adaptive detection in gaussian interference with unknown covariance after reduction by invariance in this paper we address the problem of adaptive detection in homogeneous gaussian interference with unknown covariance matrix after reduction by invariance starting from a maximal invariant statistic which contains all the information for the synthesis of an invariant detector we devise the rao test generalized likelihood ratio test glrt and durbin test moreover we compare their decision statistics with those of the receivers designed according to the same criteria from the raw data i e before reduction by invariance we prove that the glrt in the original data space is statistically equivalent to the glrt designed after reduction by invariance under a very mild assumption and coincide with the conditional uniformly most powerful invariant c umpi test obtained conditioning on an ancillary part of the maximal invariant statistic as to the rao and durbin criteria when they are applied after reduction by invariance lead to detectors different from the counterparts devised in the raw data domain at the analysis stage the performance of the receivers devised in the invariant domain is analyzed in comparison with that of the counterparts synthesized from the original observations

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

a cfar adaptive subspace detector based on a single observation in system dependent clutter background in this paper the problem of detecting target in system dependent clutter sdc background with a single observation from the test cell is researched classical detectors such as the generalized likelihood ratio detectors glrds and the adaptive matched filters amfs etc usually deal with the clutter and the noise as a whole the low rank detectors lrds make use of the low rank property of the clutter to improve the detection performance however the performance of lrds degrades when the signal is not orthogonal with respect to w r t the clutter in this paper an adaptive subspace detector for sdc sdc asd background which deals with the clutter and the noise separately is proposed the sdc asd designs the test statistic by replacing the signal and the clutter covariance matrix with their maximum likelihood estimations mles its theoretical false alarm probability and detection probability are analytically deduced analytical results show that the test statistic has the form of non central distribution besides it is shown that the sdc asd has constant false alarm rate cfar performance w r t the clutter and the noise numerical experiments are provided to validate the detection performance of the sdc asd in dealing with the target detection in sdc background less

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

analytic continuation in the case of non regular dependency on a small parameter with an application to celestial mechanics abstract we consider a non autonomous system of ordinary differential equations assume that the time dependence is periodic with a very high frequency 1 where is a small parameter and differentiability with respect to the parameter is lost when equals zero we derive from arenstorf s implicit function theorem a set of conditions to show the existence of periodic solutions these conditions look formally like the standard analytic continuation method namely checking that a certain minor does not vanish we apply this result to show the existence of a new class of periodic orbits of very large radii in the three dimensional elliptic restricted three body problem for arbitrary values of the masses of the primaries

adaptive steganalysis of least significant bit replacement in grayscale natural images this paper deals with the detection of hidden bits in the least significant bit lsb plane of a natural image the mean level and the covariance matrix of the image considered as a quantized gaussian random matrix are unknown an adaptive statistical test is designed such that its probability distribution is always independent of the unknown image parameters while ensuring a high probability of hidden bits detection this test is based on the likelihood ratio test except that the unknown parameters are replaced by estimates based on a local linear regression model it is shown that this test maximizes the probability of detection as the image size becomes arbitrarily large and the quantization step vanishes this provides an asymptotic upper bound for the detection of hidden bits based on the lsb replacement mechanism numerical results on real natural images show the relevance of the method and the sharpness of the asymptotic expression for the probability of detection

theta divisors with curve summands and the schottky problem we prove the following converse of riemann s theorem let a theta be an indecomposable principally polarized abelian variety whose theta divisor can be written as a sum of a curve and a codimension two subvariety theta c y then c is smooth a is the jacobian of c and y is a translate of w g 2 c as applications we determine all theta divisors that are dominated by a product of curves and characterize jacobians by the existence of a d dimensional subvariety with curve summand whose twisted ideal sheaf is a generic vanishing sheaf

clutter subspace estimation in low rank heterogeneous noise context this paper addresses the problem of the clutter subspace projector csp estimation in the context of a disturbance composed of a low rank lr heterogeneous clutter modeled here by a spherically invariant random vector sirv plus a white gaussian noise wgn in such context the corresponding lr adaptive filters and detectors require less training vectors than classical methods to reach equivalent performance unlike classical adaptive processes which are based on an estimate of the noise covariance matrix cm the lr processes are based on a csp estimate this csp estimate is usually derived from a singular value decomposition svd of the cm estimate however no maximum likelihood estimator mle of the cm has been derived for the considered disturbance model in this paper we introduce the fixed point equation that mle of the csp satisfies for a disturbance composed of a lr sirv clutter plus a zero mean wgn a recursive algorithm is proposed to compute this solution numerical simulations validate the introduced estimator and illustrate its interest compared to the current state of art

asymptotic properties of robust complex covariance matrix estimates in many statistical signal processing applications the estimation of nuisance parameters and parameters of interest is strongly linked to the resulting performance generally these applications deal with complex data this paper focuses on covariance matrix estimation problems in non gaussian environments and particularly the m estimators in the context of elliptical distributions first this paper extends to the complex case the results of tyler in d tyler robustness and efficiency properties of scatter matrices biometrika vol 70 no 2 p 411 1983 more precisely the asymptotic distribution of these estimators as well as the asymptotic distribution of any homogeneous function of degree 0 of the m estimates are derived on the other hand we show the improvement of such results on two applications directions of arrival doa estimation using the multiple signal classification music algorithm and adaptive radar detection based on the adaptive normalized matched filter anmf test

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

a new parametric glrt for multichannel adaptive signal detection a parametric generalized likelihood ratio test glrt for multichannel signal detection in spatially and temporally colored disturbance was recently introduced by modeling the disturbance as a multichannel autoregressive ar process the detector however involves a highly nonlinear maximum likelihood estimation procedure which was solved via a two dimensional iterative search method initialized by a suboptimal estimator in this paper we present a simplified glrt along with a new estimator for the problem both the estimator and the glrt are derived in closed form at considerably lower complexity with adequate training data the new glrt achieves a similar detection performance as the original one however for the more interesting case of limited training the original glrt may become inferior due to poor initialization because of its simpler form the new glrt also offers additional insight into the parametric multichannel signal detection problem the performance of the proposed detector is assessed using both a simulated dataset which was generated using multichannel ar models and the kassper dataset a widely used dataset with challenging heterogeneous effects found in real world environments

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

the performance of a matched subspace detector that uses subspaces estimated from finite noisy training data we analyze the performance of a matched subspace detector msd where the test signal vector is assumed to reside in an unknown low rank k subspace that must be estimated from finite noisy signal bearing training data under both a stochastic and deterministic model for the test vector subspace estimation errors due to limited training data degrade the performance of the standard plug in detector relative to that of an oracle detector to avoid some of this performance loss we utilize and extend recent results from random matrix theory rmt that precisely quantify the quality of the subspace estimate as a function of the eigen snr dimensionality of the system and the number of training samples we exploit this knowledge of the subspace estimation accuracy to derive from first principles a new rmt detector and to characterize the associated roc performance curves of the rmt and plug in detectors using more than the a critical number of informative components which depends on the training sample size and eigen snr parameters of training data will result in a performance loss that our analysis quantifies in the large system limit we validate our asymptotic predictions with simulations on moderately sized systems

performance analysis of covariance matrix estimates in impulsive noise this paper deals with covariance matrix estimates in impulsive noise environments physical models based on compound noise modeling spherically invariant random vectors sirv compound gaussian processes allow to correctly describe reality e g range power variations or clutter transitions areas in radar problems however these models depend on several unknown parameters covariance matrix statistical distribution of the texture disturbance parameters that have to be estimated based on these noise models this paper presents a complete analysis of the main covariance matrix estimates used in the literature four estimates are studied the well known sample covariance matrix mscm and a normalized version mn the fixed point fp estimate mfp and a theoretical benchmark mtfp among these estimates the only one of practical interest in impulsive noise is the fp the three others which could be used in a gaussian context are in this paper only of academic interest i e for comparison with the fp a statistical study of these estimates is performed through bias analysis consistency and asymptotic distribution this study allows to compare the performance of the estimates and to establish simple relationships between them finally theoretical results are emphasized by several simulations corresponding to real situations

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

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

hybrid detectors for subpixel targets subpixel detection is a challenging problem in hyperspectral imagery analysis since the target size is smaller than the size of a pixel detection algorithms must rely solely on spectral information a number of different algorithms have been developed over the years to accomplish this task but most detectors have taken either a purely statistical or a physics based approach to the problem we present two new hybrid detectors that take advantage of these approaches by modeling the background using both physics and statistics results demonstrate improved performance over the well known amsd and ace subpixel algorithms in experiments that include multiple targets images and area types especially when dealing with weak targets in complex backgrounds

glrt based direction detectors in homogeneous noise and subspace interference in this paper we derive and assess decision schemes to discriminate resorting to an array of sensors between the h0 hypothesis that data under test contain disturbance only i e noise plus interference and the h1 hypothesis that they also contain signal components along a direction which is a priori unknown but constrained to belong to a given subspace of the observables the disturbance is modeled in terms of complex normal random vectors plus deterministic interference assumed to belong to a known subspace we assume that a set of noise only secondary data is available which possess the same statistical characterization of noise in the cells under test at the design stage we resort to either the plain generalized likelihood ratio test glrt or the two step glrt based design procedure the performance analysis conducted resorting to simulated data shows that the one step glrt performs better than the detector relying on the two step design procedure when the number of secondary data is comparable to the number of sensors moreover it outperforms a one step glrt based subspace detector when the dimension of the signal subspace is sufficiently high

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

intersection de sous groupes et de sous varietes i we study the intersection of a subvariety x of an abelian variety a over open image in new window with the union of all the algebraic subgroups of a of given dimension d our main result states that if we remove a suitable exceptional subset from x and if d is small enough then the intersection enjoys a northcott like property the points of bounded height on it form a finite set the condition on d involves only the dimension of x and the structure of a up to isogenies we show how it can be weakened if we assume certain conjectures in the direction of an abelian version of lehmer s problem the theorem is especially meaningful when x is a curve since it is then possible to bound the height and hence to prove finiteness of the set under consideration this generalises the result of e viada on powers of elliptic curves and is analogous to work of e bombieri d masser and u zannier on tori whose general strategy we follow

subspace based adaptive generalized likelihood ratio detection subspace based adaptive detection performance is examined for the generalized likelihood ratio detector based on wilks spl lambda statistic the problem considered here is detecting the presence of one or more signals of known shape embedded in gaussian distributed noise with unknown covariance structure the data is mapped into a subspace prior to detection the probability of false alarm is independent of the subspace transformation and depends only on subspace dimension the probability of detection depends on the subspace transformation through a nonadaptive signal to noise ratio snr parameter subspace processing results in an snr loss that tends to decrease performance and a gain in statistical stability that tends to increase performance it is shown that the statistical stability effect dominates the snr loss for short data records and subspace detectors can require substantially less snr than full space detectors for equivalent performance a method for designing the subspace transformation to minimize the snr loss is proposed and illustrated through simulations

a subspace based adaptive sidelobe blanker we propose a modified version of the adaptive sidelobe blanker asb consisting of a generalized likelihood ratio test glrt based subspace detector followed by the adaptive coherence estimator the performance analysis shows that it possesses the constant false alarm rate property with respect to the unknown covariance matrix of the noise in homogeneous environment and that it guarantees a wider range of ldquodirectivityrdquo values with respect to the plain asb the probability of false alarm and the probability of detection the latter for matched signals only have been evaluated in closed form in homogeneous environment and by resorting to monte carlo simulation for the other considered cases

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

false alarm rate of the glrt for subspace signals in subspace interference plus gaussian noise in the presence of interference and gaussian noise with unknown covariance matrix a generalized likelihood ratio test glrt detector has already been developed for detecting a distributed target the target signal and interference are described with subspace models namely the target signals or interference are modeled as linear combinations of the linearly independent columns of a known subspace matrix in this paper we obtain statistical properties of this glrt detector and prove its constant false alarm rate against the noise covariance matrix moreover we derive analytical expressions for the probability of false alarm of the glrt detector specifically exact expressions for the probability of false alarm are obtained for six cases where the target subspace dimension denoted by p is 1 2 and 3 and the number of range cells denoted by h the distributed target occupies is 1 2 and 3 for the general case where p geq 4 and h geq 4 we derive an approximate expression for the probability of false alarm monte carlo simulations show that the exact expressions are valid and the accuracy of the approximate expression is acceptable for moderate or large training data size in practice these expressions can greatly facilitate the threshold setting for the glrt detector for any preassigned probability of false alarm

robust covariance matrix estimation in heterogeneous low rank context this paper addresses the problem of robust covariance matrix cm estimation in the context of a disturbance composed of a low rank lr heterogeneous clutter plus an additive white gaussian noise the lr clutter is modeled by a spherically invariant random vector with assumed high clutter to noise ratio in such a context adaptive process should require less training samples than classical methods to reach equivalent performance as in a full rank clutter configuration the main issue is that classical robust estimators of the cm cannot be computed in the undersampled configuration to overcome this issue the current approach is based on regularization methods nevertheless most of these solutions are enforcing the estimate to be well conditioned while in our context it should be lr structured this paper therefore addresses this issue and derives an algorithm to compute the maximum likelihood estimator of the cm for the considered disturbance model several relaxations and robust generalizations of the result are discussed performance is finally illustrated on numerical simulations and on a space time adaptive processing for airborne radar application

modified rao test for multichannel adaptive signal detection the problem of detecting a subspace signal is studied in colored gaussian noise with an unknown covariance matrix in the subspace model the target signal belongs to a known subspace but with unknown coordinates we first present a new derivation of the rao test based on the subspace model and then propose a modified rao test mrt by introducing a tunable parameter the mrt is more general which includes the rao test and the generalized likelihood ratio test as special cases moreover closed form expressions for the probabilities of false alarm and detection of the mrt are derived which show that the mrt bears a constant false alarm rate property against the noise covariance matrix numerical results demonstrate that the mrt can offer the flexibility of being adjustable in the mismatched case where the target signal deviates from the presumed signal subspace in particular the mrt provides better mismatch rejection capacities as the tunable parameter increases

adaptive double subspace signal detection in gaussian background part i homogeneous environments in this two part paper we consider the problem of adaptive multidimensional multichannel signal detection in gaussian noise with unknown covariance matrix the test data primary data is assumed as a collection of sample vectors arranged as the columns of a rectangular data array the rows and columns of the signal matrix are both assumed to lie in known subspaces but with unknown coordinates due to this feature of the signal structure we name this kind of signal as the double subspace signal part i of this paper focuses on the adaptive detection in homogeneous environments while part ii deals with the adaptive detection in partially homogeneous environments precisely in this part we derive the generalized likelihood ratio test glrt rao test wald test as well as their two step variations in homogeneous environments three types of spectral norm tests snts are also introduced all these detectors are shown to possess the constant false alarm rate cfar property moreover we discuss the differences between them and show how they work another contribution is that we investigate various special cases of these detectors remarkably some of them are well known existing detectors while some others are still new at the stage of performance evaluation conducted by monte carlo simulations both matched and mismatched signals are dealt with for each case more than one scenario is considered

the cfar adaptive subspace detector is a scale invariant glrt the constant false alarm rate cfar matched subspace detector cfar msd is the uniformly most powerful invariant test and the generalized likelihood ratio test glrt for detecting a target signal in noise whose covariance structure is known but whose level is unknown previously the cfar adaptive subspace detector cfar asd or adaptive coherence estimator ace was proposed for detecting a target signal in noise whose covariance structure and level are both unknown and whose covariance structure is estimated with a sample covariance matrix based on training data we show here that the cfar asd is glrt when the test measurement is not constrained to have the same noise level as the training data as a consequence this glrt is invariant to a more general scaling condition on the test and training data than the well known glrt of kelly 1986

a cfar adaptive subspace detector for first order or second order gaussian signals based on a single observation in this paper we consider the problem of detecting a signal in gaussian noise with unknown covariance matrix in partially homogeneous environments where the test and training data samples share the same noise covariance matrix up to an unknown scaling factor one solution to this problem is the adaptive subspace detector asd with a single or multiple observations however the probabilities of false alarm and detection of this asd have not been obtained yet in this paper these expressions are derived on the basis of a single observation which are confirmed with monte carlo simulations it is shown that the asd has a constant false alarm rate property with respect to both the shared noise covariance matrix structure and the independent scaling of the noise in the test data in addition we prove that for the first order model where the signal of interest is assumed to be a deterministic but unknown vector the asd derived with the generalized likelihood ratio test is consistent with that derived with an ad hoc two step design procedure

adaptive detection with bounded steering vectors mismatch angle we address the problem of detecting a signal of interest soi using multiple observations in the primary data in a background of noise with unknown covariance matrix we consider a situation where the signal s signature is not known perfectly but its angle with a nominal and known signature is bounded furthermore we consider a possible scaling inhomogeneity between the primary and the secondary noise covariance matrix first assuming that the noise covariance matrix is known we derive the generalized likelihood ratio test glrt which involves solving a semidefinite programming problem next we substitute the unknown noise covariance matrix for its estimate obtained from secondary data to yield the final detector the latter is compared with a detector that assumes a known signal s signature

mean squared error and threshold snr prediction of maximum likelihood signal parameter estimation with estimated colored noise covariances an interval error based method mie of predicting mean squared error mse performance of maximum likelihood estimators mles is extended to the case of signal parameter estimation requiring intermediate estimation of an unknown colored noise covariance matrix an intermediate step central to adaptive array detection and parameter estimation the successful application of mie requires good approximations of two quantities 1 interval error probabilities and 2 asymptotic snrrarrinfin local mse performance of the mle exact general expressions for the pairwise error probabilities that include the effects of signal model mismatch are derived herein that in conjunction with the union bound provide accurate prediction of the required interval error probabilities the crameacuter rao bound crb often provides adequate prediction of the asymptotic local mse performance of mle the signal parameters however are decoupled from the colored noise parameters in the fisher information matrix for the deterministic signal model rendering the crb incapable of reflecting loss due to colored noise covariance estimation a new modification of the crb involving a complex central beta random variable different from but analogous to the reed mallett and brennan beta loss factor provides a working solution to this problem facilitating mse prediction well into the threshold region with remarkable accuracy

reduced rank adaptive filtering a novel rank reduction scheme is introduced for adaptive filtering problems this rank reduction method uses a cross spectral metric to select the optimal lower dimensional subspace for reduced rank adaptive filtering as a function of the basis vectors of the full rank space

robust subspace learning and detection in laplacian noise and interference we address the problem of maximum likelihood subspace learning and detection in the presence of laplacian noise and interference whose subspace may be known or unknown for subspace learning the laplacian problem reduces to a maxmin convex mathematical program with polyhedral cost the minimization involves projection of the measurements onto a subspace orthogonal to the signal and interference spaces and has linear constraints while the maximization produces the subspace and has polyhedral constraints the laplacian noise model for subspace detection and estimation motivated by applications in functional magnetic resonance imaging and applicable in other areas yields maximum likelihood detectors and learned subspaces with unique structure due to the presence of corners in the polyhedrally convex optimization for instance the optimal learned subspace can consist of vectors whose elements take values of 1 or 1 only emergence of such a quantization attests to the robustness property of laplacian learning meaning that the solution is insensitive to perturbation in the data set the resulting detectors are similarly robust to false alarms and have computationally attractive properties

subspace snr maximization the constrained stochastic matched filter in this paper we propose a novel approach to perform detection of stochastic signals embedded in an additive random noise both signal and noise are considered to be realizations of zero mean random processes of which only second order statistics are known their covariance matrices the method proposed called constrained stochastic matched filter csmf is an extension of the stochastic matched filter itself derived from the matched filter the csmf is optimal in the sense that it maximizes the signal to noise ratio in a subspace whose dimension is fixed a priori in this paper after giving the reasons for our approach we show that there is neither an obvious nor analytic solution to the problem expressed then an algorithm which is proved to converge is proposed to obtain the optimal solution evaluation of the algorithm s performance is completed through estimation of receiver operating characteristic curves experiments on real signals show the improvement brought about by this method and thus its significance

on the relationship between the glrt and umpi tests for the detection of signals with unknown parameters the generalized likelihood ratio test glrt is widely used in signal processing applications such as image processing wireless communications medical imaging classification and signal detection however the glrt does not have many known properties other than that it is invariant uniformly most powerful invariant umpi for problems that fit the linear model and asymptotically n spl rarr spl infin umpi in general since it is invariant it belongs to the class of tests for which the umpi test is optimal in this paper we consider a general class of detection problems in which unknown signal parameters imply a problem invariance that can be described analytically by orthogonal subgroups this invariance is natural for problems with unknown signal parameters and for example include those of the matched subspace detectors of scharf and friedlander we derive the glrt and umpi detectors for this general signal class for the case of gaussian noise an expression is found that relates the two test statistics showing the umpi statistic to be the sum of two terms one of which is the glrt using this we find that the glrt and umpi tests are asymptotically equivalent as signal to noise ratio snr approaches infinity or as probability of false alarm approaches zero these results are illustrated by extending an example given by nicolls and de jager to show the analytic relationship between the glrt and umpi tests the results indicate that the performance between the tests becomes close at signal to noise ratios snrs associated with operating points of the receiver operating curve that are typically of interest in signal detection applications

