on a perturbed sparre andersen risk model with threshold dividend strategy and dependence in this paper we consider a sparre andersen risk model perturbed by a brownian motion where the individual claim sizes are dependent on the interclaim times we assume that dividends are paid off under a threshold strategy integral and integro differential equations satisfied by the gerber shiu functions are obtained and a solution procedure is also proposed

blind identification of mimo fir systems driven by quasistationary sources using second order statistics a frequency domain approach this paper discusses a frequency domain method for blind identification of multiple input multiple output mimo convolutive channels driven by white quasistationary sources the sources can assume arbitrary probability distributions and in some cases they can even be all gaussian distributed we also show that under slightly more restrictive assumptions the algorithm can be applied to the case when the sources are colored nonstationary signals we demonstrate that by using the second order statistics of the channel outputs under mild conditions on the nonstationarity of sources and under the condition that channel is column wise coprime the impulse response of the mimo channel can be identified up to an inherent scaling and permutation ambiguity we prove that by using the new algorithm under the stated assumptions a uniform permutation across all frequency bins is guaranteed and the inherent frequency dependent scaling ambiguities can be resolved hence no post processing is required as is the case with previous frequency domain algorithms we further present an efficient two step frequency domain algorithm for identifying the channel numerical simulations are presented to demonstrate the performance of the new algorithm

one dimensional transport equations with discontinuous coefficients we consider one dimensional linear transport equations with bounded but possibly discontinuous coefficient a the cauchy problem is studied from two different points of view in the first case we assume that a is piecewise continuous we give an existence result and a precise description of the solutions on the lines of discontinuity in the second case we assume that a satisfies a one sided lipschitz condition we give existence uniqueness and general stability results for backward lipschitz solutions and forward measure solutions by using a duality method we prove that the flux associated to these measure solutions is a product by some canonical representative of a key words linear transport equations discontinuous coefficients weak stability duality product of a measure by a discontinuous function nonnegative solutions 1991 mathematics subject classification primary 35f10 35b35 34a12 to appear in nonlinear analysis tma departement de mathematiques et applications umr cnrs 8553 ecole normale superieure et cnrs 45 rue d ulm 75230 paris cedex 05 france francois bouchut ens fr mathematiques applications et physique mathematique d orleans umr cnrs 6628 universite d orleans 45067 orleans cedex 2 france james math cnrs fr

blind deconvolution of multi input single output systems with binary sources the problem of blind source separation for multi input single output miso systems with binary inputs is treated in this paper our approach exploits the constellation properties of the successor values for each output sample in the absence of noise the successors of each output value form a characteristic finite set of clusters successor constellation the shape of this constellation is invariant of the predecessor value and it only depends on the last filter tap consequently the localization of the successors constellation can lead to the removal of the last filter tap thus reducing the length of the filter a process we call channel deflation based on the successor observation clustering soc we develop two algorithms for blind source separation soc 1 and soc 2 differing mainly on the required size of the data set furthermore the treatment of the system in the presence of noise is described using data clustering and data correction the problem of noise is attacked using a statistical mode based method moreover we correct the problem of misclassified observations using an iterative scheme based on the viterbi algorithm for the decoding of a hidden markov model hmm

on a discrete time risk model with general income and time dependent claims we consider a discrete time risk model with general premium rate and time dependent claim sizes in which the interclaim time has an impact on the subsequent claim size by studying the roots of lundberg s generalized equation we first obtain an analytical expression for the generating function of the expected discounted penalty function then it is shown that the expected discounted penalty function satisfies a defective renewal equation moreover a closed form expression for the generating function of the time to ruin is obtained when the claim sizes have discrete k m distributions numerical examples are also given to illustrate the applicability of the results obtained

bi iterative algorithm for extracting independent components from array signals it is well known that the complex valued nonunitary joint diagonalization nujd problem in blind source separation bss can be linked to the trilinear models in this paper by exploring the special structure of the nujd problem in bss we introduce a novel symmetric tri quadratic cost function and then derive a simultaneous bi iterative algorithm s bia for solving the nujd problem finally three experiments are conducted in order to show the comparatively good performance of the proposed bss algorithm

deterministic cca based algorithms for blind equalization of fir mimo channels in this paper a new deterministic technique for blind equalization of multiple input multiple output mimo channels is presented the proposed method relies on the channel order diversity of the finite impulse response mimo channel and it does not make any assumption about the spectra or the finite alphabet property of the sources assuming that the lengths of the single input multiple output channels are known or estimated a priori it is able to extract the sources up to a scale and rotation matrix ambiguity which only affects to those sources associated to single input multiple output simo channels with equal lengths unlike previously proposed techniques the method described in this paper obtains the equalizers and the best linear combination of their outputs in a single step and thus optimally the reformulation of the proposed method as a set of nested canonical correlation analysis problems is exploited to obtain efficient batch and adaptive equalization algorithms finally the performance of the proposed algorithms is evaluated by means of some simulation examples

