recent results on multiplicative noise recent developments in the analysis of langevin equations with multiplicative noise mn are reported in particular we i present numerical simulations in three dimensions showing that the mn equation exhibits like the kardar parisi zhang kpz equation both a weak coupling fixed point and a strong coupling phase supporting the proposed relation between mn and kpz ii present a dimensional and mean field analysis of the mn equation to compute critical exponents iii show that the phenomenon of the noise induced ordering transition associated with the mn equation appears only in the stratonovich representation and not in the ito one and iv report the presence of a first order like phase transition at zero spatial coupling supporting the fact that this is the minimum model for noise induced ordering transitions

shift invariant and sampling spaces associated with the fractional fourier transform domain shift invariant spaces play an important role in sampling theory multiresolution analysis and many other areas of signal and image processing a special class of the shift invariant spaces is the class of sampling spaces in which functions are determined by their values on a discrete set of points one of the vital tools used in the study of sampling spaces is the zak transform the zak transform is also related to the poisson summation formula and a common thread between all these notions is the fourier transform in this paper we extend some of these notions to the fractional fourier transform frft domain first we introduce two definitions of the discrete fractional fourier transform and two semi discrete fractional convolutions associated with them we employ these definitions to derive necessary and sufficient conditions pertaining to frft domain under which integer shifts of a function form an orthogonal basis or a riesz basis for a shift invariant space we also introduce the fractional zak transform and derive two different versions of the poisson summation formula for the frft these extensions are used to obtain new results concerning sampling spaces to derive the reproducing kernel for the spaces of fractional band limited signals and to obtain a new simple proof of the sampling theorem for signals in that space finally we present an application of our shift invariant signal model which is linked with the problem of fractional delay filtering

a generalization of joint diagonalization criteria for source separation in the field of blind source separation joint diagonalization based approaches constitute an important framework leading to useful algorithms such as the popular joint approximate diagonalization of eigenmatrices jade and simultaneous third order tensor diagonalization stotd algorithms however they are often restricted to the case of cumulants of order four in this paper we extend the results leading to jade and stotd to cumulants of any order greater than or equal to three by exhibiting a new family of contrast functions that constitutes then a unified framework for the above known results this also leads us to generalize some links between contrast functions and joint diagonalization criteria on which these algorithms are based in turn one contrast of the new family allows us to show that a function previously proposed as a separation criterion is also a contrast moreover for the two generalized jade and stotd contrasts the analytical optimal solution in the case of two sources is derived and shown to keep the same simple expression whatever the cumulant order finally some computer simulations illustrate the potential advantage one can take by considering statistics of different orders for the joint diagonalization of cumulant matrices

a finite step global convergence algorithm for the parameter estimation of multichannel ma processes an iterative algorithm for the identification of multichannel moving average ma processes using higher order statistics is proposed it is shown that the algorithm has a finite step global convergence property three multichannel ma models including one nonminimum phase ma model are estimated by this algorithm with satisfactory performances

mean squared error sampling and reconstruction in the presence of noise one of the main goals of sampling theory is to represent a continuous time function by a discrete set of samples here we treat the class of sampling problems in which the underlying function can be specified by a finite set of samples our problem is to reconstruct the signal from nonideal noisy samples which are modeled as the inner products of the signal with a set of sampling vectors contaminated by noise to mitigate the effect of the noise and the mismatch between the sampling and reconstruction vectors the samples are linearly processed prior to reconstruction considering a statistical reconstruction framework we characterize the strategies that are mean squared error mse admissible meaning that they are not dominated in terms of mse by any other linear reconstruction we also present explicit designs of admissible reconstructions that dominate a given inadmissible method adapting several classical estimation approaches to our particular sampling problem we suggest concrete admissible reconstruction methods and compare their performance the results are then specialized to the case in which the samples are processed by a digital correction filter

generalized smoothing splines and the optimal discretization of the wiener filter we introduce an extended class of cardinal l sup l splines where l is a pseudo differential operator satisfying some admissibility conditions we show that the l sup l spline signal interpolation problem is well posed and that its solution is the unique minimizer of the spline energy functional spl par ls spl par sub l2 sup 2 subject to the interpolation constraint next we consider the corresponding regularized least squares estimation problem which is more appropriate for dealing with noisy data the criterion to be minimized is the sum of a quadratic data term which forces the solution to be close to the input samples and a smoothness term that privileges solutions with small spline energies here too we find that the optimal solution among all possible functions is a cardinal l sup l spline we show that this smoothing spline estimator has a stable representation in a b spline like basis and that its coefficients can be computed by digital filtering of the input signal we describe an efficient recursive filtering algorithm that is applicable whenever the transfer function of l is rational which corresponds to the case of exponential splines we justify these algorithms statistically by establishing an equivalence between l sup l smoothing splines and the minimum mean square error mmse estimation of a stationary signal corrupted by white gaussian noise in this model based formulation the optimum operator l is the whitening filter of the process and the regularization parameter is proportional to the noise variance thus the proposed formalism yields the optimal discretization of the classical wiener filter together with a fast recursive algorithm it extends the standard wiener solution by providing the optimal interpolation space we also present a bayesian interpretation of the algorithm

l 2 sampled signal reconstruction with causality constraints part i setup and solutions this paper studies the problem of reconstructing an analog signal from its sampled measurements in which the sampler acquisition device is given and the reconstructor interpolator hold is the design parameter we formulate this problem as an l2 wiener kalman filtering like optimization problem and place the main emphasis on a systematic incorporation of causality constraints into the design procedure specifically the optimization problem is solved under the constraint that the interpolation kernel is l causal for a given i n i e that its impulse response is zero in the time interval ih where h is the sampling period we present a closed form state space solution of the problem whose computational complexity does not depend on i and which can be efficiently calculated and implemented

cumulant based blind identification of linear multi input multi output systems driven by colored inputs the blind identification problem of a linear multi input multi output mimo system is widely noticed by many researchers in diverse fields due to its relevance to blind signal separation however such a problem is ill posed and has no unique solution therefore we can only find a solution of the problem within an equivalence class we address the blind identification problem of the linear mimo system driven by unobservable colored inputs using higher order statistics hos particularly the fourth order cumulants of the outputs where the unobservable inputs are mutually independent but temporally colored linear processes we first define the set which is denoted by s of stable scalar transfer functions and then define the notion of a generalized permutation matrix which is abbreviated by a g matrix over s then it is shown that the transfer function matrix of an unknown system is identified only up to post multiplication by a g matrix this result is applied to identifying fir systems for blind signal separation

criteria for multichannel signal separation we consider the problem in which we want to separate two or more signals that are coupled to each other through an unknown multiple input multiple output linear system channel we prove that the signals can be decoupled or separated using only the condition that they are statistically independent and find even weaker sufficient conditions involving their cross polyspectra by imposing these conditions on the reconstructed signals we obtain a class of criteria for signal separation these criteria are universal in the sense that they do not require any prior knowledge or information concerning the nature of the source signals they may be communication signals or speech signals or any other 1 d or multidimensional signals e g images computationally efficient algorithms for implementing the proposed criteria that only involve the iterative solution to a linear least squares problem are presented

