anisotropic spectral spatial total variation model for multispectral remote sensing image destriping multispectral remote sensing images often suffer from the common problem of stripe noise which greatly degrades the imaging quality and limits the precision of the subsequent processing the conventional destriping approaches usually remove stripe noise band by band and show their limitations on different types of stripe noise in this paper we tentatively categorize the stripes in remote sensing images in a more comprehensive manner we propose to treat the multispectral images as a spectral spatial volume and pose an anisotropic spectral spatial total variation regularization to enhance the smoothness of solution along both the spectral and spatial dimension as a result a more comprehensive stripes and random noise are perfectly removed while the edges and detail information are well preserved in addition the split bregman iteration method is employed to solve the resulting minimization problem which highly reduces the computational load we extensively validate our method under various stripe categories and show comparison with other approaches with respect to result quality running time and quantitative assessments

multiscale image blind denoising arguably several thousands papers are dedicated to image denoising most papers assume a fixed noise model mainly white gaussian or poissonian this assumption is only valid for raw images yet in most images handled by the public and even by scientists the noise model is imperfectly known or unknown end users only dispose the result of a complex image processing chain effectuated by uncontrolled hardware and software and sometimes by chemical means for such images recent progress in noise estimation permits to estimate from a single image a noise model which is simultaneously signal and frequency dependent we propose here a multiscale denoising algorithm adapted to this broad noise model this leads to a blind denoising algorithm which we demonstrate on real jpeg images and on scans of old photographs for which the formation model is unknown the consistency of this algorithm is also verified on simulated distorted images this algorithm is finally compared with the unique state of the art previous blind denoising method

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

bayesian approaches to gaussian mixture modeling a bayesian based methodology is presented which automatically penalizes overcomplex models being fitted to unknown data we show that with a gaussian mixture model the approach is able to select an optimal number of components in the model and so partition data sets the performance of the bayesian method is compared to other methods of optimal model selection and found to give good results the methods are tested on synthetic and real data sets

global optimization of rational functions a semidefinite programming approach we consider the problem of global minimization of rational functions on unconstrained case and on an open connected semi algebraic subset of or the partial closure of such a set constrained case we show that in the univariate case n 1 these problems have exact reformulations as semidefinite programming sdp problems by using reformulations introduced in the phd thesis of jibetean 16 this extends the analogous results by nesterov 13 for global minimization of univariate polynomials for the bivariate case n 2 we obtain a fully polynomial time approximation scheme fptas for the unconstrained problem if an a priori lower bound on the infimum is known by using results by de klerk and pasechnik 1 for the np hard multivariate case we discuss semidefinite programming based relaxations for obtaining lower bounds on the infimum by using results by parrilo 15 and lasserre 12

scale space and edge detection using anisotropic diffusion a new definition of scale space is suggested and a class of algorithms used to realize a diffusion process is introduced the diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing rather than interregion smoothing it is shown that the no new maxima should be generated at coarse scales property of conventional scale space is preserved as the region boundaries in the approach remain sharp a high quality edge detector which successfully exploits global information is obtained experimental results are shown on a number of images parallel hardware implementations are made feasible because the algorithm involves elementary local operations replicated over the image

a joint inter and intrascale statistical model for bayesian wavelet based image denoising this paper presents a new wavelet based image denoising method which extends a geometrical bayesian framework the new method combines three criteria for distinguishing supposedly useful coefficients from noise coefficient magnitudes their evolution across scales and spatial clustering of large coefficients near image edges these three criteria are combined in a bayesian framework the spatial clustering properties are expressed in a prior model the statistical properties concerning coefficient magnitudes and their evolution across scales are expressed in a joint conditional model the three main novelties with respect to related approaches are 1 the interscale ratios of wavelet coefficients are statistically characterized and different local criteria for distinguishing useful coefficients from noise are evaluated 2 a joint conditional model is introduced and 3 a novel anisotropic markov random field prior model is proposed the results demonstrate an improved denoising performance over related earlier techniques

image denoising in mixed poisson gaussian noise we propose a general methodology pure let to design and optimize a wide class of transform domain thresholding algorithms for denoising images corrupted by mixed poisson gaussian noise we express the denoising process as a linear expansion of thresholds let that we optimize by relying on a purely data adaptive unbiased estimate of the mean squared error mse derived in a non bayesian framework pure poisson gaussian unbiased risk estimate we provide a practical approximation of this theoretical mse estimate for the tractable optimization of arbitrary transform domain thresholding we then propose a pointwise estimator for undecimated filterbank transforms which consists of subband adaptive thresholding functions with signal dependent thresholds that are globally optimized in the image domain we finally demonstrate the potential of the proposed approach through extensive comparisons with state of the art techniques that are specifically tailored to the estimation of poisson intensities we also present denoising results obtained on real images of low count fluorescence microscopy

optimal inversion of the anscombe transformation in low count poisson image denoising the removal of poisson noise is often performed through the following three step procedure first the noise variance is stabilized by applying the anscombe root transformation to the data producing a signal in which the noise can be treated as additive gaussian with unitary variance second the noise is removed using a conventional denoising algorithm for additive white gaussian noise third an inverse transformation is applied to the denoised signal obtaining the estimate of the signal of interest the choice of the proper inverse transformation is crucial in order to minimize the bias error which arises when the nonlinear forward transformation is applied we introduce optimal inverses for the anscombe transformation in particular the exact unbiased inverse a maximum likelihood ml inverse and a more sophisticated minimum mean square error mmse inverse we then present an experimental analysis using a few state of the art denoising algorithms and show that the estimation can be consistently improved by applying the exact unbiased inverse particularly at the low count regime this results in a very efficient filtering solution that is competitive with some of the best existing methods for poisson image denoising

mixture densities maximum likelihood and the em algorithm the problem of estimating the parameters which determine a mixture density has been the subject of a large diverse body of literature spanning nearly ninety years during the last two decades the

