subspace averaging and order determination for source enumeration in this paper we address the problem of subspace averaging with special emphasis placed on the question of estimating the dimension of the average the results suggest that the enumeration of sources in a multi sensor array which is a problem of estimating the dimension of the array manifold and as a consequence the number of radiating sources may be cast as a problem of averaging subspaces this point of view stands in contrast to conventional approaches which cast the problem as one of identifiying covariance models in a factor model we present a robust formulation of the proposed order fitting rule based on majorization minimization algorithms a key element of the proposed method is to construct a bootstrap procedure based on a newly proposed discrete distribution on the manifold of projection matrices for stochastically generating subspaces from a function of experimentally determined eigenvalues in this way the proposed subspace averaging sa technique determines the order based on the eigenvalues of an average projection matrix rather than on the likelihood of a covariance model penalized by functions of the model order by means of simulation examples we show that the proposed sa criterion is especially effective in high dimensional scenarios with low sample support

multiantenna glr detection of rank one signals with known power spectrum in white noise with unknown spatial correlation multiple antenna detection of a gaussian signal with spatial rank one in temporally white gaussian noise with arbitrary and unknown spatial covariance is considered this is motivated by spectrum sensing problems in the context of dynamic spectrum access in which several secondary networks coexist but do not cooperate creating a background of spatially correlated broadband interference when the temporal correlation of the signal of interest is assumed known up to a scale factor the corresponding generalized likelihood ratio test is shown to yield a scalar optimization problem closed form expressions of the test are obtained for the general signal spectrum case in the low signal to noise ratio snr regime as well as for signals with binary valued power spectrum in arbitrary snr the two resulting detectors turn out to be equivalent an asymptotic approximation to the test distribution for the low snr regime is derived closely matching empirical results from spectrum sensing simulation experiments

optimally distinguishable distributions a new approach to composite hypothesis testing with applications to the classical linear model the newest approach to composite hypothesis testing proposed by rissanen relies on the concept of optimally distinguishable distributions odd the method is promising but so far it has only been applied to a few simple examples we derive the odd detector for the classical linear model in this framework we provide answers to the following problems that have not been previously investigated in the literature i the relationship between odd and the widely used generalized likelihood ratio test glrt ii the connection between odd and the information theoretic criteria applied in model selection we point out the strengths and the weaknesses of the odd method in detecting subspace signals in broadband noise effects of the subspace interference are also evaluated

cfar detection strategies for distributed targets under conic constraints in this paper we deal with the problem of adaptive detection of mismatched mainlobe targets and or sidelobe interfering signals that are distributed in range to this end we investigate the impact of modeling the actual useful signal as a vector belonging to a proper cone with axis the nominal steering vector as a means to improve the robustness of the decision rule in presence of mainlobe targets similarly in order to improve the rejection capabilities of the decision rule in presence of sidelobe interferers we study the effects of replacing the usual noise only hypothesis with a noise plus interferers hypothesis where interferers belong to the complement of a cone with axis the nominal steering vector at the design stage we resort to the two step glrt based design procedure to this end we assume that a set of training data is available namely data free of signal components but sharing the same gaussian distribution of the noise in the cells under test remarkably proposed detectors possess the cfar property under the noise only hypothesis the performance assessment conducted by monte carlo simulation is aimed at assessing the effectiveness of proposed solutions also in comparison to existing ones

global regularity for a class of quasi linear local and nonlocal elliptic equations on extension domains abstract we consider the solvability of quasi linear elliptic equations with either local or nonlocal neumann robin or wentzell boundary conditions defined in the generalized sense on a bounded w 1 p extension domain whose boundary is an upper d set for an appropriate d 0 then we extend the fine regularity theory for weak solutions of the elliptic equations with the above boundary conditions known for bounded lipschitz domains to bounded w 1 p extension domains whose boundaries are upper d sets by showing that such weak solutions are globally holder continuous consequently we generalize substantially the class of bounded domains where weak solutions of boundary value problems of type neumann robin or wentzell may be uniformly continuous up to the boundary

clutter invariant atr one of the central problems in automated target recognition is to accommodate the infinite variety of clutter in real military environments the principle focus of our paper is on the construction of metric spaces where the metric measures the distance between objects of interest invariant to the infinite variety of clutter such metrics are formulated using second order random field models our results indicate that this approach significantly improves detection classification rates of targets in clutter

universal manifold embedding for geometrically deformed functions assume we have a set of observations for example images of different objects each undergoing a different geometric deformation yet all the deformations belong to the same family as a result of the action of these deformations the set of different observations on each object is generally a manifold in the ambient space of observations in this paper we show that in those cases where the set of deformations admits a finite dimensional representation there is a mapping from the space of observations to a low dimensional linear space the manifold corresponding to each object is mapped to a distinct linear subspace of euclidean space the dimension of the subspace is the same as that of the manifold this mapping which we call universal manifold embedding enables the estimation of geometric deformations using the classical linear theory the universal manifold embedding further enables the representation of the object classification and detection problems in a linear subspace matching framework the embedding of the space of observations depends on the deformation model and is independent of the specific observed object hence it is universal we study two cases of this embedding that of elastic deformations of 1 d signals and the case of affine deformations of n dimensional signals

compressed sensing with basis mismatch performance bounds and sparse based estimator compressed sensing cs is a promising emerging domain that outperforms the classical limit of the shannon sampling theory if the measurement vector can be approximated as the linear combination of few basis vectors extracted from a redundant dictionary matrix unfortunately in realistic scenario the knowledge of this basis or equivalently of the entire dictionary is often uncertain i e corrupted by a basis mismatch bm error the consequence of the bm problem is that the estimation accuracy in terms of bayesian mean square error bmse of popular sparse based estimators collapses even if the support is perfectly estimated and in the high signal to noise ratio snr regime this saturation effect considerably limits the effective viability of these estimation schemes in the first part of this work the bayesian cramer rao bound bcrb is derived for cs model with unstructured bm we show that the bcrb foresees the saturation effect of the estimation accuracy of standard sparse based estimators as for instance the omp cosamp or the bp in addition we provide an approximation of this bmse threshold in the second part and in the context of the structured bm model a new estimation scheme called bias correction estimator bice is proposed and its statistical properties are studied the bice acts as a post processing estimation layer for any sparse based estimator and mitigates considerably the bm degradation finally the bice i is a blind algorithm i e is unaware of the uncorrupted dictionary matrix ii is generic since it can be associated to any sparse based estimator iii is fast i e the additional computational cost remains low and iv has good statistical properties to illustrate our results and propositions the bice is applied in the challenging context of the compressive sampling of non bandlimited impulsive signals