multichannel signal separation methods and analysis the problem of multichannel signal separation has attracted considerable interest in recent literature a variety of methods and criteria have been proposed to solve the problem based on statistical independence between the source signals most of these criteria involve the computation of high order statistics of the observed signals we present a unified framework for many of these criteria and analyze their statistical variance

super exponential algorithms for multichannel blind deconvolution multichannel blind deconvolution has been receiving increasing attention shalvi and weinstein proposed an attractive approach to single channel blind deconvolution called the super exponential methods the objective of this correspondence is to extend the shalvi and weinstein 1993 1994 approach to the multichannel case and present super exponential algorithms for multichannel blind deconvolution we propose three approaches to multichannel blind deconvolution in the first one we present a multichannel super exponential algorithm in the second one we present a super exponential deflation algorithm in the third one we present a two stage super exponential algorithm

a general sampling theory for nonideal acquisition devices the authors first describe the general class of approximation spaces generated by translation of a function spl psi x and provide a full characterization of their basis functions they then present a general sampling theorem for computing the approximation of signals in these subspaces based on a simple consistency principle the theory puts no restrictions on the system input which can be an arbitrary finite energy signal bandlimitedness is not required in contrast to previous approaches this formulation allows for an independent specification of the sampling analysis and approximation synthesis spaces in particular when both spaces are identical the theorem provides a simple procedure for obtaining the least squares approximation of a signal they discuss the properties of this new sampling procedure and present some examples of applications involving bandlimited and polynomial spline signal representations they also define a spectral coherence function that measures the similarity between the sampling and approximation spaces and derive a relative performance bound for the comparison with the least squares solution

estimation and model selection for an ide based spatio temporal model a state space model of the stochastic spatio temporal integro difference equation ide is derived based on multidimensional sampling theory the dimensions of the state space and parameter space of the model are identified from the spatial bandwidth of the system and the support of the redistribution kernel of the ide when both the bandwidth and the kernel support are unknown a method to propose a number of state space and parameter space dimensions is presented these chosen dimensions result in a number of candidate model structures bayesian model selection making use of bayes factor the data augmentation algorithm and importance sampling is then used to identify the model best suited to represent the data in a maximum a posteriori sense

on blind multiuser forward link channel estimation by the subspace method identifiability results blind channel estimation for periodic sequence ds cdma systems can be cast into the framework of structured blind estimation of multi input multi output mimo fir systems where the structure is imposed by the user s signatures a possible approach to tackle this problem consists in looking for a structured solution to one of the blind mimo fir systems proposed previously this is the approach undertaken by several authors however most of them did not address identifiability issues in this paper we first recall and reformulate some general mimo fir identification results of meraim loubaton and moulines see ieee trans inform theory vol 43 p 499 511 1997 and point out some difficulties posed by the subspace approach next we use the above material in order to analyze the behavior of the subspace forward link channel estimate of cdma systems we derive new results showing that the subspace method is not robust to an over determination of the channel order greater than the spreading factor if however the over determination error is less than the spreading factor we show that the subspace estimate is consistent if the codes of the users are properly designed

minimax approximation of representation coefficients from generalized samples many sources of information are of analog or continuous time nature however digital signal processing applications rely on discrete data we consider the problem of approximating l2 inner products i e representation coefficients of a continuous time signal from its generalized samples adopting a robust approach we process these generalized samples in a minimax optimal sense specifically we minimize the worst approximation error of the desired representation coefficients by proper processing of the given sample sequence we then extend our results to criteria which incorporate smoothness constraints on the unknown function finally we compare our methods with the piecewise constant approximation technique commonly used for this problem and discuss the possible improvements by the suggested schemes

average sampling and reconstruction of reproducing kernel signals in mixed lebesgue spaces abstract in this paper we mainly study the average sampling and reconstruction of signals in a reproducing kernel subspace of the mixed lebesgue space l p q r m n first the sampling stability for two kinds of average sampling functionals is considered then the corresponding iterative approximation projection algorithms with exponential convergence are established finally the asymptotic pointwise error estimates are given for reconstructing a signal from its average samples corrupted by additive random noise

frequency domain blind mimo system identification based on second and higher order statistics we present a novel frequency domain framework for the identification of a multiple input multiple output mimo system driven by white mutually independent unobservable inputs the system frequency response is obtained based on singular value decomposition svd of a matrix constructed based on the power spectrum and slices of polyspectra of the system output by appropriately selecting the polyspectra slices we can create a set of such matrices each of which could independently yield the solution of they could all be combined in a joint diagonalization scheme to yield a solution with improved statistical performance the freedom to select the polyspectra slices allows us to bypass the frequency dependent permutation ambiguity that is usually associated with frequency domain svd while at the same time allows us compute and cancel the phase ambiguity an asymptotic consistency analysis of the system magnitude response estimate is performed

cardinal exponential splines part i theory and filtering algorithms causal exponentials play a fundamental role in classical system theory starting from those elementary building blocks we propose a complete and self contained signal processing formulation of exponential splines defined on a uniform grid we specify the corresponding b spline basis functions and investigate their reproduction properties green function and exponential polynomials we also characterize their stability riesz bounds we show that the exponential b spline framework allows an exact implementation of continuous time signal processing operators including convolution differential operators and modulation by simple processing in the discrete b spline domain we derive efficient filtering algorithms for multiresolution signal extrapolation and approximation extending earlier results for polynomial splines finally we present a new asymptotic error formula that predicts the magnitude and the nth order decay of the l sub 2 approximation error as a function of the knot spacing t

u invariant sampling extrapolation and causal interpolation from generalized samples causal processing of a signal s samples is crucial in on line applications such as audio rate conversion compression tracking and more this paper addresses the problems of predicting future samples and causally interpolating deterministic signals we treat a rich variety of sampling mechanisms encountered in practice namely in which each sampling function is obtained by applying a unitary operator on its predecessor examples include pointwise sampling at the output of an antialiasing filter and magnetic resonance imaging mri which correspond respectively to the translation and modulation operators from an abstract hilbert space viewpoint such sequences of functions were studied extensively in the context of stationary random processes we thus utilize powerful tools from this discipline although our problems are deterministic by nature in particular we provide necessary and sufficient conditions on the sampling mechanism such that perfect prediction is possible for cases where perfect prediction is impossible we derive the predictor minimizing the prediction error we also derive a causal interpolation method that best approximates the commonly used noncausal solution finally we study when causal processing of the samples of a signal can be performed in a stable manner

separation of independent sources from correlated inputs the characterization of independent stationary stochastic components sources is generally achieved by using the spectral matrix of partially correlated measurements which are linearly related to the components of interest in the general case where no assumptions are made concerning the way the sources are mixed on the measurements the spectral matrix is not able to extract the true sources while spectral analysis only uses second order properties of independent stochastic sources a procedure based on higher order analysis fourth order cross cumulants is developed this approach leads to a complete identification of the sources

cardinal exponential splines part ii think analog act digital by interpreting the green function reproduction property of exponential splines in signal processing terms we uncover a fundamental relation that connects the impulse responses of allpole analog filters to their discrete counterparts the link is that the latter are the b spline coefficients of the former which happen to be exponential splines motivated by this observation we introduce an extended family of cardinal splines the generalized e splines to generalize the concept for all convolution operators with rational transfer functions we construct the corresponding compactly supported b spline basis functions which are characterized by their poles and zeros thereby establishing an interesting connection with analog filter design techniques we investigate the properties of these new b splines and present the corresponding signal processing calculus which allows us to perform continuous time operations such as convolution differential operators and modulation by simple application of the discrete version of these operators in the b spline domain in particular we show how the formalism can be used to obtain exact discrete implementations of analog filters finally we apply our results to the design of hybrid signal processing systems that rely on digital filtering to compensate for the nonideal characteristics of real world analog to digital a to d and d to a conversion systems