blind source separation by nonstationarity of variance a cumulant based approach blind separation of source signals usually relies either on the nongaussianity of the signals or on their linear autocorrelations a third approach was introduced by matsuoka et al 1995 who showed that source separation can be performed by using the nonstationarity of the signals in particular the nonstationarity of their variances in this paper we show how to interpret the nonstationarity due to a smoothly changing variance in terms of higher order cross cumulants this is based on the time correlation of the squares energies of the signals and leads to a simple optimization criterion using this criterion we construct a fixed point algorithm that is computationally very efficient

blind source separation in the time frequency domain based on multiple hypothesis testing this paper considers a time frequency t f based approach for blind separation of nonstationary signals in particular we propose a time frequency point selection algorithm based on multiple hypothesis testing which allows automatic selection of auto or cross source locations in the time frequency plane the selected t f points are then used via a joint diagonalization and off diagonalization algorithm to perform source separation the proposed algorithm is developed assuming deterministic signals with additive white complex gaussian noise a performance comparison of the proposed and existing approaches is provided

a quadratic programming approach to blind equalization and signal separation blind equalization and signal separation are two well established signal processing problems in this paper we present a quadratic programming algorithm for fast blind equalization and signal separation by introducing a special non mean square error mse objective function we reformulate fractionally spaced blind equalization into an equivalent quadratic programming problem based on a clear geometric interpretation and a formal proof we show that a perfect equalization solution is obtained at every local optimum of the quadratic program because blind source separation is by nature and mathematically a closely related problem we also generalize the algorithm for blind signal separation we show that by enforcing source orthogonalization through successive processing the quadratic programming approach can be applied effectively moreover the quadratic program is easily extendible to incorporate additional practical conditions such as jamming suppression constraints we also provide evidence of good performance through computer simulations

nonorthogonal joint diagonalization by combining givens and hyperbolic rotations a new algorithm for computing the nonorthogonal joint diagonalization of a set of matrices is proposed for independent component analysis and blind source separation applications this algorithm is an extension of the jacobi like algorithm first proposed in the joint approximate diagonalization of eigenmatrices jade method for orthogonal joint diagonalization the improvement consists mainly in computing a mixing matrix of determinant one and columns of equal norm instead of an orthogonal mixing matrix this target matrix is constructed iteratively by successive multiplications of not only givens rotations but also hyperbolic rotations and diagonal matrices the algorithm performance evaluated on synthetic data compares favorably with existing methods in terms of speed of convergence and complexity

linear transport equations with μ monotone coefficients abstract we introduce the concept of a monotone function it allows us to extend the existing theory for filippov solutions to ode linear transport equations and conservation laws for a wider range of transport velocities a 1 a d and fluxes f 1 f d

local error estimates for discontinuous solutions of nonlinear hyperbolic equations let u x t be the possibly discontinuous entropy solution of a nonlinear scalar conservation law with smooth initial data suppose u varepsilon x t is the solution of an approximate viscosity regularization where varepsilon 0 is the small viscosity amplitude it is shown that by post processing the small viscosity approximation u varepsilon pointwise values of u and its derivatives with an error as close to e as desired can be recovered the analysis relies on the adjoint problem of the forward error equation which in this case amounts to a backward linear transport equation with discontinuous coefficients the novelty of our approach is to use a generalized e condition of the forward problem in order to deduce a w 1 infty energy estimate for the discontinuous backward transport equation this in turn leads to e uniform estimate on moments of the error u varepsilon u the approach presented does not follow the characteristics and therefore applies mutatis mutandis to o

robust independent component analysis by iterative maximization of the kurtosis contrast with algebraic optimal step size independent component analysis ica aims at decomposing an observed random vector into statistically independent variables deflation based implementations such as the popular one unit fastica algorithm and its variants extract the independent components one after another a novel method for deflationary ica referred to as robustica is put forward in this paper this simple technique consists of performing exact line search optimization of the kurtosis contrast function the step size leading to the global maximum of the contrast along the search direction is found among the roots of a fourth degree polynomial this polynomial rooting can be performed algebraically and thus at low cost at each iteration among other practical benefits robustica can avoid prewhitening and deals with real and complex valued mixtures of possibly noncircular sources alike the absence of prewhitening improves asymptotic performance the algorithm is robust to local extrema and shows a very high convergence speed in terms of the computational cost required to reach a given source extraction quality particularly for short data records these features are demonstrated by a comparative numerical analysis on synthetic data robustica s capabilities in processing real world data involving noncircular complex strongly super gaussian sources are illustrated by the biomedical problem of atrial activity aa extraction in atrial fibrillation af electrocardiograms ecgs where it outperforms an alternative ica based technique

