experimental evidence of stochastic resonance without tuning due to non gaussian noises in order to test theoretical predictions we have studied the phenomenon of stochastic resonance in an electronic experimental system driven by white non gaussian noise in agreement with the theoretical predictions our main findings are an enhancement of the sensibility of the system together with a remarkable widening of the response robustness this implies that even a single resonant unit can reach a marked reduction in the need for noise tuning

optimal channel switching strategy for average capacity maximization in this study an optimal channel switching strategy is proposed for average capacity maximization in the presence of average and peak power constraints necessary and sufficient conditions are derived to determine when the proposed optimal channel switching strategy can or cannot outperform the optimal single channel strategy which performs no channel switching also it is obtained that the optimal channel switching strategy can be realized by channel switching between at most two different channels in addition a low complexity optimization problem is derived to obtain the optimal channel switching strategy furthermore based on some necessary conditions that need to be satisfied by the optimal channel switching solution an alternative approach is proposed for calculating the optimal channel switching strategy numerical examples are provided to exemplify the derived theoretical results and to provide intuitive explanations

the suboptimality of randomized tests in distributed and quantized detection systems the design of decentralized or quantized detection systems requires simultaneous optimization of quantizer mappings and ultimate fusion rule it is shown that if the likelihood ratios of the unquantized or raw observations are independent and contain no point masses of probability the optimal test does not randomize this is so despite the fact that the data to be fused can be considered discrete the result is a considerable simplification in the design search

multiresolution monogenic signal analysis using the riesz laplace wavelet transform the monogenic signal is the natural 2d counterpart of the 1d analytic signal we propose to transpose the concept to the wavelet domain by considering a complexified version of the riesz transform which has the remarkable property of mapping a real valued primary wavelet basis of l2 r2 into a complex one the riesz operator is also steerable in the sense that it give access to the hilbert transform of the signal along any orientation having set those foundations we specify a primary polyharmonic spline wavelet basis of l2 r2 that involves a single mexican hat like mother wavelet laplacian of a b spline the important point is that our primary wavelets are quasi isotropic they behave like multiscale versions of the fractional laplace operator from which they are derived which ensures steerability we propose to pair these real valued basis functions with their complex riesz counterparts to specify a multiresolution monogenic signal analysis this yields a representation where each wavelet index is associated with a local orientation an amplitude and a phase we give a corresponding wavelet domain method for estimating the underlying instantaneous frequency we also provide a mechanism for improving the shift and rotation invariance of the wavelet decomposition and show how to implement the transform efficiently using perfect reconstruction filterbanks we illustrate the specific feature extraction capabilities of the representation and present novel examples of wavelet domain processing in particular a robust tensor based analysis of directional image patterns the demodulation of interferograms and the reconstruction of digital holograms

a riemannian framework for tensor computing tensors are nowadays a common source of geometric information in this paper we propose to endow the tensor space with an affine invariant riemannian metric we demonstrate that it leads to strong theoretical properties the cone of positive definite symmetric matrices is replaced by a regular and complete manifold without boundaries null eigenvalues are at the infinity the geodesic between two tensors and the mean of a set of tensors are uniquely defined etc we have previously shown that the riemannian metric provides a powerful framework for generalizing statistics to manifolds in this paper we show that it is also possible to generalize to tensor fields many important geometric data processing algorithms such as interpolation filtering diffusion and restoration of missing data for instance most interpolation and gaussian filtering schemes can be tackled efficiently through a weighted mean computation linear and anisotropic diffusion schemes can be adapted to our riemannian framework through partial differential evolution equations provided that the metric of the tensor space is taken into account for that purpose we provide intrinsic numerical schemes to compute the gradient and laplace beltrami operators finally to enforce the fidelity to the data either sparsely distributed tensors or complete tensors fields we propose least squares criteria based on our invariant riemannian distance which are particularly simple and efficient to solve

binary hypothesis testing via measure transformed quasi likelihood ratio test in this paper the gaussian quasi likelihood ratio test gqlrt for non bayesian binary hypothesis testing is generalized by applying a transform to the probability distribution of the data the proposed generalization called measure transformed gqlrt mt gqlrt selects a gaussian probability model that best empirically fits a transformed probability measure of the data by judicious choice of the transform we show that unlike the gqlrt the proposed test is resilient to outliers and involves higher order statistical moments leading to significant mitigation of the model mismatch effect on the decision performance a bayesian extension of the proposed mt gqlrt is also developed that is based on selection of a gaussian probability model that best empirically fits a transformed conditional probability distribution of the data the non bayesian and bayesian mt gqlrts are applied to signal detection and classification in simulation examples that illustrate their advantages over the standard gqlrt and other robust alternatives

