a high resolution fundamental frequency determination based on phase changes of the fourier transform the constant q transform described recently j c brown and m s puckette an efficient algorithm for the calculation of a constant q transform j acoust soc am 92 2698 2701 1992 has been adapted so that it is suitable for tracking the fundamental frequency of extremely rapid musical passages for this purpose the calculation described previously has been modified so that it is constant frequency resolution rather than constant q for lower frequency bins this modified calculation serves as the input for a fundamental frequency tracker similar to that described by brown j c brown musical fundamental frequency tracking using a pattern recognition method j acoust soc am 92 1394 1402 1992 once the fast fourier transform fft bin corresponding to the fundamental frequency is chosen by the frequency tracker an approximation is used for the phase change in the fft for a time advance of one sample to obtain an extremely precise value for this frequency graphical examples are given for musical passages by a violin executing vibrato and glissando where the fundamental frequency changes are rapid and continuous

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

parameter estimation of chirp signals the problem of the parameter estimation of chirp signals is addressed several closely related estimators are proposed whose main characteristics are simplicity accuracy and ease of online or offline implementation for moderately high signal to noise ratios they are unbiased and attain the cramer rao bound monte carlo simulations verify the expected performance of the estimators it should be easy to extend this approach to signals having polynomials of any degree in the exponent all the derivations will be done under the assumption that the signal to noise ratio is sufficiently high

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

theory and method for updating least squares finite element model of symmetric generalized centro symmetric matrices let x f be a displacement matrix and load matrix respectively c obtained by calculations or measurements is an estimate matrix of the analytical model a method is presented for correction of the model c based on the theory of inverse problem of matrices the corrected model is symmetric generalized centro symmetric with specified displacements and loads satisfying the mechanics characters of finite element model the application of the method is illustrated it is more important that a perturbation analysis is given which is not given in the earlier papers numerical results show that the method is feasible and effective

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

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

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

multiple emitter location and signal parameter estimation processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions the general problem considers sensors with arbitrary locations and arbitrary directional characteristics gain phase polarization in a noise interference environment of arbitrary covariance matrix this report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution a description is given of the multiple signal classification music algorithm which provides asymptotically unbiased estimates of 1 number of incident wavefronts present 2 directions of arrival doa or emitter locations 3 strengths and cross correlations among the incident waveforms 4 noise interference strength examples and comparisons with methods based on maximum likelihood ml and maximum entropy me as well as conventional beamforming are included an example of its use as a multiple frequency estimator operating on time series is included

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

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

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 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

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

sensitivity to basis mismatch in compressed sensing the theory of compressed sensing suggests that successful inversion of an image of the physical world broadly defined to include speech signals radar sonar returns vibration records sensor array snapshot vectors 2 d images and so on for its source modes and amplitudes can be achieved at measurement dimensions far lower than what might be expected from the classical theories of spectrum or modal analysis provided that the image is sparse in an apriori known basis for imaging problems in spectrum analysis and passive and active radar sonar this basis is usually taken to be a dft basis however in reality no physical field is sparse in the dft basis or in any apriori known basis no matter how finely we grid the parameter space the sources may not lie in the center of the grid cells and consequently there is mismatch between the assumed and the actual bases for sparsity in this paper we study the sensitivity of compressed sensing to mismatch between the assumed and the actual sparsity bases we start by analyzing the effect of basis mismatch on the best k term approximation error which is central to providing exact sparse recovery guarantees we establish achievable bounds for the l1 error of the best k term approximation and show that these bounds grow linearly with the image or grid dimension and the mismatch level between the assumed and actual bases for sparsity we then derive bounds with similar growth behavior for the basis pursuit l1 recovery error indicating that the sparse recovery may suffer large errors in the presence of basis mismatch although we present our results in the context of basis pursuit our analysis applies to any sparse recovery principle that relies on the accuracy of best k term approximations for its performance guarantees we particularly highlight the problematic nature of basis mismatch in fourier imaging where spillage from off grid dft components turns a sparse representation into an incompressible one we substantiate our mathematical analysis by numerical examples that demonstrate a considerable performance degradation for image inversion from compressed sensing measurements in the presence of basis mismatch for problem sizes common to radar and sonar

