multiscale modeling and estimation of poisson processes with application to photon limited imaging many important problems in engineering and science are well modeled by poisson processes in many applications it is of great interest to accurately estimate the intensities underlying observed poisson data in particular this work is motivated by photon limited imaging problems this paper studies a new bayesian approach to poisson intensity estimation based on the haar wavelet transform it is shown that the haar transform provides a very natural and powerful framework for this problem using this framework a novel multiscale bayesian prior to model intensity functions is devised the new prior leads to a simple bayesian intensity estimation procedure furthermore we characterize the correlation behavior of the new prior and show that it has 1 f spectral characteristics the new framework is applied to photon limited image estimation and its potential to improve nuclear medicine imaging is examined

logically rectangular grids and finite volume methods for pdes in circular and spherical domains we describe a class of logically rectangular quadrilateral and hexahedral grids for solving pdes in circular and spherical domains including grid mappings for the circle the surface of the sphere and the three dimensional ball the grids are logically rectangular and the computational domain is a single cartesian grid compared to alternative approaches based on a multiblock data structure or unstructured triangulations this approach simplifies the implementation of numerical methods and the use of adaptive refinement a more general domain with a smooth boundary can be gridded by composing one of the mappings from this paper with another smooth mapping from the circle or sphere to the desired domain although these grids are highly nonorthogonal we show that the high resolution wave propagation algorithm implemented in clawpack can be used effectively to approximate hyperbolic problems on these grids since the ratio between the largest and smallest grids is below 2 for most of our grid mappings explicit finite volume methods such as the wave propagation algorithm do not suffer from the center or pole singularities that arise with polar or latitude longitude grids numerical test calculations illustrate the potential use of these grids for a variety of applications including euler equations shallow water equations and acoustics in a heterogeneous medium pattern formation from a reaction diffusion equation on the sphere is also considered all examples are implemented in the clawpack software package and full source code is available on the web along with matlab routines for the various mappings

rational group decision making a random field ising model at t 0 abstract a modified version of a finite random field ising ferromagnetic model in an external magnetic field at zero temperature is presented to describe group decision making fields may have a non zero average a postulate of minimum inter individual conflicts is assumed interactions then produce a group polarization along one very choice which is however randomly selected a small external social pressure is shown to have a drastic effect on the polarization individual bias related to personal backgrounds cultural values and past experiences are introduced via quenched local competing fields they are shown to be instrumental in generating a larger spectrum of collective new choices beyond initial ones in particular compromise is found to results from the existence of individual competing bias conflict is shown to weaken group polarization the model yields new psychosociological insights about consensus and compromise in groups

image estimation using fast modified reduced update kalman filter the authors have proposed some modifications of the reduced update kalman filter rukf as applied to filtering of images corrupted by additive noise they have reduced the computational complexity by reducing the state dimensionality by doing so it is shown that the computational requirement is reduced by an order of magnitude while the loss of performance is only marginal next the rukf is modified using the score function based approach to accommodate non gaussian noise the image is modeled as a nonstationary mean and stationary variance autoregressive gaussian process it is shown that the stationary variance assumption is reasonable if the nonstationary mean is computed by an edge and detail preserving efficient estimator of local nonstationary mean such an estimator called the hybrid multistage medium d hmsmd filter is also described detailed experimental results are provided which indicate the success of the new filtering scheme

image contrast enhancement based on a histogram transformation of local standard deviation the adaptive contrast enhancement ace algorithm which uses contrast gains cgs to adjust the high frequency components of images is a well known technique for medical image processing conventionally the cg is either a constant or inversely proportional to the local standard deviation lsd however it is known that conventional approaches entail noise overenhancement and ringing artifacts in this paper the authors present a new ace algorithm that eliminates these problems first a mathematical model for the lsd distribution is proposed by extending hunt s 1976 image model then the cg is formulated as a function of the lsd the function which is nonlinear is determined by the transformation between the lsd histogram and a desired lsd distribution using the authors formulation it can be shown that conventional aces use linear functions to compute the new cgs it is the proposed nonlinear function that produces an adequate cg resulting in little noise overenhancement and fewer ringing artifacts finally simulations using some x ray images are provided to demonstrate the effectiveness of the the authors new algorithm

locally optimum detection of signals in a generalized observation model the random signal case locally optimum detectors for weak random signals are derived for a generalized observation model incorporating signal dependent and multiplicative noise it is shown that the locally optimum random signal detectors in the generalized observation model are interesting generalizations of those that would be obtained in the purely additive noisy signal model examples of explicit results for the locally optimum detector test statistics are given for some typical cases both asymptotic and finite sample size performances of the locally optimum detectors are considered and compared with those of other standard detector structures

a new motion compensated reduced order model kalman filter for space varying restoration of progressive and interlaced video we propose a new approach for motion compensated reduced order model kalman filtering for restoration of progressive and interlaced video in the case of interlaced inputs the proposed filter also performs deinterlacing in contrast to the literature both motion compensation and reduced order state modeling are achieved by augmenting the observation equation as opposed to modifying the state transition equation the proposed modeling which includes the two dimensional 2 d reduced order model kalman filtering romkf of angwin and kaufman 1989 as a special case results in significant performance improvement in fixed lag kalman filtering of space varying blurred images this is demonstrated by experimental results

dynamic instabilities in scalar neural field equations with space dependent delays in this paper we consider a class of scalar integral equations with a form of space dependent delay these non local models arise naturally when modelling neural tissue with active axons and passive dendrites such systems are known to support a dynamic oscillatory turing instability of the homogeneous steady state in this paper we develop a weakly nonlinear analysis of the travelling and standing waves that form beyond the point of instability the appropriate amplitude equations are found to be the coupled mean field ginzburg landau equations describing a turing hopf bifurcation with modulation group velocity of o 1 importantly we are able to obtain the coefficients of terms in the amplitude equations in terms of integral transforms of the spatio temporal kernels defining the neural field equation of interest indeed our results cover not only models with axonal or dendritic delays but those which are described by a more general distribution of delayed spatio temporal interactions we illustrate the predictive power of this form of analysis with comparison against direct numerical simulations paying particular attention to the competition between standing and travelling waves and the onset of benjamin feir instabilities

on the use of the pareto arctan distribution for describing city size in australia and new zealand abstract the circular inverse of the tangent function is used to simply derive a generalization of the pareto distribution the pareto arctan pat distribution this model includes as limiting cases pareto and zipf distributions this new probabilistic family is used to describe city size data for australia and new zealand urban agglomerations of these two countries presents similar features a few large metropolitan areas with a steadily increasing population in the last years and many small cities the pat distribution improves the performance of other traditionally used models in urban agglomeration economics such as the classical pareto lognormal and the recently proposed pareto positive stable

