block jacobi matrices and zeros of multivariate orthogonal polynomials a commuting family of symmetric matrices are called the block jacobi matrices if they are block tridiagonal they are related to multivariate orthogonal polynomials we study their eigenvalues and joint eigenvectors the joint eigenvalues of the truncated block jacobi matrices correspond to the common zeros of the multivariate orthogonal polynomials

reducing the number of multipliers in the parallel realization of half band elliptic iir filters it is shown in this correspondence that a halfband iir filter with the poles on the imaginary axis can be derived by the bilinear transformation of an elliptic minimal q factors analog prototype for an odd degree transfer function the residues at the poles are real or imaginary consequently in the parallel realization the number of multipliers can be reduced by half

entropic approach to interior point solution of linear programs we present a maxentropic approach for obtaining interior suboptimal solutions to a linear programming problem not necessarily in karmarkar s canonical form each suboptimal solution lies in the relative interior set of feasible solutions we present an application to the problem of obtaining reconstructions of minimal weighted l 1 norm of a function from the knowledge of a few of its fourier coefficients

feasibility of approximate broadband estimation of acoustic impedance profile from first principles and band limited reflection data abstractbecause seismic reflection data are band limited acoustic impedance profiles derived from them are nonunique the conventional inversion methods counter the nonuniqueness either by stabilizing the answer with respect to an initial model or by imposing mathematical constraints such as sparsity of the reflection coefficients by making a nominal assumption of an earth model locally consisting of a stack of homogeneous and horizontal layers we have formulated a set of linear equations in which the reflection coefficients are the unknowns and the recursively integrated seismic trace constitute the data drawing only on first principles the zoeppritz equation in this case the approach makes a frontal assault on the problem of reconstructing reflection coefficients from band limited data the local layer cake assumption and the strategy of seeking a singular value decomposition solution of the linear equations counter the nonuniqueness provided that the objective is to reconstruct a smooth version

commuting family of block jacobi matrices abstract the block jacobi matrices considered in this paper are a family of block tridiagonal matrices which are natural extensions of a singular jacobi matrix in the sense that they are associated with orthogonal polynomials in several variables we present the basic properties of these matrices

zero sets of bivariate hermite polynomials abstract we establish various properties for the zero sets of three families of bivariate hermite polynomials special emphasis is given to those bivariate orthogonal polynomials introduced by hermite by means of a rodrigues type formula related to a general positive definite quadratic form for this family we prove that the zero set of the polynomial of total degree n m consists of exactly n m disjoint branches and possesses n m asymptotes a natural extension of the notion of interlacing is introduced and it is proved that the zero sets of the family under discussion obey this property the results show that the properties of the zero sets considered as affine algebraic curves in r 2 are completely different for the three families analyzed

adaptive iterative algorithms for spiky deconvolution considering the joint detection estimation character that spiky deconvolution problems have an adaptively contracted projection selection operator is introduced to detect the nonzero values of the solution which can be combined with iterative algorithms to offer very efficient schemes for solving these problems a number of gradient type algorithms based on this principle are described and their performance is illustrated through simulation examples the approach is based on the idea of reducing the noise and defining the signal in an iterative form another possibility is to define the signal and reduce the overall energy outside its domain also in an iterative form this algorithm is more expensive from a computational point of view however simulations indicate that it has somewhat different properties it seems to be slightly less robust against the noise while it offers better resolution and even more accurate amplitude estimates

a technique for realizing linear phase iir filters a real time iir filter structure is presented that possesses exact phase linearity with 10 approximately 1000 times fewer general multiplies than conventional fir filters of similar performance and better magnitude characteristics than equiripple or maximally flat group delay iir filters this structure is based on a technique using local time reversal and single pass sectioned convolution methods to realized a real time recursive implementation of the noncausal transfer function h z sup 1 the time reversed section technique used to realize exactly linear phase iir filters is described the effects of finite section length on the sectional convolution are analyzed a simulation methodology is developed to address the special requirements of simulating a time reversed section filter a design example is presented with computer simulation to illustrate performance in terms of overall magnitude response and phase linearity as a function of finite section length nine example filter specifications are used to compare the performance and complexity of the time reversed section technique to those of a direct fir implementation

a neural root finder of polynomials based on root moments this letter proposes a novel neural root finder based on the root moment method rmm to find the arbitrary roots including complex ones of arbitrary polynomials this neural root finder nrf was designed based on feedforward neural networks fnn and trained with a constrained learning algorithm cla specifically we have incorporated the a priori information about the root moments of polynomials into the conventional backpropagation algorithm bpa to construct a new cla the resulting nrf is shown to be able to rapidly estimate the distributions of roots of polynomials we study and compare the advantage of the rmm based nrf over the previous root coefficient method based nrf and the traditional muller and laguerre methods as well as the mathematica roots function and the behaviors the accuracies of the resulting root finders and their training speeds of two specific structures corresponding to this fnn root finder the log and the fnn we also analyze the effects of the three controlling parameters p0 p with the cla on the two nrfs theoretically and experimentally finally we present computer simulation results to support our claims

