generalizing the hough transform to detect arbitrary shapes abstract the hough transform is a method for detecting curves by exploiting the duality between points on a curve and parameters of that curve the initial work showed how to detect both analytic curves 1 2 and non analytic curves 3 but these methods were restricted to binary edge images this work was generalized to the detection of some analytic curves in grey level images specifically lines 4 circles 5 and parabolas 6 the line detection case is the best known of these and has been ingeniously exploited in several applications 7 8 9 we show how the boundaries of an arbitrary non analytic shape can be used to construct a mapping between image space and hough transform space such a mapping can be exploited to detect instances of that particular shape in an image furthermore variations in the shape such as rotations scale changes or figure ground reversals correspond to straightforward transformations of this mapping however the most remarkable property is that such mappings can be composed to build mappings for complex shapes from the mappings of simpler component shapes this makes the generalized hough transform a kind of universal transform which can be used to find arbitrarily complex shapes

blind separation of positive sources by globally convergent gradient search the instantaneous noise free linear mixing model in independent component analysis is largely a solved problem under the usual assumption of independent nongaussian sources and full column rank mixing matrix however with some prior information on the sources like positivity new analysis and perhaps simplified solution methods may yet become possible in this letter we consider the task of independent component analysis when the independent sources are known to be nonnegative and well grounded which means that they have a nonzero pdf in the region of zero it can be shown that in this case the solution method is basically very simple an orthogonal rotation of the whitened observation vector into nonnegative outputs will give a positive permutation of the original sources we propose a cost function whose minimum coincides with nonnegativity and derive the gradient algorithm under the whitening constraint under which the separating matrix is orthogonal we further prove that in the stiefel manifold of orthogonal matrices the cost function is a lyapunov function for the matrix gradient flow implying global convergence thus this algorithm is guaranteed to find the nonnegative well grounded independent sources the analysis is complemented by a numerical simulation which illustrates the algorithm

an information maximization approach to blind separation and blind deconvolution we derive a new self organizing learning algorithm that maximizes the information transferred in a network of nonlinear units the algorithm does not assume any knowledge of the input distributions and is defined here for the zero noise limit under these conditions information maximization has extra properties not found in the linear case linsker 1989 the nonlinearities in the transfer function are able to pick up higher order moments of the input distributions and perform something akin to true redundancy reduction between units in the output representation this enables the network to separate statistically independent components in the inputs a higher order generalization of principal components analysis we apply the network to the source separation or cocktail party problem successfully separating unknown mixtures of up to 10 speakers we also show that a variant on the network architecture is able to perform blind deconvolution cancellation of unknown echoes and reverberation in a speech signal finally we derive dependencies of information transfer on time delays we suggest that information maximization provides a unifying framework for problems in blind signal processing

equivariant adaptive selective transmission in this paper we consider the problem of selective transmission the dual of the blind source separation task in which a set of independent source signals are adaptively premixed prior to a nondispersive physical mixing process so that each source can be independently monitored in the far field following similar procedures for information theoretic blind source separation we derive a stochastic gradient algorithm for iteratively estimating the premixing matrix in the selective transmission problem and through a simple modification we obtain a second algorithm whose performance is equivariant with respect to the channel s mixing characteristics the local stability conditions for the algorithms about any selective transmission solution are shown to be the same as those for similar source separation algorithms practical implementation issues are discussed including the estimation of the combined system matrix and the reordering and scaling of the received signals within the algorithm mean square error based selective transmission algorithms are also derived for performance comparison purposes simulations indicate the useful behavior of the premixing algorithms for selective transmission

source separation using a criterion based on second order statistics it is often assumed that blind separation of dynamically mixed sources cannot be done with second order statistics it is shown that separation of dynamically mixed sources indeed can be performed using second order statistics only a criterion based on second order statistics for the purpose of separating crosswise mixtures is stated the criterion is used in order to derive a gradient based separation algorithm as well as a newton type separation algorithm the uniqueness of the solution representing the separation is also investigated this reveals that 1 the channel system is parameter identifiable under weak conditions and 2 if the sources have the same color there exists at most two solutions the local convergence behavior of the proposed algorithm is studied and reveals a sufficient condition for local convergence furthermore the estimates of the channel system are shown to be consistent or to locally minimize the criterion