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

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

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

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

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

forward backward spatial smoothing techniques for coherent signal identification a spatial smoothing scheme is further investigated in the context of coherent signal classification it is shown that by making use of a set of forward and complex conjugated backward subarrays simultaneously it is always possible to estimate any k directions of arrival using at most 3k 2 sensor elements this is achieved by creating a smoothed array output covariance matrix that is structurally identical to a covariance matrix in some noncoherent situation by incorporating eigenstructure based techniques on this smoothed covariance matrix it then becomes possible to correctly identify all directions of arrival irrespective of their correlation

estimation of frequency for am fm models using the phase vocoder framework this paper proposes an extension of the applicability of phase vocoder based frequency estimators for generalized sinusoidal models which include phase and amplitude modulations a first approach called phase corrected vocoder pcv takes into account the modification of the fourier phases resulting from these modulations another approach is based on an adaptation of the principles of the time frequency reassignment and is referred to as the reassigned vocoder rv the robustness of the estimation against noise is studied both theoretically and experimentally and the performance is assessed in comparison with two state of the art algorithms an unmodified version of the reassignment method and a quadratically interpolated fast fourier transform method qifft

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

maximum likelihood parameter estimation of superimposed chirps using monte carlo importance sampling we address the problem of parameter estimation of superimposed chirp signals in noise the approach used here is a computationally modest implementation of a maximum likelihood ml technique the ml technique for estimating the complex amplitudes chirping rates and frequencies reduces to a separable optimization problem where the chirping rates and frequencies are determined by maximizing a compressed likelihood function that is a function of only the chirping rates and frequencies since the compressed likelihood function is multidimensional its maximization via a grid search is impractical we propose a noniterative maximization of the compressed likelihood function using importance sampling simulation results are presented for a scenario involving closely spaced parameters for the individual signals

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

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

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

improving the readability of time frequency and time scale representations by the reassignment method in this paper the use of the reassignment method first applied by kodera gendrin and de villedary 1976 to the spectrogram is generalized to any bilinear time frequency or time scale distribution this method creates a modified version of a representation by moving its values away from where they are computed so as to produce a better localization of the signal components we first propose a new formulation of this method followed by a thorough theoretical study of its characteristics its practical use for a large variety of known time frequency and time scale distributions is then addressed finally some experimental results are reported to demonstrate the performance of this method

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

a system of real quaternion matrix equations with applications abstract let h be the real quaternion algebra and h n m denote the set of all n m matrices over h let p h n n and q h m m be involutions i e p 2 i q 2 i a matrix a h n m is said to be p q symmetric if a paq this paper studies the system of linear real quaternion matrix equations a 1 x 1 c 1 x 1 b 1 c 2 a 2 x 2 c 3 x 2 b 2 c 4 a 3 x 1 b 3 a 4 x 2 b 4 c c we present some necessary and sufficient conditions for the existence of a solution to this system and give an expression of the general solution to the system when the solvability conditions are satisfied as applications we discuss the necessary and sufficient conditions for the system a a x c a xb b c b a c xb c c c to have a p q symmetric solution we also show an expression of the p q symmetric solution to the system when the solvability conditions are met moreover we provide an algorithm and a numerical example to illustrate our results the findings of this paper extend some known results in the literature

backward errors for eigenproblem of two kinds of structured matrices in this paper we consider backward errors in the eigenproblem of symmetric centrosymmetric and symmetric skew centrosymmetric matrices by making use of the properties of symmetric centrosymmetric and symmetric skew centrosymmetric matrices we derive explicit formulae for the backward errors of approximate eigenpairs

discrete chirp fourier transform and its application to chirp rate estimation the discrete fourier transform dft has found tremendous applications in almost all fields mainly because it can be used to match the multiple frequencies of a stationary signal with multiple harmonics in many applications wideband and nonstationary signals however often occur one of the typical examples of such signals is chirp type signals that are usually encountered in radar signal processing such as synthetic aperture radar sar and inverse sar imaging due to the motion of a target the radar return signals are usually chirps and their chirp rates include the information about the target such as the location and the velocity in this paper we study discrete chirp fourier transform dcft which is analogous to the dft besides the multiple frequency matching similar to the dft the dcft can be used to match the multiple chirp rates in a chirp type signal with multiple chirp components we show that when the signal length n is prime the magnitudes of all the sidelobes of the dcft of a quadratic chirp signal are 1 whereas the magnitude of the mainlobe of the dcft is spl radic n with this result an upper bound for the number of the detectable chirp components using the dcft is provided in terms of signal length and signal and noise powers we also show that the n point dcft performs optimally when n is a prime

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

the solvability conditions for the inverse eigenvalue problems of centro symmetric matrices this paper involves related inverse eigenvalue problems of centro symmetric matrices and their optimal approximation the sufficient and necessary conditions under which the solvable problems of inverse eigenvalue and the general provided form of the solution furthermore the algorithm to compute the optimal approximate solution and some numerical experiments are given