low power decimator design using approximated linear phase n band iir filter this correspondence presents a new design of a low power decimation filter which consists of a poly phase finite impulse response fir 4 comb filter an approximate linear phase one third band infinite impulse response iir filter and a half band fir filter a poly phase fir 4 comb filter architecture was designed which consumes 75 less power than the recursive comb filter architecture new general equations were derived for the design of 1 n band iir filters and these equations were used to design a novel approximate linear phase one third band iir filter the decimation filter is designed using simulink and dsp blockset and matlab simulations are performed to verify the phase linearity and magnitude response of the designed filter the group delay for the passband region of one third band iir filter has a negligible error of 0 009 the resulting decimation filter has 60 less hardware and consumes 67 less power than the comb fir fir decimation filter

constrained least absolute deviation neural networks it is well known that least absolute deviation lad criterion or norm used for estimation of parameters is characterized by robustness i e the estimated parameters are totally resistant insensitive to large changes in the sampled data this is an extremely useful feature especially when the sampled data are known to be contaminated by occasionally occurring outliers or by spiky noise in our previous works we have proposed the least absolute deviation neural network ladnn to solve unconstrained lad problems the theoretical proofs and numerical simulations have shown that the ladnn is lyapunov stable and it can globally converge to the exact solution to a given unconstrained lad problem we have also demonstrated its excellent application value in time delay estimation more generally a practical lad application problem may contain some linear constraints such as a set of equalities and or inequalities which is called constrained lad problem whereas the unconstrained lad can be considered as a special form of the constrained lad in this paper we present a new neural network called constrained least absolute deviation neural network cladnn to solve general constrained lad problems theoretical proofs and numerical simulations demonstrate that the proposed cladnn is lyapunov stable and globally converges to the exact solution to a given constrained lad problem independent of initial values the numerical simulations have also illustrated that the proposed cladnn can be used to robustly estimate parameters for nonlinear curve fitting which is extensively used in signal and image processing

on a class of bivariate second order linear partial difference equations and their monic orthogonal polynomial solutions abstract in this paper we classify the bivariate second order linear partial difference equations which are admissible potentially self adjoint and of hypergeometric type using vector matrix notation explicit expressions for the coefficients of the three term recurrence relations satisfied by monic orthogonal polynomial solutions are obtained in terms of the coefficients of the partial difference equation finally we make a compilation of the examples existing in the literature belonging to the class analyzed in this paper namely bivariate charlier meixner kravchuk and hahn orthogonal polynomials

multichannel spatially correlated reflectivity inversion using block sparse bayesian learning abstractthe reflectivity inversion approach based on a variety of regularization terms was extensively developed and applied to image subsurface structure in recent years in addition multichannel reflectivity inversion or deconvolution considering the lateral continuity of reflection interfaces or reflectivity in adjacent channels has been developed however these processing operations seldom adaptively judge the stratal continuity or automatically alter the parameters of the corresponding algorithm to use the special correlation of the reflection information contained in the seismic data a multichannel spatially correlated reflectivity inversion using block sparse bayesian learning bsbl is introduced the method adopts a covariance matrix that describes the spatial relationship of reflectivity and simultaneously controls the temporal sparsity with an expectation maximization algorithm we can obtain the parameters of the multichannel reflectivity model including the mean i e the estimated mul

commuting extensions and cubature formulae based on a novel point of view on 1 dimensional gaussian quadrature we present a new approach to d dimensional cubature formulae it is well known that the nodes of 1 dimensional gaussian quadrature can be computed as eigenvalues of the so called jacobi matrix the d dimensional analog is that cubature nodes can be obtained from the eigenvalues of certain mutually commuting matrices these are obtained by extending adding rows and columns to certain noncommuting matrices a1 ad related to the coordinate operators x1 xd in rd we prove a correspondence between cubature formulae and commuting extensions of a1 ad satisfying a compatibility condition which in appropriate coordinates constrains certain blocks in the extended matrices to be zero thus the problem of finding cubature formulae can be transformed to the problem of computing and then simultaneously diagonalizing commuting extensions we give a general discussion of existence and of the expected size of commuting extensions and briefly describe our attempts at computing them

a general methodology for designing globally convergent optimization neural networks we present a general methodology for designing optimization neural networks we prove that the neural networks constructed by using the proposed method are guaranteed to be globally convergent to solutions of problems with bounded or unbounded solution sets in contrast with the gradient methods whose convergence is not guaranteed we show that the proposed method contains both the gradient methods and nongradient methods employed in existing optimization neural networks as special cases based on the theoretical results of the proposed method we study the convergence and stability of general gradient models in the case of unisolated solutions using the proposed method we derive some new neural network models for a very large class of optimization problems in which the equilibrium points correspond to exact solutions and there is no variable parameter finally some numerical examples show the effectiveness of the method

projected gabor deconvolution abstractgabor deconvolution consists of approximating a nonstationary problem as several stationary subproblems via the gabor frame solving each subproblem independently and then recombining projecting the subsolutions into an approximate solution to the original nonstationary problem the approximations however cause inherent instability due to systematic errors that prevent the algorithm from converging to the true solution even for noise free cases furthermore the method will be time consuming when a nonlinear optimization is used for shaping the reflectivity structure an alternative projected gabor deconvolution is considered which is based on the gabor expansion however in contrast to the conventional form in the new method first the problem is projected into the time domain and then an inversion is performed to obtain the final reflectivity compared with the gabor deconvolution the projected alternative 1 exhibits an improved convergence property 2 is more efficient for sparse de

