ideal spatial adaptation by wavelet shrinkage summary with ideal spatial adaptation an oracle furnishes information about how best to adapt a spatially variable estimator whether piecewise constant piecewise polynomial variable knot spline or variable bandwidth kernel to the unknown function estimation with the aid of an oracle offers dramatic advantages over traditional linear estimation by nonadaptive kernels however it is a priori unclear whether such performance can be obtained by a procedure relying on the data alone we describe a new principle for spatially adaptive estimation selective wavelet reconstruction we show that variable knot spline fits and piecewise polynomial fits when equipped with an oracle to select the knots are not dramatically more powerful than selective wavelet reconstruction with an oracle we develop a practical spatially adaptive method riskshrink which works by shrinkage of empirical wavelet coefficients riskshrink mimics the performance of an oracle for selective wavelet reconstruction as well as it is possible to do so a new inequality in multivariate normal decision theory which we call the oracle inequality shows that attained performance differs from ideal performance by at most a factor of approximately 2 log n where n is the sample size moreover no estimator can give a better guarantee than this within the class of spatially adaptive procedures riskshrink is essentially optimal relying only on the data it comes within a factor log 2 n of the performance of piecewise polynomial and variableknot spline methods equipped with an oracle in contrast it is unknown how or if piecewise polynomial methods could be made to function this well when denied access to an oracle and forced to rely on data alone

analysis of multiresolution image denoising schemes using generalized gaussian and complexity priors research on universal and minimax wavelet shrinkage and thresholding methods has demonstrated near ideal estimation performance in various asymptotic frameworks however image processing practice has shown that universal thresholding methods are outperformed by simple bayesian estimators assuming independent wavelet coefficients and heavy tailed priors such as generalized gaussian distributions ggds in this paper we investigate various connections between shrinkage methods and maximum a posteriori map estimation using such priors in particular we state a simple condition under which map estimates are sparse we also introduce a new family of complexity priors based upon rissanen s universal prior on integers one particular estimator in this class outperforms conventional estimators based on earlier applications of the minimum description length mdl principle we develop analytical expressions for the shrinkage rules implied by ggd and complexity priors this allows us to show the equivalence between universal hard thresholding map estimation using a very heavy tailed ggd and mdl estimation using one of the new complexity priors theoretical analysis supported by numerous practical experiments shows the robustness of some of these estimates against mis specifications of the prior a basic concern in image processing applications

minimal coupling model of the biaxial nematic phase a minimal coupling model exhibiting isotropic uniaxial and biaxial nematic phases is analyzed in detail and its relation to existing models known in the literature is clarified its intrinsic symmetry properties are exploited to restrict the relevant ranges of coupling constants further on properties of the model are thoroughly investigated by means of bifurcation theory as proposed by kayser and raveche phys rev a 17 2067 1978 and mulder phys rev a 39 360 1989 as a first step toward this goal the bifurcation theory is applied to a general formulation of density functional theory in terms of direct correlation functions on a general formal level the theory is then analyzed to show that the bifurcation points from the reference high symmetry equilibrium phase to a low symmetry structure depend only on the properties of the one particle distribution function and the direct pair correlation function of the reference phase the character of the bifurcation whether spinodal critical tricritical isolated landau point etc depends in addition on a few higher order direct correlation functions explicit analytical results are derived for the case when only the leading l 2 terms of the potential mean field analysis or of the direct pair correlation function expansion in the symmetry adapted basis are retained formulas are compared with the numerical calculations for the mean field momentum l 2 potential model in which case they are exact in particular bifurcations from the isotropic and uniaxial nematic to the biaxial nematic phases are discussed the possibility of the recently reported nematic uniaxial nematic biaxial tricritical point a m sonnet e g virga and g e durand phys rev e 67 061701 2003 is analyzed as well

a medial axis transformation for grayscale pictures blum s medial axis transformation mat for binary pictures yields medial axis points that lie midway between opposite borders of a region or along angle bisectors this note discusses a generalization of the mat in which a score is computed for each point p of a grayscale picture based on the gradient magnitudes at pairs of points that have p as their midpoint these scores are high at points that lie midway between pairs of antiparallel edges or along angle bisectors so that they define a mat like skeleton which we may call the gradmat however this skeleton is rather sensitive to the presence of noise edges or to irregularities in the region edges and it also is subject to artifacts created by pairs of edges belonging to different objects