variational problems with two phases and their free boundaries the problem of minimizing vu 2 q2 x 2 v dx in an appropriate class of functions v is considered here q x 0 and a2 t x2 if v 0 any minimizer u is harmonic in u 0 and vu 2 has a jump a2 x 22 across the free boundary u 0 regularity and various properties are established for the minimizer u and for the free boundary introduction in this paper we consider the problem of minimizing j v f vv 2 q2 x x2 v dx vgk where q2 x 0 a22 ifu 0 and x2 u is lower semicontinuous at v 0 it is assumed that a2 0 and a a2 a22 0 the class k consists of all functions v in l loc s2 with vu g l2 i2 such that v u on a given open subset s of 3i2 and s is a domain in r the analogous problem for functions in k v k v 0 a e was studied in 1 in that paper it was proved that any local minimizer of j v in k is lipschitz continuous and if n 2 the free boundary 8 w 0 is analytic if q x is analytic the present variational problem is motivated by applications to the now of two liquids in models of jets and cavities these applications will be studied in other forthcoming papers 5 6 the present work is aimed at extending results of 1 in particular we shall establish nondegeneracy theorems the lipschitz continuity of the solution and some properties of the free boundary for n 2 the free boundary is proved to be continuously differentiable a new and rather powerful tool introduced in this paper is the monotonicity formula lemma 5 1 asserting that for a minimizer u if u x0 0 then

performance analysis of transient detectors based on a class of linear data transforms the problem of detecting short duration nonstationary signals which are commonly referred to as transients is addressed transients are characterized by a signal model containing some unknown parameters and by a model mismatch representing the difference between the model and the actual signal both linear and nonlinear signal models are considered the transients are assumed to undergo a noninvertible linear transformation prior to the application of the detection algorithm examples of such transforms include the short time fourier transform the gabor transform and the wavelet transform closed form expressions are derived for the worst case detection performance for all possible mismatch signals of a given energy these expressions make it possible to evaluate and compare the performance of various transient detection algorithms for both single channel and multichannel data numerical examples comparing the performance of detectors based on the wavelet transform and the short time fourier transform are presented

complex elliptically symmetric distributions survey new results and applications complex elliptically symmetric ces distributions have been widely used in various engineering applications for which non gaussian models are needed in this overview circular ces distributions are surveyed some new results are derived and their applications e g in radar and array signal processing are discussed and illustrated with theoretical examples simulations and analysis of real radar data the maximum likelihood ml estimator of the scatter matrix parameter is derived and general conditions for its existence and uniqueness and for convergence of the iterative fixed point algorithm are established specific ml estimators for several ces distributions that are widely used in the signal processing literature are discussed in depth including the complex t distribution k distribution the generalized gaussian distribution and the closely related angular central gaussian distribution a generalization of ml estimators the m estimators of the scatter matrix are also discussed and asymptotic analysis is provided applications of ces distributions and the adaptive signal processors based on ml and m estimators of the scatter matrix are illustrated in radar detection problems and in array signal processing applications for direction of arrival doa estimation and beamforming furthermore experimental validation of the usefulness of ces distributions for modelling real radar data is given

on element by element schur complement approximations abstract we discuss a methodology to construct sparse approximations of schur complements of two by two block matrices arising in finite element discretizations of partial differential equations earlier results from 2 are extended to more general symmetric positive definite matrices of two by two block form the applicability of the method for general symmetric and nonsymmetric matrices is analysed the paper demonstrates the applicability of the presented method providing extensive numerical experiments

spatial spectrum estimation in a location sector multiple narrowband source localization using arbitrarily configured arrays and spatial spectrum estimation is considered a new eigenspace based approach which uses projections onto a particular vector or vector set in the estimated noise only subspace is described several closest vector estimators are developed by using different measures of closeness first closest is a novel full dimensional element space approach to spatial spectrum estimation which has important performance advantages relative to pertinent established spatial spectrum estimators it incorporates a priori knowledge of the array manifold over a location sector of interest to provide snr spectral resolution thresholds which are lower than those of min norm for some arrays substantially lower second relationships between the closest approach and several established approaches to spatial spectrum estimation are established for a linear equispaced array min norm is shown to be a special case of the closest approach one which is based on projection onto a noise only subspace vector which is close to the array manifold over the entire field of view

an inhomogeneous transference principle and diophantine approximation in a landmark paper 29 d y kleinbock and g a margulis established the fundamental baker sprindzuk conjecture on homogeneous diophantine approximation on manifolds subsequently there has been dramatic progress in this area of research however the techniques developed to date do not seem to be applicable to inhomogeneous approximation consequently the theory of inhomogeneous diophantine approximation on manifolds remains essentially non existent in this paper we develop an approach that enables us to transfer homogeneous statements to inhomogeneous ones this is rather surprising as the inhomogeneous theory contains the homogeneous theory and so is more general as a consequence we establish the inhomogeneous analogue of the baker sprindzuk conjecture furthermore we prove a complete inhomogeneous version of the profound theorem of kleinbock lindenstrauss weiss 27 on the extremality of friendly measures the results obtained in this paper constitute the first step towards developing a coherent inhomogeneous theory for manifolds in line with the homogeneous theory epsrc advanced research fellow grant ep c54076x 1 research supported by epsrc grant ep e061613 1 and intas grant 03 51 5070

constructive updating downdating of oblique projectors a generalization of the gram schmidt process a generalization of the gram schmidt procedure is achieved by providing equations for updating and downdating oblique projectors the work is motivated by the problem of adaptive signal representation outside the orthogonal basis setting the proposed techniques are shown to be relevant to the problem of discriminating signals produced by different phenomena when the order of the signal model needs to be adjusted

a cfar adaptive subspace detector for second order gaussian signals we study the problem of detecting subspace signals described by the second order gaussian sog model in the presence of noise whose covariance structure and level are both unknown such a detection problem is often called gauss gauss problem in that both the signal and the noise are assumed to have gaussian distributions we propose adaptive detectors for the sog model signals based on a single observation and multiple observations with a single observation the detector can be derived in a manner similar to that of the generalized likelihood ratio test glrt but the unknown covariance structure is replaced by sample covariance matrix based on training data the proposed detectors are constant false alarm rate cfar detectors as a comparison we also derive adaptive detectors for the first order gaussian fog model based on multiple observations under the same noise condition as for the sog model with a single observation the seemingly ad hoc cfar detector for the sog model is a true glrt in that it has the same form as the glrt cfar detector for the fog model we give an approximate closed form of the probability of detection and false alarm in this case furthermore we study the proposed cfar detectors and compute the performance curves