image denoising based on wavelets and multifractals for singularity detection this paper presents a very efficient algorithm for image denoising based on wavelets and multifractals for singularity detection a challenge of image denoising is how to preserve the edges of an image when reducing noise by modeling the intensity surface of a noisy image as statistically self similar multifractal processes and taking advantage of the multiresolution analysis with wavelet transform to exploit the local statistical self similarity at different scales the pointwise singularity strength value characterizing the local singularity at each scale was calculated by thresholding the singularity strength wavelet coefficients at each scale were classified into two categories the edge related and regular wavelet coefficients and the irregular coefficients the irregular coefficients were denoised using an approximate minimum mean squared error mmse estimation method while the edge related and regular wavelet coefficients were smoothed using the fuzzy weighted mean fwm filter aiming at preserving the edges and details when reducing noise furthermore to make the fwm based filtering more efficient for noise reduction at the lowest decomposition level the mmse based filtering was performed as the first pass of denoising followed by performing the fwm based filtering experimental results demonstrated that this algorithm could achieve both good visual quality and high psnr for the denoised images

a robust real time algorithm for facial shape recovery from a single image containing cast shadow under general unknown lighting it is difficult to find a non iterative solution for statistical shape from shading sfs for a single image containing cast shadow under unknown arbitrary light conditions this is because it is not trivial to find a mapping from a convex cone in the image space to a point in the depth space to find a non iterative solution for the statistical sfs which has not been done yet to our knowledge we show that it is possible to approximate a cone of images illumination cone to a polytope by a nonlinear function which is a transform from cartesian coordinates to hyperspherical coordinates the images of a subject form a convex cone in the image space and it can be better to use the direction of an image in hyperspherical coordinates as an input feature for the mapping rather than the image itself the maximum error occurs on one of the vertices of the polytope if we choose the objective function to be the squared error of a linear function in the hyperspherical space hence we can solve the least square problem using the cost only for the vertices in deriving the solution we use the generalized rayleigh quotient canonical correlation analysis cca and prior information on input images to reduce the solution space and improve 3 d reconstruction performance in experiments the proposed scheme performs robustly under light variations and is fast enough for real time applications

noise driven anisotropic diffusion filtering of mri a new filtering method to remove rician noise from magnetic resonance images is presented this filter relies on a robust estimation of the standard deviation of the noise and combines local linear minimum mean square error filters and partial differential equations for mri as the speckle reducing anisotropic diffusion did for ultrasound images the parameters of the filter are automatically chosen from the estimated noise this property improves the convergence rate of the diffusion while preserving contours leading to more robust and intuitive filtering the partial derivative equation of the filter is extended to a new matrix diffusion filter which allows a coherent diffusion based on the local structure of the image and on the corresponding oriented local standard deviations this new filter combines volumetric planar and linear components of the local image structure the numerical scheme is explained and visual and quantitative results on simulated and real data sets are presented in the experiments the new filter leads to the best results

modeling electrocortical activity through improved local approximations of integral neural field equations neural field models of firing rate activity typically take the form of integral equations with space dependent axonal delays under natural assumptions on the synaptic connectivity we show how one can derive an equivalent partial differential equation pde model that properly treats the axonal delay terms of the integral formulation our analysis avoids the so called long wavelength approximation that has previously been used to formulate pde models for neural activity in two spatial dimensions direct numerical simulations of this pde model show instabilities of the homogeneous steady state that are in full agreement with a turing instability analysis of the original integral model we discuss the benefits of such a local model and its usefulness in modeling electrocortical activity in particular we are able to treat patchy connections whereby a homogeneous and isotropic system is modulated in a spatially periodic fashion in this case the emergence of a lattice directed traveling wave predicted by a linear instability analysis is confirmed by the numerical simulation of an appropriate set of coupled pdes

nonlinear ultrasonic image processing based on signal adaptive filters and self organizing neural networks two approaches for ultrasonic image processing are examined first signal adaptive maximum likelihood saml filters are proposed for ultrasonic speckle removal it is shown that in the case of displayed ultrasound us image data the maximum likelihood ml estimator of the original noiseless signal closely resembles the l sub 2 mean which has been proven earlier to be the ml estimator of the original signal in us b mode data thus the design of signal adaptive l sub 2 mean filters is treated for us b mode data and displayed us image data as well secondly the segmentation of ultrasonic images using self organizing neural networks nn is investigated a modification of the learning vector quantizer l sub 2 lvq is proposed in such a way that the weight vectors of the output neurons correspond to the l sub 2 mean instead of the sample arithmetic mean of the input observations the convergence in the mean and in the mean square of the proposed l sub 2 lvq nn are studied l sub 2 lvq is combined with signal adaptive filtering in order to allow preservation of image edges and details as well as maximum speckle reduction in homogeneous regions

iterative composite filtering for image restoration an algorithm solution to the noisy image restoration problem under assumptions that the image is nonstationary and that the noise process is a superposition of white and impulsive noises is proposed a composite model is used for the image in order to consider its nonstationarities in the mean and the autocorrelation separating the gross information about the image from its textural information the authors exploit the advantages of median range and levinson filters in restoring the image median statistics are used to estimate the image s gross information and to filter the impulsive noise range statistics are used to segment the textural image into approximately locally stationary images to be filtered by levenson filters the proposed restoration algorithm adapts to the nonstationarity of the image and thus it performs well the algorithm is compared with others based on either median or linear filtering alone

inelastically scattering particles and wealth distribution in an open economy using the analogy with inelastic granular gases we introduce a model for wealth exchange in society the dynamics is governed by a kinetic equation which allows for self similar solutions the scaling function has a power law tail the exponent being given by a transcendental equation in the limit of continuous trading a closed form of the wealth distribution is calculated analytically

some theoretical and numerical results for delayed neural field equations in this paper we study neural field models with delays which define a useful framework for modeling macroscopic parts of the cortex involving several populations of neurons nonlinear delayed integro differential equations describe the spatio temporal behavior of these fields using methods from the theory of delay differential equations we show the existence and uniqueness of a solution of these equations a lyapunov analysis gives us sufficient conditions for the solutions to be asymptotically stable we also present a fairly detailed study of the numerical computation of these solutions this is to our knowledge the first time that a serious analysis of the problem of the existence and uniqueness of a solution of these equations has been performed another original contribution of ours is the definition of a lyapunov functional and the result of stability it implies we illustrate our numerical schemes on a variety of examples that are relevant to modeling in neuroscience

moving window based double haar wavelet transform for image processing image denoising is a lively research field the classical nonlinear filters used for image denoising such as median filter are based on a local analysis of the pixels within a moving window recently the research of image denoising has been focused on the wavelet domain compared to the classical nonlinear filters it is based on a global multiscale analysis of images apparently the wavelet transform can be embedded in a moving window thus a moving window based local multiscale analysis is obtained in this paper based on the haar wavelet a class of nonorthogonal multichannel filter bank with its corresponding wavelet shrinkage called lee shrinkage is derived as a special case of this filter bank the double haar wavelet transform is introduced examples show that it is suitable for a moving window based local multiscale analysis used for image denoising edge detection and edge enhancement