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

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

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

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

short time fourier analysis of sampled speech the theoretical basis for the representation of a speech signal by its short time fourier transform is developed a time frequency representation for linear time varying systems is applied to the speech production model to formulate a quasi stationary representation for the speech waveform short time fourier analysis of the resulting representation yields the relationship between the short time fourier transform of the speech and the speech production model

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

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

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

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

estimating frequency by interpolation using fourier coefficients the periodogram of a time series that contains a sinusoidal component provides a crude estimate of its frequency parameter the maximizer over the fourier frequencies being within o t sup 1 of the frequency as the sample size t increases in the paper a technique for obtaining an estimator that has root mean square error of order t sup 3 2 is presented which involves only the fourier components of the time series at three frequencies the asymptotic variance of the estimator varies between roughly the asymptotic variance of the maximizer of the periodogram over all frequencies the cramer rao lower bound and three times this variance the advantage of the new estimator is its computational simplicity

a constrained matrix least squares problem in structural dynamics model updating a constrained matrix least squares problem in structural dynamics model updating is considered in this paper desired matrix properties including the satisfaction of the linear equation symmetric positive semidefiniteness and sparsity are imposed as side constraints alternating projection method is applied to solve the constrained minimization problem the results of the numerical examples show that the proposed method works well all necessary constraints are considered in our model alternating projection method is first used to update the finite element model numerical results are compared with the recent results

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

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

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

fast nearly ml estimation of the parameters of real or complex single tones or resolved multiple tones this paper presents new computationally efficient algorithms for estimating the parameters frequency amplitude and phase of one or more real tones sinusoids or complex tones cisoids in noise from a block of n uniformly spaced samples the first algorithm is an interpolator that uses the peak sample in the discrete fourier spectrum dfs of the data and its two neighbors we derive cramer rao bounds crbs for such interpolators and show that they are very close to the crb s for the maximum likelihood ml estimator the new algorithm almost reaches these bounds a second algorithm uses the five dfs samples centered on the peak to produce estimates even closer to ml enhancements are presented that maintain nearly ml performance for small values of n for multiple complex tones with frequency separations of at least 4 spl pi n rad sample unbiased estimates are obtained by incorporating the new single tone estimators into an iterative cyclic descent algorithm which is a computationally cheap nonlinear optimization single or multiple real tones are handled in the same way the new algorithms are immune to nonzero mean signals and provided n is large remain near optimal in colored and non gaussian noise

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

phase estimation of a single quasi periodic signal we propose a method for phase estimation of a single non parametric quasi periodic signal assuming signal intensities should be equal among samples of the same phase such corresponding samples are obtained by self dynamic time warping between a quasi periodic signal and a signal with multiple period shifts applied a phase sequence is then estimated in a sub sampling order using an optimization framework incorporating 1 a data term derived from the correspondences and 2 a smoothness term of the local phase evolution under 3 a monotonic increasing constraint on the phase such a phase estimation is however ill posed because of combination ambiguity between the phase evolution and the normalized periodic signal and hence can result in a biased solution therefore we introduce into the optimization framework 4 a bias correction term which imposes zero bias from the linear phase evolution analysis of the quasi periodic signals from both simulated and real data indicate the effectiveness and also potential applications of the proposed method

grid free compressive beamforming the direction of arrival doa estimation problem involves the localization of a few sources from a limited number of observations on an array of sensors thus it can be formulated as a sparse signal reconstruction problem and solved efficiently with compressive sensing cs to achieve high resolution imaging on a discrete angular grid the cs reconstruction degrades due to basis mismatch when the doas do not coincide with the angular directions on the grid to overcome this limitation a continuous formulation of the doa problem is employed and an optimization procedure is introduced which promotes sparsity on a continuous optimization variable the doa estimation problem with infinitely many unknowns i e source locations and amplitudes is solved over a few optimization variables with semidefinite programming the grid free cs reconstruction provides high resolution imaging even with non uniform arrays single snapshot data and under noisy conditions as demonstrated on experimental towed array data