detection power estimation efficiency and predictability in event related fmri experimental designs for event related functional magnetic resonance imaging can be characterized by both their detection power a measure of the ability to detect an activation and their estimation efficiency a measure of the ability to estimate the shape of the hemodynamic response randomized designs offer maximum estimation efficiency but poor detection power while block designs offer good detection power at the cost of minimum estimation efficiency periodic single trial designs are poor by both criteria we present here a theoretical model of the relation between estimation efficiency and detection power and show that the observed trade off between efficiency and power is fundamental using the model we explore the properties of semirandom designs that offer intermediate trade offs between efficiency and power these designs can simultaneously achieve the estimation efficiency of randomized designs and the detection power of block designs at the cost of increasing the length of an experiment by less than a factor of 2 experimental designs can also be characterized by their predictability a measure of the ability to circumvent confounds such as habituation and anticipation we examine the relation between detection power estimation efficiency and predictability and show that small increases in predictability can offer significant gains in detection power with only a minor decrease in estimation efficiency

oblique projections for direction of arrival estimation with prior knowledge estimation of directions of arrival doa is an important problem in various applications and a priori knowledge on the source location is sometimes available to exploit this information standard methods are based on the orthogonal projection of the steering manifold onto the noise subspace associated with the a priori known doa in this paper we derive and analyze the cramer rao bound associated with this model and in particular we point out the limitations of this approach when the known and unknown doa are closely spaced and the associated sources are uncorrelated block diagonal source covariance to fill this need we propose to integrate a priori known locations of several sources into the music algorithm based on oblique projection of the steering manifold finally we show that the proposed approach is able to almost completely cancel the influence of the known doa on the unknown ones for block diagonal source covariance and for sufficient signal to noise ratio snr

adaptive detection and estimation in the presence of useful signal and interference mismatches this paper considers adaptive detection and estimation in the presence of useful signal and interference mismatches we assume a homogeneous environment where the random disturbance components from the primary and secondary data share the same covariance matrix moreover the data under test contains a deterministic interference vector in addition to the possible useful signal we focus on the situation where an energy fraction of both the useful signal and the deterministic interference may lie outside their nominal subspaces conical uncertainty model under these conditions we devise a procedure for the computation of the joint maximum likelihood ml estimators of the useful signal and interference vectors resorting to a suitable rank one decomposition of a semidefinite program sdp problem optimal solution hence we use the aforementioned estimators for the synthesis of adaptive receivers based on different generalized likelihood ratio test glrt criteria at the analysis stage we assess the performance of the new detectors in comparison with some decision rules available in open literature

nonlinear non extensive approach for identification of structured information the problem of separating structured information representing phenomena of differing natures is considered a structure is assumed to be independent of the others if can be represented in a complementary subspace when the concomitant subspaces are well separated the problem is readily solvable by a linear technique otherwise the linear approach fails to correctly discriminate the required information hence a non extensive approach is proposed the resulting nonlinear technique is shown to be suitable for dealing with cases that cannot be tackled by the linear one

time frequency formulation design and implementation of time varying optimal filters for signal estimation this paper presents a time frequency framework for optimal linear filters signal estimators in nonstationary environments we develop time frequency formulations for the optimal linear filter time varying wiener filter and the optimal linear time varying filter under a projection side constraint these time frequency formulations extend the simple and intuitive spectral representations that are valid in the stationary case to the practically important case of underspread nonstationary processes furthermore we propose an approximate time frequency design of both optimal filters and we present bounds that show that for underspread processes the time frequency designed filters are nearly optimal we also introduce extended filter design schemes using a weighted error criterion and we discuss an efficient time frequency implementation of optimal filters using multiwindow short time fourier transforms our theoretical results are illustrated by numerical simulations

adaptive double subspace signal detection in gaussian background part ii partially homogeneous environments in this part of the paper we continue to study the problem of detecting a double subspace signal in gaussian noise precisely we address the detection problem in partially homogeneous environments where the primary and secondary data share the same covariance matrix up to an unknown scaling factor we derive the generalized likelihood ratio test glrt rao test wald test and their two step versions we also introduce three spectral norm tests snts all these detectors possess the constant false alarm rate cfar property moreover various kinds of special cases of these detectors are given at the stage of performance evaluation we consider two cases one is the case of no signal mismatch the other is more general namely the case of signal mismatch including the column space signal mismatch and row space signal mismatch

minimum ber block based precoder design for zero forcing equalization an oblique projection framework this work devises a minimum bit error rate ber block based precoder used in block transmission systems with the proposed cascaded zero forcing zf equalizer the study framework is developed as follows for a block based precoder a received signal model is formulated for the two redundancy schemes viz trailing zeros tz and cyclic prefix cp by exploiting the property of oblique projection a cascaded equalizer for block transmission systems is proposed and implemented with a scheme in which the inter block interference ibi is completely eliminated by the oblique projection and followed by a matrix degree of freedom for inter symbol interference isi equalization with the available channel state information at the transmitter side the matrix for isi equalization of the cascaded equalizer is utilized to design an optimum block based precoder such that the ber is minimized subject to the isi free and the transmission power constraints accordingly the cascaded equalizer with the isi free constraint yields a cascaded zf equalizer theoretical derivations and simulation results confirm that the proposed framework not only retains identical ber performance to previous works for cases with sufficient redundancy but also allows their results to be extended to the cases of insufficient redundancy

a quasi linear neumann problem of ambrosetti prodi type on extension domains abstract let r n be a bounded domain with the extension property whose boundary is an upper d set with respect to a measure for n 2 and d n p n we investigate the solvability of the ambrosetti prodi problem for the p laplace operator p with neumann boundary conditions using a priori estimates regularity theory a sub supersolution method and the leray schauder degree theory we obtain a necessary condition for the non existence of solutions in the weak sense the existence of at least one minimal solution and the existence of at least two distinct solutions moreover we establish global holder continuity for weak solutions of the neumann problem of ambrosetti prodi type on a large class of bad domain extending the solvability of this type of elliptic problem for the first time to a wide class of non smooth domains

convergence analysis of finite alphabet beamformers for digital cochannel signals in this paper we examine the convergence behavior of finite alphabet fa beamformers the two most popular implementations of fa beamformers for digital communication signals are the iterative least squares with projection ilsp and the minimum mean square error mmse beamformer to facilitate the analysis for the binary communications case we derive closed form expressions for the mean weight vector signal to noise ratio and signal to interference ratio for both the ilsp and mmse beamformers in terms of the bit error rate ber performance at each iteration next we generalize the analysis for the m ary pulse amplitude modulation and m ary phase shift keying cases we show that both ilsp and mmse beamformers have previously unreported bias terms in the array response vectors which are functions of the ber for each iteration furthermore as the ber becomes arbitrarily small we show that our solutions converge to the well known asymptotic expressions widely published in the literature next we provide a geometric interpretation of the effects of the noise bias vector in terms of angles between subspaces based on our analysis we were able to develop necessary and sufficient conditions for convergence in the mean we conclude with monte carlo simulations to validate our analysis

efficient application of music algorithm under the coexistence of far field and near field sources this correspondence is concerned with source localization and classification for scenarios where both the far field and near field narrowband sources may coexist we propose an efficient music based solution that requires neither a multidimensional search nor high order statistics hos we also derive the stochastic cramer rao bound crb for the problem under consideration the performance of the proposed method is compared with an existing method and with the crb