penalized maximum likelihood image reconstruction using space alternating generalized em algorithms most expectation maximization em type algorithms for penalized maximum likelihood image reconstruction converge slowly particularly when one incorporates additive background effects such as scatter random coincidences dark current or cosmic radiation in addition regularizing smoothness penalties or priors introduce parameter coupling rendering intractable the m steps of most em type algorithms this paper presents space alternating generalized em sage algorithms for image reconstruction which update the parameters sequentially using a sequence of small hidden data spaces rather than simultaneously using one large complete data space the sequential update decouples the m step so the maximization can typically be performed analytically we introduce new hidden data spaces that are less informative than the conventional complete data space for poisson data and that yield significant improvements in convergence rate this acceleration is due to statistical considerations not numerical overrelaxation methods so monotonic increases in the objective function are guaranteed we provide a general global convergence proof for sage methods with nonnegativity constraints

spatiotemporal reconstruction of list mode pet data we describe a method for computing a continuous time estimate of tracer density using list mode positron emission tomography data the rate function in each voxel is modeled as an inhomogeneous poisson process whose rate function can be represented using a cubic b spline basis the rate functions are estimated by maximizing the likelihood of the arrival times of detected photon pairs over the control vertices of the spline modified by quadratic spatial and temporal smoothness penalties and a penalty term to enforce nonnegativity randoms rate functions are estimated by assuming independence between the spatial and temporal randoms distributions similarly scatter rate functions are estimated by assuming spatiotemporal independence and that the temporal distribution of the scatter is proportional to the temporal distribution of the trues a quantitative evaluation was performed using simulated data and the method is also demonstrated in a human study using sup 11 c raclopride

image denoising using mixtures of projected gaussian scale mixtures we propose a new statistical model for image restoration in which neighborhoods of wavelet subbands are modeled by a discrete mixture of linear projected gaussian scale mixtures mpgsm in each projection a lower dimensional approximation of the local neighborhood is obtained thereby modeling the strongest correlations in that neighborhood the model is a generalization of the recently developed mixture of gsm mgsm model that offers a significant improvement both in psnr and visually compared to the current state of the art wavelet techniques however the computation cost is very high which hampers its use for practical purposes we present a fast em algorithm that takes advantage of the projection bases to speed up the algorithm the results show that when projecting on a fixed data independent basis even computational advantages with a limited loss of psnr can be obtained with respect to the bls gsm denoising method while data dependent bases of principle components offer a higher denoising performance both visually and in psnr compared to the current wavelet based state of the art denoising methods

local contrast phase descriptor for fingerprint liveness detection we propose a new local descriptor for fingerprint liveness detection the input image is analyzed both in the spatial and in the frequency domain in order to extract information on the local amplitude contrast and on the local behavior of the image synthesized by considering the phase of some selected transform coefficients these two pieces of information are used to generate a bi dimensional contrast phase histogram used as feature vector associated with the image after an appropriate feature selection a trained linear kernel svm classifier makes the final live fake decision experiments on the publicly available livdet 2011 database comprising datasets collected from various sensors prove the proposed method to outperform the state of the art liveness detection techniques highlightswe propose a new local descriptor for fingerprint liveness detection it is based on the joint use of contrast and phase information image analysis is carried out in both the spatial and the transform domains we generate a bi dimensional contrast phase histogram used as feature vector a properly trained linear kernel svm classifier makes the final live fake decision

pointwise shape adaptive dct for high quality denoising and deblocking of grayscale and color images the shape adaptive discrete cosine transform sa dct transform can be computed on a support of arbitrary shape but retains a computational complexity comparable to that of the usual separable block dct b dct despite the near optimal decorrelation and energy compaction properties application of the sa dct has been rather limited targeted nearly exclusively to video compression in this paper we present a novel approach to image filtering based on the sa dct we use the sa dct in conjunction with the anisotropic local polynomial approximation intersection of confidence intervals technique which defines the shape of the transform s support in a pointwise adaptive manner the thresholded or attenuated sa dct coefficients are used to reconstruct a local estimate of the signal within the adaptive shape support since supports corresponding to different points are in general overlapping the local estimates are averaged together using adaptive weights that depend on the region s statistics this approach can be used for various image processing tasks in this paper we consider in particular image denoising and image deblocking and deringing from block dct compression a special structural constraint in luminance chrominance space is also proposed to enable an accurate filtering of color images simulation experiments show a state of the art quality of the final estimate both in terms of objective criteria and visual appearance thanks to the adaptive support reconstructed edges are clean and no unpleasant ringing artifacts are introduced by the fitted transform

image denoising by exploring external and internal correlations single image denoising suffers from limited data collection within a noisy image in this paper we propose a novel image denoising scheme which explores both internal and external correlations with the help of web images for each noisy patch we build internal and external data cubes by finding similar patches from the noisy and web images respectively we then propose reducing noise by a two stage strategy using different filtering approaches in the first stage since the noisy patch may lead to inaccurate patch selection we propose a graph based optimization method to improve patch matching accuracy in external denoising the internal denoising is frequency truncation on internal cubes by combining the internal and external denoising patches we obtain a preliminary denoising result in the second stage we propose reducing noise by filtering of external and internal cubes respectively on transform domain in this stage the preliminary denoising result not only enhances the patch matching accuracy but also provides reliable estimates of filtering parameters the final denoising image is obtained by fusing the external and internal filtering results experimental results show that our method constantly outperforms state of the art denoising schemes in both subjective and objective quality measurements e g it achieves 2 db gain compared with bm3d at a wide range of noise levels

practical poissonian gaussian noise modeling and fitting for single image raw data we present a simple and usable noise model for the raw data of digital imaging sensors this signal dependent noise model which gives the pointwise standard deviation of the noise as a function of the expectation of the pixel raw data output is composed of a poissonian part modeling the photon sensing and gaussian part for the remaining stationary disturbances in the output data we further explicitly take into account the clipping of the data over and under exposure faithfully reproducing the nonlinear response of the sensor we propose an algorithm for the fully automatic estimation of the model parameters given a single noisy image experiments with synthetic images and with real raw data from various sensors prove the practical applicability of the method and the accuracy of the proposed model