on subspace methods for blind identification of single input multiple output fir systems blind identification of single input multiple output simo fir systems based on second order statistics has attracted a great deal of research effort we focus on subspace estimation procedures which exploit the structure of the range space of certain matrix valued statistics constructed by arranging in a prescribed order the covariance coefficients of the observations general subspace identifiability results are obtained based on properties of minimal polynomial bases of rational subspaces several subspace estimation procedures are then derived these estimators are all based on a weighted least square solution of an overdetermined system of linear equations an asymptotic statistical analysis of these estimators is carried out to evaluate the potential of these methods and the impact of the weighting

a direct algorithm for nonorthogonal approximate joint diagonalization while a pair of n n matrices can almost always be exactly and simultaneously diagonalized by a generalized eigendecomposition no exact solution exists in the case of a set with more than two matrices this problem termed approximate joint diagonalization ajd is instrumental in blind signal processing when the set of matrices to be jointly diagonalized includes at least n linearly independent matrices we propose a suboptimal but closed form solution for ajd in the direct least squares sense the corresponding non iterative algorithm is given the acronym diem diagonalization using equivalent matrices extensive numerical simulations show that diem is both fast and accurate compared to the state of the art iterative ajd algorithms

blind separation of independent sources for virtually any source probability density function the blind source separation bss problem consists of the recovery of a set of statistically independent source signals from a set of measurements that are mixtures of the sources when nothing is known about the sources and the mixture structure in the bss scenario of two noiseless real valued instantaneous linear mixtures of two sources an approximate maximum likelihood ml approach has been suggested in the literature which is only valid under certain constraints on the probability density function pdf of the sources in the present paper the expression for this ml estimator is reviewed and generalized to include virtually any source distribution an intuitive geometrical interpretation of the new estimator is also given in terms of the scatter plots of the signals involved an asymptotic performance analysis is then carried out yielding a closed form expression for the estimator asymptotic pdf simulations illustrate the behavior of the suggested estimator and show the accuracy of the asymptotic analysis in addition an extension of the method to the general bss scenario of more than two sources and two sensors is successfully implemented

nonlinear adaptive blind whitening for mimo channels a nonlinear adaptive whitening method is proposed for blind deconvolution of mimo systems by whitening the received signals in both time and space with a highly nonlinear function of the past output data the whitened signals are isi free and can be viewed as outputs of a memoryless paraunitary mixing system the convergence of the proposed recursive algorithm is proved numerical simulation shows that the whitening method proposed in the paper works well even if the output signal is corrupted by additive noise

multi input single output nonlinear blind separation of binary sources the problem of blindly separating multiple binary sources from a single nonlinear mixture is addressed through a novel clustering approach without the use of any optimization procedure the method is based on the assumption that the source probabilities are asymmetric in which case the output probability distribution can be expressed as a linear mixture of the sources we are then able to solve the problem by using a known linear multiple input single output miso blind separation method the overall procedure is very fast and in theory it works for any number of independent binary sources and for a wide range of nonlinear functions in practice the accuracy of the method depends on the estimation accuracy of the output probabilities and the cluster centers it can be quite sensitive to noise especially as the number of sources increases or the number of data samples is reduced however in our experiments we have been able to demonstrate successful separation of up to four sources

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

blind equalization of simo fir channels driven by colored signals with unknown statistics we consider the blind equalization of single input multiple output finite impulse response channel driven by colored signals the statistics of the input colored signals are unknown a priori by exploiting the inherent structural relationship between the source autocorrelation matrices of different delay lags the closed form zero forcing and minimum mean square error equalizers of desired delays are estimated from the second order statistics of the received data the blind equalizability conditions of the proposed method are investigated numerical simulation results are presented to illustrate the performance of the proposed algorithm

model selection for convolutive ica with an application to spatiotemporal analysis of eeg we present a new algorithm for maximum likelihood convolutive independent component analysis ica in which components are unmixed using stable autoregressive filters determined implicitly by estimating a convolutive model of the mixing process by introducing a convolutive mixing model for the components we show how the order of the filters in the model can be correctly detected using bayesian model selection we demonstrate a framework for deconvolving a subspace of independent components in electroencephalography eeg initial results suggest that in some cases convolutive mixing may be a more realistic model for eeg signals than the instantaneous ica model

hybrid linear and nonlinear complexity pursuit for blind source separation blind source separation bss is an increasingly popular data analysis technique with many applications several methods for bss using the statistical properties of original sources have been proposed for a famous case non gaussianity this leads to independent component analysis ica in this paper we propose a hybrid bss method based on linear and nonlinear complexity pursuit which combines three statistical properties of source signals non gaussianity linear predictability and nonlinear predictability a gradient learning algorithm is presented by minimizing a loss function simulations verify the efficient implementation of the proposed method