quantitative recurrence properties in conformal iterated function systems abstract we consider a quantitative version of poincare s recurrence theorem in a conformal iterated function system let i i be a conformal iterated function system on 0 1 d with a countable index set denote by j the attractor of let f 0 1 d r be a positive function s n f x be the sum f x f w 1 1 x f w 1 w n 1 1 x analogous to an ergodic sum and consider the set of points for which the inequality x w 1 w n 0 1 d x w 1 w n 1 x e s n f x is realized for infinitely many n n with w 1 w n n the set above contains the points x whose orbit returns very close to x infinitely many times with the quality of approximation depending on the time n and the point x this can be viewed as a quantitative version of poincare s recurrence theorem it is shown that its hausdorff dimension is the solution to some pressure function the setting considered in this paper includes the quantitative recurrence properties in the dynamical systems of b adic expansions continued fraction expansion as well as some dynamical systems defined on fractal sets applying the main result to diophantine approximation gives a partial answer to a question by k mahler

quantitative stability for the first dirichlet eigenvalue in reifenberg flat domains in rn abstract in this paper we prove that if and are close enough for the complementary hausdorff distance and their boundaries satisfy some geometrical and topological conditions then 1 1 c n where 1 resp 1 is the first dirichlet eigenvalue of the laplacian in resp and is the lebesgue measure of the symmetric difference here the constant 1 could be taken arbitrary close to 1 but strictly less and c is a constant depending on a lot of parameters including dimension n and some geometric properties of the domains

nonlinear and nonideal sampling theory and methods we study a sampling setup where a continuous time signal is mapped by a memoryless invertible and nonlinear transformation and then sampled in a nonideal manner such scenarios appear for example in acquisition systems where a sensor introduces static nonlinearity before the signal is sampled by a practical analog to digital converter we develop the theory and a concrete algorithm to perfectly recover a signal within a subspace from its nonlinear and nonideal samples three alternative formulations of the algorithm are described that provide different insights into the structure of the solution a series of oblique projections approximated projections onto convex sets and quasi newton iterations using classical analysis techniques of descent based methods and recent results on frame perturbation theory we prove convergence of our algorithm to the true input signal we demonstrate our method by simulations and explain the applicability of our theory to wiener hammerstein analog to digital hybrid systems

estimation of parameters of exponentially damped sinusoids using fast maximum likelihood estimation with application to nmr spectroscopy data we present fast maximum likelihood fml estimation of parameters of multiple exponentially damped sinusoids the fml algorithm was motivated by the desire to analyze data that have many closely spaced components such as the nmr spectroscopy data of human blood plasma the computational efficiency of fml lies in reducing the multidimensional search involved in ml estimation into multiple 1 d searches this is achieved by using our knowledge of the shape of the compressed likelihood function clf in the parameter space the proposed fml algorithm is an iterative method that decomposes the original data into its constituent signal components and estimates the parameters of the individual components efficiently using our knowledge of the shape of the clf the other striking features of the proposed algorithm are that it provides procedures for initialization has a fast converging iteration stage and makes use of the information extracted in preliminary iterations to segment the data suitably to increase the effective signal to noise ratio snr the computational complexity and the performance of the proposed algorithm are compared with other existing methods such as those based on linear prediction kiss iqml alternating projections ap and expectation maximization em

orthogonal exactly periodic subspace decomposition the detection and estimation of machine vibration multiperiodic signals of unknown periods in white gaussian noise is investigated new estimates for the subsignals signals making up the received signal and their periods are derived using an orthogonal subspace decomposition approach the concept of exactly periodic signals is introduced this in turn simplifies and enhances the understanding of periodic signals

an oblique subspace projection approach for mixed pixel classification in hyperspectral images abstract recently oblique projection has been studied for many applications in signal processing in this paper the concept of oblique projection is applied to develop an algorithm for hyperspectral image classification compared with the orthogonal subspace projector osp it can be found that osp is a priori classifier but the oblique subspace projection classifier will be referred to a posterior as a consequence the oblique subspace projector obp can be thought of as a generalized classifier including osp furthermore the estimation error from the obp can be evaluated by applying the neyman pearson detection theory to the corresponding receiver operating characteristic roc curve so the accuracy of the classification can be calculated thereafter finally some computer simulations using real airborne visible infrared image spectrometer aviris data are accomplished to justify and compare the effectiveness of the above algorithms

bi orthonormal polynomial basis function framework with applications in system identification numerical aspects are of central importance in identification and control many computations in these fields involve approximations using polynomial or rational functions that are obtained using orthogonal or oblique projections the aim of this paper is to develop a new and general theoretical framework to solve a large class of relevant problems the proposed method is built on the introduction of bi orthonormal polynomials with respect to a data dependent bi linear form this bi linear form generalises the conventional inner product and allows for asymmetric and indefinite problems the proposed approach is shown to lead to optimal numerical conditioning kappa 1 in a recent frequency domain instrumental variable system identification algorithm in comparison it is shown that these recent algorithms exhibit extremely poor numerical properties when solved using traditional approaches

robust multidimensional matched subspace classifiers based on weighted least squares we propose and design two classes of robust subspace classifiers for classification of multidimensional signals our classifiers are based on robust m estimators and the least median of squares principle and we show that they may be unified as iterated reweighted oblique subspace classifiers the performance of the proposed classifiers are demonstrated by two examples noncoherent detection of space time frequency shift keying signals and shape classification of partially occluded two dimensional 2 d objects in both cases the proposed robust subspace classifiers outperform the conventional subspace classifiers

adaptive subspace detectors we use the theory of generalized likelihood ratio tests glrts to adapt the matched subspace detectors msds of scharf 1991 and of scharf and frielander 1994 to unknown noise covariance matrices in so doing we produce adaptive msds that may be applied to signal detection for radar sonar and data communication we call the resulting detectors adaptive subspace detectors asds these include kelly s 1987 glrt and the adaptive cosine estimator ace of kaurt and scharh see ibid vol 47 p 2538 41 1999 and of scharf and mcwhorter see proc 30th asilomar conf signals syst comput pacific grove ca 1996 for scenarios in which the scaling of the test data may deviate from that of the training data we then present a unified analysis of the statistical behavior of the entire class of asds obtaining statistically identical decompositions in which each asd is simply decomposed into the nonadaptive matched filter the nonadaptive cosine or t statistic and three other statistically independent random variables that account for the performance degrading effects of limited training data

constrained maximum likelihood solution of linear equations the total least squares tls is used to solve a set of inconsistent linear equations ax spl ap y when there are errors not only in the observations y but in the modeling matrix a as well the tls seeks the least squares perturbation of both y and a that leads to a consistent set of equations when y and a have a defined structure we usually want the perturbations to also have this structure unfortunately standard tls does not generally preserve the perturbation structure so other methods are required we examine this problem using a probabilistic framework and derive an approach to determining the most probable set of perturbations given an a priori perturbation probability density function while our approach is applicable to both gaussian and non gaussian distributions we show in the uncorrelated gaussian case that our method is equivalent to several existing methods our approach is therefore more general and can be applied to a wider variety of signal processing problems

asymptotically uniformly minimax detection and isolation in network monitoring this paper addresses the problem of multiple hypothesis testing detection and isolation of mean vectors in the case of gaussian linear model with nuisance parameters an invariant constrained asymptotically uniformly minimax test is proposed to solve this problem the invariance of the test with respect to the nuisance parameters is obtained by projecting the measurement vector onto a subspace of invariant statistics the proposed test minimizes the maximum probability of false isolation uniformly with respect to the lower bounded projections of the vectors defining the alternative hypotheses this minimization is achieved provided that the signal to noise ratio snr becomes arbitrary large the asymptotic probabilities of false alarm and false isolations and their nonasymptotic bounds are analytically established to illustrate the practical relevance of the proposed test it is applied to the problem of network monitoring it is aimed to detect and isolate volume anomalies in network origin destination od traffic demands from simple link load measurements the ambient traffic i e the od traffic matrix corresponding to the nonanomalous network state is unknown and considered as a nuisance parameter an original linear parsimonious model of the ambient traffic which is indispensable for the proposed asymptotically optimal test is designed the statistical performances of this approach to detect and isolate the anomalies are evaluated by using real data from the abilene network

blind adaptation of zero forcing projections and oblique pseudo inverses for subspace detection and estimation when interference dominates noise in much of modern radar sonar and wireless communication it seems more reasonable to model measurement noise as subspace interference plus broadband noise than as colored noise this observation leads naturally to a variety of detection and estimation problems in the linear statistical model to solve these problems one requires oblique pseudo inverses oblique projections and zero forcing orthogonal projections the problem is that these operators depend on knowledge of signal and interference subspaces and this information is often not at hand more typically the signal subspace is known but the interference subspace is unknown we prove a theorem that allows these operators to be estimated directly from experimental data without knowledge of the interference subspace as a byproduct the theorem shows how signal subspace covariance may be estimated when the strict identities of the theorem are approximated then the detectors estimators and beamformers of this paper take on the form of adaptive subspace estimators detectors and capon beamformers all of which are reduced in rank the fundamental operator turns out to be a certain reduced rank wiener filter which we clarify in the course of our derivations the results of this paper form a foundation for the rapid adaptation of receivers that are then used for detection and estimation they may be applied to detection and estimation in radar sonar and hyperspectral imaging and to data decoding in multiuser communication receivers

complexity reduction for sign configurations through the kp ii equation and its information theoretic aspects we provide a combinatorial setting to explore the information content associated with the fulfillment of the kadomtsev petviashvili kp ii equation we start from a special family of solutions of kp ii namely tau functions of wronskian type a solution in this class can be expressed as a sum of exponentials and we look at combinations of signs signatures for the nonvanishing terms in this sum we prove a characterization of the signatures that return another solution of the kp ii equation they can be represented as choices of signs for columns and rows of a coefficient matrix so we recover a function satisfying the whole kp hierarchy from this single constraint the redundancy of this representation for different choices of the initial solution is investigated enumerative information theoretic and geometric aspects of this construction are discussed we provide a combinatorial setting to explore the information content associated with the fulfillment of the kadomtsev petviashvili kp ii equation we start from a special family of solutions of kp ii namely tau functions of wronskian type a solution in this class can be expressed as a sum of exponentials and we look at combinations of signs signatures for the nonvanishing terms in this sum we prove a characterization of the signatures that return another solution of the kp ii equation they can be represented as choices of signs for columns and rows of a coefficient matrix so we recover a function satisfying the whole kp hierarchy from this single constraint the redundancy of this representation for different choices of the initial solution is investigated enumerative information theoretic and geometric aspects of this construction are discussed

two dimensional direction estimation for a mixture of noncoherent and coherent signals this paper deals with the two dimensional 2 d direction of arrival doa estimation of a mixture of noncoherent including uncorrelated and partially correlated and coherent i e fully correlated narrowband signals impinging on a planar sensor array composed of two parallel uniform linear arrays ulas an oblique projection based approach for 2 d direction estimation opade is proposed by using some cross correlations between the received array data in the proposed opade the oblique projection is utilized to isolate the coherent signals from the noncoherent ones and the effect of additive noise is alleviated while the computationally intensive eigendecomposition is avoided and the estimated elevation and azimuth angles are paired automatically further an iterative alternating scheme is presented to improve the estimation accuracy of the oblique projector and hence that of the doas of coherent signals the cramer rao lower bound crb for the mixture of noncoherent and coherent signals is also derived explicitly where the prior knowledge of the signal correlation is incorporated into the 2 d doa estimation of noncoherent signals finally the effectiveness of the opade and the theoretical analysis are substantiated through numerical examples

geometry and radiometry invariant matched manifold detection consider a set of deformable objects undergoing geometric and radiometric transformations as a result of the action of these transformations the set of different realizations of each object is generally a manifold in the space of observations assuming the geometric deformations an object undergoes belong to some finite dimensional family it has been shown that the universal manifold embedding ume provides a set of nonlinear operators that universally maps each of the different manifolds where each manifold is generated by the set all of possible appearances of a single object into a distinct linear subspace of an euclidean space in this paper we generalize this framework to the case where the observed object undergoes both an affine geometric transformation and a monotonic radiometric transformation and present a novel framework for the detection and recognition of the deformable objects applying to each of the observations an operator that makes it invariant to monotonic amplitude transformations but is geometry covariant with the affine transformation the set of all possible observations on that object is mapped by the ume into a single linear subspace invariant with respect to both the geometric and radiometric transformations the embedding of the space of observations is independent of the specific observed object hence it is universal the invariant representation of the object is the basis of a matched manifold detection and tracking framework of objects that undergo complex geometric and radiometric deformations the observed surface is tessellated into a set of tiles such that the deformation of each one is well approximated by an affine geometric transformation and a monotonic transformation of the measured intensities since each tile is mapped by the radiometry invariant ume to a distinct linear subspace the detection and tracking problems are solved by evaluating distances between linear subspaces classification in this context becomes a problem of determining which labeled subspace in a grassmannian is closest to a subspace in the same grassmannian where the latter has been generated by radiometry invariant ume from an unlabeled observation

decision feedback multiuser detection a systematic approach a systematic approach to decision feedback multiuser detection is introduced for the joint detection of symbols of k simultaneously transmitting users of a synchronous correlated waveform multiple access cwma channel with gaussian noise a new performance criterion called symmetric energy is defined which is a low noise indicator of the joint error rate that at least one user is detected erroneously even the best linear detectors can perform poorly in terms of symmetric energy compared to the maximum likelihood detector a general class of decision feedback detectors dfds is defined with o k implementational complexity per user the symmetric energy of arbitrary dfd and bounds on their asymptotic effective energy aee performance are obtained along with an exact bit error rate and aee analysis for the decorrelating dfd the optimum dfd that maximizes symmetric energy is obtained each one of the k optimum decorrelating and conventional dfds that correspond to the k orders in which the users can be detected are shown to outperform the linear optimum decorrelating and conventional detectors respectively in terms of symmetric energy moreover algorithms are obtained for determining the choice of order of detection for the three dfds which guarantee that they uniformly user wise outperform their linear counterparts in addition to optimality in symmetric energy it is also shown that under certain conditions the optimum dfd achieves the aee performance of the exponentially complex maximum likelihood detector for all users simultaneously none of the results of this paper make the perfect feedback assumption the implications of our work on power control for multiuser detection are also discussed

harmonic measure on locally flat domains we will review work with tatiana toro yielding a characterizati on of those domains for which the harmonic measure has a density whose logarithm has vanishing mean oscillation

signal processing applications of oblique projection operators oblique projection operators are used to project measurements onto a low rank subspace along a direction that is oblique to the subspace they may be used to enhance signals while nulling interferences in the paper the authors give several basic results for oblique projections including formulas for constructing oblique projections with desired range and null space they analyze the algebra and geometry of oblique projections in order to understand their properties they then show how oblique projections can be used to separate signals from structured noise such as impulse noise damped or undamped interfering sinusoids such as power line interference and narrow band noise in some of the problems addressed the oblique projection provides an alternative way to implement an already known solution expressing these solutions as oblique projections brings geometrical insight to the study of the solution the geometry of oblique projections enables one to compute performance in terms of angles between signal and noise subspaces as a special case of removing impulse noise the authors can use oblique projections to interpolate missing data samples in array processing oblique projections can be used to simultaneously steer beams and nulls in communications oblique projections can be used to remove intersymbol interference

free boundary regularity for harmonic measures and poisson kernels one of the basic aims of this paper is to study the relationship between the geometry of hypersurface like subsets of euclidean space and the properties of the measures they support in this context we show that certain doubling properties of a measure determine the geometry of its support a radon measure is said to be doubling with constant c if c times the measure of the ball of radius r centered on the support is greater than the measure of the ball of radius 2r and the same center we prove that if the doubling constant of a measure on r n 1 is close to the doubling constant of the ndimensional lebesgue measure then its support is well approximated by ndimensional a ne spaces provided that the support is relatively at to start with primarily we consider sets which are boundaries of domains in r n 1 the n dimensional hausdorfi measure may not be deflned on the boundary of a domain in r n 1 thus we turn our attention to the harmonic measure which is well behaved under minor assumptions see section 3 we obtain a new characterization of locally at domains in terms of the doubling properties of their harmonic measure see section 3 along these lines we investigate how the weak regularity of the poisson kernel of a domain determines the geometry of its boundary sections 5 and 6 pursue this goal as in alt and cafiarelli s work see ac c1 c2 and also jerison s j in both cases the goal is to prove that under the appropriate technical conditions at at points of the boundary the oscillation of the poisson kernel controls the oscillation of the unit normal vector the difierence between our work and the work in ac is that we measure the oscillation in an integral sense bmo estimates

a deflation procedure for subspace decomposition a general deflation framework is described for the separation of a desired signal subspace of arbitrary dimensions from noisy multichannel observations the method simultaneously uses single and multichannel priors to split the desired and undesired subspaces even for coplanar intersecting subspaces by appropriate use of signal priors it can even extract signals from degenerate mixtures of signals and noise recorded from a few number of channels in low snr scenarios without the reduction of the data dimensions as a case study the performance of the proposed method is studied for the problem of extracting fetal cardiac signals from maternal abdominal recordings over simulated and real data a second case study deals with the degenerate problem of extracting diaphragmatic electromyogram from electrocardiograph artifacts a provisional patent application based on this method has been filed

camera model identification based on the heteroscedastic noise model the goal of this paper is to design a statistical test for the camera model identification problem the approach is based on the heteroscedastic noise model which more accurately describes a natural raw image this model is characterized by only two parameters which are considered as unique fingerprint to identify camera models the camera model identification problem is cast in the framework of hypothesis testing theory in an ideal context where all model parameters are perfectly known the likelihood ratio test lrt is presented and its performances are theoretically established for a practical use two generalized lrts are designed to deal with unknown model parameters so that they can meet a prescribed false alarm probability while ensuring a high detection performance numerical results on simulated images and real natural raw images highlight the relevance of the proposed approach

matched subspace detectors we formulate a general class of problems for detecting subspace signals in subspace interference and broadband noise we derive the generalized likelihood ratio glr for each problem in the class we then establish the invariances for the glr and argue that these are the natural invariances for the problem in each case the glr is a maximal invariant statistic and the distribution of the maximal invariant statistic is monotone this means that the glr test glrt is the uniformly most powerful invariant detector we illustrate the utility of this finding by solving a number of problems for detecting subspace signals in subspace interference and broadband noise in each case we give the distribution for the detector and compute performance curves

spectral stability estimates for the dirichlet and neumann laplacian in rough domains abstract in this paper we establish new quantitative stability estimates with respect to domain perturbations for all the eigenvalues of both the neumann and the dirichlet laplacian our main results follow from an abstract lemma stating that it is actually sufficient to provide an estimate on suitable projection operators whereas this lemma could be applied under different regularity assumptions on the domain here we use it to estimate the spectrum in lipschitz and in so called reifenberg flat domains our argument also relies on suitable extension techniques and on an estimate on the decay of the eigenfunctions at the boundary which could be interpreted as a boundary regularity result

subspace partitioning for target detection and identification detection of a given target or set of targets from observed data is a problem countered in many applications regardless of the algorithm selected detection performance can be severely degraded when the subspace defined by the target data set is singular or ill conditioned high correlations between target components and their linear combinations lead to false positives and misidentifications especially for subspace based detectors in this paper we propose a subspace partitioning scheme that allows for detection to be performed in a number of better conditioned subspaces instead of the original subspace the proposed technique is applied to raman spectroscopic data analysis through both simulation and experimental results we demonstrate the improvement in the overall detection performance when using the proposed subspace partitioning scheme in conjunction with several subspace detection methods that are commonly used in practice