a cubic b spline semi analytical algorithm for simulation of 3d steady state convection diffusion reaction problems abstract in this work a new cubic b spline based semi analytical algorithm is presented for solving 3d anisotropic convection diffusion reaction cdr problems in the inhomogeneous medium the mathematical model is expressed by the quasi linear second order elliptic partial differential equations epde with mixed derivatives and variable coefficients the final approximation is obtained as a sum of the rough primary solution and the modified spline interpolants with free parameters the primary solution mathematically satisfies boundary conditions thus the free parameters of interpolants are chosen to satisfy the governing equation in the solution domain the numerical examples demonstrate the high accuracy of the proposed method in solving 3d cdr problems in single and multi connected domains

implementation of a variable stepsize variable formula method in the time integration part of a code for treatment of long range transport of air pollutants abstract a mathematical model consisting of two partial differential equations is used to study the long range transport of sulphur di oxide and sulphate over europe the discretization of the first order space derivatives the advection terms is carried out by a pseudospectral fourier algorithm a special technique is applied in the discretization of the second order space derivatives the diffusion terms two large systems of ordinary differential equations are solved at each time step it is shown that these systems can efficiently be treated by a variable stepsize variable formula method vsvfm based on the use of predictor corrector schemes the stepsize selection strategy and the formula selection strategy are discussed in detail an attempt to carry out both an accuracy control and a stability control is made at each time step the great efficiency of the vsvfm implemented in our software as well as the reliability of the results are illustrated by numerical experiments in which real meteorological data for 1979 at the grid points of a space domain covering the whole of europe were used the main ideas implemented in the time integration part might be applied in many other situations where the systems of ordinary differential equations arising after the space discretization are only moderately stiff so that the stability requirements are dominant over the accuracy requirements on a large part of the time interval but the use of implicit time integration algorithms that require solving systems of algebraic equations at each time step is not justified as an illustration only it should be mentioned that such an application has been carried out in connection with models describing long range transport of nitrogen pollutants over europe

a new blind method for separating m 1 sources from m mixtures in this paper we consider the problem of underdetermined blind source separation ubss i e there are more sources than mixtures by exploiting the time frequency tf sparsity of the source signals some tf ubss algorithms have recently been proposed in the literature these algorithms require that the number of active sources at any tf point should not exceed one or be strictly less than the number of mixtures in this paper we show that if the number of sources is greater than the number of mixtures by one the sparsity assumption can be further relaxed especially it is allowed to have as many sources as mixtures at any tf point in this case then we propose a new tf ubss method to recover the sources the relaxation on the maximum number of active sources at tf points ensures that the tf based methods can be used in a wider range of applications

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

a constrained em algorithm for independent component analysis we introduce a novel way of performing independent component analysis using a constrained version of the expectation maximization em algorithm the source distributions are modeled as d one dimensional mixtures of gaussians the observed data are modeled as linear mixtures of the sources with additive isotropic noise this generative model is fit to the data using constrained em the simpler soft switching approach is introduced which uses only one parameter to decide on the sub or supergaussian nature of the sources we explain how our approach relates to independent factor analysis

discretization errors in the hough transform abstract straight line segments in a two dimensional image can be detected with the hough transform by searching peaks in a parameter space the influence on the hough transform of the quantization of the parameter space the quantization of the image and the width of the line segment is investigated in this paper the hough transform was improved by o gorman and clowes by taking into account the gradient direction the resulting scatter of the peaks can be reduced by using a weighting function in the transform examples of asbestos preparations are given

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

independent vector analysis identification conditions and performance bounds recently an extension of independent component analysis ica from one to multiple datasets termed independent vector analysis iva has been a subject of significant research interest iva has also been shown to be a generalization of hotelling s canonical correlation analysis in this paper we provide the identification conditions for a general iva formulation which accounts for linear nonlinear and sample to sample dependencies the identification conditions are a generalization of previous results for ica and for iva when samples are independently and identically distributed furthermore a principal aim of iva is identification of dependent sources between datasets thus we provide additional conditions for when the arbitrary ordering of the estimated sources can be common across datasets performance bounds in terms of the cramer rao lower bound are also provided for demixing matrices and interference to source ratio the performance of two iva algorithms are compared to the theoretical bounds