convergence analysis of wavelet schemes for convection reaction equations under minimal regularity assumptions in this paper we analyze convergence rates of wavelet schemes for time dependent convection reaction equations within the framework of the eulerian lagrangian localized adjoint method ellam under certain minimal assumptions that guarantee h 1 regularity of exact solutions we show that a generic ellam scheme has a convergence rate mathcal o h sqrt delta t delta t in l 2 norm then applying the theory of operator interpolation we obtain error estimates for initial data with even lower regularity namely it is shown that the error of such a scheme is mathcal o h sqrt delta t theta delta t theta for initial data in a besov space displaystyle b theta 2 q 0 theta 1 0

adaptive quasi newton algorithm for source extraction via cca approach this paper addresses the problem of adaptive source extraction via the canonical correlation analysis cca approach based on liu s analysis of cca approach we propose a new criterion for source extraction which is proved to be equivalent to the cca criterion then a fast and efficient online algorithm using quasi newton iteration is developed the stability of the algorithm is also analyzed using lyapunov s method which shows that the proposed algorithm asymptotically converges to the global minimum of the criterion simulation results are presented to prove our theoretical analysis and demonstrate the merits of the proposed algorithm in terms of convergence speed and successful rate for source extraction

generalized non orthogonal joint diagonalization with lu decomposition and successive rotations non orthogonal joint diagonalization njd free of prewhitening has been widely studied in the context of blind source separation bss and array signal processing etc however njd is used to retrieve the jointly diagonalizable structure for a single set of target matrices which are mostly formulized with a single dataset and thus is insufficient to handle multiple datasets with inter set dependences a scenario often encountered in joint bss j bss applications as such we present a generalized njd gnjd algorithm to simultaneously perform asymmetric njd upon multiple sets of target matrices with mutually linked loading matrices by using lu decomposition and successive rotations to enable j bss over multiple datasets with indication exploitation of their mutual dependences experiments with synthetic and real world datasets are provided to illustrate the performance of the proposed algorithm

a unifying information theoretic framework for independent component analysis abstract we show that different theories recently proposed for independent component analysis ica lead to the same iterative learning algorithm for blind separation of mixed independent sources we review those theories and suggest that information theory can be used to unify several lines of research pearlmutter and parra 1 and cardoso 2 showed that the infomax approach of bell and sejnowski 3 and the maximum likelihood estimation approach are equivalent we show that negentropy maximization also has equivalent properties and therefore all three approaches yield the same learning rule for a fixed nonlinearity girolami and fyfe 4 have shown that the nonlinear principal component analysis pca algorithm of karhunen and joutsensalo 5 and oja 6 can also be viewed from information theoretic principles since it minimizes the sum of squares of the fourth order marginal cumulants and therefore approximately minimizes the mutual information 7 lambert 8 has proposed different bussgang cost functions for multichannel blind deconvolution we show how the bussgang property relates to the infomax principle finally we discuss convergence and stability as well as future research issues in blind source separation

independent component analysis over galois fields of prime order we consider the framework of independent component analysis ica for the case where the independent sources and their linear mixtures all reside in a galois field of prime order p similarities and differences from the classical ica framework over the real field are explored we show that a necessary and sufficient identifiability condition is that none of the sources should have a uniform distribution we also show that pairwise independence of the mixtures implies their full mutual independence namely a nonmixing condition in the binary p 2 and ternary p 3 cases but not necessarily in higher order p 3 cases we propose two different iterative separation or identification algorithms one is based on sequential identification of the smallest entropy linear combinations of the mixtures and is shown to be equivariant with respect to the mixing matrix the other is based on sequential minimization of the pairwise mutual information measures we provide some basic performance analysis for the binary p 2 case supplemented by simulation results for higher orders demonstrating advantages and disadvantages of the proposed separation approaches

an efficient subspace method for the blind identification of multichannel fir systems we present a novel method for the blind identification of linear single input multiple output simo finite impulse response fir systems based on second order statistics our approach called the truncated transfer matrix method ttm proceeds in two major steps first the svd analysis of the lagged covariance matrix gives the subspace of the clipped system transfer matrix and second the block toeplitz structure of the transfer matrix gives extra constraints that allow us to reconstruct the matrix through the solution of a linear system of equations the proposed ttm method is analytical no optimization procedure involved and it is robust to noise we find that the method comes with an increased computational cost but it significantly outperforms state of the art second order methods in low signal to noise ratio snr situations