perception of temporally filtered x ray fluoroscopy images for noisy x ray fluoroscopy image sequences the authors quantitatively evaluated image quality after digital temporal filtering to reduce noise using an experimental paradigm called a reference test adaptive forced choice method the authors compared detectability of stationary low contrast disks in filtered and un filtered computer generated image sequences in the first experiment a low pass first order recursive filter used in x ray fluoroscopy was found to be much less effective at enhancing detectability than predicted from the reduction of display noise variance a common measurement of filter effectiveness detectability was reasonably predicted by a nonprewhitening human observer model npw hvs that included an independently determined human temporal contrast sensitivity function in another experiment designed to test models over a range of temporal frequencies the authors used paired high pass and low pass temporal filters that both reduced noise variance by 25 the high pass filter was artificially applied to the noise only and greatly improved detectability while the low pass filter had little effect the human observer model quantitatively described the measurements but classical prewhitening and nonprewhitening signal detectors did not as compared to the nonprewhitening spatio temporal matched filter human observer efficiency was low and variable at 2 1 2 9 and 0 06 for 60 frames of un filtered low pass and high pass noise respectively as compared to this detector humans were not very effective at combining information across frames on the other hand signal to noise ratios snrs from the human observer model were comparable to human performance and efficiencies were reasonably constant at 40 52 and 32 respectively the authors conclude that it is imperative to include human observer models and experiments in the analysis of noise reduction filtering of noisy image sequences such as x ray fluoroscopy

from individual choice to group decision making some universal features are independent of both the social nature of the individuals making the decision and the nature of the decision itself on this basis a simple magnet like model is built pair interactions are introduced to measure the degree of exchange among individuals while discussing an external uniform field is included to account for a possible pressure from outside individual biases with respect to the issue at stake are also included using local random fields a unique postulate of minimum conflict is assumed the model is then solved with emphasis on its psycho sociological implications counter intuitive results are obtained at this stage no new physical technicality is involved instead the full psycho sociological implications of the model are drawn few cases are then detailed to enlight them in addition several numerical experiments based on our model are shown to give both an insight on the dynamics of the model and suggest further research directions

oriented speckle reducing anisotropic diffusion ultrasound imaging systems provide the clinician with noninvasive low cost and real time images that can help them in diagnosis planning and therapy however although the human eye is able to derive the meaningful information from these images automatic processing is very difficult due to noise and artifacts present in the image the speckle reducing anisotropic diffusion filter was recently proposed to adapt the anisotropic diffusion filter to the characteristics of the speckle noise present in the ultrasound images and to facilitate automatic processing of images we analyze the properties of the numerical scheme associated with this filter using a semi explicit scheme we then extend the filter to a matrix anisotropic diffusion allowing different levels of filtering across the image contours and in the principal curvature directions we also show a relation between the local directional variance of the image intensity and the local geometry of the image which can justify the choice of the gradient and the principal curvature directions as a basis for the diffusion matrix finally different filtering techniques are compared on a 2 d synthetic image with two different levels of multiplicative noise and on a 3 d synthetic image of a y junction and the new filter is applied on a 3 d real ultrasound image of the liver

anisotropic diffusion filter with memory based on speckle statistics for ultrasound images ultrasound us imaging exhibits considerable difficulties for medical visual inspection and for development of automatic analysis methods due to speckle which negatively affects the perception of tissue boundaries and the performance of automatic segmentation methods with the aim of alleviating the effect of speckle many filtering techniques are usually considered as a preprocessing step prior to automatic analysis methods or visual inspection most of the state of the art filters try to reduce the speckle effect without considering its relevance for the characterization of tissue nature however the speckle phenomenon is the inherent response of echo signals in tissues and can provide important features for clinical purposes this loss of information is even magnified due to the iterative process of some speckle filters e g diffusion filters which tend to produce over filtering because of the progressive loss of relevant information for diagnostic purposes during the diffusion process in this paper we propose an anisotropic diffusion filter with a probabilistic driven memory mechanism to overcome the over filtering problem by following a tissue selective philosophy in particular we formulate the memory mechanism as a delay differential equation for the diffusion tensor whose behavior depends on the statistics of the tissues by accelerating the diffusion process in meaningless regions and including the memory effect in regions where relevant details should be preserved results both in synthetic and real us images support the inclusion of the probabilistic memory mechanism for maintaining clinical relevant structures which are removed by the state of the art filters

adaptive noise smoothing filter for images with signal dependent noise in this paper we consider the restoration of images with signal dependent noise the filter is noise smoothing and adapts to local changes in image statistics based on a nonstationary mean nonstationary variance nmnv image model for images degraded by a class of uncorrelated signal dependent noise without blur the adaptive noise smoothing filter becomes a point processor and is similar to lee s local statistics algorithm 16 the filter is able to adapt itself to the nonstationary local image statistics in the presence of different types of signal dependent noise for multiplicative noise the adaptive noise smoothing filter is a systematic derivation of lee s algorithm with some extensions that allow different estimators for the local image variance the advantage of the derivation is its easy extension to deal with various types of signal dependent noise film grain and poisson signal dependent restoration problems are also considered as examples all the nonstationary image statistical parameters needed for the filter can be estimated from the noisy image and no a priori information about the original image is required

simultaneous optimal segmentation and model estimation of nonstationary noisy images the authors present the class of semi markov random fields and deal in particular with the subclass of discrete valued nonsymmetric half plane unilateral markov random fields a hierarchical nonstationary mean nonstationary variance nmnv image model is proposed for the modeling of nonstationary and noisy images this model seems to be advantageous as compared to a regular nmnv model because it statistically incorporates the correlation between pixels around the boundary of two adjacent regions the hierarchical nmnv model leads to the development of an optimal algorithm that allows the simultaneous segmentation and model estimation of measured images although no theoretical result is available for the consistency of the estimated model parameters the method seems to work sufficiently well for the examples considered

nonlinear restoration of noisy images the restoration of images degraded by an additive white noise is performed by nonlinearly filtering a noisy image the standard wiener approach to this problem is modified to take into account the edge information of the image various filters of increasing complexity are derived experimental results are shown and compared to the standard wiener filter results and other earlier attempts involving nonstationary filters

image denoising a nonlinear robust statistical approach nonlinear filtering techniques based on the theory of robust estimation are introduced some deterministic and asymptotic properties are derived the proposed denoising methods are optimal over the huber spl epsi contaminated normal neighborhood and are highly resistant to outliers experimental results showing a much improved performance of the proposed filters in the presence of gaussian and heavy tailed noise are analyzed and illustrated

x ray fluoroscopy spatio temporal filtering with object detection one potential way to reduce patient and staff x ray fluoroscopy dose is to reduce the quantum exposure to the detector and compensate the additional noise with digital filtering a new filtering method spatio temporal filtering with object detection is described that reduces noise while minimizing motion and spatial blur as compared to some conventional motion detection filtering schemes this object detection method incorporates additional a priori knowledge of image content i e much of the motion occurs in isolated long thin objects catheters guide wires etc we create object likelihood images and use these to control spatial and recursive temporal filtering such as to reduce blurring the objects of interest we use automatically computed receiver operating characteristic roc curves to optimize the object likelihood enhancement method and determine that oriented matched filter kernels with 4 orientations are appropriate the matched filter kernels are simple projected cylinders we demonstrate the method on several representative x ray fluoroscopy sequences to which noise is added to simulate very low dose acquisitions with processing we find that noise variance is significantly reduced with slightly less noise reduction near moving objects we estimate an effective exposure reduction greater than 80

on the reconstruction aspects of moment descriptors the problem of reconstruction of an image from discrete and noisy data by the method of moments is examined the set of orthogonal moments based on legendre polynomials is employed a general class of signal dependent noise models is taken into account an asymptotic expansion for the global reconstruction error is established this reveals mutual relationships between a number of moments the image smoothness sampling rate and noise model characteristics the problem of an automatic data driven section of an optimal number of moments is studied this is accomplished with the help of cross validation techniques