the use of multiple criterion optimization for frequency domain design of noncausal iir filters noncausal recursive filters have recently been proposed because of their increased efficiency versus linear phase fir filters and causal iir filters 2 a general frequency domain design technique capable of exploiting the characteristics of noncausal filters is not yet available this paper proposes the use of multiple criterion optimization for the frequency domain design of noncausal iir filters a new family of filters is generated and their efficiency versus causal fir filters and iir filters is discussed

optimum binary windows for discrete fourier transforms a class of windows called binary windows for the frequency domain implementation of the discrete fourier transform is proposed while the conventional time domain windowing requires n 2 stored values of the data window and n multiplications the binary windows do not require multiplications or stored constants rather they are replaced by shift and add operations typical hardware structures are presented for efficient implementation of the binary windows

cubature formulae and orthogonal polynomials abstract the connection between orthogonal polynomials and cubature formulae for the approximation of multivariate integrals has been studied for about 100 yr the article j radon published about 50 yr ago j radon zur mechanischen kubatur monatsh math 52 1948 286 300 has been very influential in this text we describe some of the results that were obtained during the search for answers to questions raised by his article

a linear programming approach to the estimation of the power spectra of harmonic processes a new approach to the estimation of high resolution power spectra of harmonic processes is presented this approach uses linear programming lip to exploit the spiky character of the l 1 norm results for the lip power spectral estimate are contrasted with those using various formulations of the maximum entropy algorithm

linear partial q difference equations on q linear lattices and their bivariate q orthogonal polynomial solutions orthogonal polynomial solutions of an admissible potentially self adjoint linear second order partial q difference equation of the hypergeometric type in two variables on q linear lattices are analyzed a q pearson s system for the orthogonality weight function as well as for the difference derivatives of the solutions are presented giving rise to a solution of the q difference equation under study in terms of a rodrigues type formula the monic orthogonal polynomial solutions are treated in detail giving explicit formulae for the matrices in the corresponding recurrence relations they satisfy lewanowicz and wozny s lewanowicz p wozny j comput appl math 233 2010 1554 1561 have recently introduced a non monic bivariate extension of big q jacobi polynomials together with a partial q difference equation of the hypergeometric type that governs them this equation is analyzed in the last section we provide two more orthogonal polynomial solutions namely a second non monic solution from the rodrigues representation and the monic solution both from the recurrence relation that govern them and also explicitly given in terms of generalized bivariate basic hypergeometric series limit relations as email protected for the partial q difference equation and for the all three q orthogonal polynomial solutions are also presented

finite time convergent recurrent neural network with a hard limiting activation function for constrained optimization with piecewise linear objective functions this paper presents a one layer recurrent neural network for solving a class of constrained nonsmooth optimization problems with piecewise linear objective functions the proposed neural network is guaranteed to be globally convergent in finite time to the optimal solutions under a mild condition on a derived lower bound of a single gain parameter in the model the number of neurons in the neural network is the same as the number of decision variables of the optimization problem compared with existing neural networks for optimization the proposed neural network has a couple of salient features such as finite time convergence and a low model complexity specific models for two important special cases namely linear programming and nonsmooth optimization are also presented in addition applications to the shortest path problem and constrained least absolute deviation problem are discussed with simulation results to demonstrate the effectiveness and characteristics of the proposed neural network

a class of bivariate orthogonal polynomials and cubature formula the existence of gaussian cubature for a given measure depends on whether the corresponding multivariate orthogonal polynomials have enough common zeros we examine a class of orthogonal polynomials of two variables generated from that of one variable

design of multiplierless elliptic iir filters with a small quantization error we present a new technique for the design of multiplierless iir elliptic filters the multiplierless filter has all multiplication constants implemented with a small number of shifters and adders the proposed technique is based on sensitivity analysis an analytical expression for amplitude response sensitivity is derived for the filter structures consisting of two allpass subfilters in parallel it is shown that the amplitude response sensitivity to some constant x can be expressed as a product of the filter reflectance function and the phase sensitivity of the allpass section that implements the constant the closed form expressions for the phase sensitivities of the first and second order allpass sections are also developed it is shown in the paper that the n 1 2 most sensitive constants can be directly controlled by the transfer function parameters if the transfer function is derived by the bilinear transformation from an elliptic minimal q factors emqf analog prototype this way n 1 2 multiplication constants can be implemented without quantization leaving the filter characteristic strictly elliptic this is achieved for a class of low noise allpass sections and for the wave lattice digital filter as well the quantization of the remaining n 1 2 less sensitive constants is performed using the phase tolerance scheme and phase sensitivity functions the proposed design technique is straight forward and consequently very fast the application is demonstrated on the examples of narrowband wideband and halfband filters

l sub 1 and l sub infinity minimization via a variant of karmarkar s algorithm simple iterative algorithms are presented for l sub 1 and l sub infinity minimization regression based on a variant of karmarkar s linear programming algorithm although these algorithms are based on entirely different theoretical principles to the popular irls iteratively reweighted least squares algorithm they have almost identical matrix operations also presented are the results of a monte carlo study comparing the numerical convergence properties of the karmarkar algorithm for l sub 1 minimization to those of an irls and a simplex algorithm the test problem involves l sub 1 estimation of ar autoregressive model parameters the karmarkar algorithm outperformed irls by achieving higher numerical accuracy in fewer iterations techniques for reducing the computational cost per iteration of the karmarkar l sub 1 algorithm are discussed