group decorrelation enhanced subspace method for identifying fir mimo channels driven by unknown uncorrelated colored sources identification of finite impulse response fir and multiple input multiple output mimo channels driven by unknown uncorrelated colored sources is a challenging problem in this paper a group decorrelation enhanced subspace gdes method is presented the gdes method uses the idea of subspace decomposition and signal decorrelation more effectively than the joint diagonalization enhanced subspace jdes method previously reported in the literature the gdes method has a much better performance than the jdes method the correctness of the gdes method is proved assuming that 1 the channel matrix is irreducible and column reduced and 2 the source spectral matrix has distinct diagonal functions however the gdes method has an inherent ability to trade off between the required condition on the channel matrix and that on the source spectral matrix simulations show that the gdes method yields good results even when the channel matrix is not irreducible which is not possible at all for the jdes method

a two stage algorithm for mimo blind deconvolution of nonstationary colored signals a new two stage algorithm is proposed for the deconvolution of multi input multi output mimo systems with colored input signals while many blind deconvolution algorithms in the literature utilize high order statistics of the output signal for white input signals the additional information contained in colored input signals allows the design of second order statistical algorithms in fact practical signal sources such as speech signals do have distinct nonstationary colored power spectral densities we present a two stage signal separation approach in which the first step utilizes a matrix pencil between output auto correlation matrices at different delays whereas the second stage adopts a subspace method to identify and deconvolve mimo systems

blind underdetermined mixture identification by joint canonical decomposition of ho cumulants a new family of cumulant based algorithms is proposed in order to blindly identify potentially underdetermined mixtures of statistically independent sources these algorithms perform a joint canonical decomposition cand of several higher order cumulants through a cand of a three way array with special symmetries these techniques are studied in terms of identifiability performance and numerical complexity from a signal processing viewpoint the proposed methods are shown i to have a better estimation resolution and ii to be able to process more sources than the other classical cumulant based techniques second from a numerical analysis viewpoint we deal with the convergence speed of several procedures for three way array decomposition such as the acdc scheme we also show how to accelerate the iterative cand algorithms by using differently the symmetries of the considered three way array next from a multilinear algebra viewpoint the paper aims at giving some insights on the uniqueness of a joint cand of several hermitian multiway arrays compared to the cand of only one array this allows us as a result to extend the concept of virtual array va to the case of combination of several vas

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

independent component analysis by entropy bound minimization a novel differential entropy estimator is introduced where the maximum entropy bound is used to approximate the entropy given the observations and is computed using a numerical procedure thus resulting in accurate estimates for the entropy we show that such an estimator exists for a wide class of measuring functions and provide a number of design examples to demonstrate its flexible nature we then derive a novel independent component analysis ica algorithm that uses the entropy estimate thus obtained ica by entropy bound minimization ica ebm the algorithm adopts a line search procedure and initially uses updates that constrain the demixing matrix to be orthogonal for robust performance we demonstrate the superior performance of ica ebm and its ability to match sources that come from a wide range of distributions using simulated and real world data

blind identification of underdetermined mixtures by simultaneous matrix diagonalization in this paper we study simultaneous matrix diagonalization based techniques for the estimation of the mixing matrix in underdetermined independent component analysis ica this includes a generalization to underdetermined mixtures of the well known sobi algorithm the problem is reformulated in terms of the parallel factor decomposition parafac of a higher order tensor we present conditions under which the mixing matrix is unique and discuss several algorithms for its computation

estimating functions of independent component analysis for temporally correlated signals this article studies a general theory of estimating functions of independent component analysis when the independent source signals are temporarily correlated estimating functions are used for deriving both batch and on line learning algorithms and they are applicable to blind cases where spatial and temporal probability structures of the sources are unknown most algorithms proposed so far can be analyzed in the framework of estimating functions an admissible class of estimating functions is derived and related efficient on line learning algorithms are introduced we analyze dynamical stability and statistical efficiency of these algorithms different from the independently and identically distributed case the algorithms work even when only the second order moments are used the method of simultaneous diagonalization of cross covariance matrices is also studied from the point of view of estimating functions

non orthogonal joint diagonalization in the least squares sense with application in blind source separation approximate joint diagonalization of a set of matrices is an essential tool in many blind source separation bss algorithms a common measure of the attained diagonalization of the set is the weighted least squares wls criterion however most well known algorithms are restricted to finding an orthogonal diagonalizing matrix relying on a whitening phase for the nonorthogonal factor often such an approach implies unbalanced weighting which can result in degraded performance we propose an iterative alternating directions algorithm for minimizing the wls criterion with respect to a general not necessarily orthogonal diagonalizing matrix under some mild assumptions we prove weak convergence in the sense that the norm of parameters update is guaranteed to fall below any arbitrarily small threshold within a finite number of iterations we distinguish between hermitian and symmetrical problems using bss simulations results we demonstrate the improvement in estimating the mixing matrix resulting from the relaxation of the orthogonality restriction