on line blind multichannel equalization based on mutually referenced filters this paper presents a novel approach to the blind linear equalization of possibly nonminimum phase and time varying communication channels in the context of channel diversity we introduce the concept of mutually referenced equalizers mres in which several filters are considered the outputs of which act as training signals for each other a corresponding constrained multidimensional mean square error mse cost function is derived the minimization of which is shown to be a necessary and sufficient condition for equalization the links with a standard linear prediction problem are demonstrated the proposed technique exhibits properties of important practical concern 1 the proposed algorithm is globally convergent 2 simple closed form solutions exist for the mres but the mres also lend themselves readily to adaptive implementation in particular the recursive least squares rls algorithm can be used to offer optimal convergence rate 3 the mre method provides a solution for all equalization delays which results in robustness properties with respect to snr and ill defined channel lengths

linear minimax regret estimation of deterministic parameters with bounded data uncertainties we develop a new linear estimator for estimating an unknown parameter vector x in a linear model in the presence of bounded data uncertainties the estimator is designed to minimize the worst case regret over all bounded data vectors namely the worst case difference between the mean squared error mse attainable using a linear estimator that does not know the true parameters x and the optimal mse attained using a linear estimator that knows x we demonstrate through several examples that the minimax regret estimator can significantly increase the performance over the conventional least squares estimator as well as several other least squares alternatives

iterative algorithms based on multistage criteria for multichannel blind deconvolution blind deconvolution and blind equalization have been important interesting topics in diverse fields including data communication image processing and geophysical data processing recently inouye and habe introduced a multistage criterion for attaining blind deconvolution of multiple input multiple output mimo linear time invariant lti systems in this correspondence based on their criterion we present iterative algorithms for solving the blind deconvolution problem of mimo lti systems however their criterion should be subjected to several constraints of equations therefore they proposed a new constraint free multistage criterion for accomplishing the blind deconvolution of mimo lti systems based on their unconstrained criterion we show iterative algorithms for solving the blind deconvolution of multichannel lti systems

quasi interpolating spline models for hexagonally sampled data the reconstruction of a continuous domain representation from sampled data is an essential element of many image processing tasks in particular image resampling until today most image data have been available on cartesian lattices despite the many theoretical advantages of hexagonal sampling in this paper we propose new reconstruction methods for hexagonally sampled data that use the intrinsically 2 d nature of the lattice and that at the same time remain practical and efficient to that aim we deploy box spline and hex spline models which are notably well adapted to hexagonal lattices we also rely on the quasi interpolation paradigm to design compelling prefilters that is the optimal filter for a prescribed design is found using recent results from approximation theory the feasibility and efficiency of the proposed methods are illustrated and compared for a hexagonal to cartesian grid conversion problem

robust deconvolution of deterministic and random signals we consider the problem of designing an estimation filter to recover a signal x n convolved with a linear time invariant lti filter h n and corrupted by additive noise our development treats the case in which the signal x n is deterministic and the case in which it is a stationary random process both formulations take advantage of some a priori knowledge on the class of underlying signals in the deterministic setting the signal is assumed to have bounded weighted energy in the stochastic setting the power spectra of the signal and noise are bounded at each frequency the difficulty encountered in these estimation problems is that the mean squared error mse at the output of the estimation filter depends on the problem unknowns and therefore cannot be minimized beginning with the deterministic setting we develop a minimax mse estimation filter that minimizes the worst case point wise mse between the true signal x n and the estimated signal over the class of bounded norm inputs we then establish that the mse at the output of the minimax mse filter is smaller than the mse at the output of the conventional inverse filter for all admissible signals next we treat the stochastic scenario for which we propose a minimax regret estimation filter to deal with the power spectrum uncertainties this filter is designed to minimize the worst case difference between the mse in the presence of power spectrum uncertainties and the mse of the wiener filter that knows the correct power spectra the minimax regret filter takes the entire uncertainty interval into account and as demonstrated through an example can often lead to improved performance over traditional minimax mse approaches for this problem

error analysis of frame reconstruction from noisy samples this paper addresses the problem of reconstructing a continuous function defined on rd from a countable collection of samples corrupted by noise the additive noise is assumed to be i i d with mean zero and variance sigma2 we sample the continuous function on the uniform lattice 1 m zd and show for large enough m that the variance of the error between the frame reconstruction fepsiv m from noisy samples of f and the function f satisfy var fepsiv m x f x ap sigma2 md cx where cx is the best constant for every x isin rd we also prove a similar result in the case that our data are weighted average samples of corrupted by additive noise

mean field limit of systems with multiplicative noise a detailed study of the mean field solution of langevin equations with multiplicative noise is presented three different regimes depending on noise intensity weak intermediate and strong noise are identified by performing a self consistent calculation on a fully connected lattice the most interesting strong noise regime is shown to be intrinsically unstable with respect to the inclusion of fluctuations as a ginzburg criterion shows on the other hand the self consistent approach is shown to be valid only in the thermodynamic limit while for finite systems the critical behavior is found to be different in this last case the self consistent field itself is broadly distributed rather than taking a well defined mean value its fluctuations described by an effective zero dimensional multiplicative noise equation govern the critical properties these findings are obtained analytically for a fully connected graph and verified numerically both on fully connected graphs and on random regular networks the results presented here shed some doubt on what is the validity and meaning of a standard mean field approach in systems with multiplicative noise in finite dimensions where each site does not see an infinite number of neighbors but a finite one the implications of all this on the existence of a finite upper critical dimension for multiplicative noise and kardar parisi zhang problems are briefly discussed

new kurtosis optimization schemes for miso equalization this paper deals with efficient optimization of cumulant based contrast functions such a problem occurs in the blind source separation framework where contrast functions are criteria to be maximized in order to retrieve the sources more precisely we focus on the extraction of one source signal and our method applies in deflation approaches where the sources are extracted one by one we propose new methods to maximize the kurtosis contrast function these methods are intermediate between a gradient and an iterative fixed point optimization of so called reference contrasts they rely on iterative updates of the parameters which monotonically increase the contrast function value we point out the strong similarity with the expectation maximization em method and with recent generalizations referred to as minimization maximization mm we also prove the global convergence of the algorithm to a stationary point simulations confirm the convergence of our methods to a separating solution they also show experimentally that our methods have a much lower computational cost than former classical optimization methods finally simulations suggest that the methods remain valid under weaker conditions than those required for proving convergence

the uniqueness of moving average representations with independent and identically distributed random variables for non gaussian stationary time series summary full spectrum non gaussian stationary series can have at most one representation as a moving average of independent and identically distributed random variables having finite moments of all orders