widely linear equalization and blind channel identification for interference contaminated multicarrier systems this work addresses the problem of designing efficient detection techniques for multicarrier transmission systems operating in the presence of narrowband interference nbi in this case conventional linear receivers such as the zero forcing zf or the minimum mean square error mmse ones usually perform poorly since they are not capable of suppressing satisfactorily the nbi to synthesize interference resistant detection algorithms we resort to widely linear wl filtering which allows one to exploit the noncircularity property of the desired signal constellation by jointly processing the received signal and its complex conjugate version in particular we synthesize new wl zf receivers for multicarrier systems which mitigate in the minimum output energy moe sense the nbi contribution at the receiver output without requiring knowledge of the nbi statistics by exploiting the noncircularity property we also propose a new subspace based blind channel identification algorithm and derive the channel identifiability condition blind identification can be performed satisfactorily also in the presence of nbi requiring only an approximate rank determination of the nbi autocorrelation matrix the performance analysis shows that the proposed moe wl zf receiver even when implemented blindly assures a substantial improvement over the conventional linear zf and mmse ones particularly when the nbi bandwidth is very small in comparison with the intercarrier spacing and the nbi is not exactly located on a subcarrier

prewhitening for rank deficient noise in subspace methods for noise reduction a fundamental issue in connection with subspace methods for noise reduction is that the covariance matrix for the noise is required to have full rank in order for the prewhitening step to be defined however there are important cases where this requirement is not fulfilled e g when the noise has narrowband characteristics or in the case of tonal noise we extend the concept of prewhitening to include the case when the noise covariance matrix is rank deficient using a weighted pseudoinverse and the quotient singular value decomposition and we show how to formulate a general rank reduction algorithm that works also for rank deficient noise we also demonstrate how to formulate this algorithm by means of a quotient ulv decomposition which allows for faster computation and updating finally we apply our algorithm to a problem involving a speech signal contaminated by narrowband noise

the ergodic theory of shrinking targets to any dynamical system equipped with a metric we associate a class of well approximable sets in the case of an expanding rational map of the riemann sphere acting on its julia set we estimate and in some cases compute the hausdorff dimension of the associated well approximable sets the methods used show a clear link between distortion properties and the type of results obtained in this paper via ergodic theory and ubiquity

persymmetric adaptive detectors in homogeneous and partially homogeneous environments this paper addresses the problem of detecting a signal in partially homogeneous and homogeneous environments in partially homogeneous environments i e both the test data and training data share the same noise covariance matrix structure up to an unknown scaling factor a persymmetric adaptive coherence estimator per ace detector is proposed by exploiting the persymmetric structure of the covariance matrix the per ace can reduce training data requirements furthermore the expressions for the probabilities of false alarm and detection are derived along with the distribution of the loss factor in homogeneous environments a persymmetric adaptive matched filter per amf detector has been presented however its probability of detection has not been obtained yet thus we derive the expression for the probability of detection for both the per ace and per amf numerical results of these proposed expressions are confirmed with those of monte carlo trials in addition simulation results show that the proposed per ace outperforms the conventional ace in training limited scenarios

oblique projection based enumeration of mixed noncoherent and coherent narrowband signals in many application scenarios the signals impinging on the array of sensors comprise the noncoherent uncorrelated and or partially correlated signals and the coherent signals with several groups due to multipath propagation in this paper we consider the problem of estimating the number of noncoherent narrowband signals and that of coherent narrowband signals with multiple groups impinging on a planar sensor array composed of two parallel uniform linear arrays ulas and an oblique projection based enumerator for the mixed signals opems is proposed by utilizing the qr decomposition based ratio criterion qrrc for rank determination of a matrix in the opems the number of noncoherent signals and that of coherent signals in each group are estimated separately where only the elevation angles of noncoherent signals are estimated to isolate the coherent signals from the noncoherent ones and the computationally intensive and time consuming eigendecomposition procedure is avoided the consistency of the proposed opems is analyzed and its effectiveness is verified through numerical examples

analysis and design of perfusion based event related fmri experiments perfusion based functional magnetic resonance imaging fmri using arterial spin labeling asl methods has the potential to provide better localization of the functional signal to the sites of neural activity compared to blood oxygenation level dependent bold contrast fmri at present experiments using asl have been limited to simple block and periodic single trial designs we present here an adaptation of the general linear model to perfusion based fmri that enables the design and analysis of more complicated designs such as random and semirandom event related designs formulas for the least squares estimate of the perfusion response and the f statistic for the detection of a response are derived exact expressions and useful approximations for detection power and estimation efficiency are presented and it is shown that the trade off between power and efficiency for perfusion experiments is similar to that previously observed for bold experiments the least squares estimate is compared with an estimate formed from the running subtraction of tag and control images the running subtraction estimate is shown to be approximately equal to a temporally low pass filtered version of the least squares estimate numerical simulations and results from asl experiments are used to support the theoretical findings

divergence form operators in reifenberg flat domains we study the boundary regularity of solutions of elliptic operators in divergence form with c 0 coefficients or operators which are small perturbations of the laplacian in non smooth domains we show that as in the case of the laplacian there exists a close relationship between the regularity of the corresponding elliptic measure and the geometry of the domain

joint channel and symbol estimation by oblique projections the problem of simultaneous blind channel and symbol estimation of a single input multiple output simo communication channel is considered it is shown that the outer product of the channel vector and the channel input sequence can be obtained by a linear estimator that has the finite sample convergence property furthermore this estimator can be obtained by the use of oblique projections an order detection algorithm that avoids the use of subjective thresholding is also proposed applications to multiuser detection are also considered

performance analysis of a class of transient detection algorithms a unified framework the detection of short duration nonstationary signals which are commonly referred to as transients is often performed in the time frequency transform domain an analytical framework within which the performance of different detectors based on linear transforms can be easily compared for different classes of signals is developed a given class of transients is modeled as a signal existing in a linear subspace plus a mismatch signal closed form expressions are derived for the best and the worst detection performance for all possible transients in a given class using this framework the performance of detectors based on the gabor transform and on the short time fourier transform is evaluated and compared

redundancy the discrete fourier transform and impulse noise cancellation the relationship between the discrete fourier transform and error control codes is examined under certain conditions we show that discrete time sequences carry redundant information which then allow for the detection and correction of errors an application of this technique to impulse noise cancellation for pulse amplitude modulation transmission is described

two channel constrained least squares problems solutions using power methods and connections with canonical coordinates the problem of two channel constrained least squares cls filtering under various sets of constraints is considered and a general set of solutions is derived for each set of constraints the solution is determined by a coupled asymmetric generalized eigenvalue problem this eigenvalue problem establishes a connection between two channel cls filtering and transform methods for resolving channel measurements into canonical or half canonical coordinates based on this connection a unified framework for reduced rank wiener filtering is presented then various representations of reduced rank wiener filters in canonical and half canonical coordinates are introduced an alternating power method is proposed to recursively compute the canonical coordinate and half canonical coordinate mappings a deflation process is introduced to extract the mappings associated with the dominant coordinates the correctness of the alternating power method is demonstrated on a synthesized data set and conclusions are drawn