3d magnetic sparse inversion using an interior point method rock susceptibility measurements are sometimes taken on outcrop and borehole rocks and provide valuable information for constraining magnetic data inversion we present two approaches for 3d magnetic sparse inversion that effectively take advantage of the rock susceptibility information both approaches minimize a total objective function subject to bound constraints using an interior point method the first approach directly minimizes an l1 norm of the susceptibility model by keeping the bounds positive in which case the objective function is differentiable in the feasible region the second approach minimizes a more generalized lp like norm 0 p 1 of the susceptibility model by approximating the lp like norm inversion as an iteratively reweighed least squares problem moreover this approach allows the model values to be either positive or negative we also demonstrate the equivalence of the proposed approaches and the binary inversion the recovered models of both approaches are characterized by

a technique for stabilizing interval velocities from the dix equation interval velocities the velocities at which sounds travel in the earth can be computed from stacking or root mean square rms velocities by applying the dix equation dix 1955 ij j 1 rj 12tj 1 rj2tj tj 1 tj 1 2 eq 1 where rj are the stacking velocity picks tj are the associated times and ij j 1 is the average interval velocity between tj and tj 1

3d magnetic data space inversion with sparseness constraints i have developed an inversion approach that determines a 3d susceptibility distribution that produces a given magnetic anomaly the subsurface model consists of a 3d equally spaced array of dipoles the inversion incorporates a model norm that enforces sparseness and depth weighting of the solution sparseness is imposed by using the cauchy norm on model parameters the inverse problem is posed in the data space leading to a linear system of equations with dimensions based on the number of data n this contrasts with the standard least squares solution derived through operations within the m dimensional model space m being the number of model parameters hence the data space method combined with a conjugate gradient algorithm leads to computational efficiency by dealing with an n n system versus an m m one where n m tests on synthetic data show that sparse inversion produces a much more focused solution compared with a standard model space least squares inversion the inversion of aeromagnet

sparse reflectivity inversion for nonstationary seismic data abstractconventional reflectivity inversion methods are based on a stationary convolution model and theoretically require stationary seismic traces as input i e those free of attenuation and dispersion effects reflectivity inversion for nonstationary data which is typical for field surveys requires us to first compensate for the earth s q filtering effects by inverse q filtering however the attenuation compensation for inverse q filtering is inherently unstable and offers no perfect solution thus we presented a sparse reflectivity inversion method for nonstationary seismic data we referred to this method as nonstationary sparse reflectivity inversion nsri it makes the novel contribution of avoiding intrinsic instability associated with inverse q filtering by integrating the earth s q filtering operator into the stationary convolution model nsri also avoids time variant wavelets that are typically required in time variant deconvolution although nsri is initially designed for nonstationary

three points method for searching the best least absolute deviations plane in this paper a new method for estimation of optimal parameters of a best least absolute deviations plane is proposed which is based on the fact that there always exists a best least absolute deviations plane passing through at least three different data points the proposed method leads to a solution in finitely many steps moreover a modification of the aforementioned method is proposed that is especially adjusted to the case of a large number of data and the need to estimate parameters in real time both methods are illustrated by numerical examples on the basis of simulated data and by one practical example from the field of robotics

a new method for digital all pass filter design a new method for the design of digital all pass filters using chebyshev criterion is introduced it is based on a phase approximation algorithm for polynomial transfer functions the algorithm exploits a scheme of iteratively linearizing the nonlinear constraints in a nonlinear programming and converges theoretically the design method has the advantage that it finds the best uniform phase approximation to an arbitrarily specified phase response without any initial guess of the solution design examples of orders up to 80 obtained on an ibm pc xt personal computer are given to show the practicability of the method

an improved martinet parks algorithm for iir design with unequal numbers of poles and zeros the martinet parks 1978 algorithm for equiripple iir filters with unequal numbers of poles and zeros has been modified to converge for a wider range of designs including an important extraripple case several designs are compared with respect to complexity coefficient sensitivity and group delay the matlab program implementing the algorithm is available by e mail

fixed point continuation for ell_1 minimization methodology and convergence we present a framework for solving the large scale ell 1 regularized convex minimization problem min x 1 mu f x our approach is based on two powerful algorithmic ideas operator splitting and continuation operator splitting results in a fixed point algorithm for any given scalar mu continuation refers to approximately following the path traced by the optimal value of x as mu increases in this paper we study the structure of optimal solution sets prove finite convergence for important quantities and establish q linear convergence rates for the fixed point algorithm applied to problems with f x convex but not necessarily strictly convex the continuation framework motivated by our convergence results is demonstrated to facilitate the construction of practical algorithms