optimal detector randomization for multiuser communications systems optimal detector randomization is studied for the downlink of a multiuser communications system in which users can perform time sharing among multiple detectors a formulation is provided to obtain optimal signal amplitudes detectors and detector randomization factors it is shown that the solution of this joint optimization problem can be calculated in two steps resulting in significant reduction in computational complexity it is proved that the optimal solution is achieved via randomization among at most min k nd detector sets where k is the number of users and nd is the number of detectors at each receiver lower and upper bounds are derived on the performance of optimal detector randomization and it is proved that the optimal detector randomization approach can reduce the worst case average probability of error of the optimal approach that employs a single detector for each user by up to k times various sufficient conditions are obtained for the improvability and nonimprovability via detector randomization in the special case of equal crosscorrelations and noise powers a simple solution is developed for the optimal detector randomization problem and necessary and sufficient conditions are presented for the uniqueness of that solution numerical examples are provided to illustrate the improvements achieved via detector randomization

a 3 d riesz covariance texture model for prediction of nodule recurrence in lung ct this paper proposes a novel imaging biomarker of lung cancer relapse from 3 d texture analysis of ct images three dimensional morphological nodular tissue properties are described in terms of 3 d riesz wavelets the responses of the latter are aggregated within nodular regions by means of feature covariances which leverage rich intra and inter variations of the feature space dimensions when compared to the classical use of the average for feature aggregation feature covariances preserve spatial co variations between features the obtained riesz covariance descriptors lie on a manifold governed by riemannian geometry allowing geodesic measurements and differentiations the latter property is incorporated both into a kernel for support vector machines svm and a manifold aware sparse regularized classifier the effectiveness of the presented models is evaluated on a dataset of 110 patients with non small cell lung carcinoma nsclc and cancer recurrence information disease recurrence within a timeframe of 12 months could be predicted with an accuracy of 81 3 82 7 the anatomical location of recurrence could be discriminated between local regional and distant failure with an accuracy of 78 3 93 3 the obtained results open novel research perspectives by revealing the importance of the nodular regions used to build the predictive models

the mechanism of stochastic resonance it is shown that a dynamical system subject to both periodic forcing and random perturbation may show a resonance peak in the power spectrum which is absent when either the forcing or the perturbation is absent

pedestrian detection via classification on riemannian manifolds we present a new algorithm to detect pedestrian in still images utilizing covariance matrices as object descriptors since the descriptors do not form a vector space well known machine learning techniques are not well suited to learn the classifiers the space of d dimensional nonsingular covariance matrices can be represented as a connected riemannian manifold the main contribution of the paper is a novel approach for classifying points lying on a connected riemannian manifold using the geometry of the space the algorithm is tested on inria and daimlerchrysler pedestrian datasets where superior detection rates are observed over the previous approaches

fusing dependent decisions for hypothesis testing with heterogeneous sensors in this paper we consider a binary decentralized detection problem where the local sensor observations are quantized before their transmission to the fusion center sensor observations and hence their quantized versions may be heterogeneous as well as statistically dependent a composite binary hypothesis testing problem is formulated and a copula based generalized likelihood ratio test glrt based fusion rule is derived given that the local sensors are uniform multilevel quantizers an alternative computationally efficient fusion rule is also designed which involves injecting a deliberate random disturbance to the local sensor decisions before fusion although the introduction of external noise causes a reduction in the received signal to noise ratio snr it is shown that the proposed approach can result in a detection performance comparable to the glrt detector without external noise especially when the number of quantization levels is large

noise enhanced parameter estimation this paper investigates the phenomenon of noise enhanced systems for a general parameter estimation problem when the estimator is fixed and known the estimation performance before and after the addition of noise are evaluated performance comparisons are made between the original estimators and noise enhanced estimators based on different criteria the form of the optimal noise probability density function pdf is determined the results are further extended to the general case where the noise is introduced to the system via a transformation for the case where the estimator is fixed and unknown approaches are also proposed to find the optimum noise finally two illustrative examples are presented where the performance comparison is made between the optimal noise modified estimator and gaussian noise modified estimator