influence of saving propensity on the power law tail of the wealth distribution some general features of statistical multi agent economic models are reviewed with particular attention to the dependence of the equilibrium wealth distribution on the agents saving propensities it is shown that in a finite system of agents with a continuous saving propensity distribution a power law tail with pareto exponent 1 can appear also when agents do not have saving propensities distributed over the whole interval between zero and one rather a power law can be observed in a finite interval of wealth whose lower and upper ends are shown to be determined by the lower and upper cutoffs respectively of the saving propensity distribution it is pointed out that a cutoff of the power law tail can arise also through a different mechanism when the number of agents is small enough numerical simulations have been carried out by implementing a procedure for assigning saving propensities homogeneously which results in a smoother wealth distributions and correspondingly wider power law intervals than other procedures based on random algorithms

kinetic approach to long time behavior of linearized fast diffusion equations we show that the rate of convergence towards the self similar solution of certain linearized versions of the fast diffusion equation can be related to the number of moments of the initial datum that are equal to the moments of the self similar solution at a fixed time as a consequence we find an improved rate of convergence to self similarity in terms of a fourier based distance between two solutions the results are based on the asymptotic equivalence of a collisional kinetic model of boltzmann type with a linear fokker planck equation with nonconstant coefficients and make use of methods first applied to the reckoning of the rate of convergence towards equilibrium for the spatially homogeneous boltzmann equation for maxwell molecules

4dcaf a temporal approach for denoising hyperspectral image sequences abstract as a consequence of the fast development of sensor technology in the last decade it is now possible to acquire sequences of hyperspectral images at reasonable frame rates however these sequences may be significantly corrupted by noise especially when the spectral coverage of the data reaches the thermal domain while there is an abundant literature on denoising of standard video sequences or denoising of still hyperspectral images very little has been published on denoising hyperspectral sequences this paper presents a novel denoising method for actual hyperspectral sequences the approach is based on spatio spectral temporal cellular automata based filtering it presents several advantages especially the fact that the cellular automaton used is able to contemplate information concerning the type of noise present through the use of specific sequences to tune the algorithm it also considers temporal information by means of a spatio temporal neighborhood when processing each pixel of the sequence the proposed method outperforms several state of the art algorithms on both simulated and real sequences

on steady distributions of kinetic models of conservative economies we analyze the large time behavior of various kinetic models for the redistribution of wealth in simple market economies introduced in the pertinent literature in recent years as specific examples we study models with fixed saving propensity introduced by chakraborti and chakrabarti eur phys j b 17 167 170 2000 as well as models involving both exchange between agents and speculative trading as considered by cordier et al j stat phys 120 253 277 2005 we derive a sufficient criterion under which a unique non trivial stationary state exists and provide criteria under which these steady states do or do not possess a pareto tail in particular we prove the absence of pareto tails in pointwise conservative models like the one in eur phys j b 17 167 170 2000 while models with speculative trades introduced in j stat phys 120 253 277 2005 develop fat tails if the market is risky enough the results are derived by a fourier based technique first developed for the maxwell boltzmann equation gabetta et al in j stat phys 81 901 934 1995 bisi et al in j stat phys 118 1 2 301 331 2005 pareschi and toscani in j stat phys 124 2 4 747 779 2006 and from a recursive relation which allows to calculate arbitrary moments of the stationary state

explicit equilibria in a kinetic model of gambling we introduce and discuss a nonlinear kinetic equation of boltzmann type which describes the evolution of wealth in a pure gambling process where the entire sum of wealths of two agents is up for gambling and randomly shared between the agents for this equation the analytical form of the steady states is found for various realizations of the random fraction of the sum which is shared to the agents among others the exponential distribution appears as steady state in case of a uniformly distributed random fraction while gamma distribution appears for a random fraction which is beta distributed the case in which the gambling game is only conservative in the mean is shown to lead to an explicit heavy tailed distribution

interacting individuals leading to zipf s law institut de physique th eorique universit e de fribourg ch 1700 february 1 2008 we present a general approach to explain the zipf s law of city distribution if the simplestinteraction pairwise is assumed individuals tend to form cities in agreement with the well knownstatisticspacs numbers 89 50 r 05 20 y 05 40 j

unity and discord in opinion dynamics abstract we study opinion dynamics models where agents evolve via repeated pairwise interactions in the compromise model agents with sufficiently close real valued opinions average their opinions a steady state is reached with a finite number of isolated noninteracting opinion clusters parties as the initial opinion range increases the number of such parties undergoes a periodic bifurcation sequence with alternating major and minor parties in the constrained voter model there are leftists centrists and rightists a centrist and an extremist can both become centrists or extremists in an interaction while leftists and rightists do not affect each other the final state is either consensus or a frozen population of leftists and rightists the evolution in one dimension is mapped onto a constrained spin 1 ising chain with zero temperature glauber kinetics the approach to the final state exhibits a nonuniversal long time tail

nonparametric estimation in a regression model with additive and multiplicative noise abstract in this paper we consider an unknown functional estimation problem in a general nonparametric regression model with the feature of having both multiplicative and additive noise we propose two new wavelet estimators in this general context we prove that they achieve fast convergence rates under the mean integrated square error over besov spaces the obtained rates have the particularity of being established under weak conditions on the model a numerical study in a context comparable to stochastic frontier estimation with the difference that the boundary is not necessarily a production function supports the theory

testing the pareto against the lognormal distributions with the uniformly most powerful unbiased test applied to the distribution of cities fat tail distributions of sizes abound in natural physical economic and social systems the lognormal and the power laws have historically competed for recognition with sometimes closely related generating processes and hard to distinguish tail properties this state of affair is illustrated with the debate between eeckhout amer econ rev 94 1429 2004 and levy amer econ rev 99 1672 2009 on the validity of zipf s law for us city sizes by using a uniformly most powerful unbiased umpu test between the lognormal and the power laws we show that conclusive results can be achieved to end this debate we advocate the umpu test as a systematic tool to address similar controversies in the literature of many disciplines involving power laws scaling fat or heavy tails in order to demonstrate that our procedure works for data sets other than the us city size distribution we also briefly present the results obtained for the power law tail of the distribution of personal identity id losses which constitute one of the major emergent risks at the interface between cyberspace and reality

kalman filtering in two dimensions further results the two dimensional reduced update kalman filter was recently introduced the corresponding scalar filtering equations were derived for the case of estimating a gaussian signal in white gaussian noise and were shown to constitute a general nonsymmetric half plane recursive filter this paper extends the method to the deconvolution problem of image restoration this paper also provides a more thorough treatment of the uniquely two dimensional boundary condition problems numerical and subjective examples are presented

bayesian filtering of poisson noise using local statistics images recorded at low light levels inherently suffer from poisson noise a filter based on the maximum a posteriori probability map criterion is developed to remove this noise the filter is adaptive it responds to local changes in image statistics and thus removes the noise along the edges without significantly affecting the edge sharpness it does not require any a priori information about the original image because all the parameters needed for the filter are estimated from the noisy image by assuming local stationarity additionally the simple structure of the filter can be easily implemented in hardware