reconstruction of a sparse spike train from a portion of its spectrum and application to high resolution deconvolution an algorithm is proposed for the reconstruction of a sparse spike train from an incomplete set of its fourier components it is shown that as little as 20 25 percent of the fourier spectrum is sufficient in practice for a high quality reconstruction the method employs linear programming to minimize the l1 norm of the output because minimization of this norm favors solutions with isolated spikes given a wavelet this technique can be used to perform deconvolution of noisy seismograms when the desired output is a sparse spike series relative reliability of the data is assessed in the frequency domain and only the reliable spectral data are included in the calculation of the spike series equations for the unknown spike amplitudes are solved to an accuracy compatible with the uncertainties in the reliable data in examples with 10 percent random noise the output is superior to that obtained using conventional least squares techniques

multivariate orthogonal polynomials and integrable systems multivariate orthogonal polynomials in d real dimensions are considered from the perspective of the cholesky factorization of a moment matrix the approach allows for the construction of corresponding multivariate orthogonal polynomials associated second kind functions jacobi type matrices and associated three term relations and also christoffel darboux formulae the multivariate orthogonal polynomials their second kind functions and the corresponding christoffel darboux kernels are shown to be quasi determinants as well as schur complements of bordered truncations of the moment matrix quasi tau functions are introduced it is proven that the second kind functions are multivariate cauchy transforms of the multivariate orthogonal polynomials discrete and continuous deformations of the measure lead to toda type integrable hierarchy being the corresponding flows described through lax and zakharov shabat equations bilinear equations are found varying size matrix nonlinear partial difference and differential equations of the 2d toda lattice type are shown to be solved by matrix coefficients of the multivariate orthogonal polynomials the discrete flows which are shown to be connected with a gauss borel factorization of the jacobi type matrices and its quasi determinants lead to expressions for the multivariate orthogonal polynomials and their second kind functions in terms of shifted quasi tau matrices which generalize to the multidimensional realm those that relate the baker and adjoint baker functions to ratios of miwa shifted tau functions in the 1d scenario in this context the multivariate extension of the elementary darboux transformation is given in terms of quasi determinants of matrices built up by the evaluation at a poised set of nodes lying in an appropriate hyperplane in r d of the multivariate orthogonal polynomials the multivariate christoffel formula for the iteration of m elementary darboux transformations is given as a quasi determinant it is shown using congruences in the space of semi infinite matrices that the discrete and continuous flows are intimately connected and determine nonlinear partial difference differential equations that involve only one site in the integrable lattice behaving as a kadomstev petviashvili type system finally a brief discussion of measures with a particular linear isometry invariance and some of its consequences for the corresponding multivariate polynomials is given in particular it is shown that the toda times that preserve the invariance condition lay in a secant variety of the veronese variety of the fixed point set of the linear isometry

a two phase optimization neural network a novel two phase neural network that is suitable for solving a large class of constrained or unconstrained optimization problem is presented for both types of problems with solutions lying in the interior of the feasible regions the phase one structure of the network alone is sufficient when the solutions of constrained problems are on the boundary of the feasible regions the proposed two phase network is capable of achieving the exact solutions in contrast to existing optimization neural networks which can obtain only approximate solutions furthermore the network automatically provides the corresponding lagrange multiplier associated with each constraint thus for linear programming the network solves both the primal problems and their dual problems simultaneously

design of recurrent neural networks for solving constrained least absolute deviation problems recurrent neural networks for solving constrained least absolute deviation lad problems or l1 norm optimization problems have attracted much interest in recent years but so far most neural networks can only deal with some special linear constraints efficiently in this paper two neural networks are proposed for solving lad problems with various linear constraints including equality two sided inequality and bound constraints when tailored to solve some special cases of lad problems in which not all types of constraints are present the two networks can yield simpler architectures than most existing ones in the literature in particular for solving problems with both equality and one sided inequality constraints another network is invented all of the networks proposed in this paper are rigorously shown to be capable of solving the corresponding problems the different networks designed for solving the same types of problems possess the same structural complexity which is due to the fact these architectures share the same computing blocks and only differ in connections between some blocks by this means some flexibility for circuits realization is provided numerical simulations are carried out to illustrate the theoretical results and compare the convergence rates of the networks

an analysis of polynomial chaos approximations for modeling single fluid phase flow in porous medium systems we examine a variety of polynomial chaos motivated approximations to a stochastic form of a steady state groundwater flow model we consider approaches for truncating the infinite dimensional problem and producing decoupled systems we discuss conditions under which such decoupling is possible and show that to generalize the known decoupling by numerical cubature it would be necessary to find new multivariate cubature rules finally we use the acceleration of monte carlo to compare the quality of polynomial models obtained for all approaches and find that in general the methods considered are more efficient than monte carlo for the relatively small domains considered in this work a curse of dimensionality in the series expansion of the log normal stochastic random field used to represent hydraulic conductivity provides a significant impediment to efficient approximations for large domains for all methods considered in this work other than the monte carlo method

simultaneous design in both magnitude and group delay of iir and fir filters based on multiple criterion optimization this work considers the simultaneous design in both magnitude and group delay of digital transfer functions on the basis of multiple criterion optimization both causal iir filters and nonlinear phase fir filters are studied examples of the optimal tradeoff filters both fir filters and iir filters are presented and their characteristics are analyzed