macroscopic and molecular symmetries of unconventional nematic phases the effects of the molecular symmetry on macroscopic properties of conventional and unconventional nematic phases are investigated theoretically these effects concern 1 the form of the molecular orientation fluctuations 2 the thermodynamic behavior and the list of stable ordered phases 3 the effective symmetry of the molecules in the ordered phases the order parameter consists of tensors forming the main harmonics of the fluctuation distribution in conventional models valid for uniaxial molecules a single tensor is sufficient while unconventional models valid for less symmetric molecules need several tensors with the same rank we analyze the qualitative differences arising when the number of equivalent tensors varies we show how to work out complete models in the general case and to calculate the sequences of stable phases and the corresponding effective molecular symmetries this yields for each molecular group and each tensor rank a complete classification and a deep insight into the structure of thermotropic nematics this work generalizes the approach we have applied to polar nematics recently observed in polyester compounds and to unconventional uniaxial and biaxial phases of bent core materials

blind source separation based on time frequency signal representations blind source separation consists of recovering a set of signals of which only instantaneous linear mixtures are observed thus far this problem has been solved using statistical information available on the source signals this paper introduces a new blind source separation approach exploiting the difference in the time frequency t f signatures of the sources to be separated the approach is based on the diagonalization of a combined set of spatial t f distributions in contrast to existing techniques the proposed approach allows the separation of gaussian sources with identical spectral shape but with different t f localization properties the effects of spreading the noise power while localizing the source energy in the t f domain amounts to increasing the robustness of the proposed approach with respect to noise and hence improved performance asymptotic performance analysis and numerical simulations are provided

time frequency approach to underdetermined blind source separation this paper presents a new time frequency tf underdetermined blind source separation approach based on wigner ville distribution wvd and khatri rao product to separate n non stationary sources from m m n mixtures first an improved method is proposed for estimating the mixing matrix where the negative value of the auto wvd of the sources is fully considered then after extracting all the auto term tf points the auto wvd value of the sources at every auto term tf point can be found out exactly with the proposed approach no matter how many active sources there are as long as n 2m 1 further discussion about the extraction of auto term tf points is made and finally the numerical simulation results are presented to show the superiority of the proposed algorithm by comparing it with the existing ones

mesogenic lattice models with partly antinematic interactions producing uniaxial nematic phases the present paper considers nematogenic lattice models involving particles of d 2h symmetry whose centers of mass are associated with a three dimensional simple cubic lattice the pair potential is isotropic in orientation space and restricted to nearest neighbors let two orthonormal triads define orientations of a pair of interacting particles the simplest potential models proposed in the literature can be reduced to a linear combination involving the squares of the scalar products between corresponding unit vectors only and depending on three parameters by now various sets of potential parameters have been proposed and studied in the literature some of which capable of producing biaxial orientational order at sufficiently low temperature on the other hand in experimental terms mesogenic biaxial molecules mostly produce uniaxial mesophases thus we address here two very simple cases involving a nematic calamitic term as well as one model p0m or two model ppm antinematic ones whose coefficients are set equal in magnitude when only one antinematic coefficient is used the third one is set to zero the calamitic term favors the alignment of two corresponding molecular axes whereas antinematic terms or geometric constraints tend to keep two other pairs of axes mutually orthogonal the models were investigated by molecular field treatments and monte carlo simulation and found to predict a first or second order transitions between uniaxial nematic and isotropic phases the molecular field treatments yielded results in reasonable agreement with simulation

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

estimation of sparse nonnegative sources from noisy overcomplete mixtures using map in this letter we propose a new algorithm for estimating sparse nonnegative sources from a set of noisy linear mixtures in particular we consider difficult situations with high noise levels and more sources than sensors underdetermined case we show that when sources are very sparse in time and overlapped at some locations they can be recovered even with very low signal to noise ratio and by using many fewer sensors than sources a theoretical analysis based on bayesian estimation tools is included showing strong connections with algorithms in related areas of research such as ica nmf focuss and sparse representation of data with overcomplete dictionaries our algorithm uses a bayesian approach by modeling sparse signals through mixed state random variables this new model for priors imposes l0 norm based sparsity we start our analysis for the case of nonoverlapped sources 1 sparse which allows us to simplify the search of the posterior maximum avoiding a combinatorial search general algorithms for overlapped cases such as 2 sparse and k sparse sources are derived by using the algorithm for 1 sparse signals recursively additionally a combination of our map algorithm with the nn ksvd algorithm is proposed for estimating the mixing matrix and the sources simultaneously in a real blind fashion a complete set of simulation results is included showing the performance of our algorithm

extension and generalization of the gay berne potential in this paper we report a generalized form for the range parameter governing the pair interaction between soft ellipsoidal particles for nonequivalent uniaxial particles we extend the berne pechukas gaussian overlap formalism to obtain an explicit expression for this range parameter we confirm that this result is identical to that given by an approach that is not widely recognized based on an approximation to the perram wertheim hard ellipsoid contact function we further illustrate the power of the latter route by using it to write down the range parameter for the interaction between two nonequivalent biaxial particles an explicit interaction potential for nonequivalent uniaxial particles is obtained by importing the uniaxial range parameter result into the standard gay berne form a parametrization of this potential is investigated for a rod disk interaction