computing the topological pressure for intermittent maps the topological pressure is obtained as the leading zero of a dynamical zeta function we consider the problem of computing this zero when it is close to a singularity in particular we study a family of intermittent maps which we argue exhibit a branch point singularity in its zeta functions the convergence of the cycle expansion close to this point is extremely slow to deal with this problem we consider a resummation of the cycle expansion the idea is quite similar to that of pade approximants but the ansatz is a generalized series expansion around the branch point rather than a rational function the improvement on convergence of the leading zero is considerable we also briefly discuss the relation between correlation decay and the nature of the branch point

random fibonacci sequences solutions to the random fibonacci recurrence xn 1 xn xn 1 decrease increase exponentially xn exp n for sufficiently small large in the limits 0 and we expand the lyapunov exponent in powers of and 1 respectively for the classical case of 1 we obtain exact non perturbative results in particular an invariant measure associated with ricatti variable rn xn 1 xn is shown to exhibit plateaux around all rational r

an mdl framework for sparse coding and dictionary learning the power of sparse signal modeling with learned overcomplete dictionaries has been demonstrated in a variety of applications and fields from signal processing to statistical inference and machine learning however the statistical properties of these models such as underfitting or overfitting given sets of data are still not well characterized in the literature as a result the success of sparse modeling depends on hand tuning critical parameters for each data and application this work aims at addressing this by providing a practical and objective characterization of sparse models by means of the minimum description length mdl principle a well established information theoretic approach to model selection in statistical inference the resulting framework derives a family of efficient sparse coding and dictionary learning algorithms which by virtue of the mdl principle are completely parameter free furthermore such framework allows to incorporate additional prior information to existing models such as markovian dependencies or to define completely new problem formulations including in the matrix analysis area in a natural way these virtues will be demonstrated with parameter free algorithms for the classic image denoising and classification problems and for low rank matrix recovery in video applications however the framework is not limited to this imaging data and can be applied to a wide range of signal and data types and tasks

estimating generalized lyapunov exponents for products of random matrices we discuss several techniques for the evaluation of the generalized lyapunov exponents which characterize the growth of products of random matrices in the large deviation regime a monte carlo algorithm that performs importance sampling using a simple random resampling step is proposed as a general purpose numerical method which is both efficient and easy to implement alternative techniques complementing this method are presented these include the computation of the generalized lyapunov exponents by solving numerically an eigenvalue problem and some asymptotic results corresponding to high order moments of the matrix products taken together the techniques discussed in this paper provide a suite of methods which should prove useful for the evaluation of the generalized lyapunov exponents in a broad range of applications their usefulness is demonstrated on particular products of random matrices arising in the study of scalar mixing by complex fluid flows

estimating the parameters of general frequency modulated signals a general frequency modulated gfm signal characterizes the vibrations produced by compressors turbines propellers gears and other rotating machines in a dynamic environment a gfm signal is defined as the composition of a real or complex periodic or almost periodic carrier function with a real differentiable modulation function a gfm signal therefore contains sinusoids whose frequencies are possibly nonintegral multiples of a fundamental to distinguish a gfm signal from a set of unrelated sinusoids it is necessary to track them as a group this paper develops the general frequency modulation tracker gfmt for one or more gfm signals in noise using the expectation conditional maximization ecm algorithm that is an extension of the expectation maximization em algorithm three advantages of this approach are that the ratios harmonic numbers of the carrier functions do not need to be known a priori that the parameters of multiple signals are estimated simultaneously and that the gfmt algorithm exploits knowledge of the noise spectrum so that a separate normalization procedure is not required several simulated examples are presented to illustrate the algorithm s performance

improved denoising via poisson mixture modeling of image sensor noise this paper describes a study aimed at comparing the real image sensor noise distribution to the models of noise often assumed in image denoising designs a quantile analysis in pixel wavelet transform and variance stabilization domains reveal that the tails of poisson signal dependent gaussian and poisson gaussian models are too short to capture real sensor noise behavior a new poisson mixture noise model is proposed to correct the mismatch of tail behavior based on the fact that noise model mismatch results in image denoising that undersmoothes real sensor data we propose a mixture of poisson denoising method to remove the denoising artifacts without affecting image details such as edge and textures experiments with real sensor data verify that denoising for real image sensor data is indeed improved by this new technique

global analytic solutions of the radial nonlinear wave equation abstract the initial valued problem f z z 1 f z g z f z f 0 f 0 0 under suitable assumptions on the function g z f z is reduced by a well known method 2 to an operator equation of the form f n 1 f gle 1 in an abstract banach space h1 the operator n1 is a nonlinear compact and holomorphic operator defined in an open sphere centered at the origin of h1 the bar in the number means complex conjugation of and e1 is a known element in h1 the existence of a solution to the above operator equation means that there exists an analytic function f z n 1x bn zn f 0 0 which together with the first two derivatives converges absolutely for z 1 it is well known that such solutions exist under suitable assumptions on g z f z for sufficiently small here the existence of such analytic solutions is proved under more general assumptions on g z f z moreover for a given sufficiently small the theorems predict an upper bound of the solution f z for all z 1 the most important is that the existence theorems have a constructive character and can provide an answer to the question how small is the initial point f 0 as examples some equations of particular interest are studied

image denoising via sparse and redundant representations over learned dictionaries we address the image denoising problem where zero mean white and homogeneous gaussian additive noise is to be removed from a given image the approach taken is based on sparse and redundant representations over trained dictionaries using the k svd algorithm we obtain a dictionary that describes the image content effectively two training options are considered using the corrupted image itself or training on a corpus of high quality image database since the k svd is limited in handling small image patches we extend its deployment to arbitrary image sizes by defining a global image prior that forces sparsity over patches in every location in the image we show how such bayesian treatment leads to a simple and effective denoising algorithm this leads to a state of the art denoising performance equivalent and sometimes surpassing recently published leading alternative denoising methods