linear phase iir filter with equiripple stopband a simple technique of introducing transmission zeros into a low pass all pole filter function to make its stopband transmission equiripple is described the zeros are introduced through a transformation which maps the stopband of the filter onto the unit circle and the passband onto a segment of the real axis in the transformed plane the technique is used to improve the loss characteristic of all pole constant delay filters examples are included to illustrate the design procedure

linear phase low pass iir digital differentiators a novel approach to designing approximately linear phase infinite impulse response iir digital filters in the passband region is introduced the proposed approach yields digital iir filters whose numerators represent linear phase finite impulse response fir filters as an example low pass iir differentiators are introduced the range and high frequency suppression of the proposed low pass differentiators are comparable to those obtained by higher order fir low pass differentiators in addition the differentiators exhibit almost linear phases in the passband regions

high resolution three term avo inversion by means of a trivariate cauchy probability distribution three term avo inversion can be used to estimate p wave velocity s wave velocity and density perturbations from reflection seismic data the density term however exhibits little sensitivity to amplitudes and therefore its inversion is unstable one way to stabilize the density term is by including a scale matrix that provides correlation information between the three unknown avo parameters we investigate a bayesian procedure to include sparsity and a scale matrix in the three term avo inversion problem to this end we model the prior distribution of the avo parameters via a trivariate cauchy distribution we found an iterative algorithm to solve the bayesian inversion and in addition comparisons are provided with the classical inversion approach that uses a multivariate gaussian prior it is important to point out that the multivariate gaussian prior allows us to include the correlation of the avo parameters in the solution of the inverse problem the trivariate cauchy prior not only permits us

recurrence formulas for multivariate orthogonal polynomials in this paper necessary and sufficient conditions are given so that multivariate orthogonal polynomials can be generated by a recurrence formula as a consequence orthogonal polynomials of total degree n in d variables that have dim i id common zeros can now be constructed recursively the result is important to the construction of gaussian cubature formulas

an on line adaptation for discrete l_ 1 linear estimation a sequential form for the l 1 estimation problem is presented the cases of updating the optimal estimates when an extra point is to be added or when an old point is to be deleted are both presented

a sparsity regularization approach to the electromagnetic inverse scattering problem we investigate solving the electromagnetic inverse scattering problem using the distorted born iterative method dbim in conjunction with a variable selection approach known as the elastic net the elastic net applies both l 1 and l 2 penalties to regularize the system of linear equations that result at each iteration of the dbim the elastic net thus incorporates both the stabilizing effect of the l 2 penalty with the sparsity encouraging effect of the l 1 penalty the dbim with the elastic net outperforms the commonly used l 2 regularizer when the unknown distribution of dielectric properties is sparse in a known set of basis functions we consider two very different 3 d examples to demonstrate the efficacy and applicability of our approach for both examples we use a scalar approximation in the inverse solution in the first example the actual distribution of dielectric properties is exactly sparse in a set of 3 d wavelets the performances of the elastic net and l 2 approaches are compared to the ideal case where it is known a priori which wavelets are involved in the true solution the second example comes from the area of microwave imaging for breast cancer detection for a given set of 3 d gaussian basis functions we show that the elastic net approach can produce a more accurate estimate of the distribution of dielectric properties in particular the effective conductivity within an anatomically realistic 3 d numerical breast phantom in contrast the dbim with an l 2 penalty produces an estimate which suffers from multiple artifacts

multivariate orthogonal polynomials quantum decomposition deficiency rank and support of measure abstract in this paper we investigate the multivariate orthogonal polynomials based on the theory of interacting fock spaces our framework is on the same stream line of the recent paper by accardi barhoumi and dhahri 1 the classical coordinate variables are decomposed into non commuting quantum operators called creation annihilation and preservation operators in the interacting fock spaces getting the commutation relations which follow from the commuting property of the coordinate variables between themselves we can develop the reconstruction theory of the measure namely the favard s theorem we then further develop some related problems including the marginal distributions and the rank theory of the jacobi operators we will see that the deficiency rank of the jacobi operator implies that the underlying measure is supported on some algebraic surface and vice versa we will provide with some examples

bivariate second order linear partial differential equations and orthogonal polynomial solutions in this paper we construct the main algebraic and differential properties and the weight functions of orthogonal polynomial solutions of bivariate second order linear partial differential equations which are admissible potentially self adjoint and of hypergeometric type general formulae for all these properties are obtained explicitly in terms of the polynomial coefficients of the partial differential equation using vector matrix notation moreover rodrigues representations for the polynomial eigensolutions and for their partial derivatives of any order are given as illustration these results are applied to a two parameter monic appell polynomials finally the non monic case is briefly discussed 2011 elsevier inc

a new improvement to the powell and chau linear phase iir filters an improvement to the realization of the linear phase iir filters is described it is based on the rearrangement of the numerator polynomials of the iir filter functions that are used in the real time realizations proposed in literature the new realization has better total harmonic distortion when a sine input is used and it has smaller phase and group delay errors due to finite section length