inhomogeneous theory of dual diophantine approximation on manifolds the theory of inhomogeneous diophantine approximation on manifolds is developed in particular the notion of nice manifolds is introduced and the divergence part of the groshev type theory is established for all such manifolds our results naturally incorporate and generalize the homogeneous measure and dimension theorems for non degenerate manifolds established to date the results have natural applications beyond the standard inhomogeneous theory such as diophantine approximation by algebraic integers

detection of constrained subspace signals in additive infinite dimensional interference and noise the detection of constrained subspace signals in additive infinite dimensional interference and noise is motivated by consideration of multipath doppler channels subject to interference from partially overlapping frequency bands of other sources since the interference lies in an infinite dimensional subspace the standard method of projecting onto the subspace containing the signal plus interference does not yield a finite dimensional detection problem however an alternative approach may be used to extract the appropriate finite dimensional problem moreover an energy constraint may be imposed on the desired signal the generalized likelihood ratio receiver for this problem is obtained and expressions for its average probability of error are given

cfar matched direction detector in a previously published paper by besson et al we considered the problem of detecting a signal whose associated spatial signature is known to lie in a given linear subspace in the presence of subspace interference and broadband noise of known level we extend these results to the case of unknown noise level more precisely we derive the generalized likelihood ratio test glrt for this problem which provides a constant false alarm rate cfar detector it is shown that the glrt involves the largest eigenvalue and the trace of complex wishart matrices the distribution of the glrt is derived under the null hypothesis numerical simulations illustrate its performance and provide a comparison with the glrt when the noise level is known

observations on oblique projectors and pseudoinverses oblique projectors which were examined by behrens and scharf see ibid vol 42 no 6 p 1413 24 1994 are related to earlier work on oblique pseudoinverses and constrained least squares methods and are reconsidered from the standpoint of orthogonal basis vectors and qr factorizations construction algorithms are presented that are numerically more stable than the normal equations constructions previously used

the impact of temporal regularization on estimates of the bold hemodynamic response function a comparative analysis in fmri data analysis it has been shown that for a wide range of situations the hemodynamic response function hrf can be reasonably characterized as the impulse response function of a linear and time invariant system an accurate and robust extraction of the hrf is essential to infer quantitative information about the relative timing of the neuronal events in different brain regions when no assumptions are made about the hrf shape it is most commonly estimated using time windowed averaging or a least squares estimated general linear model based on either fourier or delta basis functions recently regularization methods have been employed to increase the estimation efficiency of the hrf typically these methods produce more accurate hrf estimates than the least squares approach goutte c nielsen f a hansen l k 2000 modeling the haemodynamic response in fmri using smooth fir filters ieee trans med imag 19 12 1188 1201 here we use simulations to clarify the relative merit of temporal regularization based methods compared to the least squares methods with respect to the accuracy of estimating certain characteristics of the hrf such as time to peak ttp height hr and width w of the response we implemented a bayesian approach proposed by marrelec et al marrelec g benali h ciuciu p pelegrini issac m poline j b 2003 robust estimation of the hemodynamic response function in event related bold fmri using basic physiological information hum brain mapp 19 1 17 marrelec g benali h ciuciu p poline j b bayesian estimation of the hemodynamic of the hemodynamic response function in functional mri in r f editor 2001 melville p 229 247 and its deterministic counterpart based on a combination of tikhonov regularization tikhonov a n arsenin v y 1977 solution of ill posed problems washington dc w h winston and generalized cross validation gcv wahba g 1990 spline models for observational data philadelphia siam for selecting the regularization parameter the performance of both methods is compared with least square estimates as a function of temporal resolution color and strength of the noise and the type of stimulus sequences used in almost all situations under the considered assumptions e g linearity time invariance and smooth hrf the regularization based techniques more accurately characterize the hrf compared to the least squares method our results clarify the effects of temporal resolution noise color and experimental design on the accuracy of hrf estimation

spectral stability of the neumann laplacian we prove the equivalence of hardy and sobolev type inequalities certain uniform bounds on the heat kernel and some spectral regularity properties of the neumann laplacian associated with an arbitrary region of finite measure in euclidean space we also prove that if one perturbs the boundary of the region within a uniform holder category then the eigenvalues of the neumann laplacian change by a small and explicitly estimated amount

quantitative recurrence properties for beta dynamical system abstract this note is concerned with the quantitative recurrence properties of beta dynamical system 0 1 t for general 1 the size of points with the prescribed recurrence rate is determined more precisely hausdorff dimensions of the sets x 0 1 t n x x n for infinitely many n n and x 0 1 t n x x e j 0 n 1 f t j x for infinitely many n n are obtained completely where is a positive function defined on n and f is a positive continuous function on 0 1 besides the pressure function p f t with a continuous potential f is proven to be continuous with respect to

application of manifold separation to polarimetric capon beamformer and source tracking two adaptive capon methods that jointly estimate the azimuth angle and polarization of the sources in a closed form are proposed it is shown that the azimuth angles of the sources may be estimated from the roots of a complex valued polynomial or by rooting a real valued polynomial instead the latter method is particularly useful in tracking arbitrarily polarized sources in a sequential snapshot by snapshot manner using root tracking techniques the proposed polynomial rooting based methods are applicable to polarization sensitive arrays regardless of the array geometry including conformal arrays and take into account array nonidealities a large sample analysis of the polarimetric capon method is also provided showing that it converges up to a multiplicative factor that depends on the interference plus noise power to the polarimetric music method in the high sinr regime such a result gives a new insight into the well known capon and music methods this paper also shows that employing manifold separation in robust capon beamforming as well as in transmit beamforming schemes leads to improved performance in terms of received sinr when array calibration measurements are used extensive numerical results employing real world polarimetric arrays are given results show that employing manifold separation leads to improved performance in many array processing tasks

a new subspace identification algorithm for high resolution doa estimation in this paper we propose a new direction of arrival doa estimator for sensor array processing the estimator is based on a linear algebraic connection between the standard subspace model of the array correlation matrix and a special signal plus interference model which we develop in this paper the estimator we propose is a signal subspace scaled music algorithm which we call ssmusic it is not a subspace weighted music because the scaling depends on the eigenstructure of the estimated signal subspace ssmusic has the advantage of simultaneously estimating the doa and the power of each source we employ a second order perturbation analysis of the estimator and derive stochastic representations for its bias and squared error we compare the new doa estimator with the music estimator based on these representations numerical results demonstrate the superior performance of ssmusic relative to music and the validity of the perturbation results

modified shrinking target problem in beta dynamical systems abstract in the paper we investigate a modified version of the shrinking target problem in beta dynamical systems which is induced by the transformation t x x mod 1 the hausdorff dimension of the lim sup set w f x 0 1 t n x f x n for infinitely many n n is determined where f 0 1 0 1 is a lipschitz function and is a positive function defined on n the set w f can be viewed as a dynamical analogue of the inhomogeneous diophantine approximation in which the inhomogeneous factor is allowed to vary