how to tune the system parameters to realize stochastic resonance the paper presents a numerical method of realizing stochastic resonance sr by tuning system parameters firstly a simple and effective method of evaluating the system response speed 1 is introduced then the parameter induced sr problem can be reduced to the parameter optimization problem under the condition 1 const to solve this optimization problem we put forward the following techniques i compensate the deviation from the prescribed system response speed 1 at each step ii take the curve length increment on the parameter plane as the step size in searching the maximal signal to noise ratio snr gain finally a numerical simulation confirms the effectiveness of this method

stochastic resonance in ion channels characterized by information theory we identify a unifying measure for stochastic resonance sr in voltage dependent ion channels which comprises periodic conventional aperiodic and nonstationary sr within a simplest setting the gating dynamics is governed by two state conductance fluctuations which switch at random time points between two values the corresponding continuous time point process is analyzed by virtue of information theory in pursuing this goal we evaluate for our dynamics the tau information the mutual information and the rate of information gain as a main result we find an analytical formula for the rate of information gain that solely involves the probability of the two channel states and their noise averaged rates for small voltage signals it simplifies to a handy expression our findings are applied to study sr in a potassium channel we find that sr occurs only when the closed state is predominantly dwelled upon upon increasing the probability for the open channel state the application of an extra dose of noise monotonically deteriorates the rate of information gain i e no sr behavior occurs

stochastic resonance in locally optimal detectors the aim of the paper is to show that the nonlinear effect known as stochastic resonance which corresponds to the improvement of the processing of information by noise occurs naturally in some detection problems we illustrate this by studying the problem of detecting a small amplitude sinusoid in non gaussian noise we show that in some cases the nonlinearity that appears in locally optimal detectors can be viewed as a stochastic resonator if the parameters of the locally optimal detector lod are not well tuned the performance can be improved by the addition of noise

a 3d scene registration method via covariance descriptors and an evolutionary stable strategy game theory solver in this paper we provide an integrated approach for matching patterns in scenes combining 3d and visual information for local definition of points we propose a descriptor based on the notion of covariance of features for fusion of shape and color information of 3d surfaces so called multi scale covariance descriptor mcov the intrinsic properties of this descriptor are many it is invariant to spatial rigid transformations and robust to noise and resolution changes it can also be used for characteristic point detection and lies on top of a manifold topology which allows the use of analytical metric properties this descriptor is complemented with a game theoretic approach for solving the matching correspondences under global geometric constraints this layer offers a comprehensive understanding of the scene and avoids possible mismatches due to repeated areas or symmetries which would be impossibly identified by the detector solely at a local level our solution is able to accurately match different views of a scene even under spatial transformations high noise levels and with small overlap between views outperforming state of the art approaches results are validated by comparing mcov against other state of the art 3d point descriptor methods and matching complex 3d and color scenes under several challenging conditions

adaptive stochastic resonance in noisy neurons based on mutual information noise can improve how memoryless neurons process signals and maximize their throughput information such favorable use of noise is the so called stochastic resonance or sr effect at the level of threshold neurons and continuous neurons this work presents theoretical and simulation evidence that 1 lone noisy threshold and continuous neurons exhibit the sr effect in terms of the mutual information between random input and output sequences 2 a new statistically robust learning law can find this entropy optimal noise level and 3 the adaptive sr effect is robust against highly impulsive noise with infinite variance histograms estimate the relevant probability density functions at each learning iteration a theorem shows that almost all noise probability density functions produce some sr effect in threshold neurons even if the noise is impulsive and has infinite variance the optimal noise level in threshold neurons also behaves nonlinearly as the input signal amplitude increases simulations further show that the sr effect persists for several sigmoidal neurons and for gaussian radial basis function neurons

evaluation of stochastic resonance based detectors of weak harmonic signals in additive white gaussian noise a thorough evaluation of stochastic resonance in the framework of statistical detection theory is presented both as a nonlinear signal preprocessor and as a detector the pertinent receiver operating characteristics are compared with those of the known statistically optimum detector using extensive monte carlo simulations parameter optimization and computational budget aspects are discussed

intrinsically bayesian robust kalman filter an innovation process approach in many contemporary engineering problems model uncertainty is inherent because accurate system identification is virtually impossible owing to system complexity or lack of data on account of availability time or cost the situation can be treated by assuming that the true model belongs to an uncertainty class of models in this context an intrinsically bayesian robust ibr filter is one that is optimal relative to the cost function in the classical sense and the prior distribution over the uncertainty class in the bayesian sense ibr filters have previously been found for both wiener and granulometric morphological filtering in this paper we derive the ibr kalman filter that performs optimally relative to an uncertainty class of state space models introducing the notion of bayesian innovation process and the bayesian orthogonality principle we show how the problem of designing an ibr kalman filter can be reduced to a recursive system similar to the classical kalman recursive equations except with effective counterparts such as the effective kalman gain matrix after deriving the recursive ibr kalman equations for discrete time we use the limiting method to obtain the ibr kalman bucy equations for continuous time finally we demonstrate the utility of the proposed framework for two real world problems sensor networks and gene regulatory network inference