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

a numerical method of structure preserving model updating problem and its perturbation theory a method is presented to update a special finite element fe analytical model based on matrix approximation theory with spectral constraint at first the model updating problem is treated as a matrix approximation problem dependent on the spectrum data from vibration test and modal parameter identification the optimal approximation is the first modified solution of fe model an algorithm is given to preserve the sparsity of the model by multiple correction the convergence of the algorithm is investigated and perturbation of the modified solution is analyzed finally a numerical example is provided to confirm the convergence of the algorithm and perturbation theory

a matrix inverse eigenvalue problem and its application the problem of generating a matrix a with specified eigenvalues which maps a given set of vectors of another given set is presented an existence theorem is given and proved a stable algorithm for producing the matrix a is discussed the relation between this problem and the pole assignment problem in control theory is investigated the application of this problem in the design of neural networks is discussed

sinusoidal polynomial parameter estimation using the distribution derivative in this paper we present a method to estimate the parameters of a generalized sinusoidal model a generalized sinusoid x is defined as a polynomial in the log domain with complex coefficients alphai x t exp sigmai alphai t i where i 0 q the method is based on the distribution derivative of the signal and operates in the transform domain the method is very general and can use any linear transform such as the fourier transform or the wavelet transform or even combinations of linear transforms examples with the fourier transform are given the fourier based estimation methods are evaluated using synthetic signals and have performance very close to the theoretical bound

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

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

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

compressed sensing off the grid this paper investigates the problem of estimating the frequency components of a mixture of s complex sinusoids from a random subset of n regularly spaced samples unlike previous work in compressed sensing the frequencies are not assumed to lie on a grid but can assume any values in the normalized frequency domain 0 1 an atomic norm minimization approach is proposed to exactly recover the unobserved samples and identify the unknown frequencies which is then reformulated as an exact semidefinite program even with this continuous dictionary it is shown that o slog s log n random samples are sufficient to guarantee exact frequency localization with high probability provided the frequencies are well separated extensive numerical experiments are performed to illustrate the effectiveness of the proposed method

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

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

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

the skew symmetric orthogonal solutions of the matrix equation ax b abstract an n n real matrix x is said to be a skew symmetric orthogonal matrix if xt x and xtx i using the special form of the c s decomposition of an orthogonal matrix with skew symmetric k k leading principal submatrix this paper establishes the necessary and sufficient conditions for the existence of and the expressions for the skew symmetric orthogonal solutions of the matrix equation ax b in addition in corresponding solution set of the equation the explicit expression of the nearest matrix to a given matrix in the frobenius norm have been provided furthermore the procrustes problem of skew symmetric orthogonal matrices is considered and the formula solutions are provided finally an algorithm is proposed for solving the first and third problems numerical experiments show that it is feasible

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

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

inverse eigenvalue problem in structural design a method is presented for the design of a structure with specified low order natural frequencies the method can also be used for design problems in which certain bands devoid of any frequency constraints are specified this can further be used to generate initial feasible designs for optimum design problems with frequency constraints

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

the common bisymmetric nonnegative definite solutions with extreme ranks and inertias to a pair of matrix equations abstract we in this paper consider the bisymmetric nonnegative definite solution with extremal ranks and inertias to a system of quaternion matrix equations ax c xb d we derive the extremal ranks and inertias of the common bisymmetric nonnegative definite solution to the system the general expressions of the bisymmetric nonnegative definite solution with extremal ranks and inertias to the system mentioned above are also presented in addition we give a numerical example to illustrate the results of this paper

sequential bayesian sparse signal reconstruction using array data in this paper the sequential reconstruction of source waveforms under a sparsity constraint is considered from a bayesian perspective let the wave field which is observed by a sensor array be caused by a spatially sparse set of sources a spatially weighted laplace like prior is assumed for the source field and the corresponding weighted least absolute shrinkage and selection operator lasso cost function is derived after the weighted lasso solution has been calculated as the maximum a posteriori estimate at time step k the posterior distribution of the source amplitudes is analytically approximated the weighting of the laplace like prior for time step k 1 is then fitted to the approximated posterior distribution this results in a sequential update for the lasso weights thus a sequence of weighted lasso problems is solved for estimating the temporal evolution of a sparse source field the method is evaluated numerically using a uniform linear array in simulations and applied to data which were acquired from a towed horizontal array during the long range acoustic communications experiment

on polynomial phase signals with time varying amplitudes we address the parameter estimation problem for a class of nonstationary signals modeled as polynomial phase signals with time varying amplitudes exponentially damped polynomial phase signals are treated as a special case and are analyzed in detail high order instantaneous moments provide the basic analytical tool but links are shown to exist with either the usually employed fft based technique or the high resolution kumaresan tufts 1982 music and matrix pencil methods asymptotic properties of the relevant estimators are established cramer rao lower bounds on the amplitude and phase parameter estimates are derived and computer simulations are carried out to evaluate the performance of various schemes we focus on parametric modeling of am fm signals mainly because parametric techniques offer parsimony and allow for theoretically unlimited resolution

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