the perturbed sparre andersen model with a threshold dividend strategy in this paper we consider a sparre andersen model perturbed by diffusion with generalized erlang n distributed inter claim times and a threshold dividend strategy integro differential equations with certain boundary conditions for the moment generation function and the mth moment of the present value of all dividends until ruin are derived we also derive integro differential equations with boundary conditions for the gerber shiu functions the special case where the inter claim times are erlang 2 distributed and the claim size distribution is exponential is considered in some details

penalty function based joint diagonalization approach for convolutive blind separation of nonstationary sources a new approach for convolutive blind source separation bss by explicitly exploiting the second order nonstationarity of signals and operating in the frequency domain is proposed the algorithm accommodates a penalty function within the cross power spectrum based cost function and thereby converts the separation problem into a joint diagonalization problem with unconstrained optimization this leads to a new member of the family of joint diagonalization criteria and a modification of the search direction of the gradient based descent algorithm using this approach not only can the degenerate solution induced by a null unmixing matrix and the effect of large errors within the elements of covariance matrices at low frequency bins be automatically removed but in addition a unifying view to joint diagonalization with unitary or nonunitary constraint is provided numerical experiments are presented to verify the performance of the new method which show that a suitable penalty function may lead the algorithm to a faster convergence and a better performance for the separation of convolved speech signals in particular in terms of shape preservation and amplitude ambiguity reduction as compared with the conventional second order based algorithms for convolutive mixtures that exploit signal nonstationarity

adaptive modal identification of structures with equivariant adaptive separation via independence approach abstract an efficient output only blind source separation bss method was recently introduced for the modal identification of structures bss procedures recover a set of independent sources from their unknown linear mixtures when only mixtures are observed batch data is required for the separation in traditional blind source separation methods these algorithms are however unfavorable as some sets of data are observed one after another in this paper an adaptive blind source separation technique equivariant adaptive separation via independence easi is introduced to overcome the mentioned disadvantage within the structures the easi algorithm is beneficial as it can provide solutions to real time problems while also update the un mixing matrix for each step easi not only avoids increases in size of the relevant matrices and vectors but also decreases the analysis time a synthetic example and a benchmark structure have been used in this paper to better investigate the efficiency of the proposed method the simulation results demonstrate the effectiveness of the easi algorithm in on line identification of modal parameters of structures

gerber shiu analysis in a perturbed risk model with dependence between claim sizes and interclaim times in this paper we consider a compound poisson risk model perturbed by a brownian motion we construct the bivariate cumulative distribution function of the claim size and interclaim time by farlie gumbel morgenstern copula the integro differential equations and the laplace transforms for the gerber shiu functions are obtained we also show that the gerber shiu functions satisfy some defective renewal equations for exponential claims some explicit expressions are obtained and numerical examples for the ruin probabilities are also given

hamiltonian preserving schemes for the liouville equation of geometrical optics with discontinuous local wave speeds in this paper we construct two classes of hamiltonian preserving numerical schemes for a liouville equation with discontinuous local wave speed this equation arises in the phase space description of geometrical optics and has been the foundation of the recently developed level set methods for multivalued solution in geometrical optics we extend our previous work in s jin x wen hamiltonian preserving schemes for the liouville equation with discontinuous potentials commun math sci 3 2005 285 315 for the semiclassical limit of the schrodinger equation into this system the designing principle of the hamiltonian preservation by building in the particle behavior at the interface into the numerical flux is used here and as a consequence we obtain two classes of schemes that allow a hyperbolic stability condition when a plane wave hits a flat interface the hamiltonian preservation is shown to be equivalent to snell s law of refraction in the case when the ratio of wave length over the width of the interface goes to zero when both length scales go to zero positivity and stabilities in both l 1 and l norms are established for both schemes the approach also provides a selection criterion for a unique solution of the underlying linear hyperbolic equation with singular discontinuous and measure valued coefficients benchmark numerical examples are given with analytic solution constructed to study the numerical accuracy of these schemes

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

blind separation of mixture of independent sources through a quasi maximum likelihood approach we propose two methods for separating mixture of independent sources without any precise knowledge of their probability distribution they are obtained by considering a maximum likelihood ml solution corresponding to some given distributions of the sources and relaxing this assumption afterward the first method is specially adapted to temporally independent non gaussian sources and is based on the use of nonlinear separating functions the second method is specially adapted to correlated sources with distinct spectra and is based on the use of linear separating filters a theoretical analysis of the performance of the methods has been made a simple procedure for optimally choosing the separating functions is proposed further in the second method a simple implementation based on the simultaneous diagonalization of two symmetric matrices is provided finally some numerical and simulation results are given illustrating the performance of the method and the good agreement between the experiments and the theory