3d solid texture classification using locally oriented wavelet transforms many image acquisition techniques used in biomedical imaging material analysis and structural geology are capable of acquiring 3d solid images computational analysis of these images is complex but necessary since it is difficult for humans to visualize and quantify their detailed 3d content one of the most common methods to analyze 3d data is to characterize the volumetric texture patterns texture analysis generally consists of encoding the local organization of image scales and directions which can be extremely diverse in 3d current state of the art techniques face many challenges when working with 3d solid texture where most approaches are not able to consistently characterize both scale and directional information 3d riesz wavelets can deal with both properties one key property of riesz filterbanks is steerability which can be used to locally align the filters and compare textures with arbitrary local orientations this paper proposes and compares three novel local alignment criteria for higher order 3d riesz wavelet transforms the estimations of local texture orientations are based on higher order extensions of regularized structure tensors an experimental evaluation of the proposed methods for the classification of synthetic 3d solid textures with alterations such as rotations and noise demonstrated the importance of local directional information for robust and accurate solid texture recognition these alignment methods achieved an accuracy of 0 95 in the rotated data three times more than the unaligned riesz descriptor that achieved 0 32 the accuracy obtained is better than all other techniques that are published and tested on the same database

multivariate exponential smoothing and dynamic factor model applied to hourly electricity price analysis thanks to its very simple recursive computing scheme exponential smoothing has become a popular technique to forecast time series in this work we show the advantages of its multivariate version and present some properties of the model which allows us to perform a dynamic factor analysis this analysis leads to a simple methodology to reduce the number of parameters useful when the dimension of observations is large via a linear transformation that decomposes the multivariate process into independent univariate exponential smoothing processes characterized by a single smoothing parameter that goes from zero white noise process to one random walk process a computer implementation of the expectation maximization em algorithm has been built for the maximum likelihood estimation of the models the practicality of the method is demonstrated by its application to hourly electricity price predictions in some day ahead markets such as omel powernext and nord pool markets whose forecasts are given

robust stochastic resonance for simple threshold neurons simulation and theoretical results show that memoryless threshold neurons benefit from small amounts of almost all types of additive noise and so produce the stochastic resonance or sr effect input output mutual information measures the performance of such threshold systems that use subthreshold signals the sr result holds for all possible noise probability density functions with finite variance the only constraint is that the noise mean must fall outside a forbidden threshold related interval that the user can control a new theorem shows that this condition is also necessary a corollary and simulations show that the sr effect occurs for right sided beta and weibull noise as well these sr results further hold for the entire uncountably infinite class of alpha stable probability density functions alpha stable noise densities have infinite variance and infinite higher order moments and often model impulsive noise environments the stable noise densities include the special case of symmetric bell curve densities with thick tails such as the cauchy probability density the sr result for alpha stable noise densities shows that the sr effect in threshold and thresholdlike systems is robust against occasional or even frequent violent fluctuations in noise regression analysis reveals both an exponential relationship for the optimal noise dispersion as a function of the alpha bell curve tail thickness and an approximate linear relationship for the sr maximal mutual information as a function of the alpha bell curve tail thickness

stochastic resonance in discrete time nonlinear ar 1 models this paper deals with stochastic resonance this nonlinear physical phenomenon generally occurs in bistable systems excited by random input noise plus a sinusoid through its internal dynamics such a system forces cooperation between the input noise and the input sine provided the existence of fine tuning between the power noise and the dynamics the system reacts periodically at the frequency of the sine of particular interest is the fact that the local output signal to noise ratio presents a maximum when plotted against the input noise power the system resounds stochastically continuous time systems have already been studied we study the ability of intrinsically discrete time systems general nonlinear ar 1 models to produce stochastic resonance it is then suggested that such discrete systems can be used in signal processing

detector randomization and stochastic signaling for minimum probability of error receivers optimal receiver design is studied for a communications system in which both detector randomization and stochastic signaling can be performed first it is proven that stochastic signaling without detector randomization cannot achieve a smaller average probability of error than detector randomization with deterministic signaling for the same average power constraint and noise statistics then it is shown that the optimal receiver design results in a randomization between at most two maximum a posteriori probability map detectors corresponding to two deterministic signal vectors numerical examples are provided to explain the results