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

fourth order criteria for blind sources separation various criteria based on contrast functions as well as higher order statistics are used for solving the problem of blind separation of sources in the paper for the case of instantaneous mixtures of two sources it is proved that the minimization or the cancellation of a really simple criterion a fourth order cross cumulant leads to a set of solutions whose spurious ones can be simply cancelled by using a decorrelation

blind separation of signals with mixed kurtosis signs using threshold activation functions a parameterized activation function in the form of an adaptive threshold for a single layer neural network which separates a mixture of signals with any distribution except for gaussian is introduced this activation function is particularly simple to implement since it neither uses hyperbolic nor polynomial functions unlike most other nonlinear functions used for blind separation for some specific distributions the stable region of the threshold parameter is derived and optimal values for best separation performance are given if the threshold parameter is made adaptive during the separation process the successful separation of signals whose distribution is unknown is demonstrated and compared against other known methods

blind signal separation using steepest descent method a method that significantly improves the convergence rate of the gradient based blind signal separation bss algorithm for convolutive mixtures is proposed the proposed approach is based on the steepest descent algorithm suitable for constrained bss problems where the constraints are included to ease the permutation effects associated with the convolutive mixtures in addition the method is realized using a modified golden search method plus parabolic interpolation and this allows the optimum step size to be determined with only a few calculations of the cost function evaluation of the proposed procedure in simulated environments and in a real room environment shows that the proposed method results in significantly faster convergence for the bss when compared with a fixed step size gradient based algorithm in addition for blind signal extraction where only a main speech source is desired a combined scheme consisting of the proposed bss and a postprocessor such as an adaptive noise canceller offers impressive noise suppression levels while maintaining low target signal distortion levels

a generalized contrast function and stability analysis for overdetermined blind separation of instantaneous mixtures in this letter the problem of blind separation of n independent sources from their m linear instantaneous mixtures is considered first a generalized contrast function is defined as a valuable extension of the existing classical and nonsymmetrical contrast functions it is applicable to the overdetermined blind separation m n with an unknown number of sources because not only independent components but also redundant ones are allowed in the outputs of a separation system second a natural gradient learning algorithm developed primarily for the complete case m n is shown to work as well with an n m or m m separating matrix for each optimizes a certain mutual information contrast function finally we present stability analysis for a newly proposed generalized orthogonal natural gradient algorithm which can perform the overdetermined blind separation when n is unknown obtaining an expectable result that its local stability conditions are slightly stricter than those of the conventional natural gradient algorithm using an invertible mixing matrix m n

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

algorithms for complex ml ica and their stability analysis using wirtinger calculus we derive a class of algorithms for independent component analysis ica based on maximum likelihood ml estimation and perform stability analysis of natural gradient ml ica with and without the constraint for unitary demixing matrix in the process we demonstrate how wirtinger calculus facilitates derivations and most importantly performing second order analysis in the complex domain and eliminates the need for making simplifying assumptions we derive natural gradient complex ml ica update rule and its variant with a unitary constraint as well as a newton algorithm for better convergence behavior the conditions for local stability are derived and studied using a generalized gaussian density ggd source model when the sources are circular and non gaussian we show analytically that both the ml and ml unitary ica update rules converge to the inverse of mixing matrix subject to a phase shift when the sources are noncircular and non gaussian we show that the nonunitary ml ica update rule is more stable than the ml unitary ica update rule when the sources are noncircular gaussians both update rules are stable only when the sources have distinct noncircularity indices simulation results are given to support these results

statistical dynamics of on line independent component analysis the learning dynamics of on line independent component analysis is analysed in the limit of large data dimension we study a simple hebbian learning algorithm that can be used to separate out a small number of non gaussian components from a high dimensional data set the de mixing matrix parameters are confined to a stiefel manifold of tall orthogonal matrices and we introduce a natural gradient variant of the algorithm which is appropriate to learning on this manifold for large input dimension the parameter trajectory of both algorithms passes through a sequence of unstable fixed points each described by a diffusion process in a polynomial potential choosing the learning rate too large increases the escape time from each of these fixed points effectively trapping the learning in a sub optimal state in order to avoid these trapping states a very low learning rate must be chosen during the learning transient resulting in learning time scales of o n2 or o n3 iterations where n is the data dimension escape from each sub optimal state results in a sequence of symmetry breaking events as the algorithm learns each source in turn this is in marked contrast to the learning dynamics displayed by related on line learning algorithms for multilayer neural networks and principal component analysis although the natural gradient variant of the algorithm has nice asymptotic convergence properties it has an equivalent transient dynamics to the standard hebbian algorithm