the rician inverse gaussian distribution a new model for non rayleigh signal amplitude statistics in this paper we introduce a new statistical distribution for modeling non rayleigh amplitude statistics which we have called the rician inverse gaussian riig distribution it is a mixture of the rice distribution and the inverse gaussian distribution the probability density function pdf is given in closed form as a function of three parameters this makes the pdf very flexible in the sense that it may be fitted to a variety of shapes ranging from the rayleigh shaped pdf to a noncentral spl chi sup 2 shaped pdf the theoretical basis of the new model is quite thoroughly discussed and we also give two iterative algorithms for estimating its parameters from data finally we include some modeling examples where we have tested the ability of the distribution to represent locale amplitude histograms of linear medical ultrasound data and single look synthetic aperture radar data we compare the goodness of fit of the riig model with that of the k model and in most cases the new model turns out as a better statistical model for the data we also include a series of log likelihood tests to evaluate the predictive performance of the proposed model

size distribution of cities a kinetic explanation abstract we present a kinetic approach to the formation of urban agglomerations which is based on simple rules of immigration and emigration in most cases the boltzmann type kinetic description allows to obtain within an asymptotic procedure a fokker planck equation with variable coefficients of diffusion and drift which describes the evolution in time of some probability density of the city size it is shown that in dependence of the microscopic rules of migration the equilibrium density can follow both a power law for large values of the size variable which contains as particular case a zipf s law behavior and a lognormal law for middle and low values of the size variable in particular connections between the value of pareto index of the power law at equilibrium and the disposal of the population to emigration are outlined the theoretical findings are tested with recent data of the populations of italy and switzerland

kinetic equations modelling wealth redistribution a comparison of approaches kinetic equations modelling the redistribution of wealth in simple market economies is one of the major topics in the field of econophysics we present a unifying approach to the qualitative study for a large variety of such models which is based on a moment analysis in the related homogeneous boltzmann equation and on the use of suitable metrics for probability measures in consequence we are able to classify the most important feature of the steady wealth distribution namely the fatness of the pareto tail and the dynamical stability of the latter in terms of the model parameters our results apply e g to the market model with risky investments s cordier l pareschi and g toscani j stat phys 120 253 2005 and to the model with quenched saving propensities a chatterjee b k chakrabarti and s s manna physica a 335 155 2004 also we present results from numerical experiments that confirm the theoretical predictions

pitchfork hopf bifurcations in 1d neural field models with transmission delays recently local bifurcation theory for delayed neural fields was developed in this paper we show how symmetry arguments and residue calculus can be used to simplify the computation of the spectrum in special cases and the evaluation of the normal form coefficients respectively this is done hand in hand with an extensive study of two pitchfork hopf bifurcations for a 1d neural field model with wizard hat type connectivity

standing and travelling waves in a spherical brain model the nunez model revisited the nunez model for the generation of electroencephalogram eeg signals is naturally described as a neural field model on a sphere with space dependent delays for simplicity dynamical realisations of this model either as a damped wave equation or an integro differential equation have typically been studied in idealised one dimensional or planar settings here we revisit the original nunez model to specifically address the role of spherical topology on spatio temporal pattern generation we do this using a mixture of turing instability analysis symmetric bifurcation theory centre manifold reduction and direct simulations with a bespoke numerical scheme in particular we examine standing and travelling wave solutions using normal form computation of primary and secondary bifurcations from a steady state interestingly we observe spatio temporal patterns which have counterparts seen in the eeg patterns of both epileptic and schizophrenic brain conditions

modeling the amplitude statistics of ultrasonic images in this paper a new statistical model for representing the amplitude statistics of ultrasonic images is presented the model is called the rician inverse gaussian riig distribution due to the fact that it is constructed as a mixture of the rice distribution and the inverse gaussian distribution the probability density function pdf of the riig model is given in closed form as a function of three parameters some theoretical background on this new model is discussed and an iterative algorithm for estimating its parameters from data is given then the appropriateness of the riig distribution as a model for the amplitude statistics of medical ultrasound images is experimentally studied it is shown that the new distribution can fit to the various shapes of local histograms of linearly scaled ultrasound data better than existing models a log likelihood cross validation comparison of the predictive performance of the riig the k and the generalized nakagami models turns out in favor of the new model furthermore a maximum a posteriori map filter is developed based on the riig distribution experimental studies show that the riig map filter has excellent filtering performance in the sense that it smooths homogeneous regions and at the same time preserves details

optimized wiener filter we consider using a wiener filter for denoising a set of input signals that is degraded by additive white gaussian noise the wiener filter is designed to minimize the mean square error and it requires the knowledge of covariance of input signals and variance of the noise the mean square error is defined as a distance between input signals and input signals estimated by the wiener filter from noisy output signals although we have to infer input signals from only noisy output signals the input signals are required for the evaluation of the mean square error we reformulate the mean square error using noisy output signals and the covariance of the input signals the covariance of the input signals is estimated by minimizing the mean square error we apply our method to the case when an input signal is not generated by the assumed prior probability in particular we apply our method to image restoration and obtain good estimation results

the visual cortex as a crystal a theory of pattern formation in primary visual cortex v1 is presented that takes into account its crystalline like structure the cortex is partitioned into fundamental domains or hypercolumnsof a lattice describing the distribution of singularities or pinwheels in the orientation preference map each hypercolumn is modelled as a network of orientation and spatial frequency selective cells organised around a pair of pinwheels which are associated with high and low spatial frequency domains respectively the network topology of the hypercolumn is taken to be a sphere with the pinwheels located at the poles of the sphere interactions between hypercolumns are mediated by anisotropic long range lateral connections that link cells with similar feature preferences using weakly nonlinear analysis we investigate the spontaneous formation of cortical activity patterns through the simultaneous breaking of an internal o 3 symmetry and a discrete lattice symmetry the resulting patterns are characterised by states in which each hypercolumn exhibits a tuned response to both orientation and spatial frequency and the distribution of optimal responses across hypercolumns is doubly periodic or quasi periodic with respect to the underlying lattice 2002 published by elsevier science b v

master equation for a kinetic model of a trading market and its analytic solution we analyze an ideal gas like model of a trading market with quenched random saving factors for its agents and show that the steady state income m distribution p m in the model has a power law tail with pareto index nu exactly equal to unity confirming the earlier numerical studies on this model the analysis starts with the development of a master equation for the time development of p m precise solutions are then obtained in some special cases

zipf s law in city size from a resource utilization model we study a resource utilization scenario characterized by intrinsic fitness to describe the growth and organization of different cities we consider a model for resource utilization where many restaurants compete as in a game to attract customers using an iterative learning process results for the case of restaurants with uniform fitness are reported when fitness is uniformly distributed it gives rise to a zipf law for the number of customers we perform an exact calculation for the utilization fraction for the case when choices are made independent of fitness a variant of the model is also introduced where the fitness can be treated as an ability to stay in the business when a restaurant loses customers its fitness is replaced by a random fitness the steady state fitness distribution is characterized by a power law while the distribution of the number of customers still follows the zipf law implying the robustness of the model our model serves as a paradigm for the emergence of zipf law in city size distribution

