the sftf algorithm a numerically stabilized version of the classical ftf algorithm the roundoff error generation on the other hand seems somewhat smaller for relatively long filters the computational complexity of the new algorithm is smaller than that of the well known lms algorithm rendering it especially suitable for applications such as acoustic echo cancellation

time second order finite difference finite element algorithm for nonlinear time fractional diffusion problem with fourth order derivative term abstract in this article we study and analyze a galerkin mixed finite element mfe method combined with time second order discrete scheme for solving nonlinear time fractional diffusion equation with fourth order derivative term we firstly introduce an auxiliary variable u reduce the fourth order problem into a coupled system with two equations discretize the obtained coupled system at time t k 2 by a second order difference scheme with second order approximation for fractional derivative then formulate mixed weak formulation and fully discrete mfe scheme further we give the detailed proof for stability of scheme the existence and uniqueness of mfe solution and a priori error estimates finally by some numerical computations we test the theoretical results which illustrate that we can obtain the numerical results for two variables moreover we arrive at second order time convergence orders which are higher than the ones yielded by the l 1 approximation

human ankle joint stiffness over the full range of muscle activation levels abstract system identification techniques have been used to track changes in dynamic stiffness of the human ankle joint over a wide range of muscle contraction levels subjects lay supine on an experimental table with their left foot encased in a rigid low inertia cast which was fixed to an electro hydraulic actuator operating as a position servo subjects generated tonic plantarflexor or dorsiflexor torques of different magnitudes ranging from rest to maximum voluntary contractions mvc during repeated presentations of a stochastic ankle angular position perturbation compliance impulse response functions irf were determined from every 2 5 s perturbation sequence the gain g natural freqency n and damping parameters of the second order model providing the best fit to each irf were determined and used to compute the corresponding inertial i viscous b and elastic k stiffness parameters the behaviour of these parameters with mean torque was found to follow two simple rules first the elastic parameter k increased in proportion to mean ankle torque as it was varied from rest to mvc these changes were considerable involving increases of more than an order of magnitude second the damping parameter remained almost invariant over the entire range of contractions despite the dramatic changes in k

geometric invariant features in the radon transform domain for near duplicate image detection radon transform has been widely used in content based image representation due to its excellent geometric properties in this paper we propose a family of geometric invariant features based on radon transform for near duplicate image detection according to the theoretical analysis between geometric operations translation scaling and rotation and radon transform we present a geometric invariant feature model based on the feature model we developed four kinds of geometric invariant features in addition a uniform sampling technique is introduced to combine different features the comprehensive performance of the combined feature is better than that of a single one extensive experiments show that the proposed features are robust not only to rotation and scaling but also to other operations such as compression noise contamination blurring illumination modification cropping etc and achieve strong competitive performance compared with the state of the art image features