adaptive blind separation with an unknown number of sources the blind source separation bss problem with an unknown number of sources is an important practical issue that is usually skipped by assuming that the source number n is known and equal to the number m of sensors this letter studies the general bss problem satisfying m n first it is shown that the mutual information of outputs of the separation network is a cost function for bss provided that the mixing matrix is of full column rank and the m m separating matrix is nonsingular the mutual information reaches its local minima at the separation points where the m outputs consist of n desired source signals and m n redundant signals second it is proved that the natural gradient algorithm proposed primarily for complete bss m n can be generalized to deal with the overdetermined bss problem m n but it would diverge inevitably due to lack of a stationary point to overcome this shortcoming we present a modified algorithm which can perform bss steadily and provide the desired source signals at specified channels if some matrix is designed properly finally the validity of the proposed algorithm is confirmed by computer simulations on artificially synthesized data

super exponential methods for blind deconvolution a class of iterative methods for solving the blind deconvolution problem i e for recovering the input of an unknown possibly nonminimum phase linear system by observation of its output is presented these methods are universal do not require prior knowledge of the input distribution are computationally efficient and statistically stable and converge to the desired solution regardless of initialization at a very fast rate the effects of finite length of the data finite length of the equalizer and additive noise in the system on the attainable performance intersymbol interference are analyzed it is shown that in many cases of practical interest the performance of the proposed methods is far superior to linear prediction methods even for minimum phase systems recursive and sequential algorithms are also developed which allow real time implementation and adaptive equalization of time varying systems

adaptive online learning algorithms for blind separation maximum entropy and minimum mutual information there are two major approaches for blind separation maximum entropy me and minimum mutual information mmi both can be implemented by the stochastic gradient descent method for obtaining the demixing matrix the mi is the contrast function for blind separation the entropy is not to justify the me the relation between me and mmi is first elucidated by calculating the first derivative of the entropy and proving that the mean subtraction is necessary in applying the me and at the solution points determined by the mi the me will not update the demixing matrix in the directions of increasing the cross talking second the natural gradient instead of the ordinary gradient is introduced to obtain efficient algorithms because the parameter space is a riemannian space consisting of matrices the mutual information is calculated by applying the gram charlier expansion to approximate probability density functions of the outputs finally we propose an efficient learning algorithm that incorporates with an adaptive method of estimating the unknown cumulants it is shown by computer simulation that the convergence of the stochastic descent algorithms is improved by using the natural gradient and the adaptively estimated cumulants

determination of the attitude of 3d objects from a single perspective view a method for finding analytical solutions to the problem of determining the attitude of a 3d object in space from a single perspective image is presented its principle is based on the interpretation of a triplet of any image lines as the perspective projection of a triplet of linear ridges of the object model and on the search for the model attitude consistent with these projections the geometrical transformations to be applied to the model to bring it into the corresponding location are obtained by the resolution of an eight degree equation in the general case using simple logical rules it is shown on examples related to polyhedra that this approach leads to results useful for both location and recognition of 3d objects because few admissible hypotheses are retained from the interpolation of the three line segments line matching by the prediction verification procedure is thus less complex

sequential blind extraction of instantaneously mixed sources this paper presents a general approach to sequential blind extraction of instantaneously mixed sources for several major ill conditioned cases as well as the regular case of full column rank mixing matrices four ill conditioned cases are considered the mixing matrix is square but singular the number of sensors is less than that of sources the number of sensors is larger than that of sources but the column rank of the mixing matrix is deficient and the number of sources is unknown and the column rank of the mixing matrix is deficient first a solvability analysis is presented for a general case a necessary and sufficient condition for extractability is derived a sequential blind extraction approach is then proposed to extract all theoretically separable sources next a principle and a cost function based on fourth order cumulants are presented for blind source extraction by minimizing the cost function under a nonsingularity constraint of the extraction matrix all theoretically separable sources can be extracted sequentially finally simulation results are presented to demonstrate the validity and performance of the blind source extraction approach