city size distributions for india and china this paper studies the size distributions of urban agglomerations for india and china we have estimated the scaling exponent for zipf s law with the indian census data for the years of 1981 2001 and the chinese census data for 1990 and 2000 along with the biased linear fit estimate the maximum likelihood estimate for the pareto and tsallis q exponential distribution has been computed for india the scaling exponent is in the range of 1 88 2 06 and for china it is in the interval 1 82 2 29 the goodness of fit tests of the estimated distributions are performed using the kolmogorov smirnov statistic

on a kinetic model for a simple market economy in this paper we consider a simple kinetic model of economy involving both exchanges between agents and speculative trading we show that the kinetic model admits non trivial quasi stationary states with power law tails of pareto type in order to do this we consider a suitable asymptotic limit of the model yielding a fokker planck equation for the distribution of wealth among individuals for this equation the stationary state can be easily derived and shows a pareto power law tail numerical results confirm the previous analysis

iterative least squares estimators in nonlinear image restoration the concept of iterative least squares estimation as applied to nonlinear image restoration is considered regarding the convergence analysis of nonlinear iterative algorithms the potential of the global convergence theorem gct is explored the theoretical analysis is performed on a general class of nonlinear algorithms which defines a signal dependent linear mapping of the residual the descent properties of two normed functions are considered furthermore a procedure for the selection of the iteration parameter is introduced the steepest descent sd iterative approach for the solution of the least squares optimization problem is introduced the convergence properties of the particular algorithm are readily derived on the basis of the generalized analysis and the gct the factors that affect the convergence rate of the sd algorithm are thoroughly studied in the case of the sd algorithm structural modifications are proposed and two hybrid sd algorithms attain convergence in a more uniform fashion with respect to their entries in general the algorithms achieve larger convergence rates than the conventional sd technique

invariants equivariants and characters in symmetric bifurcation theory in the analysis of stability in bifurcation problems it is often assumed that the appropriate reduced equations are in normal form in the presence of symmetry the truncated normal form is an equivariant polynomial map therefore the determination of invariants and equivariants of the group of symmetries of the problem is an important step in general these are hard problems of invariant theory and in most cases they are tractable only through symbolic computer programs nevertheless it is desirable to obtain some of the information about invariants and equivariants without actually computing them for example the number of linearly independent homogeneous invariants or equivariants of a certain degree generating functions for these dimensions are generally known as molien functions we obtain formulae for the number of linearly independent homogeneous invariants or equivariants for hopf bifurcation in terms of characters we also show how to construct molien functions for invariants and equivariants for hopf bifurcation our results are then applied to the computation of the number of invariants and equivariants for hopf bifurcation for several finite groups and the continuous group o 3

image reconstruction and restoration overview of common estimation structures and problems developments in the theory of image reconstruction and restoration over the past 20 or 30 years are outlined particular attention is paid to common estimation structures and to practical problems not properly solved yet the problem of image reconstruction and restoration is first formulated some of the current regularization approaches used to solve the problem are then described the concepts of a priori information and compound criterion are introduced a bayesian interpretation of the regularization techniques is given which clarifies the role of the tuning parameters and indicates how they could be estimated the practical aspects of computing the solution first when the hyperparameters are known and second when they must be estimated are then considered conclusions are drawn and points that still need to be investigated are outlined

adaptive nonlinear image restoration by a modified kalman filtering approach an adaptive nonlinear kalman type filter is presented for the restoration of two dimensional images degraded by general image formation system degradations and additive white noise a vector difference equation model is used to model the degradation process the object plane distribution function is partitioned into disjoint regions based on the amount of spatial activity in the image and difference equation models are used to characterize this nonstationary object plane distribution function features of the restoration filter include the ability to account for the response of the human visual system to additive noise in an image a two dimensional interpolation scheme to improve the estimates of the initial states in each region and a nearest neighbor algorithm to choose the previous state of vector for the state of pixel i j

asymptotic properties of the inelastic kac model we discuss the asymptotic behavior of certain models of dissipative systems obtained from a suitable modification of kac caricature of a maxwellian gas it is shown that global equilibria different from concentration are possible if the energy is not finite these equilibria are distributed like stable laws and attract initial densities which belong to the normal domain of attraction if the initial density is assumed of finite energy with higher moments bounded it is shown that the solution converges for large time to a profile with power law tails these tails are heavily dependent of the collision rule

statistic based map image reconstruction from poisson data using gibbs priors a statistical method for selecting the gibbs parameter in map image restoration from poisson data using gibbs priors is presented the gibbs parameter determines the degree to which the prior influences the restoration the presented method yields a map restored image minimally influenced by the prior for which a statistic falls within an appropriate confidence interval the method assumes that a close approximation to the blurring function is known a simple iterative feedback algorithm is presented to statistically select the parameter as the map image restoration is being performed this algorithm is heuristically based on a model reference control formulation but it requires only a minimal number of iterations for the parameter to settle to its statistically specified value the performance of the statistical method for selecting the prior parameter and that of the iterative feedback algorithm are demonstrated using both 2 d and 3 d images

a new image smoothing method based on a simple model of spatial processing in the early stages of human vision the difficulty of preserving edges is central to the problem of smoothing images the main problem is that of distinguishing between meaningful contours and noise so that the image can be smoothed without loss of details substantial efforts have been devoted to solving this difficult problem and a plethora of filtering methods have been proposed in the literature non linear filters have proved to be more efficient than their linear counterparts here a new nonlinear filter for noise smoothing is introduced this filter is based on the psychophysical phenomenon of human visual contrast sensitivity results on real images are presented to demonstrate the validity of our approach compared to other known filtering methods

pareto tails and lognormal body of us cities size distribution abstract we consider a distribution which consists of lower tail pareto lognormal body and upper tail pareto to estimate the size distribution of all us cities this distribution fits the data more accurately than a distribution that comprises of only lognormal and the upper tail pareto

speckle suppression in sar images using the 2 d garch model a novel bayesian based speckle suppression method for synthetic aperture radar sar images is presented that preserves the structural features and textural information of the scene first the logarithmic transform of the original image is analyzed into the multiscale wavelet domain we show that the wavelet coefficients of sar images have significantly non gaussian statistics that are best described by the 2 d garch model by using the 2 d garch model on the wavelet coefficients we are capable of taking into account important characteristics of wavelet coefficients such as heavy tailed marginal distribution and the dependencies between the coefficients furthermore we use a maximum a posteriori map estimator for estimating the clean image wavelet coefficients finally we compare our proposed method with various speckle suppression methods applied on synthetic and actual sar images and we verify the performance improvement in utilizing the new strategy

conciliatory and contradictory dynamics in opinion formation abstract in this article we use a kinetic description to study the effect of different psychologies on the evolution of the opinion with respect to a binary choice in a closed group we show that the interaction between individuals with different reactions regarding the exchange of opinion induces certain phenomena such as the concentration of opinions or the cyclic in time behaviour of the distribution function we provide an existence and uniqueness result for the model and numerically test it in some relevant cases