steerable pyramids and tight wavelet frames in l_ 2 bbr d we present a functional framework for the design of tight steerable wavelet frames in any number of dimensions the 2 d version of the method can be viewed as a generalization of simoncelli s steerable pyramid that gives access to a larger palette of steerable wavelets via a suitable parametrization the backbone of our construction is a primal isotropic wavelet frame that provides the multiresolution decomposition of the signal the steerable wavelets are obtained by applying a one to many mapping n th order generalized riesz transform to the primal ones the shaping of the steerable wavelets is controlled by an m m unitary matrix where m is the number of wavelet channels that can be selected arbitrarily this allows for a much wider range of solutions than the traditional equiangular configuration steerable pyramid we give a complete functional description of these generalized wavelet transforms and derive their steering equations we describe some concrete examples of transforms including some built around a mallat type multiresolution analysis of l2 rd and provide a fast fourier transform based decomposition algorithm we also propose a principal component based method for signal adapted wavelet design finally we present some illustrative examples together with a comparison of the denoising performance of various brands of steerable transforms the results are in favor of an optimized wavelet design equalized principal component analysis which consistently performs best

noise benefits in combined nonlinear bayesian estimators this paper investigates the benefits of intentionally adding noise to a bayesian estimator which comprises a linear combination of a number of individual bayesian estimators that are perturbed by mutually independent noise sources and multiplied by a set of adjustable weighting coefficients we prove that the bayes risk for the mean square error mse criterion is minimized when the same optimum weighting coefficients are assigned to the identical estimators in the combiner this property leads to a simplified analysis of the noise benefit to the mse of the combined bayesian estimator even when the number of individual estimators tends to infinity it is shown that for a sufficiently large number of individual estimators the mse of the designed bayesian estimator approaches a plateau for a wide range of added noise levels this robust feature facilitates the incorporation of the added noise into the design of bayesian estimators without tuning the noise level for an easily implementable bayesian estimator composed of quantizers the benefit of the symmetric scale family noise is demonstrated and the optimal noise probability density function is approximated by solving a constrained nonlinear optimization problem we further extend this potential bayesian estimator to the nonlinear filter design finally examples of the noise benefits in random parameter estimation and nonlinear filtering support the theoretical analyses

theory of stochastic resonance in signal transmission by static nonlinear systems a deterministic periodic signal plus a stationary random noise is applied to a static nonlinearity taking the form of a monovariable arbitrary function on real numbers the property of noise enhanced signal transmission through stochastic resonance is studied for this class of static nonlinear systems a theory is developed that provides expressions for the output autocorrelation function power spectral density signal to noise ratio and input output phase shift in the presence of a periodic input a noise distribution and a static nonlinearity all three being arbitrary both white and colored input noises are successively considered for white input noise exact expressions are derived in a discrete time framework directly confrontable to simulations or experiments the theory is applied to describe stochastic resonance in various examples of static nonlinear systems for instance a diode nonlinearity in addition confrontations with experiments and simulations are given that support the theory in particular interesting effects are reported such as a signal to noise ratio larger at the output than at the input or stochastic resonance at zero frequency finally the validity of the theory is extended to dynamic nonlinear systems that can be decomposed into a static nonlinearity followed by an arbitrary dynamic linear system s1063 651x 97 12002 5

theory of the stochastic resonance effect in signal detection part ii variable detectors in part i of this paper ldquotheory of the stochastic resonance effect in signal detection part i fixed detectors rdquo ieee transactions on signal processing vol 55 no 7 pt 1 pp 3172 3184 the mechanism of the stochastic resonance sr effect for a fixed detector has been examined this paper analyzes the stochastic resonance sr effect under the condition that the detector structure or its parameters can also be changed the detector optimization problem with sr noise under both neyman pearson and bayesian criteria is examined in the bayesian approach when the prior probabilities are unknown the minimax approach is adopted the form of the optimal noise pdf along with the corresponding detector as well as the maximum achievable performance are determined the developed theory is then applied to a general class of weak signal detection problems under the assumptions that the sample size n is large enough and the test statistics satisfies the conditions of central limit theorem the optimal sr noise is shown to be a constant vector and independent of the signal strength for both neyman pearson and bayesian criteria illustrative examples are presented where performance comparisons are made between the original detector and the optimal sr noise modified detector for different types of sr noise