generic vanishing and minimal cohomology classes on abelian varieties we establish a and conjecture further relationship between the existence of subvarieties representing minimal cohomology classes on principally polarized abelian varieties and the generic vanishing of the cohomology of twisted ideal sheaves the main ingredient is the generic vanishing criterion established in pareschi g and popa m gv sheaves fourier mukai transform and generic vanishing preprint math ag 0608127 based on the fourier mukai transform

diffuse multipath exploitation for adaptive radar detection we deal with the problem of detecting point like targets in diffuse multipath environments modeling the target echo as the superposition of a deterministic signal with an unknown scaling factor due to the direct path plus a zero mean complex circular symmetric gaussian random vector with an unknown covariance matrix accounting for the echoes from the glistening surface we devise a constrained generalized likelihood ratio test glrt for the resulting hypothesis testing problem enforcing the primary data covariance matrix due to both interference and multipath echoes to belong to a neighborhood of the secondary data sample covariance matrix remarkably the proposed decision scheme ensures the desirable constant false alarm rate cfar property with respect to the unknown parameters of the interference the performance assessment conducted on simulated data in terms of detection probability also in comparison with existing solutions highlights the effectiveness of the new approach to cope with diffuse multipath phenomena

adaptive threshold estimation via extreme value theory determining a detection threshold to automatically maintain a low false alarm rate is a challenging problem in a number of different applications the underlying parametric assumptions of most automatic target detection algorithms are invalid therefore thresholds derived using these incorrect distribution assumptions do not produce desirable results when applied to real sensor data monte carlo methods for threshold determination work well but tend to perform poorly when targets are present in order to mitigate these effects we propose an algorithm using extreme value theory through the use of the generalized pareto distribution gpd and a kolmogorov smirnov statistical test unlike previous work based on gpd estimates this algorithm incorporates a way to adaptively maintain low false alarm rates in the presence of targets both synthetic and real world detection results demonstrate the usefulness of this algorithm

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

a maximal invariant framework for adaptive detection with structured and unstructured covariance matrices we introduce a framework for exploring array detection problems in a reduced dimensional space by exploiting the theory of invariance in hypothesis testing this involves calculating a low dimensional basis set of functions called the maximal invariant the statistics of which are often tractable to obtain thereby making analysis feasible and facilitating the search for tests with some optimality property using this approach we obtain a locally most powerful invariant test for the unstructured covariance case and show that all invariant tests can be expressed in terms of the previously published kelly s generalized likelihood ratio glrt and robey s adaptive matched filter amf test statistics applying this framework to structured covariance matrices corresponding to stochastic interferers in a known subspace for which the glrt is unavailable we obtain the maximal invariant and propose several new invariant detectors that are shown to perform as well or better than existing ad hoc detectors these invariant tests are unaffected by most nuisance parameters hence the variation in the level of performance is sharply reduced this framework facilitates the search for such tests even when the usual glrt is unavailable

statistical analysis of the nonhomogeneity detector for non gaussian interference backgrounds we derive the nonhomogeneity detector nhd for non gaussian interference scenarios and present a statistical analysis of the method the non gaussian interference scenario is assumed to be modeled by a spherically invariant random process sirp we present a method for selecting representative homogeneous training data based on our statistical analysis of the nhd for finite sample support used in covariance estimation in particular an exact theoretical expression for the nhd test statistic probability density function pdf is derived performance analysis of the nhd is presented using both simulated data and measured data from the multichannel airborne radar measurement mcarm program a performance comparison with existing nhd approaches is also included

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

invariance and optimality of cfar detectors in binary composite hypothesis tests we investigate the relationship between constant false alarm rate cfar and invariant tests we introduce the minimal invariant group mig we show that for a family of distributions the unknown parameters are eliminated from the distribution of the maximal invariant statistic under the mig while the maximum information of the observed signal is preserved we prove that any invariant test with respect to mig is cfar and conversely for any cfar test an invariant statistic exists with respect to an mig under some mild conditions moreover for a given cfar test we propose a systematic method for deriving an enhanced test i e a function of observations exists such that the likelihood ratio lr of the maximal invariant of its mig gives an enhanced test furthermore we introduce the uniformly most powerful cfar ump cfar test as the optimal cfar bound among all cfar tests we then prove that the ump cfar test for the minimally invariant hypothesis testing problem is given by the lr of the maximal invariant under mig for some problems this test mp cfar depends on the unknown parameters of the alternative hypothesis however provides an upper performance bound for all suboptimal cfar tests we also propose three suboptimal novel cfar tests among which one is asymptotically optimal

theoremes de connexite pour les produits d espaces projectifs et les grassmanniennes we give a numerical condition on the images of two morphisms to a grassmannian or a product of projective spaces that ensures that their fibered product is connected thereby extending connectedness results of fulton and hansen this result is valid over any algebraically closed field it yields a condition on the class of an irreducible subvariety of a grassmannian that implies that it is simply connected this applies in particular to fano varieties of certain hypersurfaces in a projective space

deformation theory generic vanishing theorems and some conjectures of enriques catanese and beauville introduction 389 w notation and conventions 392 w deformations of cohomology groups 392 w generic vanishing criteria for topologically trivial line bundles 397 w a nakano type generic vanishing theorem 401 w an application to surfaces 405 references 407

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

optimal design of large dimensional adaptive subspace detectors this paper addresses the design of adaptive subspace matched filter asmf detectors in the presence of a mismatch in the steering vector these detectors are coined as adaptive in reference to the step of utilizing an estimate of the clutter covariance matrix using training data of signal free observations to estimate the clutter covariance matrix we employ regularized covariance estimators that by construction force the eigenvalues of the covariance estimates to be greater than a positive scalar rho while this feature is likely to increase the bias of the covariance estimate it presents the advantage of improving its conditioning thus making the regularization suitable for handling high dimensional regimes in this paper we consider the setting of the regularization parameter and the threshold for asmf detectors in both gaussian and compound gaussian clutters in order to allow for a proper selection of these parameters it is essential to analyze the false alarm and detection probabilities for tractability such a task is carried out under the asymptotic regime in which the number of observations and their dimensions grow simultaneously large thereby allowing us to leverage existing results from random matrix theory simulation results are provided in order to illustrate the relevance of the proposed design strategy and to compare the performances of the proposed asmf detectors versus adaptive normalized matched filter anmf detectors under mismatch scenarios

maximal invariants and performance of some invariant hypothesis tests for an adaptive detection problem maximal invariants for adaptive detection of a signal in unknown interference from multiple observations is derived given coherent samples from p sets of observations it is shown that a maximal invariant statistic for the detection problem is a 2p 1 dimensional vector comprising the eigenvalues of two hermitian positive definite matrices obtained from the data set two invariant detectors well known for p 1 are generalized for the case of multiple observations and closed form expressions for the probability of detection and probability of false alarm are derived along with the distributions of the signal to interference plus noise loss factors several novel invariant detectors are constructed from the maximal invariants and the receiver operating characteristics of the detectors compared

doubly symmetric periodic solutions of the spatial restricted three body problem abstract the existence of two new families of periodic solutions to the spatial restricted three body problem is shown these solutions are independent of the mass ratio of the primaries have large inclinations and are symmetric with respect to two coordinate planes in one family the infinitesimal particle is very far from the primaries and in the other family the infinitesimal is very close to one of the primaries

adaptive detection of a signal known only to lie on a line in a known subspace when primary and secondary data are partially homogeneous this paper deals with the problem of detecting a signal known only to lie on a line in a subspace in the presence of unknown noise using multiple snapshots in the primary data to account for uncertainties about a signal s signature we assume that the steering vector belongs to a known linear subspace furthermore we consider the partially homogeneous case for which the covariance matrix of the primary and the secondary data have the same structure but possibly different levels this provides an extension to the framework considered by bose and steinhardt the natural invariances of the detection problem are studied which leads to the derivation of the maximal invariant then a detector is proposed that proceeds in two steps first assuming that the noise covariance matrix is known the generalized likelihood ratio test glrt is formulated then the noise covariance matrix is replaced by its sample estimate based on the secondary data to yield the final detector the latter is compared with a similar detector that assumes the steering vector to be known

kernel spectral matched filter for hyperspectral imagery in this paper a kernel based nonlinear spectral matched filter is introduced for target detection in hyperspectral imagery which is implemented by using the ideas in kernel based learning theory a spectral matched filter is defined in a feature space of high dimensionality which is implicitly generated by a nonlinear mapping associated with a kernel function a kernel version of the matched filter is derived by expressing the spectral matched filter in terms of the vector dot products form and replacing each dot product with a kernel function using the so called kernel trick property of the mercer kernels the proposed kernel spectral matched filter is equivalent to a nonlinear matched filter in the original input space which is capable of generating nonlinear decision boundaries the kernel version of the linear spectral matched filter is implemented and simulation results on hyperspectral imagery show that the kernel spectral matched filter outperforms the conventional linear matched filter

glrt based adaptive detection algorithms for range spread targets we address adaptive detection of a range spread target or targets embedded in gaussian noise with unknown covariance matrix to this end we assume that cells referred to in the following as secondary data that are free of signal components are available those secondary data are supposed to possess either the same covariance matrix or the same structure of the covariance matrix of the cells under test in this context we design detectors relying on the generalized likelihood ratio test glrt and on a two step glrt based design procedure remarkably both criteria lead to receivers ensuring the constant false alarm rate cfar property with respect to the unknown quantities a thorough performance assessment of the proposed detection strategies together with the evaluation of their processing cost highlights that the two step design procedure is to be preferred with respect to the plain glrt in fact the former leads to detectors that achieve satisfactory performance under several situations of practical interest and are simpler to implement than those designed resorting to the latter

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

optimality of high resolution array processing using the eigensystem approach in the classical approach to underwater passive listening the medium is sampled in a convenient number of look directions from which the signals are estimated in order to build an image of the noise field in contrast a modern trend is to consider the noise field as a global entity depending on few parameters to be estimated simultaneously in a gaussian context it is worthwhile to consider the application of likelihood methods in order to derive a detection test for the number of sources and estimators for their locations and spectral levels this paper aims to compute such estimators when the wavefront shapes are not assumed known a priori this justifies results previously found using the asymptotical properties of the eigenvalue eigenvector decomposition of the estimated spectral density matrix of the sensor signals they have led to a variety of high resolution array processing methods more specifically a covariance matrix test for equality of the smallest eigenvalues is presented for source detection for source localization a best fit method and a test of orthogonality between the smallest eigenvectors and the source vectors are discussed

first kind symmetric periodic solutions of the generalized van der waals hamiltonian the aim of this paper is to prove the existence of a new symmetric family of periodic solutions of the generalized van der waals hamiltonian in fact we prove the existence of several families of first kind symmetric periodic solutions as continuation of circular orbits of the kepler problem in the spatial case

a robust matched detector we address the matched detector problem in the case the signal to be detected is imperfectly known while in the standard detector the signal is known to lie along a particular direction we consider the case where this direction is known up to additive white gaussian noise this somehow amounts to assuming that the signal lies in a cone the aperture of which depends upon the level of uncertainty we build the associated generalized likelihood ratio glr analyze its statistical properties indicate how to set the threshold to achieve a given false alarm rate and how to predict the associated probability of detection the so obtained detector reduces to the conventional one when the uncertainty vanishes and we analyze its behavior when the level of uncertainty which has to be known a priori is mis evaluated it appears that the sensitivity of the detector is quite low with respect to this kind of errors more importantly several realistic examples are presented that indicate that the proposed detector remains quite efficient when the true signals are far from being of the assumed model and whatever the model of the uncertainty actually is it is this robustness that makes the detector valuable

regularized m estimators of scatter matrix in this paper a general class of regularized m estimators of scatter matrix are proposed that are suitable also for low or insufficient sample support small n and large p problems the considered class constitutes a natural generalization of m estimators of scatter matrix maronna 1976 and are defined as a solution to a penalized m estimation cost function using the concept of geodesic convexity we prove the existence and uniqueness of the regularized m estimators of scatter and the existence and uniqueness of the solution to the corresponding m estimating equations under general conditions unlike the non regularized m estimators of scatter the regularized estimators are shown to exist for any data configuration an iterative algorithm with proven convergence to the solution of the regularized m estimating equation is also given since the conditions for uniqueness do not include the regularized versions of tyler s m estimator necessary and sufficient conditions for their uniqueness are established separately for the regularized tyler s m estimators we also derive a simple closed form and data dependent solution for choosing the regularization parameter based on shape matrix matching in the mean squared sense finally some simulations studies illustrate the improved accuracy of the proposed regularized m estimators of scatter compared to their non regularized counterparts in low sample support problems an example of radar detection using normalized matched filter nmf illustrate that an adaptive nmf detector based on regularized m estimators are able to maintain accurately the preset cfar level