image classification using spectral and spatial information based on mrf models a new criterion for classifying multispectral remote sensing images or textured images by using spectral and spatial information is proposed the images are modeled with a hierarchical markov random field mrf model that consists of the observed intensity process and the hidden class label process the class labels are estimated according to the maximum a posteriori map criterion but some reasonable approximations are used to reduce the computational load a stepwise classification algorithm is derived and is confirmed by simulation and experimental results

the distribution of all french communes a composite parametric approach abstract the distribution of the size of all french settlements communes from 1962 to 2012 is examined by means of a three parameter composite lognormal pareto distribution this model is based on a lognormal density up to an unknown threshold value and a pareto density thereafter recent findings have shown that the untruncated settlement size data is in excellent agreement with the lognormal distribution in the lower and central parts of the empirical distribution but it follows a power law in the upper tail for that reason this probabilistic family that nests both models seems appropriate to describe urban agglomeration in france the outcomes of this paper reveal that for the early periods 1962 1975 the upper quartile of the commune size data adheres closely to a power law distribution whereas for later periods 2006 2012 most of the city size dynamics is explained by a lognormal model

image sequence filtering in quantum limited noise with applications to low dose fluoroscopy clinical angiography requires hundreds of x ray images putting the patients and particularly the medical staff at risk dosage reduction involves an inevitable sacrifice in image quality in this work the latter problem is addressed by first modeling the signal dependent poisson distributed noise that arises as a result of this dosage reduction the commonly utilized noise model for single images is shown to be obtainable from the new model stochastic temporal filtering techniques are proposed to enhance clinical fluoroscopy sequences corrupted by quantum mottle the temporal versions of these filters as developed here are more suitable for filtering image sequences as correlations along the time axis can be utilized for these dynamic sequences the problem of displacement field estimation is treated in conjunction with the filtering stage to ensure that the temporal correlations are taken along the direction of motion to prevent object blur

effects of the turnover rate on the size distribution of firms an application of the kinetic exchange models abstract we address the issue of the distribution of firm size to this end we propose a model of firms in a closed conserved economy populated with zero intelligence agents who continuously move from one firm to another we then analyze the size distribution and related statistics obtained from the model there are three well known statistical features obtained from the panel study of the firms i e the power law in size in terms of income and or employment the laplace distribution in the growth rates and the slowly declining standard deviation of the growth rates conditional on the firm size first we show that the model generalizes the usual kinetic exchange models with binary interaction to interactions between an arbitrary number of agents when the number of interacting agents is in the order of the system itself it is possible to decouple the model we provide exact results on the distributions which are not known yet for binary interactions our model easily reproduces the power law for the size distribution of firms zipf s law the fluctuations in the growth rate falls with increasing size following a power law though the exponent does not match with the data however the distribution of the difference of the firm size in this model has laplace distribution whereas the real data suggests that the difference of the log of sizes has the same distribution

partition based weighted sum filters for image restoration we develop the concept of partitioning the observation space to build a general class of filters referred to as partition based weighted sum pws filters in the general framework each observation vector is mapped to one of m partitions comprising the observation space and each partition has an associated filtering function we focus on partitioning the observation space utilizing vector quantization and restrict the filtering function within each partition to be linear in this formulation a weighted sum of the observation samples forms the estimate where the weights are allowed to be unique within each partition the partitions are selected and weights tuned by training on a representative set of data it is shown that the proposed data adaptive processing allows for greater detail preservation when encountering nonstationarities in the data and yields superior results compared to several previously defined filters optimization of the pws filters is addressed and experimental results are provided illustrating the performance of pws filters in the restoration of images corrupted by gaussian noise

wavelet domain filtering for photon imaging systems many imaging systems rely on photon detection as the basis of image formation one of the major sources of error in these systems is poisson noise due to the quantum nature of the photon detection process unlike additive gaussian white noise the variance of poisson noise is proportional to the underlying signal intensity and consequently separating signal from noise is a very difficult task in this paper we perform a novel gedankenexperiment to devise a new wavelet domain filtering procedure for noise removal in photon imaging systems the filter adapts to both the signal and the noise and balances the trade off between noise removal and excessive smoothing of image details designed using the statistical method of cross validation the filter is simultaneously optimal in a small sample predictive sum of squares sense and asymptotically optimal in the mean square error sense the filtering procedure has a simple interpretation as a joint edge detection estimation process moreover we derive an efficient algorithm for performing the filtering that has the same order of complexity as the fast wavelet transform itself the performance of the new filter is assessed with simulated data experiments and tested with actual nuclear medicine imagery

practical signal dependent noise parameter estimation from a single noisy image the additive white gaussian noise is widely assumed in many image processing algorithms however in the real world the noise from actual cameras is better modeled as signal dependent noise sdn in this paper we focus on the sdn model and propose an algorithm to automatically estimate its parameters from a single noisy image the proposed algorithm identifies the noise level function of signal dependent noise assuming the generalized signal dependent noise model and is also applicable to the poisson gaussian noise model the accuracy is achieved by improved estimation of local mean and local noise variance from the selected low rank patches we evaluate the proposed algorithm with both synthetic and real noisy images experiments demonstrate that the proposed estimation algorithm outperforms the state of the art methods

kinetic models of opinion formation in the presence of personal conviction we consider a nonlinear kinetic equation of boltzmann type which takes into account the influence of conviction during the formation of opinion in a system of agents which interact through the binary exchanges introduced by toscani g toscani commun math sci 4 481 2006 the original exchange mechanism which is based on the human tendency to compromise and change of opinion through self thinking is here modified in the parameters of the compromise and diffusion terms which now are assumed to depend on the personal degree of conviction the numerical simulations show that the presence of conviction has the potential to break symmetry and to produce clusters of opinions the model is partially inspired by the recent work l pareschi and g toscani phil trans r soc a 372 20130396 2014 in which the role of knowledge in the formation of wealth distribution has been investigated

kinetic models for the trading of goods in this paper we introduce kinetic equations for the evolution of the probability distribution of two goods among a huge population of agents the leading idea is to describe the trading of these goods by means of some fundamental rules in price theory in particular by using cobb douglas utility functions for the binary exchange and the edgeworth box for the description of the common exchange area in which utility is increasing for both agents this leads to a boltzmann type equation in which the post interaction variables depend in a nonlinear way from the pre interaction ones other models will be derived by suitably linearizing this boltzmann equation in presence of uncertainty in the exchanges it is shown that the solution to some of the linearized kinetic equations develop pareto tails where the pareto index depends on the ratio between the gain and the variance of the uncertainty in particular the result holds true for the solution of a drift diffusion equation of fokker planck type obtained from the linear boltzmann equation as the limit of quasi invariant trades

noise level estimation for natural images based on scale invariant kurtosis and piecewise stationarity noise level estimation is crucial in many image processing applications such as blind image denoising in this paper we propose a novel noise level estimation approach for natural images by jointly exploiting the piecewise stationarity and a regular property of the kurtosis in bandpass domains we design a k means based algorithm to adaptively partition an image into a series of non overlapping regions each of whose clean versions is assumed to be associated with a constant but unknown kurtosis throughout scales the noise level estimation is then cast into a problem to optimally fit this new kurtosis model in addition we develop a rectification scheme to further reduce the estimation bias through noise injection mechanism extensive experimental results show that our method can reliably estimate the noise level for a variety of noise types and outperforms some state of the art techniques especially for non gaussian noises