independent component analysis and simultaneous third order tensor diagonalization comon s 1994 well known scheme for independent component analysis ica is based on the maximal diagonalization in a least squares sense of a higher order cumulant tensor in a previous paper we proved that for fourth order cumulants the computation of an elementary jacobi rotation is equivalent to the computation of the best rank 1 approximation of a fourth order tensor in this paper we show that for third order tensors the computation of an elementary jacobi rotation is again equivalent to a best rank 1 approximation however here it is a matrix that has to be approximated this favorable computational load makes it attractive to do something third order like for fourth order cumulant tensors as well we show that simultaneous optimal diagonalization of third order tensor slices of the fourth order cumulant is a suitable strategy this simultaneous third order tensor diagonalization approach stotd is similar in spirit to the efficient jade algorithm

waveform preserving blind estimation of multiple independent sources the problem of blind estimation of source signals is to estimate the source signals without knowing the characteristics of the transmission channel it is shown that the minimum variance unbiased estimates can be obtained if and only if the transmission channel can be identified blindly it is shown that the channel can be blindly identified if and only if there is not more than one gaussian source this condition suggests that waveform preserving blind estimation can be achieved over a wide range of signal processing applications including those cases in which the source signals have identical nongaussian distributions the constructive proof of the necessary and sufficient condition serves as a foundation for the development of waveform preserving blind signal estimation algorithms examples are presented to demonstrate the applications of the theoretical results

systems with multiplicative noise critical behavior from kpz equation and numerics we show that certain critical exponents of systems with multiplicative noise can be obtained from exponents of the kpz equation numerical simulations in 1d confirm this prediction and yield other exponents of the multiplicative noise problem the numerics also verify an earlier prediction of the divergence of the susceptibility over an entire range of control parameter values and show that the exponent governing the divergence in this range varies continuously with control parameter

reconstruction of nonuniformly sampled bandlimited signals by means of digital fractional delay filters this paper considers the problem of reconstructing a class of nonuniformly sampled bandlimited signals of which a special case occurs in e g time interleaved analog to digital converter adc systems due to time skew errors to this end we propose a synthesis system composed or digital fractional delay filters the overall system i e nonuniform sampling and the proposed synthesis system can be viewed as a generalization of time interleaved adc systems to which the former reduces as a special case compared with existing reconstruction techniques our method has major advantages from an implementation point of view to be precise 1 we can perform the reconstruction as well as desired in a certain sense by properly designing the digital fractional delay filters and 2 if properly implemented the fractional delay filters need not be redesigned in case the time skews are changed the price to pay for these attractive features is that we need to use a slight oversampling it should be stressed however that the oversampling factor is less than two as compared with the nyquist rate the paper includes error and quantization noise analysis the former is useful in the analysis of the quantization noise and when designing practical fractional delay filters approximating the ideal filters

the estimation of the fourth order cumulant for dependent data consistency and asymptotic normality let xi be a stationary dependent random process with finite eight order moments for broad classes of processes mixing and strongly mixing we obtain the convergence in probability with sharp rates of the estimate of the fourth order cumulant from n observations xi i 1 n we also establish the asymptotic distribution of the estimation error the asymptotic expression of the variance is explicitly specified

generalized identifiability conditions for blind convolutive mimo separation this correspondence deals with the problem of source separation in the case where the output of a multivariate convolutive mixture is observed we propose novel and generalized conditions for the blind identifiability of a separating system the results are based on higher order statistics and are valid in the case of stationary but not necessarily i i d signals in particular we extend recent results based on second order statistics only the approach relies on the use of so called reference signals our new results also show that only weak conditions are required on the reference signals this is illustrated by simulations and opens up the possibility of developing new methods

mimo ar system identification and blind source separation for gmm distributed sources the problem of blind source separation bss and system identification for multiple input multiple output mimo auto regressive ar mixtures is addressed in this paper two new time domain algorithms for system identification and bss are proposed based on the gaussian mixture model gmm for sources distribution both algorithms are based on the generalized expectation maximization gem method for joint estimation of the mimo ar model parameters and the gmm parameters of the sources the first algorithm is derived under the assumption of unstructured input signal statistics while the second algorithm incorporates the prior knowledge about the structure of the input signal statistics due to the statistically independent source assumption these methods are tested via simulations using synthetic and audio signals the system identification performances are tested by comparison between the state transition matrix estimation using the proposed algorithms and the well known multidimensional yule walker solution followed by an instantaneous bss method the results show that the proposed algorithms outperform the yule walker based approach the bss performances were compared to other convolutive bss methods the results show that the proposed algorithms achieve higher signal to interference ratio sir compared to the other tested methods

multichannel arma processes parametric modeling of multichannel time series is accomplished by using higher than second order statistics hos of the observed nongaussian data cumulants of vector processes are defined using a kronecker product formulation and consistency of their sample estimators is addressed identifiability results in connection with the hos based parameter estimation of causal and noncausal multivariate arma processes are established estimates of the parameters of causal arma models are obtained as the solution to a set of linear equations whereas those of noncausal arma models are obtained as the solution to a cumulant matching algorithm conventional approaches based on second order statistics can identify a multichannel system only to within post multiplication by a unimodular matrix hos based methods yield solutions that are unique to within post multiplication by an extended permutation matrix additionally the multiminimum phase assumption can be relaxed and the observations may be contaminated with colored gaussian noise frequency domain methods for nonparametric system identification are discussed briefly simulations results validating the multichannel parameter estimation algorithms are provided

maximum standardized cumulant deconvolution of non gaussian linear processes a linear process is represented as a driving white noise convolved with a system response sequence the concept of natural peakedness of a system response sequence is defined and its properties are investigated utilizing natural peakedness the convergence theory of maximum standardized cumulant deconvolution is established and the uniqueness theorem of non gaussian linear process representations is proved in addition autoregressive models on a countable abelian group are defined and the relation between cumulant deconvolution and autoregressive models is given

unbiased adaptive estimations of the fourth order cumulant for real random zero mean signal in this paper a consistent efficient estimator of the fourth order cumulant for real discrete time random i i d at least up to order 8 zero mean signal is proposed in both batch and adaptive versions in batch version the proposed estimator is not only consistent but also unbiased and efficient the systematical theoretical and experimental studies with comparisons between the proposed estimator and three other estimators of the fourth order cumulant the natural or the traditional one the trivial unbiased estimator for the known power case and the fourth k statistics are undertaken for both normal and uniform processes then the adaptive versions of the estimators all except the fourth k statistics are given and studied in detail the convergence in mean and the convergence in mean square analyses are performed for them first theoretically then empirically finally the whole set of analyses carried out for both batch and adaptive versions shows that from many points of view the proposed estimator is interesting for use in versatile signal processing applications especially in real time and short term ones

sampling and reconstruction of signals in a reproducing kernel subspace of lp rd in this paper we consider sampling and reconstruction of signals in a reproducing kernel subspace of lp rd 1 p associated with an idempotent integral operator whose kernel has certain off diagonal decay and regularity the space of p integrable non uniform splines and the shift invariant spaces generated by finitely many localized functions are our model examples of such reproducing kernel subspaces of lp rd we show that a signal in such reproducing kernel subspaces can be reconstructed in a stable way from its samples taken on a relatively separated set with sufficiently small gap we also study the exponential convergence consistency and the asymptotic pointwise error estimate of the iterative approximation projection algorithm and the iterative frame algorithm for reconstructing a signal in those reproducing kernel spaces from its samples with sufficiently small gap