a constructive approach for finding arbitrary roots of polynomials by neural networks this paper proposes a constructive approach for finding arbitrary real or complex roots of arbitrary real or complex polynomials by multilayer perceptron network mlpn using constrained learning algorithm cla which encodes the a priori information of constraint relations between root moments and coefficients of a polynomial into the usual bp algorithm bpa moreover the root moment method rmm is also simplified into a recursive version so that the computational complexity can be further decreased which leads the roots of those higher order polynomials to be readily found in addition an adaptive learning parameter with the cla is also proposed in this paper an initial weight selection method is also given finally several experimental results show that our proposed neural connectionism approaches with respect to the nonneural ones are more efficient and feasible in finding the arbitrary roots of arbitrary polynomials

spiking band limited traces with a relative entropy algorithm a novel method for the inversion of band limited seismic traces to full bandwidth reflectivity traces is based on a probabilistic spiky model of the reflectivity trace in which position indicators and amplitudes of the spikes occur as random variables and relies on relative entropy inference from information theory first an a priori model for general reflectivity traces in the prospect is derived from nearby wells second the a priori distribution is updated into an a posteriori distribution for the specific trace being studied by the addition of the fourier data of the seismic trace within a passband uncertainty about the fourier coefficients can be accounted for by specification of a noise variance which implicitly is infinite outside the passband the update with relative entropy inference is justified because of its relationship with bayesian inference application of maximum a posteriori map estimation to the a posteriori distribution results in the most likely spiky reflectivity trace of f

recursive processing by noncausal digital filters digital filters having exactly linear phase are usually realized by nonrecursive systems however the filter degree and thus the expense becomes rather large in the case of steep filters with high attenuation in the stopband this paper deals with an alternative possibility using noncausal recursive systems after known methods are generalized suitable algorithms are proposed and systematic errors are investigated finally the method is compared with nonrecursive filtering

nonlinear identification with local model networks using gtls techniques and equality constraints local model networks approximate a nonlinear system through multiple local models fitted within a partition space the main advantage of this approach is that the identification of complex nonlinear processes is alleviated by the integration of structured knowledge about the process this paper extends these concepts by the integration of quantitative process knowledge into the identification procedure quantitative knowledge describes explicit dependences between inputs and outputs and is integrated in the parameter estimation process by means of equality constraints for this purpose a constrained generalized total least squares algorithm for local parameter estimation is presented furthermore the problem of proper integration of constraints in the partitioning process is treated where an expectation maximization procedure is combined with constrained parameter estimation the benefits and the applicability of the proposed concepts are demonstrated by means of two illustrative examples and a practical application using real measurement data

design of computationally efficient elliptic iir filters with a reduced number of shift and add operations in multipliers in this paper a new design method for elliptic iir filters that provides the implementation of half of the multiplication constants with few shifters and adders is proposed an iir filter when derived by the bilinear transformation from an elliptic minimal q factor analog prototype has its z plane poles on the circle that is orthogonal to the unit circle and has the center on the real axis of the plane due to this property the center of the circle can be used as a parameter for the representation of a pole whereas the second parameter is the radius of the pole it is shown in this paper that the center of the circle is uniquely determined by the frequency for which the filter attenuation is 3 db this result is used for the realization based on the parallel connection of two all pass networks it is shown that all second order all pass sections can be implemented with one common multiplication constant determined by the center of the circle the design method is presented that by an appropriate distribution of a margin in the filter performance predetermines the value of the common constant according to the desired number of shift and add operations this way half of the multipliers are replaced with a limited number of shifters and adders conventional computer programs for iir elliptic digital filters can be used the direct approach for the distribution of the z plane poles among two all pass functions is developed the application and efficiency of the proposed design method are demonstrated by examples

a technique to truncate iir filter impulse response and its application to real time implementation of linear phase iir filters a technique for realizing linear phase infinite impulse response iir filters has been proposed by powell and chau 1991 and gives a real time implementation of h z sup 1 spl middot h z where h z is a causal iir filter function in their system the input signal is divided into l sample sections time reversed section convolved with h z and time reversed again the signal is then filtered by h z to give the system output with a processing delay of 3l 1 samples however the group delay response of the system exhibits a minor sinusoidal variation superimposed on some constant value this variation will degrade image quality in image processing and signal quality in signal transmission applications furthermore the output of the system contains harmonic distortion for a sinusoidal input the main drawbacks of powell and chau s technique are the large processing delay of 3l 1 samples and the accompanying phase and harmonic distortions a smaller processing delay increases the phase and harmonic distortions yet the amplitude response remains acceptable previously the present authors presented a method of reducing the processing delay by shortening the section length by an integer factor n using a structure with increased number of paths for the time reversed signal the authors consider how to reduce the phase and harmonic distortions we examined the operation of the sectioned convolution and analyzed it based on a state space representation then we found that the cause of the distortions is a periodic variation of the impulse response length in the sectioned convolution to overcome this problem a technique is devised to realize a recursive circuit having a truncated impulse response with a fixed length l a system applying this technique to the powell chau system is demonstrated to exhibit perfect linear phase characteristic and produce virtually no harmonic distortion therefore the section length l can be reduced without limitation due to phase and harmonic distortions two methods for reducing the increased computational complexity of this technique assuming fixed l are developed and simulations are performed for the proposed system to confirm the expected improvements

