improved estimation of eigenvalues and eigenvectors of covariance matrices using their sample estimates the problem of estimating the eigenvalues and eigenvectors of the covariance matrix associated with a multivariate stochastic process is considered the focus is on finite sample size situations whereby the number of observations is limited and comparable in magnitude to the observation dimension using tools from random matrix theory and assuming a certain eigenvalue splitting condition new estimators of the eigenvalues and eigenvectors of the covariance matrix are derived that are shown to be consistent in a more general asymptotic setting than the traditional one indeed these estimators are proven to be consistent not only when the sample size increases without bound for a fixed observation dimension but also when the observation dimension increases to infinity at the same rate as the sample size numerical evaluations indicate that the estimators have an excellent performance in small sample size scenarios where the observation dimension and the sample size are comparable in magnitude

covariance regularization by thresholding this paper considers regularizing a covariance matrix of p variables estimated from n observations by hard thresholding we show that the thresholded estimate is consistent in the operator norm as long as the true covariance matrix is sparse in a suitable sense the variables are gaussian or sub gaussian and log p n 0 and obtain explicit rates the results are uniform over families of covariance matrices which satisfy a fairly natural notion of sparsity we discuss an intuitive resampling scheme for threshold selection and prove a general cross validation result that justifies this approach we also compare thresholding to other covariance estimators in simulations and on an example from climate data 1 introduction estimation of covariance matrices is important in a number of areas of statistical analysis including dimension reduction by principal component analysis pca classification by linear or quadratic discriminant analysis lda and qda establishing independence and conditional independence relations in the context of graphical models and setting confidence intervals on linear functions of the means of the components in recent years many application areas where these tools are used have been dealing with very high dimensional datasets and sample sizes can be very small relative to dimension examples include genetic data brain imaging spectroscopic imaging climate data and many others it is well known by now that the empirical covariance matrix for samples of size n from a p variate gaussian distribution np p is not a good estimator of the population covariance if p is large many results in random matrix theory illustrate this from the classical mary law 29 to the more recent work of johnstone and his students on the theory of the largest eigenvalues 12 23 30 and associated eigenvectors 24 however with the exception of a method for estimating the covariance spectrum 11 these probabilistic results do not offer alternatives to the sample covariance matrix alternative estimators for large covariance matrices have therefore attracted a lot of attention recently two broad classes of covariance estimators have emerged those that rely on a natural ordering among variables and assume that variables

decision based order statistic filters the authors propose two adaptive order statistic filters which generate outputs based on the results of hypothesis tests to reduce edge shifting of the median filter a modified median filter mmf is proposed first a hypothesis test is applied to detect the edge location then whenever an edge is detected the mmf generates the output by modifying the median output based on a comparison of median value to the current input value the mmf can retain more fine details than the median filter with the same window size as well as reduce the output mean square error which is caused mainly by edge shifting to suppress nonimpulsive noise as well as impulsive noise an l type structure is combined with the mmf the proposed filter generates the output by using asymmetric alpha trimming on the mmf output in addition to noise suppression it can enhance the gradient of blurred edges provided that the size of the window is greater than the transition width of the blurred edges experimental results for one and two dimensional signals are presented

an adaptive order statistic noise filter for gamma corrected image sequences original video signals are often corrupted by a certain amount of noise originating from the camera electronics as a result of the gamma correction in cameras the observed noise is signal dependent we present a spatio temporal order statistic os noise filter that takes into account the gamma correction in the camera the calculation of the filter coefficients requires higher order order statistics hoos of the noise process we make use of a range test rt to determine locally from which neighboring signal values an estimate should be formed the noise filter that we arrive at is adaptive and computationally efficient

modified subspace algorithms for doa estimation with large arrays this paper proposes the use of a new generalized asymptotic paradigm in order to analyze the performance of subspace based direction of arrival doa estimation in array signal processing applications instead of assuming that the number of samples is high whereas the number of sensors antennas remains fixed the asymptotic situation analyzed herein assumes that both quantities tend to infinity at the same rate this asymptotic situation provides a more accurate description of a potential situation where these two quantities are finite and hence comparable in magnitude it is first shown that both music and ssmusic are inconsistent when the number of antennas sensors increases without bound at the same rate as the sample size this is done by analyzing and deriving closed form expressions for the two corresponding asymptotic cost functions by examining these asymptotic cost functions one can establish the minimum number of samples per antenna needed to resolve closely spaced sources in this asymptotic regime next two alternative estimators are constructed that are strongly consistent in the new asymptotic situation i e they provide consistent doa estimates not only when the number of snapshots goes to infinity but also when the number of sensors antennas increases without bound at the same rate these estimators are inspired by the theory of g estimation and are therefore referred to as g music and g ssmusic respectively simulations show that the proposed algorithms outperform their traditional counterparts in finite sample size situations although they still present certain limitations