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

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

scale and orientation invariant generalized hough transform a new approach abstract the conventional generalized hough transform ght is useful for detecting or locating translated 2 dimensional 2d object shapes however a weakness of the conventional ght is that a brute force approach is usually required to handle shape scaling and rotation resulting in the use of a 4d hough counting space hcs a new version of the ght called scale and orientation invariant ght soight is proposed to remove this weakness the improvement is based on the use of half lines and circles to replace the displacement vectors used in the conventional ght for cell value incrementation the required dimensionality of the hcs for the soight is reduced to 2d so that the storage and computation requirements for cell value incrementation and maximum detection in the hcs can be reduced effectively some experimental results are included to demonstrate the applicability of the proposed soight

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

an iterative hough procedure for three dimensional object recognition abstract this paper describes an iterative hough procedure for recognizing images of three dimensional objects straight line segments in the image are matched by finding the parameters of a viewing transformation of a three dimensional model consisting of line segments assuming the scale of the object is known there are three orientation and two translation parameters to be estimated initially a sparse regular subset of parameters and transformations is evaluated for goodness of fit then the procedure is repeated by successively subdividing the parameter space near current best estimates or peaks

least squares finite element method for the advection diffusion equation the space time least squares finite element methods are constructed for the advection diffusion equation by using both linear shape functions and quadratic b spline shape functions two test problems are studied to demonstrate the accuracy of the present methods results of the two schemes have been compared

solution of nonlinear evolution problems by parallelized collocation interpolation methods abstract this paper deals with the solution of initial boundary value problems for nonlinear evolution equations the solution technique is based on collocation interpolation methods which are improved in order to reduce computational errors at fixed discretizations of the independent variables the method consists in parallelizing the approximation of the space derivatives so that the same approximation is reached by a lower number of collocation points and hence by a lower computation time the analysis includes a theoretical and computational estimate both of the approximation error and of the computational time

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

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 linear non gaussian acyclic model for causal discovery in recent years several methods have been proposed for the discovery of causal structure from non experimental data such methods make various assumptions on the data generating process to facilitate its identification from purely observational data continuing this line of research we show how to discover the complete causal structure of continuous valued data under the assumptions that a the data generating process is linear b there are no unobserved confounders and c disturbance variables have non gaussian distributions of non zero variances the solution relies on the use of the statistical method known as independent component analysis and does not require any pre specified time ordering of the variables we provide a complete matlab package for performing this lingam analysis short for linear non gaussian acyclic model and demonstrate the effectiveness of the method using artificially generated data and real world data

quartic and quintic b spline methods for advection diffusion equation differential quadrature methods based on b spline functions of degree four and five have been introduced to solve advection diffusion equation numerically two initial boundary value problems modeling the transportation of a concentration and distribution of an initial pulse are simulated using both methods the errors of the numerical results obtained by both methods have been computed stability analysis for both methods is also studied by the use of matrix stability

equivariant adaptive source separation source separation consists of recovering a set of independent signals when only mixtures with unknown coefficients are observed this paper introduces a class of adaptive algorithms for source separation that implements an adaptive version of equivariant estimation and is henceforth called equivariant adaptive separation via independence easi the easi algorithms are based on the idea of serial updating this specific form of matrix updates systematically yields algorithms with a simple structure for both real and complex mixtures most importantly the performance of an easi algorithm does not depend on the mixing matrix in particular convergence rates stability conditions and interference rejection levels depend only on the normalized distributions of the source signals closed form expressions of these quantities are given via an asymptotic performance analysis the theme of equivariance is stressed throughout the paper the source separation problem has an underlying multiplicative structure the parameter space forms a matrix multiplicative group we explore the favorable consequences of this fact on implementation performance and optimization of easi algorithms

solution of nonlinear initial value problems by the spline based differential quadrature method the spline based differential quadrature method sdqm is applied to the solution of nonlinear initial value problems explicit expressions of weighting coefficients for approximation of derivatives are presented dynamic systems with duffing type nonlinearity are solved to demonstrate the effectiveness of the method numerical results of three examples show that the spline based differential quadrature method is versatile and stable in the solution of nonlinear initial value problems it can be counted on to achieve satisfactory accuracy for long term integration