a blind source separation technique using second order statistics separation of sources consists of recovering a set of signals of which only instantaneous linear mixtures are observed in many situations no a priori information on the mixing matrix is available the linear mixture should be blindly processed this typically occurs in narrowband array processing applications when the array manifold is unknown or distorted this paper introduces a new source separation technique exploiting the time coherence of the source signals in contrast with other previously reported techniques the proposed approach relies only on stationary second order statistics that are based on a joint diagonalization of a set of covariance matrices asymptotic performance analysis of this method is carried out some numerical simulations are provided to illustrate the effectiveness of the proposed method

sequential blind source separation based exclusively on second order statistics developed for a class of periodic signals a sequential algorithm for the blind separation of a class of periodic source signals is introduced in this paper the algorithm is based only on second order statistical information and exploits the assumption that the source signals have distinct periods separation is performed by sequentially converging to a solution which in effect diagonalizes the output covariance matrix constructed at a lag corresponding to the fundamental period of the source we select the one with the smallest period simulation results for synthetic signals and real electrocardiogram recordings show that the proposed algorithm has the ability to restore statistical independence and its performance is comparable to that of the equivariant adaptive source separation easi algorithm a benchmark high order statistics based sequential algorithm with similar computational complexity the proposed algorithm is also shown to mitigate the limitation that the easi algorithm can separate at most one gaussian distributed source furthermore the steady state performance of the proposed algorithm is compared with that of easi and the block based second order blind identification sobi method

projection pursuit based method for blind separation of nonnegative sources this paper presents a projection pursuit pp based method for blind separation of nonnegative sources first the available observation matrix is mapped to construct a new mixing model in which the inaccessible source matrix is normalized to be column sum to 1 then the pp method is proposed to solve this new model where the mixing matrix is estimated column by column through tracing the projections to the mapped observations in specified directions which leads to the recovery of the sources the proposed method is much faster than chan s method which has similar assumptions to ours due to the usage of optimal projection it is also more advantageous in separating cross correlated sources than the independence and uncorrelation based methods as it does not employ any statistical information of the sources furthermore the new method does not require the mixing matrix to be nonnegative simulation results demonstrate the superior performance of our method

blind channel identification with colored sources by exploiting properties of companion matrices this paper proposes a new second order statistics based method for blind multiple input multiple output mimo finite impulse response fir channel estimation driven by colored sources it is assumed that the second order statistics sos of the input sources are known a priori by exploiting the new derived properties of the companion matrices an original proof for the uniqueness of the system solution is provided which serves as a theoretical basis for the proposed new method that admits a closed form solution the corresponding identifiability conditions and the computational complexity of the proposed method are discussed and compared with other existing method numerical simulation results are presented to illustrate the performance of the proposed algorithm

blind source separation by sparse decomposition in a signal dictionary the blind source separation problem is to extract the underlying source signals from a set of linear mixtures where the mixing matrix is unknown this situation is common in acoustics radio medical signal and image processing hyperspectral imaging and other areas we suggest a two stage separation process a priori selection of a possibly overcomplete signal dictionary for instance a wavelet frame or a learned dictionary in which the sources are assumed to be sparsely representable followed by unmixing the sources by exploiting the their sparse representability we consider the general case of more sources than mixtures but also derive a more efficient algorithm in the case of a nonovercomplete dictionary and an equal numbers of sources and mixtures experiments with artificial signals and musical sounds demonstrate significantly better separation than other known techniques

a note on stone s conjecture of blind signal separation stone s method is one of the novel approaches to the blind source separation bss problem and is based on stone s conjecture however this conjecture has not been proved we present a simple simulation to demonstrate that stone s conjecture is incorrect we then modify stone s conjecture and prove this modified conjecture as a theorem which can be used a basis for bss algorithms

a sequential subspace method for blind identification of general fir mimo channels this correspondence addresses the problem of blindly identifying multiple input multiple output mimo finite impulse response fir channels without the conventional assumption of identical column degrees a subspace based algorithm is developed that identifies the channel s columns sequentially from the lowest degree columns to the highest degree ones compared with the previous generalized subspace method by gorokhov and loubaton 1997 the new method is simpler and more accurate