weighted sobolev spaces with applications to singular nonlinear boundary value problems abstract variational methods are used in a weighted sobolev space to prove the existence of solutions for a certain class of singular nonlinear ordinary differential equations

nonparametric multiscale blind estimation of intensity frequency dependent noise the camera calibration parameters and the image processing chain which generated a given image are generally not available to the receiver this happens for example with scanned photographs and for most jpeg images these images have undergone various nonlinear contrast changes and also linear and nonlinear filters to deal with remnant noise in such images we introduce a general nonparametric intensity and frequency dependent noise model we demonstrate by simulated and experiments with real images that this model which requires the estimation of more than 1000 parameters performs an efficient noise estimation the proposed noise model is a patch model its estimation can therefore be used as a preliminary step to any patch based denoising method our noise estimation method introduces several new tools for performing this complex estimation one of them is a new sparse patch distance function permitting to find noisy patches with similar underlying geometry a validation of the noise model and of its estimation method is obtained by comparing its results to ground truth noise curves for both raw and jpeg encoded images and by visual inspection of the denoising results of real images a fair comparison with the state of the art is also performed

computation of growth rates of random sequences with multi step memory we extend the generating function approach to the computation of growth rate of random fibonacci sequences with long memory functional iteration equations are obtained and its general form is conjectured and proved based on which an asymptotic representation of the growth rate is obtained the validity of both the derived and the conjectured formula are verified upon comparison with monte carlo simulation a numerical scheme of the functional iteration is designed and implemented successfully

multipatch unbiased distance non local adaptive means with wavelet shrinkage many existing non local means nlm methods either use euclidean distance to measure the similarity between patches or compute weight omega ij only once and keep it unchanged during the subsequent denoising iterations or use only the structure information of the denoised image to update weight omega ij these may lead to the limited denoising performance to address these issues this paper proposes the non local adaptive means nlam for image denoising nlam treats weight omega ij as an optimization variable and iteratively updates its value we then introduce three unbiased distances namely pixel pixel patch patch and coupled unbiased distances these unbiased distances are more robust to measure the image pixel patch similarity than euclidean distance using the coupled unbiased distance we propose the unbiased distance non local adaptive means ud nlam because ud nlam uses only a single patch size to compute weight omega ij we introduce multipatch ud nlam mud nlam to adapt different noise levels to further improve denoising performance we then propose a new denoising method called mud nlam with wavelet shrinkage mud nlam ws experimental results show that the proposed nlam ud nlam and mud nlam outperform existing nlm methods and mud nlam ws achieves a better performance than the state of the art denoising methods

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

optimal spatial adaptation for patch based image denoising a novel adaptive and patch based approach is proposed for image denoising and representation the method is based on a pointwise selection of small image patches of fixed size in the variable neighborhood of each pixel our contribution is to associate with each pixel the weighted sum of data points within an adaptive neighborhood in a manner that it balances the accuracy of approximation and the stochastic error at each spatial position this method is general and can be applied under the assumption that there exists repetitive patterns in a local neighborhood of a point by introducing spatial adaptivity we extend the work earlier described by buades et al which can be considered as an extension of bilateral filtering to image patches finally we propose a nearly parameter free algorithm for image denoising the method is applied to both artificially corrupted white gaussian noise and real images and the performance is very close to and in some cases even surpasses that of the already published denoising methods

novel computation of the growth rate of generalized random fibonacci sequences a new formulation is proposed for the computation of average growth rates of generalized random fibonacci sequences based on the new formula a novel numerical scheme is designed and successfully implemented and interesting analytic asymptotic expansions are obtained for several examples

bounded self weights estimation method for non local means image denoising using minimax estimators a non local means nlm filter is a weighted average of a large number of non local pixels with various image intensity values the nlm filters have been shown to have powerful denoising performance excellent detail preservation by averaging many noisy pixels and using appropriate values for the weights respectively the nlm weights between two different pixels are determined based on the similarities between two patches that surround these pixels and a smoothing parameter another important factor that influences the denoising performance is the self weight values for the same pixel the recently introduced local james stein type center pixel weight estimation method ljs outperforms other existing methods when determining the contribution of the center pixels in the nlm filter however the ljs method may result in excessively large self weight estimates since no upper bound is assumed and the method uses a relatively large local area for estimating the self weights which may lead to a strong bias in this paper we investigated these issues in the ljs method and then propose a novel local self weight estimation methods using direct bounds lmm db and reparametrization lmm rp based on the baranchik s minimax estimator both the lmm db and lmm rp methods were evaluated using a wide range of natural images and a clinical mri image together with the various levels of additive gaussian noise our proposed parameter selection methods yielded an improved bias variance trade off a higher peak signal to noise psnr ratio and fewer visual artifacts when compared with the results of the classical nlm and ljs methods our proposed methods also provide a heuristic way to select a suitable global smoothing parameters that can yield psnr values that are close to the optimal values

estimation of gaussian poissonian gaussian and processed visual noise and its level function we propose a method for estimating the image and video noises of different types white gaussian signal independent mixed poissonian gaussian signal dependent or processed non white our method also estimates the noise level function nlf of these types we do so by classifying image patches based on their intensity and variance in order to find homogeneous regions that best represent the noise we assume that the noise variance is a piecewise linear function of intensity in each intensity class to find noise representative regions noisy signal free patches are first nominated in each intensity class next clusters of connected patches are weighted where the weights are calculated based on the degree of similarity to the noise model the highest ranked cluster defines the peak noise variance and other selected clusters are used to approximate the nlf the more information we incorporate such as temporal data and camera settings the more reliable the estimation becomes to account for the processed noise i e remaining after in camera processing we consider the ratio of low to high frequency energies we address noise variations along video signals using a temporal stabilization of the estimated noise objective and subjective simulations demonstrate that the proposed method outperforms other noise estimation techniques both in accuracy and speed