quadratic higher order criteria for iterative blind separation of a mimo convolutive mixture of sources this paper deals with the problem of source separation in the case when the observations result from a multiple input multiple output convolutive mixing system in a blind framework higher order contrast functions have been proved to be efficient for extracting sources inspired by a semiblind approach we propose new contrast functions for blind signal separation that make use of reference signals the main advantage of this approach consists in the quadratic form of these criteria the extraction of one source hence reduces to a simple optimization task for which fast and efficient algorithms are available the separation of the other sources from the mixture is then carried out by an iterative deflation method furthermore these contrasts are shown to be valid for both independent identically distributed i i d and non i i d source signals the performance offered by these criteria is investigated through simulations they appear as very appealing tools compared with some classical contrast functions

nonuniform sampling and reconstruction in shift invariant spaces this article discusses modern techniques for nonuniform sampling and reconstruction of functions in shift invariant spaces it is a survey as well as a research paper and provides a unified framework for uniform and nonuniform sampling and reconstruction in shift invariant subspaces by bringing together wavelet theory frame theory reproducing kernel hilbert spaces approximation theory amalgam spaces and sampling inspired by applications taken from communication astronomy and medicine the following aspects will be emphasized a the sampling problem is well defined within the setting of shift invariant spaces b the general theory works in arbitrary dimension and for a broad class of generators c the reconstruction of a function from any sufficiently dense nonuniform sampling set is obtained by efficient iterative algorithms these algorithms converge geometrically and are robust in the presence of noise d to model the natural decay conditions of real signals and images the sampling theory is developed in weighted l p spaces

performance bounds and design criteria for estimating finite rate of innovation signals in this paper we consider the problem of estimating finite rate of innovation fri signals from noisy measurements and specifically analyze the interaction between fri techniques and the underlying sampling methods we first obtain a fundamental limit on the estimation accuracy attainable regardless of the sampling method next we provide a bound on the performance achievable using any specific sampling approach essential differences between the noisy and noise free cases arise from this analysis in particular we identify settings in which noise free recovery techniques deteriorate substantially under slight noise levels thus quantifying the numerical instability inherent in such methods this instability which is only present in some families of fri signals is shown to be related to a specific type of structure which can be characterized by viewing the signal model as a union of subspaces finally we develop a methodology for choosing the optimal sampling kernels for linear reconstruction based on a generalization of the karhunen loeve transform the results are illustrated for several types of time delay estimation problems

regularization theory in image restoration the stabilizing functional approach several aspects of the application of regularization theory in image restoration are presented this is accomplished by extending the applicability of the stabilizing functional approach to 2 d ill posed inverse problems inverse restoration is formulated as the constrained minimization of a stabilizing functional the choice of a particular quadratic functional to be minimized is related to the a priori knowledge regarding the original object through a formulation of image restoration as a maximum a posteriori estimation problem this formulation is based on image representation by certain stochastic partial differential equation image models the analytical study and computational treatment of the resulting optimization problem are subsequently presented as a result a variety of regularizing filters and iterative regularizing algorithms are proposed a relationship between the regularized solutions proposed and optimal wiener estimation is identified the filters and algorithms proposed are evaluated through several experimental results

blind separation of instantaneous mixtures of nonstationary sources most source separation algorithms are based on a model of stationary sources however it is a simple matter to take advantage of possible nonstationarities of the sources to achieve separation this paper develops novel approaches in this direction based on the principles of maximum likelihood and minimum mutual information these principles are exploited by efficient algorithms in both the off line case via a new joint diagonalization procedure and in the on line case via a newton like procedure some experiments showing the good performance of our algorithms and evidencing an interesting feature of our methods are presented their ability to achieve a kind of super efficiency the paper concludes with a discussion contrasting separating methods for non gaussian and nonstationary models and emphasizing that as a matter of fact what makes the algorithms work is strictly speaking not the nonstationarity itself but rather the property that each realization of the source signals has a time varying envelope

a linear time varying system framework for noniterative discrete time band limited signal extrapolation a technique for the analysis and design of noniterative algorithms for discrete time band limited signal extrapolation is described the approach involves modeling the extrapolation process as a linear time varying ltv system or filter together with a previously developed fourier theory for ltv systems this model provides a frequency domain transfer function representation for the extrapolation system this representation serves as a powerful tool for characterizing and comparing the reconstruction properties of several well known least squares optimal algorithms for band limited extrapolation moreover the frequency domain setting provides a conceptually attractive means for understanding the process of extrapolation itself additionally a least squares approximation methodology for designing ltv filters for band limited extrapolation is developed the design technique is shown to unify a broad class of algorithms for extrapolating discrete time data and further to provide a means for designing new and improved extrapolation algorithms

unbiased efficient estimator of the fourth order cumulant for random zero mean non i i d signals particular case of ma stochastic process non gaussian processes may require not only the information provided by first two moments but also that given by the higher order statistics in particular by the third and fourth order moments or cumulants this paper addresses a fourth order cumulant estimation problem for real discrete time random non i i d signal that can be approximated as an ma stochastic process an unbiased estimator is proposed studied and compared to two other frequently used estimators of the fourth order cumulant natural estimator and fourth k statistics statistical comparative studies are undertaken from both bias and mse points of view for different distribution laws and ma filters algorithms aiming to reduce computational complexity of the proposed estimator as well as that of the fourth k statistics bias are also provided

image reconstruction and restoration overview of common estimation structures and problems developments in the theory of image reconstruction and restoration over the past 20 or 30 years are outlined particular attention is paid to common estimation structures and to practical problems not properly solved yet the problem of image reconstruction and restoration is first formulated some of the current regularization approaches used to solve the problem are then described the concepts of a priori information and compound criterion are introduced a bayesian interpretation of the regularization techniques is given which clarifies the role of the tuning parameters and indicates how they could be estimated the practical aspects of computing the solution first when the hyperparameters are known and second when they must be estimated are then considered conclusions are drawn and points that still need to be investigated are outlined

a family of frequency and time domain contrasts for blind separation of convolutive mixtures of temporally dependent signals this paper addresses the problem of blind separation of convolutive mixtures via contrast maximization new frequency domain contrast functions are constructed based on higher order spectra of the observations they allow to separate mixtures of sources that are spatially independent and temporally possibly nonlinear processes using parseval s formula the former criteria yield a general class of time domain contrasts which extends to the convolutive case results that have been previously obtained in the context either of instantaneous mixtures or of independent and identically distributed i i d sources a monte carlo simulation study is carried out for comparison between the different contrasts thus providing a guideline about the choice of an appropriate contrast

new processing techniques based on the constant modulus adaptive algorithm this paper presents three extensions of the constant modulus algorithm cma introduced in an earlier paper as a means of correcting degradations in constant enyelope waveforms as originally formulated the cma employs an fir filter with complex coefficients and accepts complex quadrature input data in this paper first a real input real coefficient version of the algorithm is shown to perform arbitrarily close to the fully complex version secondly the algorithm is extended for the enhancement of signals having a nonconstant but known envelope as might arise in data signals with pulse shaping lastly a multichannel version of cma wherein several observations are linearly combined is presented for joint adaptation of multiple filters this approach can be used for example as a means of spatial or polarization beamsteering to reject additive interferers and compensate for channel induced polarization rotation