towards a mathematical theory of super resolution this paper develops a mathematical theory of super resolution broadly speaking super resolution is the problem of recovering the fine details of an object the high end of its spectrum from coarse scale information only from samples at the low end of the spectrum suppose we have many point sources at unknown locations in 0 1 and with unknown complex valued amplitudes we only observe fourier samples of this object up to a frequency cutoff fc we show that one can super resolve these point sources with infinite precision i e recover the exact locations and amplitudes by solving a simple convex optimization problem which can essentially be reformulated as a semidefinite program this holds provided that the distance between sources is at least 2 fc this result extends to higher dimensions and other models in one dimension for instance it is possible to recover a piecewise smooth function by resolving the discontinuity points with infinite precision as well we also show that the theory and methods are robust to noise in particular in the discrete setting we develop some theoretical results explaining how the accuracy of the super resolved signal is expected to degrade when both the noise level and the super resolution factor vary 2014 wiley periodicals inc

a high performance neural network for solving linear and quadratic programming problems two classes of high performance neural networks for solving linear and quadratic programming problems are given we prove that the new system converges globally to the solutions of the linear and quadratic programming problems in a neural network network parameters are usually not specified the proposed models can overcome numerical difficulty caused by neural networks with network parameters and obtain desired approximate solutions of the linear and quadratic programming problems

automatic phase correction of common midpoint stacked data the residual wavelet on a processed seismic section is often not zero phase despite all efforts to make it so in this paper we adopt the convolutional model for the processed seismogram assume that the residual phase shift can be approximated by a frequency independent constant and use the varimax norm to generate an algorithm to estimate the residual phase directly application of our algorithm to reflectivities from well logs suggests that it should work in the majority of cases so long as the reflectivity is non gaussian an application of our algorithm to stacked data enhances the interpretability of the seismic section and leads to an improved match between the recovered relative acoustic impedance and a measured velocity log

gaussian cubature and bivariate polynomial interpolation gaussian cubature is used to study bivariate polynomial interpolation based on the common zeros of quasi orthogonal polynomials

minimum entropy deconvolution with frequency domain constraints a method for reconstructing the reflectivity spectrum using the minimum entropy criterion is presented the algorithm fmed described is compared with the classical minimum entropy deconvolution med as well as with the linear programming lp and autoregressive ar approaches the med is performed by maximizing an entropy norm with respect to the coefficients of a linear operator that deconvolves the seismic trace by comparison the approach presented here maximizes the norm with respect to the missing frequencies of the reflectivity series spectrum this procedure reduces to a nonlinear algorithm that is able to carry out the deconvolution of band limited data avoiding the inherent limitations of linear operators the proposed method is illustrated under a variety of synthetic examples field data are also used to test the algorithm the results show that the proposed method is an effective way to process band limited data the fmed and the lp arise from similar conceptions both methods seek an extremum of a particular norm subjected to frequency constraints in the lp approach the linear programming problem is solved using an adaptation of the simplex method which is a very expensive procedure the fmed uses only two fast fourier transforms ffts per iteration hence the computational cost of the inversion is reduced

a new approach to the realization of low sensitivity iir digital filters a new implementation of an iir digital filter transfer function is presented that is structurally passive and hence has extremely low pass band sensitivity the structure is based on a simple parallel interconnection of two all pass sections with each section implemented in a structurally lossless manner the structure shares a number of properties in common with wave lattice digital filters computer simulation results verifying the low sensitivity feature are included along with results on roundoff noise dynamic range interaction a large number of alternatives is available for the implementation of the all pass sections giving rise to the well known wave lattice digital filters as a specific instance of the implementation

recovery of a sparse spike time series by l sub 1 norm deconvolution an l sub 1 norm minimization scheme is applied to the determination of the impulse response vector h of flaws detected in practical examples of ultrasonic nondestructive evaluation in candu nuclear reactors for each problem parametric programming is applied to find the optimum value of the damping parameter that will yield the best estimate of h according to a quantified performance factor this performance factor is based on a quantified analysis of the transitions in estimates of h as the damping parameter is varied over a wide range of possible values it is shown that for the examined cases in which the true impulse response is a sparsely filled spike strain the l sub 1 norm provides significantly better results than the more commonly used l sub 2 norm minimization schemes these results are shown to be consistent with theoretical predictions

approximating surfaces by the moving least absolute deviations method in this paper we are going to consider the problem of global data approximation on the basis of data containing outliers for that purpose a new method entitled the moving least absolute deviations method is proposed in the region of data in the network of knots weighted least absolute deviations local planes are constructed by means of which a global approximant is defined the method is tested on the well known franke s function an application in gridding of sonar data is also shown

simultaneous deconvolution and wavelet inversion as a global optimization estimates of the source wavelet and band limited earth reflectivity are obtained simultaneously from an optimization of deconvolution outputs similar to minimum entropy deconvolution med the only inputs required beyond the observed seismogram are wavelet length and an inversion parameter cooling rate the objective function to be minimized is a measure of the spikiness of the deconvolved seismogram i assume that the wavelet whose deconvolution from the data results in the most spike like trace is the best wavelet estimate because this is a highly nonlinear problem simulated annealing is used to solve it the procedure yields excellent results on synthetic data and disparate field data sets is robust in the presence of noise and is fast enough to operate in a desktop computer environment