linear quadratic noise smoothing filters for quantum limited images we consider the use of nonlinear estimators for the noise smoothing of images obtained under quantum limited imaging conditions a volterra expansion is investigated from which a set of linear quadratic filters is derived using higher order statistics the filters are applicable for single frame and multiple frames of a single scene imaged under low light levels

sar image regularization with fast approximate discrete minimization synthetic aperture radar sar images like other coherent imaging modalities suffer from speckle noise the presence of this noise makes the automatic interpretation of images a challenging task and noise reduction is often a prerequisite for successful use of classical image processing algorithms numerous approaches have been proposed to filter speckle noise markov random field mrf modelization provides a convenient way to express both data fidelity constraints and desirable properties of the filtered image in this context total variation minimization has been extensively used to constrain the oscillations in the regularized image while preserving its edges speckle noise follows heavy tailed distributions and the mrf formulation leads to a minimization problem involving nonconvex log likelihood terms such a minimization can be performed efficiently by computing minimum cuts on weighted graphs due to memory constraints exact minimization although theoretically possible is not achievable on large images required by remote sensing applications the computational burden of the state of the art algorithm for approximate minimization namely the alpha expansion is too heavy specially when considering joint regularization of several images we show that a satisfying solution can be reached in few iterations by performing a graph cut based combinatorial exploration of large trial moves this algorithm is applied to joint regularization of the amplitude and interferometric phase in urban area sar images

wavelet based sar image despeckling and information extraction using particle filter this paper proposes a new wavelet based synthetic aperture radar sar image despeckling algorithm using the sequential monte carlo method a model based bayesian approach is proposed this paper presents two methods for sar image despeckling the first method called wggpf models a prior with generalized gaussian gg probability density function pdf and the second method called wgmpf models prior with a generalized gaussian markov random field ggmrf the likelihood pdf is modeled using a gaussian pdf the ggmrf model is used because it enables texture parameter estimation the prior is modeled using gg pdf when texture parameters are not needed a particle filter is used for drawing particles from the prior for different shape parameters of gg pdf when the ggmrf prior is used the particles are drawn from prior in order to estimate noise free wavelet coefficients and for those coefficients the texture parameter is changed in order to obtain the best textural parameters the texture parameters are changed for a predefined set of shape parameters of ggmrf the particles with the highest weights represents the final noise free estimate with corresponding textural parameters the despeckling algorithms are compared with the state of the art methods using synthetic and real sar data the experimental results show that the proposed despeckling algorithms efficiently remove noise and proposed methods are comparable with the state of the art methods regarding objective measurements the proposed wgmpf preserves textures of the real high resolution sar images well

image denoising based on multiscale singularity detection for cone beam ct breast imaging it was recently reported that the real time flat panel detector based cone beam computed tomography cbct breast imaging can help improve the detectability of small breast tumors with an x ray dose comparable to that of the conventional mammography in this paper an efficient denoising algorithm is proposed to further reduce the x ray exposure level required by a cbct scan to acquire acceptable image quality the proposed wavelet based denoising algorithm possesses three significant characteristics 1 wavelet coefficients at each scale are classified into two categories irregular coefficients and edge related and regular coefficients 2 noise in irregular coefficients is reduced as much as possible without producing artifacts to the denoised images and 3 for the edge related and regular coefficients if they are at the first decomposition level they are further denoised otherwise no modifications are made to them so as to obtain good visual quality for diagnosis by applying the proposed denoising algorithm to the filtered projection images the x ray exposure level necessary for the cbct scan can he reduced by up to 60 while obtaining clinically acceptable image quality this denoising result indicates that in the clinical application of cbct breast imaging the patient radiation dose can be significantly reduced

patch based nonlocal functional for denoising fluorescence microscopy image sequences we present a nonparametric regression method for denoising 3 d image sequences acquired via fluorescence microscopy the proposed method exploits the redundancy of the 3 d time information to improve the signal to noise ratio of images corrupted by poisson gaussian noise a variance stabilization transform is first applied to the image data to remove the dependence between the mean and variance of intensity values this preprocessing requires the knowledge of parameters related to the acquisition system also estimated in our approach in a second step we propose an original statistical patch based framework for noise reduction and preservation of space time discontinuities in our study discontinuities are related to small moving spots with high velocity observed in fluorescence video microscopy the idea is to minimize an objective nonlocal energy functional involving spatio temporal image patches the minimizer has a simple form and is defined as the weighted average of input data taken in spatially varying neighborhoods the size of each neighborhood is optimized to improve the performance of the pointwise estimator the performance of the algorithm which requires no motion estimation is then evaluated on both synthetic and real image sequences using qualitative and quantitative criteria

the size distributions of all indian cities abstract we apply five distributions lognormal double pareto lognormal lognormal upper tail pareto pareto tails lognormal and pareto tails lognormal with differentiability restrictions to estimate the size distribution of all indian cities since india contains numerous small cities it is important to explicitly model the lower tail behavior for studying the distribution of all indian cities our results rigorously confirm using both graphical and formal statistical tests that among these five distributions pareto tails lognormal is a better suited parametrization of the indian city size data verifying that the indian city size distribution exhibits a strong reverse pareto in the lower tail lognormal in the mid range body and pareto in the upper tail

sar image segmentation based on level set approach and cal g _a 0 model this paper proposes an image segmentation method for synthetic aperture radar sar exploring statistical properties of sar data to characterize image regions we consider cal g a 0 distribution parameters for sar image segmentation combined to the level set framework the cal g a 0 distribution belongs to a class of cal g distributions that have been successfully used to model different regions in amplitude sar images for data modeling purpose such statistical data model is fundamental to deriving the energy functional to perform region mapping which is input into our level set propagation numerical scheme that splits sar images into homogeneous heterogeneous and extremely heterogeneous regions moreover we introduce an assessment procedure based on stochastic distance and the cal g a 0 model to quantify the robustness and accuracy of our approach our results demonstrate the accuracy of the algorithms regarding experiments on synthetic and real sar data

on the estimation of the coefficient of variation for anisotropic diffusion speckle filtering in this paper we focus on the problem of speckle removal by means of anisotropic diffusion and specifically on the importance of the correct estimation of the statistics involved first we derive an anisotropic diffusion filter that does not depend on a linear approximation of the speckle model assumed which is the case of a previously reported filter namely srad then we focus on the problem of estimation of the coefficient of variation of both signal and noise and of noise itself our experiments indicate that neighborhoods used for parameter estimation do not need to coincide with those used in the diffusion equations then we show that as long as the estimates are good enough the filter proposed here and the srad perform fairly closely a fact that emphasizes the importance of the correct estimation of the coefficients of variation

nonlocal means based speckle filtering for ultrasound images in image processing restoration is expected to improve the qualitative inspection of the image and the performance of quantitative image analysis techniques in this paper an adaptation of the nonlocal nl means filter is proposed for speckle reduction in ultrasound us images originally developed for additive white gaussian noise we propose to use a bayesian framework to derive a nl means filter adapted to a relevant ultrasound noise model quantitative results on synthetic data show the performances of the proposed method compared to well established and state of the art methods results on real images demonstrate that the proposed method is able to preserve accurately edges and structural details of the image