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

perspective transformation invariant generalized hough transform for perspective planar shape detection and matching abstract in the real world most object shapes are perspectively transformed when imaged how to recognize or locate such shapes in images is interesting and important the conventional generalized hough transform ght is useful for detecting or locating translated two dimensional 2d planar shapes however it cannot be used for detecting perspectively transformed planar shapes a new version of the ght called perspective transformation invariant generalized hough transform ptight is proposed to remove this weakness the ptight is based on the use of a new perspective reference table that is built up by applying both forward and inverse perspective transformations on a given template shape image from all viewing directions and positions due to the use of the point spread function to express the perspective reference table the required dimensionality of the hough counting space hcs for the ptight is reduced to 2d after performing the ptight on an input image the peaks in the hcs whose values are larger than a threshold is picked out as the candidate locations of the perspective shape to be detected in the input images by performing an inverse ptight on the candidates one of the candidate locations whose corresponding shape matches best with the input shape is selected and the desired parameters of the perspective transformation can be obtained some experimental results are included to demonstrate the applicability of the proposed ptight

a novel blind deconvolution scheme for image restoration using recursive filtering we present a novel blind deconvolution technique for the restoration of linearly degraded images without explicit knowledge of either the original image or the point spread function the technique applies to situations in which the scene consists of a finite support object against a uniformly black grey or white background this occurs in certain types of astronomical imaging medical imaging and one dimensional 1 d gamma ray spectra processing among others the only information required are the nonnegativity of the true image and the support size of the original object the restoration procedure involves recursive filtering of the blurred image to minimize a convex cost function we prove convexity of the cost function establish sufficient conditions to guarantee a unique solution and examine the performance of the technique in the presence of noise the new approach is experimentally shown to be more reliable and to have faster convergence than existing nonparametric finite support blind deconvolution methods for situations in which the exact object support is unknown we propose a novel support finding algorithm

independent factor analysis we introduce the independent factor analysis ifa method for recovering independent hidden sources from their observed mixtures ifa generalizes and unifies ordinary factor analysis fa principal component analysis pca and independent component analysis ica and can handle not only square noiseless mixing but also the general case where the number of mixtures differs from the number of sources and the data are noisy ifa is a two step procedure in the first step the source densities mixing matrix and noise covariance are estimated from the observed data by maximum likelihood for this purpose we present an expectation maximization em algorithm which performs unsupervised learning of an associated probabilistic model of the mixing situation each source in our model is described by a mixture of gaussians thus all the probabilistic calculations can be performed analytically in the second step the sources are reconstructed from the observed data by an optimal nonlinear estimator a variational approximation of this algorithm is derived for cases with a large number of sources where the exact algorithm becomes intractable our ifa algorithm reduces to the one for ordinary fa when the sources become gaussian and to an em algorithm for pca in the zero noise limit we derive an additional em algorithm specifically for noiseless ifa this algorithm is shown to be superior to ica since it can learn arbitrary source densities from the data beyond blind separation ifa can be used for modeling multidimensional data by a highly constrained mixture of gaussians and as a tool for nonlinear signal encoding

evam an eigenvector based algorithm for multichannel blind deconvolution of input colored signals a new algorithm is proposed for the deconvolution of an unknown possibly colored gaussian or nonstationary signal that is observed through two or more unknown channels described by rational system transfer functions more specifically not only the root pole and zero locations but also the orders of the channel transfer functions are unknown it is assumed that the channel orders may be overestimated the proposed algorithm estimates the orders and root locations of the channel transfer functions therefore it can also be used in multichannel system identification problems the input signal is allowed to be nonstationary and the channel transfer functions may be a nonminimum phase as well as noncausal hence the proposed algorithm is particularly suitable for applications such as dereverberation of speech signals recorded through multiple microphones several experimental results indicate improvement compared to the existing methods in the literature

a differential quadrature algorithm for simulations of nonlinear schrodinger equation numerical simulations of nonlinear schrodinger equation are studied using differential quadrature method based on cosine expansion propogation of a soliton interaction of two solitons birth of standing and mobile solitons and bound state solutions are simulated the accuracy of the method dq is measured using maximum error norm the results are compared with some earlier works the lowest two conserved quantities are computed numerically for all cases