inequalities and monotonicity properties for zeros of hermite functions we study the variation of the zeros of the hermite function h t with respect to the positive real variable we show that for each nonnegative integer n h t has exactly n 1 real zeros when n n 1 and that each zero increases from i1 to 1 as increases we establish a formula for the derivative of a zero with respect to the parameter this derivative is a completely monotonic function of by products include some results on the regular sign behaviour of difierences of zeros of hermite polynomials as well as a proof of some inequalities related to work of w k hayman and e l ortiz for the largest zero of h t similar results on zeros of certain con uent hypergeometric functions are given too these specialize to results on the flrst second etc positive zeros of hermite polynomials

analysis of error in reconstruction of two dimensional signals from irregularly spaced samples we consider the problem of estimating a band limited two dimensional 2 d signal based on a finite set of irregularly spaced samples we derive the minimum mean squared error estimator of the form of a sum of weighted interpolating functions that are identical in shape but are centered at the irregularly spaced sample points and show that this estimator is identical to the minimum energy band limited interpolator that has been previously obtained by others the relation between the mean squared error and the set of irregularly spaced sampling points is studied using the minimax principle the maximum of the mean squared error over a class of signals is minimized by proper choice of the set of sampling points three criteria for evaluating the performance of the sampling point set are derived from a candidate group of sets of irregularly spaced sampling points these criteria may be used to select that point set which is optimal for recovery over a class of signals

regularized interpolation for noisy images interpolation is the means by which a continuously defined model is fit to discrete data samples when the data samples are exempt of noise it seems desirable to build the model by fitting them exactly in medical imaging where quality is of paramount importance this ideal situation unfortunately does not occur in this paper we propose a scheme that improves on the quality by specifying a tradeoff between fidelity to the data and robustness to the noise we resort to variational principles which allow us to impose smoothness constraints on the model for tackling noisy data based on shift rotation and scale invariant requirements on the model we show that the lp norm of an appropriate vector derivative is the most suitable choice of regularization for this purpose in addition to tikhonov like quadratic regularization this includes edge preserving total variation like tv regularization we give algorithms to recover the continuously defined model from noisy samples and also provide a data driven scheme to determine the optimal amount of regularization we validate our method with numerical examples where we demonstrate its superiority over an exact fit as well as the benefit of tv like nonquadratic regularization over tikhonov like quadratic regularization

cumulant based identification of multichannel moving average models given cumulants of a stationary perhaps noisy non gaussian r variate moving average ma q process identifiability conditions are studied under which the ma coefficient matrices the input statistics and the order q can be uniquely determined the selection of a unique representative from the equivalence class corresponding to a given cumulant structure involves fewer restrictions than that corresponding to a given covariance structure two algorithms are derived for estimating the possibly nonminimum phase ma coefficient matrices

identification and deconvolution of multichannel linear non gaussian processes using higher order statistics and inverse filter criteria this paper is concerned with the problem of estimation and deconvolution of the matrix impulse response function of a multiple input multiple output mimo system given only the measurements of the vector output of the system the system is assumed to be driven by a temporally i i d and spatially independent non gaussian vector sequence which is not observed an iterative inverse filter criteria based approach is developed using the third order or the fourth order normalized cumulants of the inverse filtered data at zero lag stationary points of the proposed cost functions are investigated the approach is input iterative i e the input sequences are extracted and removed one by one the matrix impulse response is then obtained by cross correlating the extracted inputs with the observed outputs identifiability conditions are analyzed the strong consistency of the proposed approach is also briefly discussed computer simulation examples are presented to illustrate the proposed approaches

general approach to blind source separation this paper identifies and studies two major issues in the blind source separation problem separability and separation principles we show that separability is an intrinsic property of the measured signals and can be described by the concept of m row decomposability introduced in this paper we also show that separation principles can be developed by using the structure characterization theory of random variables in particular we show that these principles can be derived concisely and intuitively by applying the darmois skitovich theorem which is well known in statistical inference theory and psychology some new insights are gained for designing blind source separation filters

a general algebraic algorithm for blind extraction of one source in a mimo convolutive mixture the paper deals with the problem of blind source extraction from a multiple input multiple output mimo convolutive mixture we define a new criterion for source extraction which uses higher order contrast functions based on so called reference signals it generalizes existing reference based contrasts in order to optimize the new criterion we propose a general algebraic algorithm based on best rank 1 tensor approximation computer simulations illustrate the good behavior and the interest of our algorithm in comparison with other approaches

blind equalization of mimo fir channels driven by white but higher order colored source signals the goal of the article is to find a minimal amount of statistical information or a much weaker condition about source signals for which blind equalization is possible for multiple input multiple output finite impulse response mimo fir channels first a sufficiently broad framework is set up within which such a theoretical problem is well posed within this framework it is shown that second order statistics sos alone are not sufficient for blind equalization when the source signals are white additional higher order statistics hos are needed then we show that the only additional higher order statistical information needed is spatial fourth order cumulants though it has not yet been proved to be minimal it is interesting to note that this is the same as the weakest known condition on the source signals even for an instantaneous mixture we then show a necessary and sufficient condition for blind equalization when the source signals are white and spatially fourth order uncorrelated based on this condition criterion a for blind equalization of mimo fir channels is developed by exploiting the temporal fourth order statistics finally based on this criterion a new necessary and sufficient condition in terms of cumulants for the blind equalization of mimo fir channels is obtained

source separation in post nonlinear mixtures we address the problem of separation of mutually independent sources in nonlinear mixtures first we propose theoretical results and prove that in the general case it is not possible to separate the sources without nonlinear distortion therefore we focus our work on specific nonlinear mixtures known as post nonlinear mixtures these mixtures constituted by a linear instantaneous mixture linear memoryless channel followed by an unknown and invertible memoryless nonlinear distortion are realistic models in many situations and emphasize interesting properties i e in such nonlinear mixtures sources can be estimated with the same indeterminacies as in instantaneous linear mixtures the separation structure of nonlinear mixtures is a two stage system namely a nonlinear stage followed by a linear stage the parameters of which are updated to minimize an output independence criterion expressed as a mutual information criterion the minimization of this criterion requires knowledge or estimation of source densities or of their log derivatives a first algorithm based on a gram charlier expansion of densities is proposed unfortunately it fails for hard nonlinear mixtures a second algorithm based on an adaptive estimation of the log derivative of densities leads to very good performance even with hard nonlinearities experiments are proposed to illustrate these results

sampling and reconstruction of signals in function spaces associated with the linear canonical transform the linear canonical transform lct has been shown to be useful and powerful in signal processing optics etc many results of this transform are already known including sampling theory most existing sampling theories of the lct consider the class of bandlimited signals however in the real world many analog signals arising in engineering applications are non bandlimited in this correspondence we propose a sampling and reconstruction strategy for a class of function spaces associated with the lct which can provide a suitable and realistic model for real applications first we introduce definitions of semi and fully discrete convolutions for the lct then we derive necessary and sufficient conditions pertaining to the lct under which integer shifts of a chirp modulated function generate a riesz basis for the function spaces by applying the results we present a more comprehensive sampling theory for the lct in the function spaces and further a sampling theorem which recovers a signal from its own samples in the function spaces is established moreover some sampling theorems for shift invariant spaces and some existing sampling theories for bandlimited signals associated with the fourier transform ft the fractional ft or the lct are noted as special cases of the derived results finally some potential applications of the derived theory are presented