nonlocal image restoration with bilateral variance estimation a low rank approach simultaneous sparse coding ssc or nonlocal image representation has shown great potential in various low level vision tasks leading to several state of the art image restoration techniques including bm3d and lssc however it still lacks a physically plausible explanation about why ssc is a better model than conventional sparse coding for the class of natural images meanwhile the problem of sparsity optimization especially when tangled with dictionary learning is computationally difficult to solve in this paper we take a low rank approach toward ssc and provide a conceptually simple interpretation from a bilateral variance estimation perspective namely that singular value decomposition of similar packed patches can be viewed as pooling both local and nonlocal information for estimating signal variances such perspective inspires us to develop a new class of image restoration algorithms called spatially adaptive iterative singular value thresholding saist for noise data saist generalizes the celebrated bayesshrink from local to nonlocal models for incomplete data saist extends previous deterministic annealing based solution to sparsity optimization through incorporating the idea of dictionary learning in addition to conceptual simplicity and computational efficiency saist has achieved highly competent often better objective performance compared to several state of the art methods in image denoising and completion experiments our subjective quality results compare favorably with those obtained by existing techniques especially at high noise levels and with a large amount of missing data

a fast parallel algorithm for blind estimation of noise variance a blind noise variance algorithm that recovers the variance of noise in two steps is proposed the sample variances are computed for square cells tessellating the noise image several tessellations are applied with the size of the cells increasing fourfold for consecutive tessellations the four smallest sample variance values are retained for each tessellation and combined through an outlier analysis into one estimate the different tessellations thus yield a variance estimate sequence the value of the noise variance is determined from this variance estimate sequence the blind noise variance algorithm is applied to 500 noisy 256 256 images in 98 of the cases the relative estimation error was less than 0 2 with an average error of 0 06 application of the algorithm to differently sized images is also discussed

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

automatic parameter selection for denoising algorithms using a no reference measure of image content across the field of inverse problems in image and video processing nearly all algorithms have various parameters which need to be set in order to yield good results in practice usually the choice of such parameters is made empirically with trial and error if no ground truth reference is available some analytical methods such as cross validation and stein s unbiased risk estimate sure have been successfully used to set such parameters however these methods tend to be strongly reliant on restrictive assumptions on the noise and also computationally heavy in this paper we propose a no reference metric q which is based upon singular value decomposition of local image gradient matrix and provides a quantitative measure of true image content i e sharpness and contrast as manifested in visually salient geometric features such as edges in the presence of noise and other disturbances this measure 1 is easy to compute 2 reacts reasonably to both blur and random noise and 3 works well even when the noise is not gaussian the proposed measure is used to automatically and effectively set the parameters of two leading image denoising algorithms ample simulated and real data experiments support our claims furthermore tests using the tid2008 database show that this measure correlates well with subjective quality evaluations for both blur and noise distortions

an em approach for time variant poisson gaussian model parameter estimation the problem of estimating the parameters of a poisson gaussian model from experimental data has recently raised much interest in various applications for instance in confocal fluorescence microscopy in this context a field of independent random variables is observed which is varying both in time and space each variable is a sum of two components one following a poisson and the other a gaussian distribution in this paper a general formulation is considered where the associated poisson process is nonstationary in space and also exhibits an exponential decay in time whereas the gaussian component corresponds to a stationary white noise with arbitrary mean to solve the considered parametric estimation problem we follow an iterative expectation maximization em approach the parameter update equations involve deriving finite approximation of infinite sums expressions for the maximum error incurred in the process are also given since the problem is non convex we pay attention to the em initialization using a moment based method where recent optimization tools come into play we carry out a performance analysis by computing the cramer rao bounds on the estimated variables the practical performance of the proposed estimation procedure is illustrated on both synthetic data and real fluorescence macroscopy image sequences the algorithm is shown to provide reliable estimates of the mean variance of the gaussian noise and of the scale parameter of the poisson component as well as of its exponential decay rate in particular the mean estimate of the poisson component can be interpreted as a good quality denoised version of the data

homogeneity localization using particle filters with application to noise estimation this paper proposes a method for localizing homogeneity and estimating additive white gaussian noise awgn variance in images the proposed method uses spatially and sparsely scattered initial seeds and utilizes particle filtering techniques to guide their spatial movement towards homogeneous locations this way the proposed method avoids the need to perform the full search associated with block based noise estimation methods to achieve this the paper proposes for the particle filter a dynamic model and a homogeneity observation model based on laplacian structure detectors the variance of awgn is robustly estimated from the variances of blocks in the detected homogeneous areas a proposed adaptive trimmed mean based robust estimator is used to account for the reduction in estimation samples from the full search approach our results show that the proposed method reduces the number of homogeneity measurements required by block based methods while achieving more accuracy

a class of singular nonlinear boundary value problems abstract variational methods are used in a weighted sobolev space to prove the existence of solutions with any prescribed number of zeros for a class of singular nonlinear second order differential equations

random fibonacci sequences and the number 1 13198824 begin abstract for the familiar fibonacci sequence defined by f 1 f 2 1 and f n f n 1 f n 2 for n 2 f n increases exponentially with n at a rate given by the golden ratio 1 sqrt 5 2 1 61803398 ldots but for a simple modification with both additions and subtractions the it random fibonacci sequences defined by t 1 t 2 1 and for n 2 t n pm t n 1 pm t n 2 where each pm sign is independent and either or with probability 1 2 it is not even obvious if abs t n should increase with n our main result is that begin equation sqrt n abs t n rightarrow 1 13198824 ldots text as n rightarrow infty end equation with probability 1 finding the number 1 13198824 ldots involves the theory of random matrix products stern brocot division of the real line a fractal like measure a computer calculation and a rounding error analysis to validate the computer calculation end abstract

gaussian mixture modeling by exploiting the mahalanobis distance in this paper the expectation maximization em algorithm for gaussian mixture modeling is improved via three statistical tests the first test is a multivariate normality criterion based on the mahalanobis distance of a sample measurement vector from a certain gaussian component center the first test is used in order to derive a decision whether to split a component into another two or not the second test is a central tendency criterion based on the observation that multivariate kurtosis becomes large if the component to be split is a mixture of two or more underlying gaussian sources with common centers if the common center hypothesis is true the component is split into two new components and their centers are initialized by the center of the old component candidate for splitting otherwise the splitting is accomplished by a discriminant derived by the third test this test is based on marginal cumulative distribution functions experimental results are presented against seven other em variants both on artificially generated data sets and real ones the experimental results demonstrate that the proposed em variant has an increased capability to find the underlying model while maintaining a low execution time

