computation of error bounds for p matrix linear complementarity problems we give new error bounds for the linear complementarity problem where the involved matrix is a p matrix computation of rigorous error bounds can be turned into a p matrix linear interval system moreover for the involved matrix being an h matrix with positive diagonals an error bound can be found by solving a linear system of equations which is sharper than the mathias pang error bound preliminary numerical results show that the proposed error bound is efficient for verifying accuracy of approximate solutions

a class of linear complementarity problems solvable in polynomial time we describe a condition number for the linear complementarity problem lcp which characterizes the degree of difficulty for its solution when a potential reduction algorithm is used consequently we develop a class of lcps solvable in polynomial time the result suggests that the convexity or positive semidefiniteness of the lcp may not be the basic issue that separates lcps solvable and not solvable in polynomial time

a generalized approach to direction finding with reference to the recently developed estimation of signal parameters using a rotational invariance techniques esprit it is pointed out that other operators can be used to generate the matrix pencil by way of example the moving window operator is discussed

calculation of the fisher information matrix for multidimensional data sets data sets that are acquired in many practical systems can be described as the output of a multidimensional linear separable denominator system with gaussian measurement noise an important example is nuclear magnetic resonance nmr spectroscopy in nmr spectroscopy high accuracy parameter estimation is of central importance a classical result on the crame spl acute r rao lower bound states that the inverse of the fisher information matrix fim provides a lower bound for the covariance of any unbiased estimator of the parameter vector the calculation of the fim is therefore of central importance for an assessment of the accuracy with which parameters can be estimated it is shown how the fim can be expressed using the matrices that determine the system that generates the data set for uniformly sampled data it is shown how the fim can be expressed through the solutions of lyapunov equations the novel techniques are demonstrated with an example arising from nmr spectroscopy

on bandwidth choice for spatial data density estimation bandwidth choice is crucial in spatial kernel estimation in exploring non gaussian complex spatial data the paper investigates the choice of adaptive and non adaptive bandwidths for density estimation given data on a spatial lattice an adaptive bandwidth depends on local data and hence adaptively conforms with local features of the spatial data we propose a spatial cross validation scv choice of a global bandwidth this is done first with a pilot density involved in the expression for the adaptive bandwidth the optimality of the procedure is established and it is shown that a non adaptive bandwidth choice comes out as a special case although the cross validation idea has been popular for choosing a non adaptive bandwidth in data driven smoothing of independent and time series data its theory and application have not been much investigated for spatial data for the adaptive case there is little theory even for independent data conditions that ensure asymptotic optimality of the scv selected bandwidth are derived actually also extending time series and independent data optimality results further for the adaptive bandwidth with an estimated pilot density oracle properties of the resultant density estimator are obtained asymptotically as if the true pilot were known numerical simulations show that finite sample performance of the scv adaptive bandwidth choice works quite well it outperforms the existing r routines such as the rule of thumb and the so called second generation sheather jones bandwidths for moderate and big data sets an empirical application to a set of spatial soil data is further implemented with non gaussian features significantly identified

multidimensional frequency estimation with finite snapshots in the presence of identical frequencies recently an eigenvector based algorithm has been developed for multidimensional frequency estimation with a single snapshot of data mixture unlike most existing algebraic approaches that estimate frequencies from eigenvalues the eigenvector based algorithm achieves automatic frequency pairing without joint diagonalization of multiple matrices but it fails when there exist identical frequencies in certain dimensions because eigenvectors are not linearly independent anymore in this paper we develop an eigenvector based algorithm for multidimensional frequency estimation with finite data snapshots we also analyze the identifiability id and performance of the proposed algorithm it is shown that our algorithm offers the most relaxed statistical id condition for multidimensional frequency estimation from finite snapshots more important we introduce complex weighting factors so that the algorithm is still operational when there exist identical frequencies in one or more dimensions furthermore the weighting factors are optimized to minimize the mean square errors of the frequency estimates simulation results show that the proposed algorithm offers competitive performance when compared to existing algebraic approaches but at lower complexity

estimating the parameters of exponentially damped sinusoids and pole zero modeling in noise we have presented techniques 1 6 based on linear prediction lp and singular value decomposition svd for accurate estimation of closely spaced frequencies of sinusoidal signals in noise in this note we extend these techniques to estimate the parameters of exponentially damped sinusoidal signals in noise the estimation procedure presented here makes use of backward prediction in addition to svd first the method is applied to data consisting of one and two exponentially damped sinusoids the choice of one and two signal components facilitates the comparison of estimation error in pole damping factors and pole frequencies to the appropriate cramer rao cr bounds and to traditional methods of linear prediction second our method is applied to an example due to steiglitz 8 in which the data consists of noisy values of the impulse response samples composed of many exponentially damped sinusoids of a linear system having both poles and zeros the poles of the system are accurately determined by our method and the zeros are obtained subsequently using shanks method

esprit a subspace rotation approach to estimation of parameters of cisoids in noise the application of a subspace invariance approach esprit to the estimation of parameters frequencies and powers of cisoids in noise is described esprit exploits an underlying rotational invariance of signal subspaces spanned by two temporally displaced data sets the new approach has several advantages including improved resolution over pisarenko s technique for harmonic retrieval

music for multidimensional spectral estimation stability and super resolution this paper presents a performance analysis of the multiple signal classification music algorithm applied on d dimensional single snapshot spectral estimation while s true frequencies are located on the continuum of a bounded domain inspired by the matrix pencil form we construct a d fold hankel matrix from the measurements and exploit its vandermonde decomposition in the noiseless case music amounts to identifying a noise subspace evaluating a noise space correlation function and localizing frequencies by searching the s smallest local minima of the noise space correlation function in the noiseless case 2s d measurements guarantee an exact reconstruction by music as the noise space correlation function vanishes exactly at true frequencies when noise exists we provide an explicit estimate on the perturbation of the noise space correlation function in terms of noise level dimension d the minimum separation among frequencies the maximum and minimum amplitudes while frequencies are separated by 2 rayleigh length rl at each direction as a by product the maximum and minimum non zero singular values of the multidimensional vandermonde matrix whose nodes are on the unit sphere are estimated under a gap condition of the nodes under the 2 rl separation condition if noise is i i d gaussian we show that perturbation of the noise space correlation function decays like sqrt log bf n bf n as the sample size bf n increases when the separation among frequencies drops below 2 rl our numerical experiments show that the noise tolerance of music obeys a power law with the minimum separation of frequencies