ensemble learning for independent component analysis it is well known that the applicability of independent component analysis ica to high dimensional pattern recognition tasks such as face recognition often suffers from two problems one is the small sample size problem the other is the choice of basis functions or independent components both problems make ica classifier unstable and biased in this paper we propose an enhanced ica algorithm by ensemble learning approach named as random independent subspace ris to deal with the two problems firstly we use the random resampling technique to generate some low dimensional feature subspaces and one classifier is constructed in each feature subspace then these classifiers are combined into an ensemble classifier using a final decision rule extensive experimentations performed on the feret database suggest that the proposed method can improve the performance of ica classifier

nonstationary source separation using sequential and variational bayesian learning independent component analysis ica is a popular approach for blind source separation where the mixing process is assumed to be unchanged with a fixed set of stationary source signals however the mixing system and source signals are nonstationary in real world applications e g the source signals may abruptly appear or disappear the sources may be replaced by new ones or even moving by time this paper presents an online learning algorithm for the gaussian process gp and establishes a separation procedure in the presence of nonstationary and temporally correlated mixing coefficients and source signals in this procedure we capture the evolved statistics from sequential signals according to online bayesian learning the activity of nonstationary sources is reflected by an automatic relevance determination which is incrementally estimated at each frame and continuously propagated to the next frame we employ the gp to characterize the temporal structures of time varying mixing coefficients and source signals a variational bayesian inference is developed to approximate the true posterior for estimating the nonstationary ica parameters and for characterizing the activity of latent sources the differences between this ica method and the sequential monte carlo ica are illustrated in the experiments the proposed algorithm outperforms the other ica methods for the separation of audio signals in the presence of different nonstationary scenarios

biaxial and uniaxial phases produced by partly repulsive mesogenic models involving d2h molecular symmetries the present paper considers biaxial nematogenic lattice models involving particles of d 2h symmetry whose centers of mass are associated with a three dimensional simple cubic lattice the pair potential is isotropic in orientation space and restricted to nearest neighbors let two orthonormal triads define orientations of a pair of interacting particles the investigated potential models are quadratic with respect to the nine scalar products between the two sets of unit vectors actually based on available geometric identities these expressions can be reduced to diagonal form containing only the scalar products between corresponding unit vectors and depending on three parameters over the years this comparatively simple functional form has also proven to be rather versatile by now various sets of potential parameters capable of producing mesogenic behavior of some kind have been proposed and studied in the literature a new and simplified form was recently proposed and investigated by sonnet virga durand and de matteis a m sonnet e g virga and g e durand phys rev e 67 061701 2003 g de matteis and e g virga phys rev e 71 061703 2005 and is known to support a biaxial phase at sufficiently low temperature following the idea of the above authors we have studied a more extended range of parameters including cases where biaxiality cannot be sustained in the pair ground state in cases where a biaxial phase survives an appropriate mean field analysis may predict the existence of a direct second order transition to the isotropic phase as well as a second order sequence isotropic to uniaxial to biaxial a second order phase transition is also predicted which involves isotropic and uniaxial phases only monte carlo simulations have been carried out as well for a few points in the parameter space and found to produce results which partly confirm mean field predictions

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

hidden markov models for wavelet based blind source separation in this paper we consider the problem of blind source separation in the wavelet domain we propose a bayesian estimation framework for the problem where different models of the wavelet coefficients are considered the independent gaussian mixture model the hidden markov tree model and the contextual hidden markov field model for each of the three models we give expressions of the posterior laws and propose appropriate markov chain monte carlo algorithms in order to perform unsupervised joint blind separation of the sources and estimation of the mixing matrix and hyper parameters of the problem indeed in order to achieve an efficient joint separation and denoising procedures in the case of high noise level in the data a slight modification of the exposed models is presented the bernoulli gaussian mixture model which is equivalent to a hard thresholding rule in denoising problems a number of simulations are presented in order to highlight the performances of the aforementioned approach 1 in both high and low signal to noise ratios and 2 comparing the results with respect to the choice of the wavelet basis decomposition

wavelet based statistical signal processing using hidden markov models wavelet based statistical signal processing techniques such as denoising and detection typically model the wavelet coefficients as independent or jointly gaussian these models are unrealistic for many real world signals we develop a new framework for statistical signal processing based on wavelet domain hidden markov models hmms that concisely models the statistical dependencies and non gaussian statistics encountered in real world signals wavelet domain hmms are designed with the intrinsic properties of the wavelet transform in mind and provide powerful yet tractable probabilistic signal models efficient expectation maximization algorithms are developed for fitting the hmms to observational signal data the new framework is suitable for a wide range of applications including signal estimation detection classification prediction and even synthesis to demonstrate the utility of wavelet domain hmms we develop novel algorithms for signal denoising classification and detection