a transfer operator approach to random fibonacci sequences we consider two stochastic variants of a fibonacci sequence generated by xn 1 xn xn 1 and xn 1 xn xn 1 respectively both the sequences begin with x0 x1 1 and the signs in each iteration are independently chosen with probability p for we focus on the generalized lyapunov exponent q of xn which gives the growth when q 0 or decay when q 0 rate of the ensemble average of xn q when n by using a technique that reduces the non increasing segments in the sequences we map the random sequences to a product of random 2 2 nonnegative matrices which is closely related to the farey fraction spin chain model we show that there exists a critical value q below which the ensemble average of xn q is dominated by the non increasing or linearly increasing samples and hence q is a constant both q and q and its derivatives can be precisely calculated with the transfer operator method moreover when q is a positive integer q is exactly determined by a system of polynomial equations the analysis can be readily generalized to the random sequence generated by xn 1 2cos k xn xn 1 or xn 1 2cos k xn xn 1 for any integer k 3

maximum likelihood estimation of k distribution parameters via the expectation maximization algorithm maximum likelihood ml estimates of k distribution parameters are derived using the expectation maximization em approach this approach demonstrates the computational advantages compared with 2 d numerical maximization of the likelihood function using a nelder mead approach for large datasets the em approach yields more accurate estimates than those of a non ml estimation technique

anisotropic second and fourth order diffusion models based on convolutional virtual electric field for image denoising this paper proposes novel second order and fourth order anisotropic diffusion models for image denoising these two models are based on convolutional virtual electric field convef the proposed second order anisotropic diffusion model was introduced by introducing the convef into the perona malik p m equation and the fourth order one is coined by combining convef and the you kaveh y k equation the employment of the convef model allows to improve the estimation of high order derivatives and makes the proposed methods more robust to noise in addition the proposed convef based y k model is an anisotropic diffusion equation which can avoid the over smoothness of edges and provide better edge protection capability except for better denoising some experiments are conducted to demonstrate the efficiency of the proposed methods

skellam shrinkage wavelet based intensity estimation for inhomogeneous poisson data the ubiquity of integrating detectors in imaging and other applications implies that a variety of real world data are well modeled as poisson random variables whose means are in turn proportional to an underlying vector valued signal of interest in this article we first show how the so called skellam distribution arises from the fact that haar wavelet and filterbank transform coefficients corresponding to measurements of this type are distributed as sums and differences of poisson counts we then provide two main theorems on skellam shrinkage one showing the near optimality of shrinkage in the bayesian setting and the other providing for unbiased risk estimation in a frequentist context these results serve to yield new estimators in the haar transform domain including an unbiased risk estimate for shrinkage of haar fisz variance stabilized data along with accompanying low complexity algorithms for inference we conclude with a simulation study demonstrating the efficacy of our skellam shrinkage estimators both for the standard univariate wavelet test functions as well as a variety of test images taken from the image processing literature confirming that they offer some performance improvements over existing alternatives

on the structure of vector quantizers vector quantization is intrinsically superior to predictive coding transform coding and other suboptimal and em ad hoc procedures since it achieves optimal rate distortion performance subject only to a constraint on memory or block length of the observable signal segment being encoded the key limitation of existing techniques is the very large randomly generated code books which must be stored and the computational complexity of the associated encoding procedures the quantization operation is decomposed into its rudimentary structural components this leads to a simple and elegant approach to derive analytical properties of optimal quantizers some useful properties of quantizers and algorithmic approaches are given which are relevant to the complexity of both storage and processing in the encoding operation highly disordered quantizers which have been designed using a clustering algorithm are considered finally lattice quantizers are examined which circumvent the need for a code book by using a highly structured code based on lattices the code vectors are algorithmically generated in a simple manner rather than stored in a code book and fast algorithms perform the encoding algorithm with negligible complexity

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

on the cycle expansion for the lyapunov exponent of a product of random matrices the cycle expansion of the thermodynamical zeta function for the lyapunov exponent of a product of random matrices typically converges exponentially with the maximal cycle length mainieri 1992 phys rev lett 68 1965 in this paper we show that the convergent exponents are given by the spectrum of a properly defined evolution operator which describes how a steady distribution of vector direction is established under the action of random matrices the exponential decay terms are automatically eliminated in the cycle expansion of the spectral determinant which greatly accelerates the convergence provided all matrix elements are positive numbers as a marginal case the random fibonacci series is studied in detail and it is shown that this method is helpful

a global sparse gradient based coupled system for image denoising abstract we consider a coupled system for image denoising which consists of an anisotropic diffusion equation and a global sparse gradient model gsg the global sparse gradient model is used to estimate the edge map from the noisy image accurately and robustly the anisotropic diffusion process is guided by the edge map furthermore we prove the existence and uniqueness of the solutions of the coupled system with dirichlet initial boundary value problem finally comparing with the edge indicators based on local methods experimental results demonstrate that our proposed method has the state of the art performance among the pde based anisotropic diffusion approaches both in objective measurement and visual evaluation

space alternating generalized expectation maximization algorithm the expectation maximization em method can facilitate maximizing likelihood functions that arise in statistical estimation problems in the classical em paradigm one iteratively maximizes the conditional log likelihood of a single unobservable complete data space rather than maximizing the intractable likelihood function for the measured or incomplete data em algorithms update all parameters simultaneously which has two drawbacks 1 slow convergence and 2 difficult maximization steps due to coupling when smoothness penalties are used the paper describes the space alternating generalized em sage method which updates the parameters sequentially by alternating between several small hidden data spaces defined by the algorithm designer the authors prove that the sequence of estimates monotonically increases the penalized likelihood objective derive asymptotic convergence rates and provide sufficient conditions for monotone convergence in norm two signal processing applications illustrate the method estimation of superimposed signals in gaussian noise and image reconstruction from poisson measurements in both applications the sage algorithms easily accommodate smoothness penalties and converge faster than the em algorithms