clt for linear spectral statistics of large dimensional sample covariance matrices let bn 1 n t1 2nxnx nt1 2n where xn xij is n n with i i d complex standardized entries having finite fourth moment and t1 2n is a hermitian square root of the nonnegative definite hermitian matrix tn the limiting behavior as n with n n approaching a positive constant of functionals of the eigenvalues of bn where each is given equal weight is studied due to the limiting behavior of the empirical spectral distribution of bn it is known that these linear spectral statistics converges a s to a nonrandom quantity this paper shows their rate of convergence to be 1 n by proving after proper scaling that they form a tight sequence moreover if exppx211 0 and expp x11 4 2 or if x11 and tn are real and exppx411 3 they are shown to have gaussian limits

generalization of median root prior reconstruction penalized iterative algorithms for image reconstruction in emission tomography contain conditions on which kind of images are accepted as solutions the penalty term has commonly been a function of pairwise pixel differences in the activity in a local neighborhood such that smooth images are favored attempts to ensure better edge and detail preservation involve difficult tailoring of parameter values or the penalty function itself the previously introduced median root prior mrp favors locally monotonic images mrp preserves sharp edges while reducing locally nonmonotonic noise at the same time quantitative properties of mrp are good because differences in the neighboring pixel values are not penalized as such the median is used as an estimate for a penalty reference against which the pixel value is compared when setting the penalty in order to generalize the class of mrp type of priors the standard median was replaced by other order statistic operations the l and finite impulse response median hybrid fmh filters they allow for smoother appearance as they apply linear weighting together with robust nonlinear operations the images reconstructed using the new mrp l and mrp fmh priors are visually more conventional good quantitative properties of mrp are not significantly altered by the new priors

on morphological operators based on rank filters rank order morphological operators have been designed to better cope with shape variations and noise than the corresponding operators with plain structuring elements in this paper starting from a brief historical overview of rank order filters and erosions dilations in digital image processing rank order based morphological operators are surveyed we also highlight the relations between these operators and show that many are similar if not equivalent an extensive bibliography is provided

microstatistics in signal decomposition and the optimal filtering problem the author introduces and analyzes a large class of nonlinear filters which are based on signal decomposition and where the estimation in the decomposed space uses linear combinations of either the observation vector the sorted observation vector or in general a nonlinear transformation of the observation vector thus nonlinear filter response characteristics are achieved but with the machinery of linear systems theory available for their optimization and design it is shown that linear filters are a subclass of microstatistic filters and that the optimal linear filter solution is suboptimal in the decomposed signal space the filtering problem reduces to a set of filters operating on the decomposed signals the output is a weighted sum of the decomposed filtered signals the optimal interconnection structure between decomposed signals has complexity o m 1 where m is the cardinality of the decomposition the formulation is given for a radix 1 decomposition and generalized for a radix q decomposition computer simulations illustrate the performance

locally monotonic regression the concept of local monotonicity appears in the study of the set of root signals of the median filter and provides a measure of the smoothness of the signal the median filter is a suboptimal smoother under this measure of smoothness since a filter pass does necessarily yield a locally monotonic output even if a locally monotonic output does result there is no guarantee that it will possess other desirable properties such as optimal similarity to the original signal locally monotonic regression is a technique for the optimal smoothing of finite length discrete real signals under such a criterion a theoretical framework in which the existence of locally monotonic regression is proved and algorithms for their computation are given regression is considered as an approximation problem in r sub n the criterion of approximation is derived from a semimetric and the approximating set is the collection of signals sharing the property of being locally monotonic

mathematical programming algorithms for regression based nonlinear filtering in r sup n this paper is concerned with regression under a sum of partial order constraints examples include locally monotonic piecewise monotonic runlength constrained and unimodal and oligomodal regression these are of interest not only in nonlinear filtering but also in density estimation and chromatographic analysis it is shown that under a least absolute error criterion these problems can be transformed into appropriate finite problems which can then be efficiently solved via dynamic programming techniques although the result does not carry over to least squares regression hybrid programming algorithms can be developed to solve least squares counterparts of certain problems in the class