simultaneous seismic data denoising and reconstruction via multichannel singular spectrum analysis we present a rank reduction algorithm that permits simultaneous reconstruction and random noise attenuation of seismic records we based our technique on multichannel singular spectrum analysis mssa the technique entails organizing spatial data at a given temporal frequency into a block hankel matrix that in ideal conditions is a matrix of rank k where k is the number of plane waves in the window of analysis additive noise and missing samples will increase the rank of the block hankel matrix of the data consequently rank reduction is proposed as a means to attenuate noise and recover missing traces we present an iterative algorithm that resembles seismic data reconstruction with the method of projection onto convex sets in addition we propose to adopt a randomized singular value decomposition to accelerate the rank reduction stage of the algorithm we apply mssa reconstruction to synthetic examples and a field data set synthetic examples were used to assess the performance of the method in two

rational modeling by pencil of functions method pole zero modeling of signals such as an electromagnetic scatterer response is considered in this paper it is shown by use of the pencil of functions theorem that a the true parameters can be recovered in the ideal case where the signal is the impulse reponse of a rational function h z and b the parameters are optimal in the functional dependence sense when the observed data are corrupted by additive noise or by systematic error although the computations are more involved than in all pole modeling they are considerably less than those required in iterative schemes of pole zero modeling the advantages of the method are demonstrated by a simulation example and through application to the electromagnetic response of a scatterer the paper also includes very recent and promising results on a new approach to noise correction in contradistinction with spectral subtraction techniques where only amplitude information is emphasized and phase is ignored we propose a method that a estimates the noise spectral density for the data frame and then b performs the subtraction of the noise correlation matrix from the gram matrix of the signal

on svd for estimating generalized eigenvalues of singular matrix pencil in noise several algorithms for estimating generalized eigenvalues ges of singular matrix pencils perturbed by noise are reviewed the singular value decomposition svd is explored as the common structure in the three basic algorithms direct matrix pencil algorithm pro esprit and tls esprit it is shown that several svd based steps inherent in the algorithms are equivalent to the first order approximation in particular the pro esprit and its variant tls pro esprit are shown to be equivalent and the tls esprit and its earlier version ls esprit are shown to be asymptotically equivalent to the first order approximation for the problem of estimating superimposed complex exponential signals the state space algorithm is shown to be also equivalent to the previous matrix pencil algorithms to the first order approximation the second order perturbation and the threshold phenomenon are illustrated by simulation results based on a damped sinusoidal signal an improved state space algorithm is found to be the most robust to noise

perturbation analysis of tk method for harmonic retrieval problems the authors present a first order perturbation analysis of the tufts kumaresan tk 1980 method used to estimate frequencies of complex sinusoids in small additive noise several fundamental properties are presented and proved further illustrations are provided through numerical examples

design of two dimensional rectangular array beamformers with partial adaptivity this paper considers the problem of designing a two dimensional 2 d rectangular array beamformer with partial adaptivity using the eigenstructure of the signal data received by a 2 d rectangular array beamformer we first show that the optimal weight matrix when using full adaptivity can be obtained from a set of singular vectors then the design problem of using partial adaptivity is formulated as a result the optimal solution for the partially adaptive weight matrix can be found by solving two basic problems namely determining the proper dimension of the partially adaptive weight matrix and the set of the singular vectors we develop the detection formulas for the information theoretic criteria aic and mdl to find the proper dimension next an efficient method is presented so that the optimal solution for the set of the singular vectors can be found analytically we also investigate the required computational complexity it is shown that 2 d partially adaptive beamforming using the proposed technique requires less computational complexity than 2 d fully adaptive beamforming using conventional techniques moreover computer simulations demonstrate that the proposed 2 d partially adaptive technique provides satisfactory array performance when compared with conventional fully adaptive techniques

effect of dependence on stochastic measures of accuracy of density estimations in kernel density estimation those data values that make a nondegenerate contribution to the estimator computed at a given point tend to be spaced well apart this property has the effect of suppressing many of the conventional consequences of long range dependence for example slower rates of convergence which might otherwise be revealed by a traditional lossor risk based assessment of performance from that viewpoint dependence has to be very long range indeed before a density estimator experiences any first order effects however an analysis in terms of the convergence rate for a particular realization rather than the rate averaged over all realizations reveals a very different picture we show that from that viewpoint and in the context of functions of gaussian processes effects on rates of convergence can become apparent as soon as the boundary between short and long range dependence is crossed for example the distance between ise and mise optimal bandwidths is generally of larger order for long range dependent data we shed new light on cross validation too in particular we show that the variance of the cross validation bandwidth is generally larger for long range dependent data and that the first order properties of this bandwidth do not depend on how many data are left out when constructing the cross validation criterion moreover for long range dependent data the cross validation bandwidth is usually perfectly negatively correlated in the limit with the optimal stochastic bandwidth

a preconditioned two step modulus based matrix splitting iteration method for linear complementarity problem abstract in this paper a preconditioned two step modulus based matrix splitting iteration method for linear complementarity problems associated with an m matrix is proposed the convergence analysis of the presented method is given in particular we provide a comparison theorem between preconditioned two step modulus based gauss seidel ptmgs iteration method and two step modulus based gauss seidel tmgs iteration method which shows that ptmgs method improves the convergence rate of original tmgs method for linear complementarity problem numerical tested examples are used to illustrate the theoretical analysis

an infinity norm bound for the inverse of dashnic zusmanovich type matrices with applications abstract an upper bound for the infinity norm for the inverse of dashnic zusmanovich type matrices is given it is proved that the upper bound is sharper than the well known varah s bound for strictly diagonally dominant matrices by introducing a new subclass of p matrices dashnic zusmanovich type b matrices dz type b matrices and using the proposed infinity norm bound an error bound is given for the linear complementarity problems of dz type b matrices we also give a new pseudospectra localization to measure the distance to instability

on the resolvability of normally distributed vector parameter estimates this paper presents a metric useful in analyzing the resolution of multidimensional vector parameter estimators that produce normal estimates this metric is based on the distance between ellipsoidal confidence regions about each of the parameters when the ellipsoids are disjoint the parameters are deemed resolvable this paper presents a method for finding the noise level at which all of the ellipsoids are disjoint but at least two are tangent this is deemed the resolution threshold noise level the underlying mathematical result treats the problem of finding a dilation noise level at which two coupled quadratic equations have a unique solution

maximum likelihood estimation of 2 d superimposed exponential signals the problem of maximum likelihood estimation of the parameters i e frequencies amplitudes and noise variance of 2 d superimposed exponential signals is considered in this paper a polynomial rooting approach is proposed to obtain the estimates of the 2 d frequencies strong consistency and limiting distribution are established for the estimates of the parameters furthermore the covariance matrix of the limiting distribution attains the cramer rao lower bound

multidimensional esprit for damped and undamped signals algorithm computations and perturbation analysis in this paper we present and analyze the performance of multidimensional esprit n d esprit method for estimating parameters of n d superimposed damped and or undamped exponentials n d esprit algorithm is based on low rank decomposition of multilevel hankel matrices formed by the n d data in order to reduce the computational complexity for large signals we propose a fast n d esprit using truncated singular value decomposition svd then through a first order perturbation analysis we derive simple expressions of the variance of the estimates in n d multiple tones case these expressions do not involve the factors of the svd we also derive closed form expressions of the variances of the complex modes frequencies and damping factors estimates in the n d single tone case computer results are presented to show effectiveness of the fast version of n d esprit and verify theoretical expressions

least squares estimation of 2 d sinusoids in colored noise asymptotic analysis this paper considers the problem of estimating the parameters of real valued two dimensional 2 d sinusoidal signals observed in colored noise this problem is a special case of the general problem of estimating the parameters of a real valued homogeneous random field with mixed spectral distribution from a single observed realization of it the large sample properties of the least squares ls estimator of the parameters of the sinusoidal components are derived making no assumptions on the type of the probability distribution of the observed field it is shown that if the disturbance field satisfies a combination of conditions comprised of a strong mixing condition and a condition on the order of its uniformly bounded moments the normalized estimation error of the ls estimator is consistent asymptotically normal with zero mean and a normalized asymptotic covariance matrix for which a simple expression is derived it is further shown that the ls estimator is asymptotically unbiased the normalized asymptotic covariance matrix is block diagonal where each block corresponds to the parameters of a different sinusoidal component assuming further that the colored noise field is gaussian the ls estimator of the sinusoidal components is shown to be asymptotically efficient

near maximal 2 d sinusoid identification from limited data we describe a novel method to identify a large number of two dimensional 2 d sinusoids from very limited data starting with the noiseless exponential superposition model we derive the 2 d linear prediction equations for the data and present a general 2 d exponential identification algorithm based on one dimensional 1 d rooting techniques then we enhance this general algorithm for the special case of 2 d sinusoid identification by using conjugate reverse data to increase the number of identifiable sinusoids and by using fft to avoid polynomial rooting noise is handled by least squares solutions of the linear prediction equations and the polynomial equations numerical simulations demonstrate that our algorithm provides a competitive alternative to existing algorithms

cramer rao bound on the estimation accuracy of complex valued homogeneous gaussian random fields this paper considers the problem of the achievable accuracy in jointly estimating the parameters of a complex valued two dimensional 2 d gaussian and homogeneous random field from a single observed realization of it based on the 2 d wold decomposition the field is modeled as a sum of purely indeterministic evanescent and harmonic components using this parametric model we first solve a key problem common to many open problems in parametric estimation of homogeneous random fields that of expressing the field mean and covariance functions in terms of the model parameters employing the parametric representation of the observed field mean and covariance we derive a closed form expression for the fisher information matrix fim of complex valued homogeneous gaussian random fields with mixed spectral distribution consequently the cramer rao lower bound on the error variance in jointly estimating the model parameters is evaluated

esprit estimation of signal parameters via rotational invariance techniques an approach to the general problem of signal parameter estimation is described the algorithm differs from its predecessor in that a total least squares rather than a standard least squares criterion is used although discussed in the context of direction of arrival estimation esprit can be applied to a wide variety of problems including accurate detection and estimation of sinusoids in noise it exploits an underlying rotational invariance among signal subspaces induced by an array of sensors with a translational invariance structure the technique when applicable manifests significant performance and computational advantages over previous algorithms such as mem capon s mlm and music

pseudo maximum likelihood estimation in two classes of semiparametric diffusion models abstract two classes of semiparametric diffusion models are considered where either the drift or the diffusion term is parameterized while the other term is left unspecified we propose a pseudo maximum likelihood estimator pmle of the parametric component that maximizes the likelihood with a preliminary estimator of the unspecified term plugged in it is demonstrated how models and estimators can be used in a two step specification testing strategy of semiparametric and fully parametric models and shown that approximate simulated versions of the pmle inherit the properties of the actual but infeasible estimator a simulation study investigates the finite sample performance of the pmle

an efficient approach for two dimensional parameter estimation of a single tone in this paper parameter estimation of a two dimensional 2 d single damped real complex tone in the presence of additive white gaussian noise is addressed by utilizing the rank one property of the 2 d noise free data matrix the damping factor and frequency for each dimension are estimated in a separable manner from the principal left and right singular vectors according to an iterative weighted least squares procedure the remaining parameters are then obtained straightforwardly using standard least squares the biases as well as variances of the damping factor and frequency estimates are also derived which show that they are approximately unbiased and their performance achieves crame r rao lower bound crlb at sufficiently large signal to noise ratio snr and or data size conditions we refer the proposed approach to as principal singular vector utilization for modal analysis puma which performs estimation in a fast and accurate manner the development and analysis can easily be adapted for a tone which is undamped in at least one dimension furthermore comparative simulation results with several conventional 2 d estimators and crlb are included to corroborate the theoretical development of the puma approach as well as to demonstrate its superiority

two dimensional discrete complex image method dcim for closed form green s function of arbitrary 3d structures in general multilayered media the traditional discrete complex image method dcim is not efficient when the source and field points are in different layers because all the spatial coordinates can not be analytically included in the image terms in spatial domain a two dimensional method 2d dcim is introduced in this paper in the new methodology we reorganize the spectral kernel as a 2d function we use the 2d matrix pencil method 2d mpm to fit this 2d function and to generate a set of complex images independent of any spatial coordinates the closed form spatial domain green s function can be obtained for arbitrary locations of source and field points in general multilayered media compared with traditional 1d dcim we do not have to run mpm for each vertical combination of source and field points the efficiency of the matrix filling kernel of method of moments mom is significantly improved

vandermonde decomposition of multilevel toeplitz matrices with application to multidimensional super resolution the vandermonde decomposition of toeplitz matrices discovered by caratheodory and fejer in the 1910s and rediscovered by pisarenko in the 1970s forms the basis of modern subspace methods for 1 d frequency estimation many related numerical tools have also been developed for multidimensional md especially 2 d frequency estimation however a fundamental question has remained unresolved as to whether an analog of the vandermonde decomposition holds for multilevel toeplitz matrices in the md case in this paper an affirmative answer to this question and a constructive method for finding the decomposition are provided when the matrix rank is lower than the dimension of each toeplitz block a numerical method for searching for a decomposition is also proposed when the matrix rank is higher the new results are applied to study the md frequency estimation within the recent super resolution framework a precise formulation of the atomic ell 0 norm is derived using the vandermonde decomposition practical algorithms for frequency estimation are proposed based on the relaxation techniques extensive numerical simulations are provided to demonstrate the effectiveness of these algorithms compared with the existing atomic norm and subspace methods

nonparametric estimation of time varying parameters under shape restrictions in recent years a lot of econometric literature has been devoted to estimating time varying coefficients in regression models here a new method based on smoothers is proposed which is able to introduce shape restrictions over the coefficients the statistical properties of the estimator are obtained for very general situations including locally stationary regressors in particular the procedure provides consistent results for time varying autoregressive models the practical problem of implementation is also addressed a data driven method for selecting the control parameters is provided together with an algorithm that reduces the computational cost a simulation study and an application to real data supports the theoretical results

total least squares approach for frequency estimation using linear prediction the resolution of the estimated closely spaced frequencies of the multiple sinusoids degrades as the signal to noise ratio snr of the received signal becomes low this resolution can be improved by using the total least squares tls method in solving the linear prediction lp equation this approach makes use of the singular value decomposition svd of the augmented matrix for low rank approximation to reduce the noise effect from both the observation vector and the lp data matrix simultaneously comparison is made to the principle eigenvector pe method of tufts and kumaresan both on theoretical and experimental grounds the tls algorithm exhibits superior performance over the pe method where low rank approximation is applied to the data matrix only

matrix pencil method for estimating parameters of exponentially damped undamped sinusoids in noise a study of a matrix pencil method for estimating frequencies and damping factors of exponentially damped and or undamped sinusoids in noise is presented comparison of this method to a polynomial method svd prony method shows that the matrix pencil method and the polynomial method are two special cases of a matrix prediction approach and that the pencil method is more efficient in computation and less restrictive about signal probes it is found through perturbation analysis and simulation that for signals with unknown damping factors the pencil method is less sensitive to noise than the polynomial method an expression of the cramer rao bound for the exponential signals is presented

estimating two dimensional frequencies by matrix enhancement and matrix pencil a new method called the matrix enhancement and matrix pencil memp method is presented for estimating two dimensional 2 d frequencies in the memp method an enhanced matrix is constructed from the data samples and then the matrix pencil approach is used to extract out the 2 d sinusoids from the principal eigenvectors of the enhanced matrix the memp method yields the estimates of the 2 d frequencies efficiently without solving the roots of a 2 d polynomial or searching in a 2 d space it is shown that the memp method can be faster than a 2 d fft method if the number of the 2 d sinusoids is much smaller than the data set simulation results are provided to show that the accuracy of the memp method can be very close to the cramer rao lower bound

an efficient two dimensional frequency estimator the problem of two dimensional frequency estimation of a sinusoid embedded in complex white gaussian noise is addressed a frequency estimator and its statistical performance are derived the estimator is demonstrated to be an efficient estimator it achieves the cramer rao bound for high signal to noise ratios the results of a computer simulator which compares the variance with that of the maximum likelihood estimator and the theoretical two dimensional cramer rao bound are presented

a comparison of error bounds for linear complementarity problems of h matrices we give new error bounds for the linear complementarity problem when the involved matrix is an h matrix with positive diagonals we find classes of h matrices for which the new bounds improve considerably other previous bounds we also show advantages of these new bounds with respect the computational cost a new perturbation bound of h matrices linear complementarity problems is also presented

function estimation via wavelet shrinkage for long memory data in this article we study function estimation via wavelet shrinkage for data with long range dependence we propose a fractional gaussian noise model to approximate nonparametric regression with long range dependence and establish asymptotics for minimax risks because of long range dependence the minimax risk and the minimax linear risk converge to 0 at rates that differ from those for data with independence or short range dependence wavelet estimates with best selection of resolution leveldependent threshold achieve minimax rates over a wide range of spaces cross validation for dependent data is proposed to select the optimal threshold the wavelet estimates significantly outperform linear estimates the key to proving the asymptotic results is a wavelet vaguelette decomposition which decorrelates fractional gaussian noise such wavelet vaguelette decomposition is also very useful in fractal signal processing

three dimensional textured image blocks model based on wold decomposition in this paper we present a new parametric modeling of three dimensional homogeneous volumes of textured images 3d texture based on 3d wold decomposition for discrete processes this decomposition additively separates any 3d discrete homogeneous process into three mutually orthogonal components a purely indeterministic a remote past type deterministic and an evanescent component the evanescent component can be further decomposed into two orthogonal components called type 1 evanescent and type 2 evanescent assuming that the 3d image volume is a finite realization of a discrete homogeneous stochastic process the 3d texture field can be uniquely represented as a sum of four mutually orthogonal components with different spectral properties the aim of this paper is to present new parametric models able to describe both the spectral support and spatial characteristics of each component a spectral decomposition algorithm to separate a 3d texture into structured and unstructured parts is also proposed

detection of signals by information theoretic criteria a new approach is presented to the problem of detecting the number of signals in a multichannel time series based on the application of the information theoretic criteria for model selection introduced by akaike aic and by schwartz and rissanen mdl unlike the conventional hypothesis testing based approach the new approach does not requite any subjective threshold settings the number of signals is obtained merely by minimizing the aic or the mdl criteria simulation results that illustrate the performance of the new method for the detection of the number of signals received by a sensor array are presented

strong consistency of the over and underdetermined lse of 2 d exponentials in white noise we consider the problem of least squares estimation of the parameters of two dimensional 2 d exponential signals observed in the presence of an additive noise field when the assumed number of exponentials is incorrect we consider both the case where the number of exponential signals is underestimated and the case where the number of exponential signals is overestimated in the case where the number of exponential signals is underestimated we prove the almost sure convergence of the least squares estimates lse to the parameters of the dominant exponentials in the case where the number of exponential signals is overestimated the estimated parameter vector obtained by the least squares estimator contains a subvector that converges almost surely to the correct parameters of the exponentials

joint angle and delay estimation using shift invariance techniques in a multipath communication scenario it is often relevant to estimate the directions and relative delays of each multipath ray we derive a closed form subspace based method for the simultaneous estimation of these parameters from an estimated channel impulse response using knowledge of the transmitted pulse shape function the algorithm uses a two dimensional 2 d esprit like shift invariance technique to separate and estimate the phase shifts due to delay and direction of incidence with automatic pairing of the two parameter sets improved resolution is obtained by enlarging the data matrix with shifted and conjugated copies of itself

pairwise local fisher and naive bayes improving two standard discriminants abstract the fisher discriminant is probably the best known likelihood discriminant for continuous data another benchmark discriminant is the naive bayes which is based on marginals only in this paper we extend both discriminants by modeling dependence between pairs of variables in the continuous case this is done by local gaussian versions of the fisher discriminant in the discrete case the naive bayes is extended by taking geometric averages of pairwise joint probabilities we also indicate how the two approaches can be combined for mixed continuous and discrete data the new discriminants show promising results in a number of simulation experiments and real data illustrations

density estimation in the l infty norm for dependent data with applications to the gibbs sampler this paper investigates the density estimation problem in the lx norm for dependent data it is shown that the iid optimal minimax rates are also optimal for smooth classes of stationary sequences satisfying certain 8 mixing or absolutely regular conditions moreover for given 3 mixing coefficients bounds on uniform convergence rates of kernel estimators are computed in terms of the mixing coefficients the rates and the bounds obtained are not only for estimating the density but also for its derivatives the results are then applied to give uniform convergence rates in problems associated with the gibbs sampler

error bounds for the linear complementarity problem with a p matrix abstract we introduce a fundamental quantity associated with a p matrix and show how this quantity is useful in deriving error bounds for the linear complementarity problem of the p type we also obtain upper and lower bounds for the quantity introduced

statistical analysis of an eigendecomposition based method for 2 d frequency estimation abstract an eigendecomposition based method for two dimensional frequency estimation is analyzed in this paper this method to be referred to as matrix pencil mp method computes a smoothed data covariance matrix then its eigendecomposition and then the two dimensional frequencies via a mp approach the mp method is now known to be more efficient in computation than many other methods and able to provide a near optimum performance for relatively large signal to noise ratio snr the aim of this paper is to provide a further analysis of the mp method assuming a moderate snr to make the problem tractable a large two dimensional data set is considered in this paper a number of fundamental relations inherent in the mp method are revealed which lead to a general expression of the large sample covariances of the estimated two dimensional frequencies the large sample covariances are reduced to a very simple form for the single two dimensional frequency case the theoretical covariances are verified by the simulation results

an algorithm for pole zero modeling and spectral analysis an explicit connection between fitting exponential models and pole zero models to observed data is made the fitting problem is formulated as a constrained nonlinear minimization problem this problem is then solved using a simplified iterative algorithm the algorithm is applied to simulated data and the performance of the algorithm is compared to previous results

error bounds for the linear complementarity problem with a σ sdd matrix abstract we give new error bounds for the linear complementarity problem when the involved matrix is a sdd matrix with positive diagonals the new bounds can improve considerably other previous bounds we also find a subclass of sdd matrices for which the new bound is very simple

statistical analysis of effective singular values in matrix rank determination a major problem in using svd singular value decomposition as a tool in determining the effective rank of a perturbed matrix is that of distinguishing between significantly small and significantly large singular values to the end conference regions are derived for the perturbed singular values of matrices with noisy observation data the analysis is based on the theories of perturbations of singular values and statistical significance test threshold bounds for perturbation due to finite precision and i i d random models are evaluated in random models the threshold bounds depend on the dimension of the matrix the noisy variance and predefined statistical level of significance results applied to the problem of determining the effective order of a linear autoregressive system from the approximate rank of a sample autocorrelation matrix are considered various numerical examples illustrating the usefulness of these bounds and comparisons to other previously known approaches are given

estimation of frequencies and damping factors by two dimensional esprit type methods in this paper we consider two dimensional 2 d signals modeled by the sum of damped cisoids we propose two high resolution approaches to estimate their frequencies and damping factors both high resolution methods are based on the shift invariance structure of the signal subspace related to each dimension the first one estimates the frequency components in both dimensions as in the matrix enhancement and matrix pencil memp method before pairing them with a new algorithm the second one consists of the direct estimation of the signal frequency pairs without an additional step to pair the frequencies related to each dimension we show how these methods can estimate the scattering points of radar images

sensor array signal processing via a procrustes rotations based eigenanalysis of the esprit data pencil the authors propose the procrustes rotation based esprit algorithm pro esprit for estimating characteristic parameters associated with a scene of radiating sources given data derived from two identical sensor arrays the x and y arrays which are displaced relative to one another pro esprit uses the inherent redundancy built into the esprit array system to compensate for deviations from the ideal array model this redundancy is manifested by two fundamental properties of the noiseless x and y data matrices comprising the esprit data pencil a they have the same row space the signal subspace and 2 they have the same column space the source subspace these properties are utilized by invoking two primary tools 1 the solution to the procrustes problem for optimally approximating an invariant subspace rotation and 2 the total least squares method for perturbing each of two estimates of a common subspace in a minimal fashion until the two perturbed spaces are the same

the evanescent field transform for estimating the parameters of homogeneous random fields with mixed spectral distributions parametric modeling and estimation of complex valued homogeneous random fields with mixed spectral distributions is a fundamental problem in two dimensional 2 d signal processing the parametric model under consideration results from the 2 d wold type decomposition of the random field the same model naturally arises as the physical model in problems of space time adaptive processing of airborne radar a computationally efficient algorithm for estimating the parameters of the field components is presented the algorithm is based on a nonlinear operator that uniquely maps each evanescent component to a single exponential the exponential s spatial frequency is a function of the spectral support parameters of the evanescent component hence employing this operator the problem of estimating the spectral support parameters of an evanescent field is replaced by the simpler problem of estimating the spatial frequency of a 2 d exponential the properties of the operator are analyzed the algorithm performance is illustrated and investigated using monte carlo simulations

off the grid line spectrum denoising and estimation with multiple measurement vectors compressed sensing suggests that the required number of samples for reconstructing a signal can be greatly reduced if it is sparse in a known discrete basis yet many real world signals are sparse in a continuous dictionary one example is the spectrally sparse signal which is composed of a small number of spectral atoms with arbitrary frequencies on the unit interval in this paper we study the problem of line spectrum denoising and estimation with an ensemble of spectrally sparse signals composed of the same set of continuous valued frequencies from their partial and noisy observations two approaches are developed based on atomic norm minimization and structured covariance estimation both of which can be solved efficiently via semidefinite programming the first approach aims to estimate and denoise the set of signals from their partial and noisy observations via atomic norm minimization and recover the frequencies via examining the dual polynomial of the convex program we characterize the optimality condition of the proposed algorithm and derive the expected error rate for denoising demonstrating the benefit of including multiple measurement vectors the second approach aims to recover the population covariance matrix from the partially observed sample covariance matrix by motivating its low rank toeplitz structure without recovering the signal ensemble performance guarantee is derived with a finite number of measurement vectors the frequencies can be recovered via conventional spectrum estimation methods such as music from the estimated covariance matrix finally numerical examples are provided to validate the favorable performance of the proposed algorithms with comparisons against several existing approaches

two dimensional grid free compressive beamforming compressive beamforming realizes the direction of arrival doa estimation and strength quantification of acoustic sources by solving an underdetermined system of equations relating microphone pressures to a source distribution via compressive sensing the conventional method assumes doas of sources to lie on a grid its performance degrades due to basis mismatch when the assumption is not satisfied to overcome this limitation for the measurement with plane microphone arrays a two dimensional grid free compressive beamforming is developed first a continuum based atomic norm minimization is defined to denoise the measured pressure and thus obtain the pressure from sources next a positive semidefinite programming is formulated to approximate the atomic norm minimization subsequently a reasonably fast algorithm based on alternating direction method of multipliers is presented to solve the positive semidefinite programming finally the matrix enhancement and matrix pencil method is introduced to process the obtained pressure and reconstruct the source distribution both simulations and experiments demonstrate that under certain conditions the grid free compressive beamforming can provide high resolution and low contamination imaging allowing accurate and fast estimation of two dimensional doas and quantification of source strengths even with non uniform arrays and noisy measurements

hammerstein system identification with the nearest neighbor algorithm the nonlinear characteristic in a hammerstein system i e a system in which a nonlinear memoryless subsystem and a linear dynamic are connected in a cascade is recovered with the nonparametric nearest neighbor regression estimate the a priori information is nonparametric both the nonlinear characteristic and the impulse response are completely unknown and can be of any form local and global properties of the estimate are examined whatever the probability density of the input signal the estimate converges at every continuity point of the characteristic as well as in the global sense we derive the asymptotic bias and variance of the proposed estimate as a result the optimal rate of convergence is established that additionally is independent of the shape of the input density results of numerical simulations are also presented

a general preconditioner for linear complementarity problem with an m matrix abstract in this paper we first present a general preconditioner p for solving linear complementarity problem lcp associated with an m matrix a and a vector f and prove that the lcp a f is equivalent to the lcp p a p f then based on this general preconditioner p two preconditioned ssor methods for solving the linear complementarity problems are proposed we show that this general preconditioner p accelerates the convergence of two ssor methods under the assumption that p a is a z matrix in addition we also give a practically concrete choice for the preconditioner p satisfying aforementioned assumption numerical examples are used to illustrate the theoretical results obtained

doa estimation of wideband sources using a harmonic source model and uniform linear array we consider the problem of estimation of the doas of multiple wideband sources incident on a uniform linear array ula in the presence of spatially and temporally white gaussian noise wgn the approach presented builds up on the iqml algorithm suggested by bresler and macovski 1986 for the case of narrowband doa estimation it is shown that the concept of an arma model for the observed data vector for the narrowband case can be generalized to model an appropriately stacked space time data vector obtained by combining the space time samples the coefficients of the corresponding 2 d predictor polynomial can be used to represent the null subspace of the wideband array steering matrix and rooting of the polynomial at each frequency separately gives the doa estimates these separate estimates at multiple frequencies are combined into a single doa estimate in a least squares sense this leads to the formulation of an iqml like procedure for the spatial parameter estimation of wideband sources like its narrowband counterpart the proposed approach is applicable to both noncoherent and coherent sources the performance of the proposed method is studied via extensive computer simulations and by comparison with the cramer rao bounds

on the accuracy of the kumaresan tufts method for estimating complex damped exponentials recently kumaresan and tufts kt presented a method for estimating the parameters of damped exponential waveforms in additive white noise the kt method uses singular value decomposition svd of the data matrix with truncation and backward prediction to improve the accuracy of the estimates the kt method was demonstrated to have a very good performance in comparison to traditional methods used for the same problem e g prony s method kumaresan and tufts also showed by numerical simulations that the variances of the estimates obtained by their method approaches the cramer rao lower bounds for selected test cases in this correspondence we provide a quantitative accuracy analysis of the kt method the analysis is based on first order taylor series approximations of the estimated parameters around their true values no assumptions are made on the number of data points used but it is assumed that the noise level is small enough for the first order approximations to be valid results of the analysis are illustrated by some numerical examples these results confirm the good performance of the kt method and show the effect of the user chosen parameters on the accuracy of the estimates

error bounds for linear complementarity problems of db matrices doubly b matrices db matrices which properly contain b matrices are introduced by pena 2003 2 in this paper we present error bounds for the linear complementarity problem when the matrix involved is a db matrix and a new bound for linear complementarity problem of a b matrix the numerical examples show that the bounds are sharp

blind high resolution localization and tracking of multiple frequency hopped signals this paper considers the problem of blind localization and tracking of multiple frequency hopped spread spectrum signals using a uniform linear antenna array without knowledge of hopping patterns or directions of arrival as a preprocessing step we propose to identify a hop free subset of data by discarding high entropy spectral slices from the spectrogram high resolution localization is then achieved via either quadrilinear regression of four way data generated by capitalizing on both spatial and temporal shift invariance or a new maximum likelihood ml based two dimensional 2 d harmonic retrieval algorithm the latter option achieves the best known model identifiability bound while remaining close to the cramer rao bound even at low signal to noise ratios snrs following beamforming using the recovered directions a dynamic programming approach is developed for joint ml estimation of signal frequencies and hop instants in single user tracking the efficacy of the proposed algorithms is illustrated in pertinent simulations

approximate maximum likelihood algorithms for two dimensional frequency estimation of a complex sinusoid starting with the maximum likelihood ml formulation three iterative algorithms for approximate ml frequency estimation of a two dimensional 2 d complex sinusoid in white gaussian noise are developed mean and variance analyses of the proposed methods are provided which show that they are approximately unbiased and their performance achieves cramer rao lower bound crlb at sufficiently high signal to noise ratio snr conditions computer simulation results are included to corroborate the theoretical development as well as to contrast the performance of the proposed algorithms with kay s estimators and the crlb

exact maximum likelihood parameter estimation of superimposed exponential signals in noise a unified framework for the exact maximum likelihood estimation of the parameters of superimposed exponential signals in noise encompassing both the time series and the array problems is presented an exact expression for the ml criterion is derived in terms of the linear prediction polynomial of the signal and an iterative algorithm for the maximization of this criterion is presented the algorithm is equally applicable in the case of signal coherence in the array problem simulation shows the estimator to be capable of providing more accurate frequency estimates than currently existing techniques the algorithm is similar to those independently derived by kumaresan et al in addition to its practical value the present formulation is used to interpret previous methods such as prony s pisarenko s and modifications thereof

comments on estimation of frequencies and damping factors by two dimensional esprit type methods for original paper see rouquette and najim ieee trans signal process vol 49 no 1 p 237 45 2001 the original authors present two high resolution approaches to estimate two dimensional 2 d signal parameters the first approach decomposes the 2 d estimation problem into two one dimensional 1 d ones estimates the 1 d frequencies with the memp method and then forms correct pairs using a new pairing scheme introduced in vanpoucke et al 1994 the second method the 2 d esprit method directly estimates the 2 d frequencies it is shown that both methods are more accurate than the related methods the present authors note that the original paper appears to have a key error in the permutation matrix specification of the first method in this comment they derive the correct one with the performance simulations

using the em algorithm to increase the number of signals estimable by 2 d parametric techniques this paper provides an easy method for increasing the number of modes estimable by 2 d parameter estimation schemes which use a single snapshot of the data for data of size m sub 1 spl times m sub 2 few of these techniques allow the number of modes to exceed m sub 1 and or m sub 2 as these restrictions are not inherent to the model but the algorithms themselves this problem is circumvented by treating the observed data as an incomplete version of a larger data set an existing 2 d parameter estimation scheme is then used for the maximization m step of the expectation maximization em algorithm in this way one can increase the number of modes the scheme can estimate without changing the scheme itself

infimum of error bounds for linear complementarity problems of σ sdd and σ1 ssd matrices abstract in 2013 18 garcia esnaola and pena presented error bounds for the linear complementarity problems of sdd and 1 ssd matrices respectively these bounds all involve a parameter on an open interval it is shown in this paper that the infimum of these error bounds as a function of the parameter exists and then is determined numerical examples are given to verify the theoretical results

first order singular basis functions for corner diffraction analysis using the method of moments this paper presents a set of divergence conforming basis functions to model the behavior of surface currents near the edges and corners of an infinitely thin perfectly conducting polygonal flat plate the basis functions are derived by imposing the edge and corner conditions on the first order basis functions current distributions obtained using the new set of basis functions are compared with the exact solutions for several scattering configurations even though the proposed basis functions are not highest order complete they provide accurate results without incurring complexity in the analysis or additional computational requirements

joint scattering center enumeration and parameter estimation in gtd model in this article a novel multistage clean based method based on generalized likelihood ratio test glrt is proposed for scattering centers enumeration and their parameter estimation to analyze the performance of the proposed scattering center enumeration algorithm the probability density function pdf of the glrt is derived for both the known noise variance case and the unknown noise variance case in addition we derived a closed form for the probability of correct enumeration of scattering centers obtained in the case of the known model parameter a method to reduce the computational complexity of the proposed algorithm has also been introduced despite the conventional methods which are based on the damped exponential models the proposed method uses the geometrical theory of diffraction gtd model whose performance does not degrade as the bandwidth increases the simulation results show an appropriate performance of this method at low signal to noise ratio snr situations

estimation of two dimensional frequencies using modified matrix pencil method the problem of multiple two dimensional 2 d sinusoidal frequency estimation is considered a modified matrix pencil method is proposed to simultaneously estimate the frequency pairs in the signal thereby bypassing the computationally expensive pairing operation as seen in the literature simulation results show that the accuracy of the estimates for each frequency from our technique is better than or comparable to that of existing methods and the variance of the estimates are close to the crameacuter rao bound simulation results also show that our method provides accurate and consistent frequency estimation results that other methods cannot provide with less or comparable computational complexity

plane wave least squares reverse time migration with a preconditioned stochastic conjugate gradient method abstractthis study derives a preconditioned stochastic conjugate gradient cg method that combines stochastic optimization with singular spectrum analysis ssa denoising to improve the efficiency and image quality of plane wave least squares reverse time migration plsrtm this method reduces the computational costs of plsrtm by applying a controlled group sampling method to a sufficiently large number of plane wave sections and accelerates the convergence using a hybrid of stochastic descent sd iteration and cg iteration however the group sampling also produces aliasing artifacts in the migration results we use ssa denoising as a preconditioner to remove the artifacts moreover we implement the preconditioning on the take off angle domain common image gathers cigs for better results we conduct numerical tests using the marmousi model and sigsbee2a salt model and compare the results of this method with those of the sd method and the cg method the results demonstrate that our method efficientl

an eigenvector based approach for multidimensional frequency estimation with improved identifiability this paper presents an algebraic method for two dimensional 2 d and multidimensional frequency estimation by exploiting eigenvector structure the algorithm is based on multidimensional smoothing and data folding and offers significantly improved identifiability id over existing algebraic approaches thus is termed the improved multidimensional folding imdf algorithm the id performance and computational complexity of the proposed algorithm are analyzed in detail in the 2 d case it is shown that with the imdf algorithm up to approximately 0 34m1 m2 1 2 d frequencies can be uniquely resolved with probability one from an m1 by m2 data mixture assuming m1gesm2 while the most relaxed id bound offered by existing algebraic approaches is approximately m1m2 4 unlike most eigenvalue techniques that usually require an extra frequency association step the imdf algorithm achieves automatic frequency pairing once an eigenvalue decomposition problem is solved because frequencies are estimated from the eigenvectors instead of the eigenvalues theoretical analysis and simulation results demonstrate its competitive performance compared to the crameacuter rao bound crb

computationally efficient subspace based method for two dimensional direction estimation with l shaped array in order to mitigate the effect of additive noises and reduce the computational burden we propose a new computationally efficient cross correlation based two dimensional 2 d direction of arrivals doas estimation code method for noncoherent narrowband signals impinging on the l shaped sensor array structured by two uniform linear arrays ulas by estimating the azimuth and elevation angles independently with a one dimensional 1 d subspace based estimation technique without eigendecomposition where the null spaces are obtained through a linear operation of the matrices formed from the cross correlation matrix between the received data of two ulas then the pair matching of estimated azimuth and elevation angles is accomplished by searching the minimums of a cost function of the azimuth and elevation angles where the computationally intensive and time consuming eigendecomposition process is avoided further the asymptotic mean square error mse expressions of the azimuth and elevation estimates are derived the effectiveness of proposed method and the theoretical analysis are verified through numerical examples and it is shown that the proposed code method performs well at low signal to noise ratio snr and with a small number of snapshots

exact sampling results for some classes of parametric nonbandlimited 2 d signals we present sampling results for certain classes of two dimensional 2 d signals that are not bandlimited but have a parametric representation with a finite number of degrees of freedom while there are many such parametric signals it is often difficult to propose practical sampling schemes therefore we will concentrate on those classes for which we are able to give exact sampling algorithms and reconstruction formulas we analyze in detail a set of 2 d diracs and extend the results to more complex objects such as lines and polygons unlike most multidimensional sampling schemes the methods we propose perfectly reconstruct such signals from a finite number of samples in the noiseless case some of the techniques we use are already encountered in the context of harmonic retrieval and error correction coding in particular singular value decomposition svd based methods and the annihilating filter approach are both explored as inherent parts of the developed algorithms potentials and limitations of the algorithms in the noisy case are also pointed out applications of our results can be found in astronomical signal processing image processing and in some classes of identification problems

bounds on the accuracy of estimating the parameters of discrete homogeneous random fields with mixed spectral distributions this paper considers the achievable accuracy in jointly estimating the parameters of a real valued two dimensional 2 d homogeneous random field with mixed spectral distribution from a single observed realization of it on the basis of a 2 d wold like decomposition the field is represented as a sum of mutually orthogonal components of three types purely indeterministic harmonic and evanescent an exact form of the cramer rao lower bound on the error variance in jointly estimating the parameters of the different components is derived it is shown that the estimation of the harmonic component is decoupled from that of the purely indeterministic and the evanescent components moreover the bound on the parameters of the purely indeterministic and the evanescent components is independent of the harmonic component numerical evaluation of the bounds provides some insight into the effects of various parameters on the achievable estimation accuracy

a fast reduced rank interpolation method for prestack seismic volumes that depend on four spatial dimensions rank reduction strategies can be employed to attenuate noise and for prestack seismic data regularization we present a fast version of cadzow reduced rank reconstruction method cadzow reconstruction is implemented by embedding 4d spatial data into a level four block toeplitz matrix rank reduction of this matrix via the lanczos bidiagonalization algorithm is used to recover missing observations and to attenuate random noise the computational cost of the lanczos bidiagonalization is dominated by the cost of multiplying a level four block toeplitz matrix by a vector this is efficiently implemented via the 4d fast fourier transform the proposed algorithm significantly decreases the computational cost of rank reduction methods for multidimensional seismic data denoising and reconstruction synthetic and field prestack data examples are used to examine the effectiveness of the proposed method

nonlinear additive arx models abstract we consider in this article a class of nonlinear additive autoregressive models with exogenous variables for nonlinear time series analysis and propose two modeling procedures for building such models the procedures proposed use two backfitting techniques the ace and bruto algorithms to identify the nonlinear functions involved and use the methods of best subset regression and variable selection in regression analysis to determine the final model simulated and real examples are used to illustrate the analysis

high snr perturbation in single 2 d frequency estimate using matrix pencil an exact and most revealing expression of the high signal to noise snr first order perturbation variance of the single 2d frequency estimate using the matrix enhancement and matrix pencil memp method is provided this expression is a general form consistent with several previously reported expressions for the 1d frequency case based on this expression the statistical efficiency of the memp method is discussed the optimum efficiency of the memp method is shown to be achieved by its 1d specialized version

separation and reconstruction of simultaneous source data via iterative rank reduction abstractwe have developed a rank reduction algorithm based on singular spectrum analysis ssa that is capable of suppressing the interferences generated by simultaneous source acquisition we evaluated an inversion scheme that minimizes the misfit between predicted and observed blended data in t x domain subject to a low rank constraint that is applied to data in the f x domain in particular we developed an iterative algorithm by adopting the projected gradient method with the ssa filter acting as the projection operator this method entails extracting small patches of data from a common receiver gather and organizing the spatial data at a given monochromatic frequency into a hankel matrix for the ideal unblended data hankel matrices extracted from the data are of low rank the incoherent interferences in common receiver domain caused by simultaneously fired shots increase the rank of the aforementioned hankel matrices therefore rank reduction filtering is an effective way to annihilate source inte

on bandwidth choice in nonparametric regression with both short and long range dependent errors we analyse methods based on the block bootstrap and leave out cross validation for choosing the bandwidth in nonparametric regression when errors have an almost arbitrarily long range of dependence a novel analytical device for modelling the dependence structure of errors is introduced this allows a concise theoretical description of the way in which the range of dependence affects optimal bandwidth choice it is shown that provided block length or leave out number respectively are chosen appropriately both techniques produce first order optimal bandwidths nevertheless the block bootstrap has far better empirical properties particularly under long range dependence

application of the matrix pencil method for estimating the sem singularity expansion method poles of source free transient responses from multiple look directions the matrix pencil method has been utilized for estimating the natural resonances from different transient responses recorded along multiple look directions as a function of time after the incident field has passed the structure the novelty of this article is that a single estimate for all the poles are done utilizing multiple transient waveforms emanating from the structure along multiple look directions the sem poles are independent of the angle at which the transient response is recorded the only difference between the various waveforms are that the residues at the various poles are of different magnitudes some of the residues may even be zero for some of the poles indicating that the contribution from certain sem poles may not be significant along that look direction here all the waveforms are utilized providing a single estimate for the poles without performing an arithmetic mean of the various waveforms

robust reduced rank filtering for erratic seismic noise attenuation abstractsingular spectrum analysis ssa or cadzow reduced rank filtering is an efficient method for random noise attenuation ssa starts by embedding the seismic data into a hankel matrix rank reduction of this hankel matrix followed by antidiagonal averaging is utilized to estimate an enhanced seismic signal rank reduction is often implemented via the singular value decomposition svd the svd is a nonrobust matrix factorization technique that leads to suboptimal results when the seismic data are contaminated by erratic noise the term erratic noise designates non gaussian noise that consists of large isolated events with known or unknown distribution we adopted a robust low rank factorization that permitted use of the ssa filter in situations in which the data were contaminated by erratic noise in our robust ssa method we replaced the quadratic error criterion function that yielded the truncated svd solution by a bisquare function the hankel matrix was then approximated by the product of two low

on rank of block hankel matrix for 2 d frequency detection and estimation for detection and estimation of 2 d frequencies from a 2 d array of data using a subspace decomposition method one needs to construct a block hankel matrix for reliable detection and estimation the rank of the block hankel matrix should be made equal to the number of 2 d frequencies inherent in the data in the absence of noise in this work we provide the conditions for achieving the desired rank