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

a coordinate descent algorithm for complex joint diagonalization under hermitian and transpose congruences abstract this paper deals with the problem of joint complexmatrix diagonalization by considering both the hermitian andtranspose congruences we address the general case where thesearched diagonalizing matrix is apriori nonunitary based onthe minimization of a quadratic criterion we propose a ex ible algorithm in the sense that it allows to directly consider arectangular diagonalizing matrix and to take into considerationboth the hermitian and transpose congruences within the sameframework the proposed algorithm is a coordinate descentalgorithm that is based on an approximate criterion leading to theanalytical derivation of the minima arguments computer simu lations are drawn to illustrate the usefulness and performancesof the algorithm and a comparison to state of the art algorithmsis presented finally an application to independent componentanalysis based on fourth order statistics is also presented index terms blind source separation complex symmetric ma trices hermitian matrices independent component analysis jointdiagonalization

blind separation of sound sources from the principle of least spatial entropy abstract the aim of the paper is to offer a method for separating incoherent and compact sound sources which may overlap in both the space and frequency domains this is found of interest in acoustical applications involving the identification and ranking of sound sources stemming from different physical origins the principle proceeds in two steps the first one being reminiscent to source reconstruction e g as in near field acoustical holography and the second one to blind source separation specifically the source mixture is first expanded into a linear combination of spatial basis functions whose coefficients are set by backpropagating the pressures measured by an array of microphones to the source domain this leads to a formulation similar but no identical to blind source separation in the second step these coefficients are blindly separated into uncorrelated latent variables assigned to incoherent virtual sources these are shown to be defined up to an arbitrary rotation a unique set of sound sources is finally recovered by searching for that rotation by conjugate gradient descent in the stiefel manifold of unitary matrices which maximizes their spatial compactness as measured either by their spatial variance or their spatial entropy this results in the proposal of two separation criteria coined least spatial variance and least spatial entropy respectively the same concept of spatial entropy which is central to the paper is also exploited in defining a new criterion the entropic l curve dedicated to determining the number of active sound sources the idea consists in considering the number of sources that achieves the best compromise between a low spatial entropy as expected from compact sources and a low statistical entropy as expected from a low residual error the proposed methodology is validated on both laboratory experiments and numerical data and illustrated on an industrial example concerned with the ranking of sound sources on a diesel engine at the same time its robustness to the estimated number of active sources is demonstrated

underdetermined blind modal identification of structures by earthquake and ambient vibration measurements via sparse component analysis abstract sparse component analysis sca approach was adopted to handle underdetermined blind modal identification of structures where the number of sensors is less than the number of active modes to exploit the sparsity of structural responses in time frequency domain short time fourier transform stft was used in this study the proposed sca based approach has two main stages modal matrix estimation and modal displacement estimation in the first stage hierarchical clustering algorithm was used to estimate the modal matrix the clustering algorithm was preceded by a preprocessing step to select the points in time frequency domain that only one mode makes contribution in the responses these points were fed to the clustering algorithm as an input performing this analysis enhanced the modal matrix estimation accuracy and reduced the computational cost while conducting clustering analysis having estimated mixing matrix the complex valued modal responses in the transformed domain were recovered via smoothed zero norm sl 0 algorithm in a broad sense using the sl 0 algorithm permits researchers to use any kind of transform in seeking sparsity regardless of obtaining real valued or complex valued signals in transformed domain natural frequencies and damping ratios were extracted from the recovered modal responses performance of the proposed method was investigated using a synthetic example and a benchmark structure with earthquake and ambient excitation respectively

statistical inference for independent component analysis application to structural var models abstract the well known problem of non identifiability of structural var models disappears if the structural shocks are independent and if at most one of them is gaussian in that case the relevant estimation technique is the independent component analysis ica since the introduction of ica by comon 1994 various semi parametric estimation methods have been proposed for orthogonalizing the error terms these methods include pseudo maximum likelihood pml approaches and recursive pml the aim of our paper is to derive the asymptotic properties of the pml approaches in particular to study their consistency we conduct monte carlo studies exploring the relative performances of these methods finally an application based on real data shows that structural var models can be estimated without additional identification restrictions in the non gaussian case and that the usual restrictions can be tested

on the renewal risk model under a threshold strategy in this paper we consider the renewal risk process under a threshold dividend payment strategy for this model the expected discounted dividend payments and the gerber shiu expected discounted penalty function are investigated integral equations integro differential equations and some closed form expressions for them are derived when the claims are exponentially distributed it is verified that the expected penalty of the deficit at ruin is proportional to the ruin probability

regularized spectral matching for blind source separation application to fmri imaging the main contribution of this paper is to present a bayesian approach for solving the noisy instantaneous blind source separation problem based on second order statistics of the time varying spectrum the success of the blind estimation relies on the nonstationarity of the second order statistics and their intersource diversity choosing the time frequency domain as the signal representation space and transforming the data by a short time fourier transform stft our method presents a simple em algorithm that can efficiently deal with the time varying spectrum diversity of the sources the estimation variance of the stft is reduced by averaging across time frequency subdomains the algorithm is demonstrated on a standard functional resonance imaging fmri experiment involving visual stimuli in a block design explicitly taking into account the noise in the model the proposed algorithm has the advantage of extracting only relevant task related components and considers the remaining components artifacts to be noise