fluctuations of an improved population eigenvalue estimator in sample covariance matrix models this paper provides a central limit theorem for a consistent estimator of population eigenvalues with large multiplicities based on sample covariance matrices the focus is on limited sample size situations whereby the number of available observations is comparable in magnitude to the observation dimension an exact expression as well as an empirical asymptotically accurate approximation of the limiting variance is derived simulations are performed that corroborate the theoretical claims

analysis of preflow push algorithms for maximum network flow we study the class of preflow push algorithms recently introduced by goldberg and tarjan for solving the maximum network flow problem on a weighted digraph g v e we improve goldberg and tarjanis o n3 time bound for the maximum distance preflow push algorithm to o n2 m and show that this bound is tight by constructing a parametrized worst case network we then develop the maximal excess preflow push algorithm and show that it achieves a bound of o n2 m pushes based on this we develop a maximum network flow algorithm for the synchronous distributed model of computation that uses at most o n2 m messages and o n2 time thereby improving upon the best previously known algorithms for this model

improving gil werman algorithm for running min and max filters the current best bound on the number of comparison operations needed to compute the running maximum or minimum over a p element sliding data window is approximately three comparisons per output sample this bound is probabilistic for some algorithms and is derived for their complexities on the average for independent identically distributed i i d input signals the worst case complexities of these algorithms are o p the worst case complexity c sub r 3 4 p comparisons per output sample for 1d signals is achieved in the gil werman algorithm 1993 in this correspondence we propose a modification of the gil werman algorithm with the same worst case complexity but with a lower average complexity a theoretical analysis shows that using the proposed modification the complexities of sliding max or min 1d and 2d filters over i i d signals are reduced to c sub 1 2 5 3 5 p 1 p sup 2 and c sub 2 5 7 p 2 p sup 2 comparisons per output sample on the average respectively simulations confirm the theoretical results moreover experiments show that even for highly correlated data namely for real images the behavior of the algorithm remains the same as for i i d signals

on techniques for detecting circumscribed masses in mammograms a method for detecting one type of breast tumor circumscribed masses in mammograms is presented it relies on a combination of criteria used by experts including the shape brightness contrast and uniform density of tumor areas the method uses modified median filtering to enhance mammogram images and template matching to detect the tumors in the template matching step suspicious areas are identified by thresholding the cross correlation values and a percentile method is used to determine a threshold for each film in addition two tests are used to remove false alarms from the resulting candidates the results obtained by applying these techniques to a set of test images are described they are judged encouraging

multistage order statistic filters for image sequence processing the application of multistage order statistic filters mos to the task of noise suppression in time varying imagery is studied it is shown that mos filters efficiently preserve image structures under motion without motion compensation preprocessing in particular the families of multistage median and weighted median filters are considered motion preservation and statistical smoothing measures are derived it is shown that spatiotemporal filtering allows for a significant improvement over both spatial and temporal filtering in terms of output image resolution and noise suppression

fast algorithms for training stack filters stack filters constitute a class of nonlinear digital filters possessing a weak superposition property in the paper fast algorithms for training stack filters are introduced the first algorithm is based on a technique previously developed similar to the previous algorithm this improved method requires only simple arithmetic operations increment decrement and local comparison the spl epsiv convergence property of the fast algorithm is established in addition two fast training algorithms are developed for a subclass of stack filters called weighted order statistic filters these fast algorithms are variants of the lms and rls algorithms in linear filters all three fast algorithms developed exploit the repetition property of the training input the factor of speedup is approximately the ratio between the number of quantization levels of the input and the window size

a family of nonlinear filters with data dependent coefficients a new family of data dependent nonlinear filters ddnl is presented coefficients are computed locally and the absolute distance between signal samples is used to determine a rank order dependent weighting function the new filters have very good performance regarding noise suppression and impulse rejection and at the same time provide better edge preservation than the averager and other linear smoothers

a new approach for mutual information analysis of large dimensional multi antenna channels this paper adresses the behavior of the mutual information of correlated multiple input multiple output mimo rayleigh channels when the numbers of transmit and receive antennas converge to infin at the same rate using a new and simple approach based on poincare nash inequality and on an integration by parts formula it is rigorously established that the mutual information when properly centered and rescaled converges to a standard gaussian random variable simple expressions for the centering and scaling parameters are provided these results confirm previous evaluations based on the powerful but nonrigorous replica method it is believed that the tools that are used in this paper are simple robust and of interest for the communications engineering community