recursive expectation maximization em algorithms for time varying parameters with applications to multiple target tracking we investigate the application of expectation maximization em algorithms to the classical problem of multiple target tracking mtt for a known number of targets conventional algorithms which deal with this problem have a computational complexity that depends exponentially on the number of targets and usually divide the problem into a localization stage and a tracking stage the new algorithms achieve a linear dependency and integrate these two stages three optimization criteria are proposed using deterministic and stochastic dynamic models for the targets

pure let image deconvolution we propose a non iterative image deconvolution algorithm for data corrupted by poisson or mixed poisson gaussian noise many applications involve such a problem ranging from astronomical to biological imaging we parameterize the deconvolution process as a linear combination of elementary functions termed as linear expansion of thresholds this parameterization is then optimized by minimizing a robust estimate of the true mean squared error the poisson unbiased risk estimate each elementary function consists of a wiener filtering followed by a pointwise thresholding of undecimated haar wavelet coefficients in contrast to existing approaches the proposed algorithm merely amounts to solving a linear system of equations which has a fast and exact solution simulation experiments over different types of convolution kernels and various noise levels indicate that the proposed method outperforms the state of the art techniques in terms of both restoration quality and computational complexity finally we present some results on real confocal fluorescence microscopy images and demonstrate the potential applicability of the proposed method for improving the quality of these images

growth and decay of random fibonacci sequences for 0 they grow exponentially by formulating the problem as a markov chain involving random matrix products and computing its invariant measure a fractal the lyapunov constant limn x n 1 n is determined numerically for a wide range of values and its dependence on is observed to be non smooth the limit is defined in the almost sure sense this generalizes recent work of viswanath who proved 1 1 131 988 24 by a simple rescaling these results also apply to the more general random recurrence x n 1 x n x n 1 for fixed and these random recurrence relations have links with many fields including ergodic theory dynamical systems heavy tailed statistics spectral theory continued fractions and condensed matter physics

global optimization with polynomials and the problem of moments we consider the problem of finding the unconstrained global minimum of a real valued polynomial p x mathbb r n to mathbb r as well as the global minimum of p x in a compact set k defined by polynomial inequalities it is shown that this problem reduces to solving an often finite sequence of convex linear matrix inequality lmi problems a notion of karush kuhn tucker polynomials is introduced in a global optimality condition some illustrative examples are provided

image denoising by sparse 3 d transform domain collaborative filtering we propose a novel image denoising strategy based on an enhanced sparse representation in transform domain the enhancement of the sparsity is achieved by grouping similar 2d image fragments e g blocks into 3d data arrays which we call groups collaborative altering is a special procedure developed to deal with these 3d groups we realize it using the three successive steps 3d transformation of a group shrinkage of the transform spectrum and inverse 3d transformation the result is a 3d estimate that consists of the jointly filtered grouped image blocks by attenuating the noise the collaborative filtering reveals even the finest details shared by grouped blocks and at the same time it preserves the essential unique features of each individual block the filtered blocks are then returned to their original positions because these blocks are overlapping for each pixel we obtain many different estimates which need to be combined aggregation is a particular averaging procedure which is exploited to take advantage of this redundancy a significant improvement is obtained by a specially developed collaborative wiener filtering an algorithm based on this novel denoising strategy and its efficient implementation are presented in full detail an extension to color image denoising is also developed the experimental results demonstrate that this computationally scalable algorithm achieves state of the art denoising performance in terms of both peak signal to noise ratio and subjective visual quality

wavelets ridgelets and curvelets for poisson noise removal in order to denoise poisson count data we introduce a variance stabilizing transform vst applied on a filtered discrete poisson process yielding a near gaussian process with asymptotic constant variance this new transform which can be deemed as an extension of the anscombe transform to filtered data is simple fast and efficient in very low count situations we combine this vst with the filter banks of wavelets ridgelets and curvelets leading to multiscale vsts ms vsts and nonlinear decomposition schemes by doing so the noise contaminated coefficients of these ms vst modified transforms are asymptotically normally distributed with known variances a classical hypothesis testing framework is adopted to detect the significant coefficients and a sparsity driven iterative scheme reconstructs properly the final estimate a range of examples show the power of this ms vst approach for recovering important structures of various morphologies in very low count images these results also demonstrate that the ms vst approach is competitive relative to many existing denoising methods

detection of random signals in gaussian mixture noise a locally optimal detection algorithm for random signals in dependent noise is derived and applied to independent identically distributed complex valued gaussian mixture noise the resulting detector is essentially a weighted sum of power detectors the power detector is the locally optimal detector for random signals in gaussian noise the weighting functions are modified to enhance the detection performance for small sample sizes an implementation of the mixture detector using the expectation maximization algorithm is described moments of these detectors are calculated from piecewise polynomial approximations of the weighting functions the sum of sufficiently many independent identically distributed detector outputs is then approximated by a normal distribution probability distributions are also derived for the power detector in gaussian mixture noise for a particular set of noise parameters the theoretical distributions are compared with those obtained from monte carlo simulation and seen to be quite close the theoretical distributions are then used to compare the performance of the mixture and power detectors in gaussian mixture noise over a range of parameters and to assess the impact of parameter error on detection performance in this study the signal gain of the mixture detectors varies from 15 to 38 db and the degradation of the probability of detection due to parameter estimation error is relatively minor