a globally convergent approach for blind mimo adaptive deconvolution we discuss the blind deconvolution of multiple input multiple output mimo linear convolutional mixtures and propose a set of hierarchical criteria motivated by the maximum entropy principle the proposed criteria are based on the constant modulus cm criterion in order to guarantee that all minima achieve perfectly restoration of different sources the approach is moreover robust to errors in channel order estimation practical implementation is addressed by a stochastic adaptive algorithm with a low computational cost complete convergence proofs based on the characterization of all extrema are provided the efficiency of the proposed method is illustrated by numerical simulations

quantitative error analysis for the reconstruction of derivatives we present a general fourier based method which provides an accurate prediction of the approximation error when the derivative of a signal s t is continuously reconstructed from uniform point samples or generalized measurements on s this formalism applies to a wide class of convolution based techniques it provides a key tool the frequency error kernel for designing computationally efficient reconstruction schemes which are near optimal in the least squares sense

criteria for blind deconvolution of multichannel linear time invariant systems blind deconvolution and equalization of linear time invariant systems have widely received attention in various fields such as data communication image processing and geophysical data processing shalvi and weinstein 1990 proposed certain criteria for blind deconvolution of nonminimum phase linear time invariant systems their work is however restricted to the single channel or scalar case this correspondence extends the shalvi weinstein approach to the multichannel case we propose a multistage maximization criterion and a single stage maximization criterion for attaining multichannel blind deconvolution under the normalized condition specified later they are shown to be equivalent

noninvertible gabor transforms time frequency analysis such as the gabor transform plays an important role in many signal processing applications the redundancy of such representations is often directly related to the computational load of any algorithm operating in the transform domain to reduce complexity it may be desirable to increase the time and frequency sampling intervals beyond the point where the transform is invertible at the cost of an inevitable recovery error in this paper we initiate the study of recovery procedures for noninvertible gabor representations we propose using fixed analysis and synthesis windows chosen e g according to implementation constraints and to process the gabor coefficients prior to synthesis in order to shape the reconstructed signal we develop three methods for signal recovery the first follows from the consistency requirement namely that the recovered signal has the same gabor representation as the input signal the second is based on minimization of a worst case error last we develop a recovery technique based on the assumption that the input signal lies in some subspace of l2 we show that for each of the criteria the manipulation of the transform coefficients amounts to a 2d twisted convolution which we show how to perform using a filter bank when the undersampling factor is an integer the processing reduces to standard 2d convolution we provide simulation results demonstrating the advantages and weaknesses of each of the algorithms

fourth order blind identification of underdetermined mixtures of sources fobium for about two decades numerous methods have been developed to blindly identify overdetermined p spl les n mixtures of p statistically independent narrowband nb sources received by an array of n sensors these methods exploit the information contained in the second order so the fourth order fo or both the so and fo statistics of the data however in practical situations the probability of receiving more sources than sensors increases with the reception bandwidth and the use of blind identification bi methods able to process underdetermined mixtures of sources for which p n may be required although such methods have been developed over the past few years they all present serious limitations in practical situations related to the radiocommunications context for this reason the purpose of this paper is to propose a new attractive bi method exploiting the information contained in the fo data statistics only that is able to process underdetermined mixtures of sources without the main limitations of the existing methods provided that the sources have different trispectrum and nonzero kurtosis with the same sign a new performance criterion that is able to quantify the identification quality of a given source and allowing the quantitative comparison of two bi methods for each source is also proposed in the paper finally an application of the proposed method is presented through the introduction of a powerful direction finding method built from the blindly identified mixture matrix

deconvolution and estimation of transfer function phase and coefficients for nongaussian linear processes nongaussian linear processes are considered it is shown that the phase of the transfer function can be estimated under broad conditions this is not true of gaussian linear processes and in this sense gaussian linear processes are atypical the asymptotic behavior of a phase estimate is determined the phase estimates make use of bispectral estimates these ideas are applied to a problem of deconvolution which is effective even when the transfer function is not minimum phase a number of computational illustrations are given

moving average restoration of bandlimited signals from noisy observations the purpose of this paper is to describe the extension of the whittaker shannon sampling theorem to reconstruction of bandlimited functions in the presence of zero mean uncorrelated noise it is shown that the classical whittaker shannon sampling scheme is not consistent in the case of noisy measurements and new reconstruction algorithms based on the moving average smoothing are proposed the weak and strong consistency of the algorithms is established and the rate of convergence is investigated the theory is verified in the computer simulations

high rate interpolation of random signals from nonideal samples we address the problem of reconstructing a random signal from samples of its filtered version using a given interpolation kernel in order to reduce the mean squared error mse when using a nonoptimal kernel we propose a high rate interpolation scheme in which the interpolation grid is finer than the sampling grid a digital correction system that processes the samples prior to their multiplication with the shifts of the interpolation kernel is developed this system is constructed such that the reconstructed signal is the linear minimum mse lmmse estimate of the original signal given its samples an analytic expression for the mse as a function of the interpolation rate is provided which leads to an explicit condition such that the optimal mse is achieved with the given nonoptimal kernel simulations confirm the reduction in mse with respect to a system with equal sampling and reconstruction rates

critical wetting of a class of nonequilibrium interfaces a mean field picture a self consistent mean field method is used to study critical wetting transitions under nonequilibrium conditions by analyzing kardar parisi zhang kpz interfaces in the presence of a bounding substrate in the case of positive kpz nonlinearity a single gaussian regime is found on the contrary interfaces corresponding to negative nonlinearities lead to three different regimes of critical behavior for the surface order parameter i a trivial gaussian regime ii a weak fluctuation regime with a trivially located critical point and nontrivial exponents and iii a highly nontrivial strong fluctuation regime for which we provide a full solution by finding the zeros of parabolic cylinder functions these analytical results are also verified by solving numerically the self consistent equation in each case analogies with and differences from equilibrium critical wetting as well as nonequilibrium complete wetting are also discussed

nonideal sampling and interpolation from noisy observations in shift invariant spaces digital analysis and processing of signals inherently relies on the existence of methods for reconstructing a continuous time signal from a sequence of corrupted discrete time samples in this paper a general formulation of this problem is developed that treats the interpolation problem from ideal noisy samples and the deconvolution problem in which the signal is filtered prior to sampling in a unified way the signal reconstruction is performed in a shift invariant subspace spanned by the integer shifts of a generating function where the expansion coefficients are obtained by processing the noisy samples with a digital correction filter several alternative approaches to designing the correction filter are suggested which differ in their assumptions on the signal and noise the classical deconvolution solutions least squares tikhonov and wiener are adapted to our particular situation and new methods that are optimal in a minimax sense are also proposed the solutions often have a similar structure and can be computed simply and efficiently by digital filtering some concrete examples of reconstruction filters are presented as well as simple guidelines for selecting the free parameters e g regularization of the various algorithms