a robust approach to independent component analysis of signals with high level noise measurements we propose a robust approach for independent component analysis ica of signals where observations are contaminated with high level additive noise and or outliers the source signals may contain mixtures of both sub gaussian and super gaussian components and the number of sources is unknown our robust approach includes two procedures in the first procedure a robust prewhitening technique is used to reduce the power of additive noise the dimensionality and the correlation among sources a cross validation technique is introduced to estimate the number of sources in this first procedure in the second procedure a nonlinear function is derived using the parameterized t distribution density model this nonlinear function is robust against the undue influence of outliers fundamentally moreover the stability of the proposed algorithm and the robust property of misestimating the parameters kurtosis have been studied by combining the t distribution model with a family of light tailed distributions sub gaussian model we can separate the mixture of sub gaussian and super gaussian source components through the analysis of artificially synthesized data and real world magnetoencephalographic meg data we illustrate the efficacy of this robust approach

hierarchy of orientational phases and axial anisotropies in the gauge theoretical description of generalized nematic liquid crystals the paradigm of spontaneous symmetry breaking encompasses the breaking of the rotational symmetries text o 3 of isotropic space to a discrete subgroup i e a three dimensional point group the subgroups form a rich hierarchy and allow for many different phases of matter with orientational order such spontaneous symmetry breaking occurs in nematic liquid crystals and a highlight of such anisotropic liquids is the uniaxial and biaxial nematics generalizing the familiar uniaxial and biaxial nematics to phases characterized by an arbitrary point group symmetry referred to as generalized nematics leads to a large hierarchy of phases and possible orientational phase transitions we discuss how a particular class of nematic phase transitions related to axial point groups can be efficiently captured within a recently proposed gauge theoretical formulation of generalized nematics k liu j nissinen r j slager k wu and j zaanen phys rev x 6 041025 2016 these transitions can be introduced in the model by considering anisotropic couplings that do not break any additional symmetries by and large this generalizes the well known uniaxial biaxial nematic phase transition to any arbitrary axial point group in three dimensions we find in particular that the generalized axial transitions are distinguished by two types of phase diagrams with intermediate vestigial orientational phases and that the window of the vestigial phase is intimately related to the amount of symmetry of the defining point group due to inherently growing fluctuations of the order parameter this might explain the stability of the observed uniaxial biaxial phases as compared to the yet to be observed other possible forms of generalized nematic order with higher point group symmetries

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

segmentation of images having unimodal distributions a gradient relaxation method based on maximizing a criterion function is studied and compared to the nonlinear probabilistic relaxation method for the purpose of segmentation of images having unimodal distributions although both methods provide comparable segmentation results the gradient method has the additional advantage of providing control over the relaxation process by choosing three parameters which can be tuned to obtain the desired segmentation results at a faster rate examples are given on two different types of scenes

denoising and recognition using hidden markov models with observation distributions modeled by hidden markov trees hidden markov models have been found very useful for a wide range of applications in machine learning and pattern recognition the wavelet transform has emerged as a new tool for signal and image analysis learning models for wavelet coefficients have been mainly based on fixed length sequences but real applications often require to model variable length very long or real time sequences in this paper we propose a new learning architecture for sequences analyzed on short term basis but not assuming stationarity within each frame long term dependencies will be modeled with a hidden markov model which in each internal state will deal with the local dynamics in the wavelet domain using a hidden markov tree the training algorithms for all the parameters in the composite model are developed using the expectation maximization framework this novel learning architecture could be useful for a wide range of applications we detail two experiments with artificial and real data model based denoising and speech recognition denoising results indicate that the proposed model and learning algorithm are more effective than previous approaches based on isolated hidden markov trees in the case of the doppler benchmark sequence with 1024 samples and additive white noise the new method reduced the mean squared error from 1 0 to 0 0842 the proposed methods for feature extraction modeling and learning increased the phoneme recognition rates in 28 13 with better convergence than models based on gaussian mixtures

universal mean field phase diagram for biaxial nematics obtained from a minimax principle we study a class of quadratic hamiltonians which describe both fully attractive and partly repulsive molecular interactions characteristic of biaxial liquid crystal molecules to treat the partly repulsive interactions we establish a minimax principle for the associated mean field free energy we show that the phase diagram described by sonnet et al phys rev e 67 061701 2003 is universal our predictions are in good agreement with the recent observations on both v shaped and tetrapodal molecules

high order contrasts for independent component analysis this article considers high order measures of independence for the independent component analysis problem and discusses the class of jacobi algorithms for their optimization several implementations are discussed we compare the proposed approaches with gradient based techniques from the algorithmic point of view and also on a set of biomedical data

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed