adaptive bayesian wavelet shrinkage abstract when fitting wavelet based models shrinkage of the empirical wavelet coefficients is an effective tool for denoising the data this article outlines a bayesian approach to shrinkage obtained by placing priors on the wavelet coefficients the prior for each coefficient consists of a mixture of two normal distributions with different standard deviations the simple and intuitive form of prior allows us to propose automatic choices of prior parameters these parameters are chosen adaptively according to the resolution level of the coefficients typically shrinking high resolution frequency coefficients more heavily assuming a good estimate of the background noise level we obtain closed form expressions for the posterior means and variances of the unknown wavelet coefficients the latter may be used to assess uncertainty in the reconstruction several examples are used to illustrate the method and comparisons are made with other shrinkage methods

a new stochastic cellular automaton model on traffic flow and its jamming phase transition a general stochastic traffic cellular automaton ca model which includes the slow to start effect and driver s perspective is proposed in this paper it is shown that this model includes well known traffic ca models such as the nagel schreckenberg model the quick start model and the slow to start model as specific cases fundamental diagrams of this new model clearly show metastable states around the critical density even when the stochastic effect is present we also obtain analytic expressions of the phase transition curve in phase diagrams by using approximate flow density relations at boundaries these phase transition curves are in excellent agreement with numerical results

discontinuous transition from free flow to synchronized flow induced by short range interaction between vehicles in a three phase traffic flow model abstract in this paper we incorporate a limitation on the interaction range between neighboring vehicles into the cellular automaton model proposed by gao and jiang et al k gao r jiang s x hu b h wang and q s wu phys rev e 76 2007 026105 which was established within the framework of kerner s three phase traffic theory and has been shown to be able to reproduce the three phase traffic flow this modification eliminates an unrealistic phenomenon found in the previous model where the velocity adaptation effect between neighboring vehicles can exist even if those vehicles are infinitely far away from each other therefore in the improved model we regulate that such interactions can only occur within a finite distance for simplicity we suppose a constant value to describe this distance in this paper as a result when compared to the previous model the improved model mainly simulates the following results which are believed to be an improvement 1 the improved model successfully reproduces the expected discontinuous transition from free flow to synchronized flow and the related moving synchronized flow pattern which are both absent in the original model but have been observed in real traffic 2 the improved model simulates the correlation functions time headway distributions and optimal velocity functions which are all more consistent with the empirical data than the previous model and most of the other models published before 3 together with the previous two models considering the velocity difference effect this model finally accomplishes a significative process of developing traffic flow models from the traditional fundamental diagram approach to the three phase traffic theory this process should be helpful for us to understand the traffic dynamics and mechanics further and deeper

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

estimation of the mean of a multivariate normal distribution estimation of the means of independent normal random variables is considered using sum of squared errors as loss an unbiased estimate of risk is obtained for an arbitrary estimate and certain special classes of estimates are then discussed the results are applied to smoothing by use of moving averages and to trimmed analogs of the james stein estimate a suggestion is made for calculating approximate confidence sets for the mean vector centered at an arbitrary estimate

cellular automaton model with velocity adaptation in the framework of kerner s three phase traffic theory received 8 february 2007 revised manuscript received 5 june 2007 published 13 august 2007in this paper we propose a cellular automata ca model for traf c ow in the framework of kerner sthree phase traf c theory we mainly consider the velocity difference effect on the randomization of vehicles the presented model is equivalent to a combination of two ca models i e the kerner klenov wolf kkwca model and the nagel schreckenberg ns ca model with slow to start effect with a given probability vehicle dynamical rules are changed over time randomly between the rules of the ns model and the rules ofthe kkw model due to the rules of the kkw model the speed adaptation effect of three phase traf c theoryis automatically taken into account and our model can show synchronized ow due to the rules of the nsmodel our model can show wide moving jams the effect of switching from the rules of the kkw model tothe rules of the ns model provides equivalent effects to the acceleration noise in the kkw model numericalsimulations are performed for both periodic and open boundaries conditions the results are consistent with thewell known results of the three phase traf c theory published before doi 10 1103 physreve 76 026105 pacs number s 89 40 a 45 70 vn 05 40 a 02 60 cb

harmonic analysis filtering techniques for forced and decaying homogeneous isotropic turbulence harmonic analysis filtering methods are used to decompose 3d forced and decaying turbulent fields into coherent and incoherent parts the filtering methods are the curvelets wavelet and dual tree complex wavelet filtering techniques the methods are applied against the velocity fields of forced and decaying homogeneous isotropic turbulence the velocity fields are generated using the lattice boltzmann method lbm with a resolution of 128 3 where the taylor micro scale reynolds numbers are 72 and 29 for forced and decaying fields respectively the main objective of this study is to use other different filtering methods rather than depending only on wavelet and fourier decompositions using different filtering methods may help in turbulence modeling improving our knowledge about the structure of turbulent flow choosing the appropriate filtering method and extracting general characteristics of the flow under study results show that the coherent and the random incoherent fields contribute to all scales in the inertial range but the statistical behavior is different for each field the three filtering methods approximately identify the coherent fields with the same geometrical shapes of the organized vortical structures the statistical properties such as flatness skewness and spectrum of the extracted fields coherent and incoherent parts are also investigated for each filtering method the joint pdfs between the third and second invariants of the velocity gradient tensor are also studied the joint pdfs for the coherent parts are found similar to previous topological studies of isotropic turbulence however the incoherent pdfs show different topological features

empirical test for cellular automaton models of traffic flow based on a detailed microscopic test scenario motivated by recent empirical studies of single vehicle data several cellular automaton models for traffic flow are compared we find three levels of agreement with the empirical data 1 models that do not reproduce even qualitatively the most important empirical observations 2 models that are on a macroscopic level in reasonable agreement with the empirics and 3 models that reproduce the empirical data on a microscopic level as well our results are not only relevant for applications but also shed light on the relevant interactions in traffic flow

wavelets meet burgulence cvs filtered burgers equation numerical experiments with the one dimensional inviscid burgers equation show that filtering the solution at each time step in a way similar to cvs coherent vortex simulation gives the solution of the viscous burgers equation the cvs filter used here is based on a complex valued translation invariant wavelet representation of the velocity from which one selects the wavelet coefficients having modulus larger than a threshold whose value is iteratively estimated the flow evolution is computed from either deterministic or random initial conditions considering both white noise and brownian motion

llsure local linear sure based edge preserving image filtering in this paper we propose a novel approach for performing high quality edge preserving image filtering based on a local linear model and using the principle of stein s unbiased risk estimate as an estimator for the mean squared error from the noisy image only we derive a simple explicit image filter which can filter out noise while preserving edges and fine scale details moreover this filter has a fast and exact linear time algorithm whose computational complexity is independent of the filtering kernel size thus it can be applied to real time image processing tasks the experimental results demonstrate the effectiveness of the new filter for various computer vision applications including noise reduction detail smoothing and enhancement high dynamic range compression and flash no flash denoising

preconditioning multichannel adaptive filtering algorithms using evd and svd based signal prewhitening and system decoupling abstract it is well known that the convergence rate of multichannel lms based algorithms is limited by the correlation properties of the reference signals and the cross coupling within the plant dynamics these factors give rise to excessive eigenvalue spread and slow convergence rate of a gradient descent algorithm a preconditioning technique is developed in this study for the multichannel lms algorithm so as to improve its convergence rate signal prewhitening and system decoupling are the two key elements of the proposed techniques preconditioning filters are first formulated in the frequency domain by using eigenvalue decomposition and singular value decomposition these filters are then transformed into the time domain with causality taken into account the preconditioning filters are incorporated into a multichannel lms algorithm where the reference signals are prewhitened and the plants are decoupled prior to the adaptation process simulations for a two channel one listener cross talk cancellation problem illustrate the effectiveness of the preconditioning technique in improving the convergence rate of the adaptive algorithms

a new sure approach to image denoising interscale orthonormal wavelet thresholding this paper introduces a new approach to orthonormal wavelet image denoising instead of postulating a statistical model for the wavelet coefficients we directly parametrize the denoising process as a sum of elementary nonlinear processes with unknown weights we then minimize an estimate of the mean square error between the clean image and the denoised one the key point is that we have at our disposal a very accurate statistically unbiased mse estimate stein s unbiased risk estimate that depends on the noisy image alone not on the clean one like the mse this estimate is quadratic in the unknown weights and its minimization amounts to solving a linear system of equations the existence of this a priori estimate makes it unnecessary to devise a specific statistical model for the wavelet coefficients instead and contrary to the custom in the literature these coefficients are not considered random any more we describe an interscale orthonormal wavelet thresholding algorithm based on this new approach and show its near optimal performance both regarding quality and cpu requirement by comparing it with the results of three state of the art nonredundant denoising algorithms on a large set of test images an interesting fallout of this study is the development of a new group delay based parent child prediction in a wavelet dyadic tree

pde based image restoration a hybrid model and color image denoising the paper is concerned with pde based image restoration a new model is introduced by hybridizing a nonconvex variant of the total variation minimization tvm and the motion by mean curvature mmc in order to deal with the mixture of the impulse and gaussian noises reliably we suggest the essentially nondissipative enod difference schemes for the mmc component to eliminate the impulse noise with a minimum ideally no introduction of dissipation the mmc tvm hybrid model and the enod schemes are applied for both gray scale and color images for color image denoising we consider the chromaticity brightness decomposition with the chromaticity formulated in the angle domain an incomplete crank nicolson alternating direction implicit time stepping procedure is adopted to solve those differential equations efficiently numerical experiments have shown that the new hybrid model and the numerical schemes can remove the mixture of the impulse and gaussian noises efficiently and reliably preserving edges quite satisfactorily

wavelet thresholding of multivalued images in this paper a denoising technique for multivalued images exploiting interband correlations is proposed a redundant wavelet transform is applied and denoising is applied by thresholding wavelet coefficients specific functions of the wavelet coefficients are defined that exploit interscale and or interband correlation of the signal three functions are studied the square of the wavelet coefficients products of coefficients at adjacent scales and products of coefficients from different bands for these functions the signal and noise probability density functions pdf become more separated the high signal correlation between bands is exploited by summing these products over all bands in this way separating noise and signal pdfs even more the noise pdf of the proposed quantities is derived analytically and from this a wavelet threshold is derived the technique is demonstrated to outperform single band wavelet thresholding on multispectral remote sensing images and on multimodal mri images

a nonlinear stein based estimator for multichannel image denoising the use of multicomponent images has become widespread with the improvement of multisensor systems having increased spatial and spectral resolutions however the observed images are often corrupted by an additive gaussian noise in this paper we are interested in multichannel image denoising based on a multiscale representation of the images a multivariate statistical approach is adopted to take into account both the spatial and the intercomponent correlations existing between the different wavelet subbands more precisely we propose a new parametric nonlinear estimator which generalizes many reported denoising methods the derivation of the optimal parameters is achieved by applying stein s principle in the multivariate case experiments performed on multispectral remote sensing images clearly indicate that our method outperforms conventional wavelet denoising techniques

the sure let approach to image denoising we propose a new approach to image denoising based on the image domain minimization of an estimate of the mean squared error stein s unbiased risk estimate sure unlike most existing denoising algorithms using the sure makes it needless to hypothesize a statistical model for the noiseless image a key point of our approach is that although the nonlinear processing is performed in a transformed domain typically an undecimated discrete wavelet transform but we also address nonorthonormal transforms this minimization is performed in the image domain indeed we demonstrate that when the transform is a ldquotightrdquo frame an undecimated wavelet transform using orthonormal filters separate subband minimization yields substantially worse results in order for our approach to be viable we add another principle that the denoising process can be expressed as a linear combination of elementary denoising processes linear expansion of thresholds let armed with the sure and let principles we show that a denoising algorithm merely amounts to solving a linear system of equations which is obviously fast and efficient quite remarkably the very competitive results obtained by performing a simple threshold image domain sure optimized on the undecimated haar wavelet coefficients show that the sure let principle has a huge potential

statistical extraction and filtering of multi scale vortical structures in isotropic turbulence a consistent method for extracting and filtering the isotropic turbulence into multi scale fields with the identification of its coherent and incoherent parts is proposed the extraction and filtering processes are done simultaneously in fourier space three fields are extracted using sharp cutoff wave numbers and the organized coherent and random incoherent parts are identified at each scale the proposed method is applied against the velocity fields of forced homogeneous turbulence with two different resolutions 128 3 and 256 3 a statistical thresholding method using the energy spectrum function is also suggested and applied in fourier space to identify the coherent and incoherent parts most methods studied in the literature focused on filtering the flow field into the coherent and incoherent parts only while some others tackled the extraction of the different scales without identifying the coherent and incoherent parts in this study the velocity fields are transformed into fourier space and the multi scales are identified at different cutoff wave numbers with the addition of a threshold filtering to recognize the coherent and incoherent parts at the same time then the inverse fourier transform is applied where the velocity fields are transformed back to physical space and the q identification method is used to visualize all fields it is found that the incoherent parts at the large and intermediate scales are different from that found at the fine scale case few incoherent regions can be found in the large scale field and these incoherent regions increase in the medium case in the fine scale case the incoherent regions reach its maximum existence and they are distributed in all regions of the flow statistical features such as the velocity derivatives skewness the flatness and the probability distribution function pdf for all fields are extensively discussed and compared with previous efforts the introduced method may help in developing a mixed method that can handle the two processes extracting and filtering at the same time and it is important to highlight the direct contribution of the incoherent part at different wave numbers stages

the curvelet transform for image denoising we describe approximate digital implementations of two new mathematical transforms namely the ridgelet transform and the curvelet transform our implementations offer exact reconstruction stability against perturbations ease of implementation and low computational complexity a central tool is fourier domain computation of an approximate digital radon transform we introduce a very simple interpolation in the fourier space which takes cartesian samples and yields samples on a rectopolar grid which is a pseudo polar sampling set based on a concentric squares geometry despite the crudeness of our interpolation the visual performance is surprisingly good our ridgelet transform applies to the radon transform a special overcomplete wavelet pyramid whose wavelets have compact support in the frequency domain our curvelet transform uses our ridgelet transform as a component step and implements curvelet subbands using a filter bank of a spl grave trous wavelet filters our philosophy throughout is that transforms should be overcomplete rather than critically sampled we apply these digital transforms to the denoising of some standard images embedded in white noise in the tests reported here simple thresholding of the curvelet coefficients is very competitive with state of the art techniques based on wavelets including thresholding of decimated or undecimated wavelet transforms and also including tree based bayesian posterior mean methods moreover the curvelet reconstructions exhibit higher perceptual quality than wavelet based reconstructions offering visually sharper images and in particular higher quality recovery of edges and of faint linear and curvilinear features existing theory for curvelet and ridgelet transforms suggests that these new approaches can outperform wavelet methods in certain image reconstruction problems the empirical results reported here are in encouraging agreement

a hybrid convex variational model for image restoration we propose a new hybrid model for variational image restoration using an alternative diffusion switching non quadratic function with a parameter the parameter is chosen adaptively so as to minimize the smoothing near the edges and allow the diffusion to smooth away from the edges this model belongs to a class of edge preserving regularization methods proposed in the past the f function formulation this involves a minimizer to the associated energy functional we study the existence and uniqueness of the energy functional of the model using real and synthetic images we show that the model is effective in image restoration

a nonlinear primal dual method for total variation based image restoration we present a new method for solving total variation tv minimization problems in image restoration the main idea is to remove some of the singularity caused by the nondifferentiability of the quantity nabla u in the definition of the tv norm before we apply a linearization technique such as newton s method this is accomplished by introducing an additional variable for the flux quantity appearing in the gradient of the objective function which can be interpreted as the normal vector to the level sets of the image u our method can be viewed as a primal dual method as proposed by conn and overton a primal dual interior point method for minimizing a sum of euclidean norms preprint 1994 and andersen ph d thesis odense university denmark 1995 for the minimization of a sum of euclidean norms in addition to possessing local quadratic convergence experimental results show that the new method seems to be globally convergent

image denoising using scale mixtures of gaussians in the wavelet domain we describe a method for removing noise from digital images based on a statistical model of the coefficients of an overcomplete multiscale oriented basis neighborhoods of coefficients at adjacent positions and scales are modeled as the product of two independent random variables a gaussian vector and a hidden positive scalar multiplier the latter modulates the local variance of the coefficients in the neighborhood and is thus able to account for the empirically observed correlation between the coefficient amplitudes under this model the bayesian least squares estimate of each coefficient reduces to a weighted average of the local linear estimates over all possible values of the hidden multiplier variable we demonstrate through simulations with images contaminated by additive white gaussian noise that the performance of this method substantially surpasses that of previously published methods both visually and in terms of mean squared error

robustness of the filtered x lms algorithm part i necessary conditions for convergence and the asymptotic pseudospectrum of toeplitz matrices errors in the secondary path model of the filtered x lms fxlms algorithm will lead to its divergence when the eigenvalues of the cross correlation matrix between the estimated filtered reference and the true filtered reference signals are not all located in the right half plane this cross correlation matrix has a block toeplitz structure whose dimension is determined by the number of adaptive filter coefficients using results on the asymptotic pseudospectrum of toeplitz matrices a frequency domain condition on the model is derived to ensure stability the condition is sufficient and necessary for a large number of filter coefficients a transient analysis shows that the sufficient condition given by wang and ren 1999 is only necessary to prevent an initial increase of the error in the adaptive filter coefficients critical behavior

a new cellular automata model including a decelerating damping effect to reproduce kerner s three phase theory abstract most of the conventional traffic cellular automaton ca models based on the nagel schreckenberg model nasch model have two problems an unrealistic deceleration dynamics when a vehicle agent collides with a preceding vehicle in a stopping event and the problem with reproducing the synchronized flow in kerner s three phase theory in this paper a revised stochastic nishinari fukui schadschneider s nfs model belonging to the class of nasch models is presented the proposed ca model where a random braking effect is improved by considering the dependency on the velocity difference and heading distance with a preceding vehicle is confirmed to overcome the two above mentioned drawbacks

anisotropic diffusion of multivalued images with applications to color filtering a general framework for anisotropic diffusion of multivalued images is presented we propose an evolution equation where at each point in time the directions and magnitudes of the maximal and minimal rate of change in the vector image are first evaluated these are given by eigenvectors and eigenvalues of the first fundamental form in the given image metric then the image diffuses via a system of coupled differential equations in the direction of minimal change the diffusion strength is controlled by a function that measures the degree of dissimilarity between the eigenvalues we apply the proposed framework to the filtering of color images represented in cie l a b space

frequency domain adaptation of causal digital filters the adaptation of causal fir digital filters in the discrete frequency domain is considered and it is shown how the bin normalized form of the lms algorithm can converge to a biased solution for problems such as linear prediction a discrete frequency domain version of newton s algorithm is derived and it is demonstrated how this can converge to the optimal causal solution even for linear prediction problems the algorithm employs a spectral factorization of the estimated power spectral density of the reference signal the entirely noncausal part of which is used before the causality constraint in the adaptation algorithm and the entirely causal part is applied after the causality constraint the spectral factors can be calculated online from a recursive estimate of the power spectral density without too great a loss of convergence speed the extension of the algorithm to the adaptation of feedforward controllers is also described in which case the spectral factors of the reference signals filtered by the plant response are required and these are shown to be equal to the spectral factors of the reference signal multiplied by the minimum phase part or the plant frequency response

optimal controllers and adaptive controllers for multichannel feedforward control of stochastic disturbances a time domain formulation for the multichannel feedforward control problem is used to derive an optimally condition for the least squares controller it is also used to motivate an instantaneous steepest descent algorithm for the adaptation of the controller which is known as the filtered error lms algorithm the convergence rate of this algorithm is limited by the correlation properties of each reference signal their cross correlation properties and the dynamics and coupling within the plant response an expression is then derived for the transfer function of the optimum least squares controller this suggests a new architecture for the adaptive controller whose convergence rate is not limited by the factors mentioned above a set of white and uncorrelated reference signals are generated to drive a modified matrix of control filters whose outputs are multiplied by the inverse of the minimum phase part of the plant response matrix before being fed to the physical plant the error signals from the plant are then used to update this controller after being fed through the time reverse transpose of the all pass part of the plant matrix the relationship is also discussed between this architecture and that using a singular value decomposition of the plant response which is used to control tonal disturbances

bivariate shrinkage functions for wavelet based denoising exploiting interscale dependency most simple nonlinear thresholding rules for wavelet based denoising assume that the wavelet coefficients are independent however wavelet coefficients of natural images have significant dependencies we only consider the dependencies between the coefficients and their parents in detail for this purpose new non gaussian bivariate distributions are proposed and corresponding nonlinear threshold functions shrinkage functions are derived from the models using bayesian estimation theory the new shrinkage functions do not assume the independence of wavelet coefficients we show three image denoising examples in order to show the performance of these new bivariate shrinkage rules in the second example a simple subband dependent data driven image denoising system is described and compared with effective data driven techniques in the literature namely visushrink sureshrink bayesshrink and hidden markov models in the third example the same idea is applied to the dual tree complex wavelet coefficients

weighted and extended total variation for image restoration and decomposition in various information processing tasks obtaining regularized versions of a noisy or corrupted image data is often a prerequisite for successful use of classical image analysis algorithms image restoration and decomposition methods need to be robust if they are to be useful in practice in particular this property has to be verified in engineering and scientific applications by robustness we mean that the performance of an algorithm should not be affected significantly by small deviations from the assumed model in image processing total variation tv is a powerful tool to increase robustness in this paper we define several concepts that are useful in robust restoration and robust decomposition we propose two extended total variation models weighted total variation wtv and extended total variation etv we state generic approaches the idea is to replace the tv penalty term with more general terms the motivation is to increase the robustness of rof rudin osher fatemi model and to prevent the staircasing effect due to this method moreover rewriting the non convex sublinear regularizing terms as wtv we provide a new approach to perform minimization via the well known chambolle s algorithm the implementation is then more straightforward than the half quadratic algorithm the behavior of image decomposition methods is also a challenging problem which is closely related to anisotropic diffusion etv leads to an anisotropic decomposition close to edges improving the robustness it allows to respect desired geometric properties during the restoration and to control more precisely the regularization process we also discuss why compression algorithms can be an objective method to evaluate the image decomposition quality

color image enhancement via chromaticity diffusion a novel approach for color image denoising is proposed in this paper the algorithm is based on separating the color data into chromaticity and brightness and then processing each one of these components with partial differential equations or diffusion flows in the proposed algorithm each color pixel is considered as an n dimensional vector the vectors direction a unit vector gives the chromaticity while the magnitude represents the pixel brightness the chromaticity is processed with a system of coupled diffusion equations adapted from the theory of harmonic maps in liquid crystals this theory deals with the regularization of vectorial data while satisfying the intrinsic unit norm constraint of directional data such as chromaticity both isotropic and anisotropic diffusion flows are presented for this n dimensional chromaticity diffusion flow the brightness is processed by a scalar median filter or any of the popular and well established anisotropic diffusion flows for scalar image enhancement we present the underlying theory a number of examples and briefly compare with the current literature

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

stochastic optimal velocity model and its long lived metastability in this paper we propose a stochastic cellular automaton model of traffic flow extending two exactly solvable stochastic models i e the asymmetric simple exclusion process and the zero range process moreover it is regarded as a stochastic extension of the optimal velocity model in the fundamental diagram flux density diagram our model exhibits several regions of density where more than one stable state coexists at the same density in spite of the stochastic nature of its dynamical rule moreover we observe that two long lived metastable states appear for a transitional period and that the dynamical phase transition from a metastable state to another metastable stable state occurs sharply and spontaneously

dual norms and image decomposition models following a recent work by y meyer decomposition models into a geometrical component and a textured component have recently been proposed in image processing in such approaches negative sobolev norms have seemed to be useful to modelize oscillating patterns in this paper we compare the properties of various norms that are dual of sobolev or besov norms we then propose a decomposition model which splits an image into three components a first one containing the structure of the image a second one the texture of the image and a third one the noise our decomposition model relies on the use of three different semi norms the total variation for the geometrical component a negative sobolev norm for the texture and a negative besov norm for the noise we illustrate our study with numerical examples

wavelet thresholding for multiple noisy image copies this correspondence addresses the recovery of an image from its multiple noisy copies the standard method is to compute the weighted average of these copies since the wavelet thresholding technique has been shown to effectively denoise a single noisy copy we consider in this paper combining the two operations of averaging and thresholding because thresholding is a nonlinear technique averaging then thresholding or thresholding then averaging produce different estimators by modeling the signal wavelet coefficients as laplacian distributed and the noise as gaussian our investigation finds the optimal ordering to depend on the number of available copies and on the signal to noise ratio we then propose thresholds that are nearly optimal under the assumed model for each ordering with the optimal and near optimal thresholds the two methods yield similar performance and both show considerable improvement over merely averaging

estimating the probability of the presence of a signal of interest in multiresolution single and multiband image denoising we develop three novel wavelet domain denoising methods for subband adaptive spatially adaptive and multivalued image denoising the core of our approach is the estimation of the probability that a given coefficient contains a significant noise free component which we call signal of interest in this respect we analyze cases where the probability of signal presence is 1 fixed per subband 2 conditioned on a local spatial context and 3 conditioned on information from multiple image bands all the probabilities are estimated assuming a generalized laplacian prior for noise free subband data and additive white gaussian noise the results demonstrate that the new subband adaptive shrinkage function outperforms bayesian thresholding approaches in terms of mean squared error the spatially adaptive version of the proposed method yields better results than the existing spatially adaptive ones of similar and higher complexity the performance on color and on multispectral images is superior with respect to recent multiband wavelet thresholding

adapting to unknown smoothness via wavelet shrinkage abstract we attempt to recover a function of unknown smoothness from noisy sampled data we introduce a procedure sureshrink that suppresses noise by thresholding the empirical wavelet coefficients the thresholding is adaptive a threshold level is assigned to each dyadic resolution level by the principle of minimizing the stein unbiased estimate of risk sure for threshold estimates the computational effort of the overall procedure is order n log n as a function of the sample size n sureshrink is smoothness adaptive if the unknown function contains jumps then the reconstruction essentially does also if the unknown function has a smooth piece then the reconstruction is essentially as smooth as the mother wavelet will allow the procedure is in a sense optimally smoothness adaptive it is near minimax simultaneously over a whole interval of the besov scale the size of this interval depends on the choice of mother wavelet we know from a previous paper by the authors that traditional smoot

multiple shrinkage and subset selection in wavelets this paper discusses bayesian methods for multiple shrinkage estimation in wavelets wavelets are used in applications for data denoising via shrinkage of the coefficients towards zero and for data compression by shrinkage and setting small coefficients to zero we approach wavelet shrinkage by using bayesian hierarchical models assigning a positive prior probability to the wavelet coefficients being zero the resulting estimator for the wavelet coefficients is a multiple shrinkage estimator that exhibits a wide variety of nonlinear patterns we discuss fast computational implementations with a focus on easy to compute analytic approximations as well as importance sampling and markov chain monte carlo methods multiple shrinkage estimators prove to have excellent mean squared error performance in reconstructing standard test functions we demonstrate this in simulated test examples comparing various implementations of multiple shrinkage to commonly used shrinkage rules finally we illustrate our approach with an application to the so called glint data

orthonormal bases of compactly supported wavelets we construct orthonormal bases of compactly supported wavelets with arbitrarily high regularity the order of regularity increases linearly with the support width we start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction the construction then follows from a synthesis of these different approaches

on a class of ill posed minimization problems in image processing in this paper we show that minimization problems involving sublinear regularizing terms are ill posed in general although numerical experiments in image processing give very good results the energies studied here are inspired by image restoration and image decomposition rewriting the nonconvex sublinear regularizing terms as weighted total variations we give a new approach to perform minimization via the well known chambolle s algorithm the approach developed here provides an alternative to the well known half quadratic minimization one

bayesian tree structured image modeling using wavelet domain hidden markov models wavelet domain hidden markov models have proven to be useful tools for statistical signal and image processing the hidden markov tree hmt model captures the key features of the joint probability density of the wavelet coefficients of real world data one potential drawback to the hmt framework is the need for computationally expensive iterative training to fit an hmt model to a given data set e g using the expectation maximization algorithm we greatly simplify the hmt model by exploiting the inherent self similarity of real world images the simplified model specifies the hmt parameters with just nine meta parameters independent of the size of the image and the number of wavelet scales we also introduce a bayesian universal hmt uhmt that fixes these nine parameters the uhmt requires no training of any kind while extremely simple we show using a series of image estimation denoising experiments that these new models retain nearly all of the key image structure modeled by the full hmt finally we propose a fast shift invariant hmt estimation algorithm that outperforms other wavelet based estimators in the current literature both visually and in mean square error

runge kutta type total variation regularization for nonlinear inverse problems in this paper we construct a runge kutta type total variation regularization for the nonlinear ill posed problems this method resembles runge kutta type iteration with the bregman distance as a regularization functional in the presence of noise with noise level we prove this method to be convergent under appropriate stopping rule furthermore some numerical experiments are presented to verify this method to be more suitable for problems with discontinuous solutions rk type tv regularization for the nonlinear ill posed problems is constructed this method introduced bregman distance as regularization functional under appropriate stopping rule this method with noise is convergent numerical tests testify the method for problems with discontinuous solutions

building robust wavelet estimators for multicomponent images using stein s principle multichannel imaging systems provide several observations of the same scene which are often corrupted by noise in this paper we are interested in multispectral image denoising in the wavelet domain we adopt a multivariate statistical approach in order to exploit the correlations existing between the different spectral components our main contribution is the application of stein s principle to build a new estimator for arbitrary multichannel images embedded in additive gaussian noise simulation tests carried out on optical satellite images show that the proposed method outperforms conventional wavelet shrinkage techniques

application of the lattice boltzmann method to transition in oscillatory channel flow in this study the applicability of the lattice boltzmann method to oscillatory channel flow with a zero mean velocity has been evaluated the model has been compared to exact analytical solutions in the laminar case re 100 where re is the reynolds number based on the stokes layer for the womersley parameter 1 31 in this regime there was good agreement between numerical and exact analytical solutions the model was then applied to study the primary instability of oscillatory channel flow with a zero mean velocity for these transitionary flows the parameters were varied in the range 400 re 1000 and 4 16 disturbances superimposed on the numerical solution triggered the two dimensional primary instability this phenomenon has not been numerically evaluated over the range of or re currently investigated the results are consistent with quasi steady linear stability theories and previous numerical investigations

edge preserving image denoising via optimal color space projection denoising of color images can be done on each color component independently recent work has shown that exploiting strong correlation between high frequency content of different color components can improve the denoising performance we show that for typical color images high correlation also means similarity and propose to exploit this strong intercolor dependency using an optimal luminance color difference space projection experimental results confirm that performing denoising on the projected color components yields superior denoising performance both in peak signal to noise ratio and visual quality sense compared to that of existing solutions we also develop a novel approach to estimate directly from the noisy image data the image and noise statistics which are required to determine the optimal projection

sure let multichannel image denoising interscale orthonormal wavelet thresholding we propose a vector matrix extension of our denoising algorithm initially developed for grayscale images in order to efficiently process multichannel e g color images this work follows our recently published sure let approach where the denoising algorithm is parameterized as a linear expansion of thresholds let and optimized using stein s unbiased risk estimate sure the proposed wavelet thresholding function is pointwise and depends on the coefficients of same location in the other channels as well as on their parents in the coarser wavelet subband a nonredundant orthonormal wavelet transform is first applied to the noisy data followed by the subband dependent vector valued thresholding of individual multichannel wavelet coefficients which are finally brought back to the image domain by inverse wavelet transform extensive comparisons with the state of the art multiresolution image denoising algorithms indicate that despite being nonredundant our algorithm matches the quality of the best redundant approaches while maintaining a high computational efficiency and a low cpu memory consumption an online java demo illustrates these assertions

wavelet thresholding via a bayesian approach we discuss a bayesian formalism which gives rise to a type of wavelet threshold estimation in nonparametric regression a prior distribution is imposed on the wavelet coefficients of the unknown response function designed to capture the sparseness of wavelet expansion that is common to most applications for the prior specified the posterior median yields a thresholding procedure our prior model for the underlying function can be adjusted to give functions falling in any specific besov space we establish a relationship between the hyperparameters of the prior model and the parameters of those besov spaces within which realizations from the prior will fall such a relationship gives insight into the meaning of the besov space parameters moreover the relationship established makes it possible in principle to incorporate prior knowledge about the function s regularity properties into the prior model for its wavelet coefficients however prior knowledge about a function s regularity properties might be difficult to elicit with this in mind we propose a standard choice of prior hyperparameters that works well in our examples several simulated examples are used to illustrate our method and comparisons are made with other thresholding methods we also present an application to a data set that was collected in an anaesthesiological study

on a weighted total variation minimization problem abstract the present article is devoted to the study of a constrained weighted total variation minimization problem which may be viewed as a relaxation of a generalized cheeger problem and is motivated by landslide modeling using the fact that the set of minimizers is invariant by a wide class of monotone transformations we prove that level sets of minimizers are generalized cheeger sets and obtain qualitative properties of the minimizers they are all bounded and all achieve their essential supremum on a set of positive measure

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