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

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

faster independent component analysis by preconditioning with hessian approximations independent component analysis ica is a technique for unsupervised exploration of multichannel data that is widely used in observational sciences in its classic form ica relies on modeling the data as linear mixtures of nongaussian independent sources the maximization of the corresponding likelihood is a challenging problem if it has to be completed quickly and accurately on large sets of real data this problem has been addressed by resorting to quasi newton methods which rely on sparse approximations of the hessian of the log likelihood however those approximations are not accurate when the ica model does not hold exactly as is often the case for real datasets we propose a new algorithm dubbed picard which makes use of sparse approximate hessians only as a preconditioner to the l bfgs algorithm refining the hessian approximation from a memory of the past iterates extensive numerical comparisons to several algorithms of the same class demonstrate the superior performance of the proposed technique especially on real data

stochastic trapping in a solvable model of on line independent component analysis previous analytical studies of on line independent component analysis ica learning rules have focused on asymptotic stability and efficiency in practice the transient stages of learning are often more significant in determining the success of an algorithm this is demonstrated here with an analysis of a hebbian ica algorithm which can find a small number of nongaussian components given data composed of a linear mixture of independent source signals an idealized data model is considered in which the sources comprise a number of nongaussian and gaussian sources and a solution to the dynamics is obtained in the limit where the number of gaussian sources is infinite previous stability results are confirmed by expanding around optimal fixed points where a closed form solution to the learning dynamics is obtained however stochastic effects are shown to stabilize otherwise unstable suboptimal fixed points conditions required to destabilize one such fixed point are obtained for the case of a single nongaussian component indicating that the initial learning rate required to escape successfully is very low o n 2 where n is the data dimension resulting in very slow learning typically requiring o n3 iterations simulations confirm that this picture holds for a finite system

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

globally convergent blind source separation based on a multiuser kurtosis maximization criterion we consider the problem of recovering blindly i e without the use of training sequences a number of independent and identically distributed source user signals that are transmitted simultaneously through a linear instantaneous mixing channel the received signals are hence corrupted by interuser interference iui and we can model them as the outputs of a linear multiple input multiple output mimo memoryless system assuming the transmitted signals to be mutually independent i i d and to share the same non gaussian distribution a set of necessary and sufficient conditions for the perfect blind recovery up to scalar phase ambiguities of all the signals exists and involves the kurtosis as well as the covariance of the output signals we focus on a straightforward blind constrained criterion stemming from these conditions from this criterion we derive an adaptive algorithm for blind source separation which we call the multiuser kurtosis muk algorithm at each iteration the algorithm combines a stochastic gradient update and a gram schmidt orthogonalization procedure in order to satisfy the criterion s whiteness constraints a performance analysis of its stationary points reveals that the muk algorithm is free of any stable undesired local stationary points for any number of sources hence it is globally convergent to a setting that recovers them all

a theoretical analysis of piezoelectric composite laminate with larger amplitude deflection effect part ii hermite differential quadrature method and application incorporating the effects of larger amplitude deflection and electro elastical properties of piezoelectric lamina the hamilton s variation principle was used to deduce the fundamental formulations of smart anisotropic composite plate in part i in terms of reddy s simple higher order theory in order to solve the five highly coupled nonlinear partial differential equations with complicated overlapping boundary conditions a novel numerical method hermite differential quadrature hdq method was developed to implement the differential equations with complicated overlapping boundary conditions based on the presently developed hdq method any orders derivatives of the unknown functions or any boundary conditions can be point collocation based discretized by a set of point values along x and y direction then a system of complete algebraic nonlinear equations can be constructed to calculate out the final point values of the mid plane displacements by using the governing equations and relative boundary conditions with hdq method finally some detailed numerical examples for the anisotropic piezoelectric composite laminate with the distributed poling directions of piezoelectric layer and fiber orientations of composite layers were studied to validate the developed theoretical analysis model and hdq numerical method