nonideal sampling and regularization theory shannon s sampling theory and its variants provide effective solutions to the problem of reconstructing a signal from its samples in some shift invariant space which may or may not be bandlimited in this paper we present some further justification for this type of representation while addressing the issue of the specification of the best reconstruction space we consider a realistic setting where a multidimensional signal is prefiltered prior to sampling and the samples are corrupted by additive noise we adopt a variational approach to the reconstruction problem and minimize a data fidelity term subject to a tikhonov like continuous domain l2 regularization to obtain the continuous space solution we present theoretical justification for the minimization of this cost functional and show that the globally minimal continuous space solution belongs to a shift invariant space generated by a function generalized b spline that is generally not bandlimited when the sampling is ideal we recover some of the classical smoothing spline estimators the optimal reconstruction space is characterized by a condition that links the generating function to the regularization operator and implies the existence of a b spline like basis to make the scheme practical we specify the generating functions corresponding to the most popular families of regularization operators derivatives iterated laplacian as well as a new generalized one that leads to a new brand of matern splines we conclude the paper by proposing a stochastic interpretation of the reconstruction algorithm and establishing an equivalence with the minimax and minimum mean square error mmse wiener solutions of the generalized sampling problem

source extraction by maximizing the variance in the conditional distribution tails this paper presents a method for signal extraction based on conditional second order moments of the output of the extraction filter the estimator of the filter is derived from an approximate maximum likelihood criterion conditioned on a presence indicator of the source of interest the conditional moment is shown to be a contrast function under the conditions that 1 all cross moments of the same order between the source signal of interest and the other source signals are null and 2 that the source of interest has the largest conditional moment among all sources for the two source two observation case this allows us to derive the theoretical recovery bounds of the contrast when the conditional cross moment does not vanish a comparison with empirical results confirms these bounds simulations show that the estimator is quite robust to additive gaussian distributed noise also through simulations we show that the error level induced by a rough approximation of the presence indicator shows a strong similarity with that of additive noise the robustness with respect both to noise and to inaccuracies in the prior information about the source presence guarantees a wide applicability of the proposed method

sampling from a system theoretic viewpoint part i concepts and tools this paper is first in a series of papers studying a system theoretic approach to the problem of reconstructing an analog signal from its samples the idea borrowed from earlier treatments in the control literature is to address the problem as a hybrid model matching problem in which performance is measured by system norms in this paper we present the paradigm and revise underlying technical tools such as the lifting technique and some topics of the operator theory this material facilitates a systematic and unified treatment of a wide range of sampling and reconstruction problems recovering many hitherto considered different solutions and leading to new results some of these applications are discussed in the second part

a minimum squared error framework for generalized sampling we treat the problem of reconstructing a signal from its nonideal samples where the sampling and reconstruction spaces as well as the class of input signals can be arbitrary subspaces of a hilbert space our formulation is general and includes as special cases reconstruction from finitely many samples as well as uniform sampling of continuous time signals which are not necessarily bandlimited to obtain a good approximation of the signal in the reconstruction space from its samples we suggest two design strategies that attempt to minimize the squared norm error between the signal and its reconstruction the approaches we propose differ in their assumptions on the input signal if the signal is known to lie in an appropriately chosen subspace then we propose a method that achieves the minimal squared error on the other hand when the signal is not restricted we show that the minimal norm reconstruction cannot generally be obtained instead we suggest minimizing the worst case squared error between the reconstructed signal and the best possible but usually unattainable approximation of the signal within the reconstruction space we demonstrate both theoretically and through simulations that the suggested methods can outperform the consistent reconstruction approach previously proposed for this problem

postfiltering versus prefiltering for signal recovery from noisy samples we consider the extension of the whittaker shannon ws reconstruction formula to the case of signals sampled in the presence of noise and which are not necessarily band limited observing that in this situation the classical sampling expansion yields inconsistent reconstruction we introduce a class of signal recovery methods with a smooth correction of the interpolation series two alternative data smoothing methods are examined based either on a global postfiltering or a local data presmoothing we assess the accuracy of the methods by the global l sub 2 error both band limited and non band limited signals are considered a general class of correlated noise processes is taken into account the weak and strong rates of convergence of the algorithms are established and their relative efficiency is discussed the influence of noise memory and its moment structure on the accuracy is thoroughly examined

fast acquisition and reconstruction of optical coherence tomography images via sparse representation in this paper we present a novel technique based on compressive sensing principles for reconstruction and enhancement of multi dimensional image data our method is a major improvement and generalization of the multi scale sparsity based tomographic denoising msbtd algorithm we recently introduced for reducing speckle noise our new technique exhibits several advantages over msbtd including its capability to simultaneously reduce noise and interpolate missing data unlike msbtd our new method does not require an a priori high quality image from the target imaging subject and thus offers the potential to shorten clinical imaging sessions this novel image restoration method which we termed sparsity based simultaneous denoising and interpolation sbsdi utilizes sparse representation dictionaries constructed from previously collected datasets we tested the sbsdi algorithm on retinal spectral domain optical coherence tomography images captured in the clinic experiments showed that the sbsdi algorithm qualitatively and quantitatively outperforms other state of the art methods

robust mean squared error estimation in the presence of model uncertainties we consider the problem of estimating an unknown parameter vector x in a linear model that may be subject to uncertainties where the vector x is known to satisfy a weighted norm constraint we first assume that the model is known exactly and seek the linear estimator that minimizes the worst case mean squared error mse across all possible values of x we show that for an arbitrary choice of weighting the optimal minimax mse estimator can be formulated as a solution to a semidefinite programming problem sdp which can be solved very efficiently we then develop a closed form expression for the minimax mse estimator for a broad class of weighting matrices and show that it coincides with the shrunken estimator of mayer and willke with a specific choice of shrinkage factor that explicitly takes the prior information into account next we consider the case in which the model matrix is subject to uncertainties and seek the robust linear estimator that minimizes the worst case mse across all possible values of x and all possible values of the model matrix as we show the robust minimax mse estimator can also be formulated as a solution to an sdp finally we demonstrate through several examples that the minimax mse estimator can significantly increase the performance over the conventional least squares estimator and when the model matrix is subject to uncertainties the robust minimax mse estimator can lead to a considerable improvement in performance over the minimax mse estimator

new criteria for blind deconvolution of nonminimum phase systems channels a necessary and sufficient condition for blind deconvolution without observing the input of nonminimum phase linear time invariant systems channels is derived based on this condition several optimization criteria are proposed and their solution is shown to correspond to the desired response these criteria involve the computation only of second and fourth order moments implying a simple tap update procedure the proposed methods are universal in the sense that they do not impose any restrictions on the probability distribution of the unobserved input sequence it is shown that in several important cases e g when the additive noise is gaussian the proposed criteria are essentially unaffected

linear bispectrum of signals and identification of nonminimum phase fir systems driven by colored input the identification of non minimum phase finite impulse response fir systems driven by third order stationary colored signals that are not linear processes is addressed modeling the linear part of the bispectrum of a signal is discussed the bispectrum of a signal is decomposed into two multiplicative factors the linear bispectrum is defined as the factor of the bispectrum that can exactly be modeled using a third order white noise driven linear shift invariant lsi system the linear bispectrum of the output of the unknown lsi system is represented using an arma autoregressive moving average model where the ma parameters correspond to the unknown fir system impulse response coefficients and the ar parameters model the linear bispectrum of the input signal an algorithm for identifying the ma and ar parameters is given how the proposed method is different from fitting an arma model directly to the bicumulants or the bispectrum of the system output is discussed the method is applied to blur identification