jpeg compression history estimation for color images we routinely encounter digital color images that were previously compressed using the joint photographic experts group jpeg standard en route to the image s current representation the previous jpeg compression s various settings termed its jpeg compression history ch are often discarded after the jpeg decompression step given a jpeg decompressed color image this paper aims to estimate its lost jpeg ch we observe that the previous jpeg compression s quantization step introduces a lattice structure in the discrete cosine transform dct domain this paper proposes two approaches that exploit this structure to solve the jpeg compression history estimation chest problem first we design a statistical dictionary based chest algorithm that tests the various chs in a dictionary and selects the maximum a posteriori estimate second for cases where the dct coefficients closely conform to a 3 d parallelepiped lattice we design a blind lattice based chest algorithm the blind algorithm exploits the fact that the jpeg ch is encoded in the nearly orthogonal bases for the 3 d lattice and employs novel lattice algorithms and recent results on nearly orthogonal lattice bases to estimate the ch both algorithms provide robust jpeg chest performance in practice simulations demonstrate that jpeg chest can be useful in jpeg recompression the estimated ch allows us to recompress a jpeg decompressed image with minimal distortion large signal to noise ratio and simultaneously achieve a small file size

noise parameter estimation for poisson corrupted images using variance stabilization transforms noise is present in all images captured by real world image sensors poisson distribution is said to model the stochastic nature of the photon arrival process and agrees with the distribution of measured pixel values we propose a method for estimating unknown noise parameters from poisson corrupted images using properties of variance stabilization with a significantly lower computational complexity and improved stability the proposed estimation technique yields noise parameters that are comparable in accuracy to the state of art methods

automatic estimation and removal of noise from a single image image denoising algorithms often assume an additive white gaussian noise awgn process that is independent of the actual rgb values such approaches cannot effectively remove color noise produced by today s ccd digital camera in this paper we propose a unified framework for two tasks automatic estimation and removal of color noise from a single image using piecewise smooth image models we introduce the noise level function nlf which is a continuous function describing the noise level as a function of image brightness we then estimate an upper bound of the real nlf by fitting a lower envelope to the standard deviations of per segment image variances for denoising the chrominance of color noise is significantly removed by projecting pixel values onto a line fit to the rgb values in each segment then a gaussian conditional random field gcrf is constructed to obtain the underlying clean image from the noisy input extensive experiments are conducted to test the proposed algorithm which is shown to outperform state of the art denoising algorithms

the random fibonacci recurrence and the visible points of the plane in this letter we show a connection between the random fibonacci recurrence and the visible points of the plane in particular we show that by suitably modifying the rules of the random fibonacci map there is a unique correspondence between the visible points points with relative prime coordinates of the first quadrant and the vertices of a self similar graph what we call the fibonacci graph the proposed random recurrence can then be interpreted as a random walk on this graph

zeta function for the lyapunov exponent of a product of random matrices a cycle expansion for the lyapunov exponent of a product of random matrices is derived the formula is nonperturbative and numerically effective which allows the lyapunov exponent to be computed to high accuracy in particular the free energy and heat capacity are computed for the one dimensional ising model with quenched disorder the formula is derived by using a bernoulli dynamical system to mimic the randomness

entire fredholm determinants for evaluation of semiclassical and thermodynamical spectra proofs that fredholm determinants of transfer operators for hyperbolic flows are entire can be extended to a large new class of multiplicative evolution operators we construct such operators both for the gutzwiller semiclassical quantum mechanics and for classical thermodynamic formalism and introduce a new functional determinant which is expected to be entire for axiom a flows and whose zeros coincide with the zeros of the gutzwiller voros zeta function

image noise level estimation by principal component analysis the problem of blind noise level estimation arises in many image processing applications such as denoising compression and segmentation in this paper we propose a new noise level estimation method on the basis of principal component analysis of image blocks we show that the noise variance can be estimated as the smallest eigenvalue of the image block covariance matrix compared with 13 existing methods the proposed approach shows a good compromise between speed and accuracy it is at least 15 times faster than methods with similar accuracy and it is at least two times more accurate than other methods our method does not assume the existence of homogeneous areas in the input image and hence can successfully process images containing only textures

an infinite transfer matrix approach to the product of random 2 2 positive matrices this paper concerns the efficient and precise determination of the laypunov exponent and other statistical properties of a product of random 2 2 matrices by considering the ensemble average of an infinite series of regular functions and its iteration we construct a transfer matrix which is shown to be a trace class operator in a hilbert space given that the positiveness of the random matrices is assumed this fact gives a theoretical explanation of the superior convergence of the cycle expansion of the lyapunov exponent bai 2007 j phys a math theor 40 8315 a numerical method based on the infinite transfer matrix is applied to a one dimensional ising model with a random field and a generalized fibonacci sequence it is found that in the presence of continuous distribution of a disorder or degenerated random matrix the transfer matrix approach is more efficient than the cycle expansion method

low rank decomposition based restoration of compressed images via adaptive noise estimation images coded at low bit rates in real world applications usually suffer from significant compression noise which significantly degrades the visual quality traditional denoising methods are not suitable for the content dependent compression noise which usually assume that noise is independent and with identical distribution in this paper we propose a unified framework of content adaptive estimation and reduction for compression noise via low rank decomposition of similar image patches we first formulate the framework of compression noise reduction based upon low rank decomposition compression noises are removed by soft thresholding the singular values in singular value decomposition of every group of similar image patches for each group of similar patches the thresholds are adaptively determined according to compression noise levels and singular values we analyze the relationship of image statistical characteristics in spatial and transform domains and estimate compression noise level for every group of similar patches from statistics in both domains jointly with quantization steps finally quantization constraint is applied to estimated images to avoid over smoothing extensive experimental results show that the proposed method not only improves the quality of compressed images obviously for post processing but are also helpful for computer vision tasks as a pre processing method

eigenvector statistics of the product of ginibre matrices we develop a method to calculate left right eigenvector correlations of the product of m independent n n complex ginibre matrices for illustration we present explicit analytical results for the vector overlap for a couple of examples for small m and n we conjecture that the integrated overlap between left and right eigenvectors is given by the formula o 1 m 2 n 1 and support this conjecture by analytical and numerical calculations we derive an analytical expression for the limiting correlation density as n for the product of ginibre matrices as well as for the product of elliptic matrices in the latter case we find that the correlation function is independent of the eccentricities of the elliptic laws