application of partition based median type filters for suppressing noise in images an adaptive median based filter is proposed for removing noise from images specifically the observed sample vector at each pixel location is classified into one of m mutually exclusive partitions each of which has a particular filtering operation the observation signal space is partitioned based an the differences defined between the current pixel value and the outputs of cwm center weighted median filters with variable center weights the estimate at each location is formed as a linear combination of the outputs of those cwm filters and the current pixel value to control the dynamic range of filter outputs a location invariance constraint is imposed upon each weighting vector the weights are optimized using the constrained lms least mean square algorithm recursive implementation of the new filter is then addressed the new technique consistently outperforms other median based filters in suppressing both random valued and fixed valued impulses and it also works satisfactorily in reducing gaussian noise as well as mixed gaussian and impulse noise

random matrix approach to cross correlations in financial data we analyze cross correlations between price fluctuations of different stocks using methods of random matrix theory rmt using two large databases we calculate cross correlation matrices c of returns constructed from i 30 min returns of 1000 us stocks for the 2 yr period 1994 1995 ii 30 min returns of 881 us stocks for the 2 yr period 1996 1997 and iii 1 day returns of 422 us stocks for the 35 yr period 1962 1996 we test the statistics of the eigenvalues lambda i of c against a null hypothesis a random correlation matrix constructed from mutually uncorrelated time series we find that a majority of the eigenvalues of c fall within the rmt bounds lambda lambda for the eigenvalues of random correlation matrices we test the eigenvalues of c within the rmt bound for universal properties of random matrices and find good agreement with the results for the gaussian orthogonal ensemble of random matrices implying a large degree of randomness in the measured cross correlation coefficients further we find that the distribution of eigenvector components for the eigenvectors corresponding to the eigenvalues outside the rmt bound display systematic deviations from the rmt prediction in addition we find that these deviating eigenvectors are stable in time we analyze the components of the deviating eigenvectors and find that the largest eigenvalue corresponds to an influence common to all stocks our analysis of the remaining deviating eigenvectors shows distinct groups whose identities correspond to conventionally identified business sectors finally we discuss applications to the construction of portfolios of stocks that have a stable ratio of risk to return less

the wmmr filters a class of robust edge enhancers the authors develop a class of filters called weighted majority of m values with minimum range wmmr sup m that have the same impulse rejection properties as the median they demonstrate a subclass of these filters wmmr that may be optimized for edge enhancement in one dimension in that their output converges to the closest perfect edge one of these filters is shown to restore a class of noisy edges to the closest perfect edge on one pass applications in one and two dimensions are discussed and a two dimensional simulation is provided comparing the wmmr to other filters for smoothing and edge enhancement

a class of rank order smoothers smoothers or nonlinear filters that make estimates purely on the basis of rank and temporal order determinations among members of the input data are inherently robust and compatible with vlsi implementations the classic example is the moving median smoother but it is possible to define others which have significantly different attributes both in relation to the statistical estimation problem and in relation to hardware implications attributes offered in the latter category which are especially desirable in systolic vlsi include essentially recursive operation and elimination of the interactions between rank and temporal ordering requirements which are a feature of median smoothers experimental results indicate significantly improved response to noisy steps for these smoothers in comparison to median smoothers of comparable rectangular pulse detection capabilities

generalized mean median filtering for robust frequency selective applications huber proposed the pepsi family of epsi contaminated normal distributions to model environments characterized by heavy tailed distributions based on this two component mixture distribution mean median mem filters were proposed the mem filter output is a combination of the sample mean and the sample median where observation samples are weighted uniformly this property of mem filters constrains them to the class of smoothers lacking frequency selective filtering capabilities this paper extends mem filtering to the weighted sum median wsm filtering structure admitting real valued weights thereby enabling more general filtering characteristics i e bandpass and high pass filtering the proposed filter structure is also well motivated from a presented maximum likelihood ml estimate analysis under epsi contaminated statistics the ml analysis demonstrates the need for a combination of weighted sum ws and weighted median wm type filters for processing of signals corrupted by epsi contaminated noise the wsm filter is statistically analyzed through the determination of filter output variance and breakdown probability the combination parameter alpha is optimized to minimize the filter output variance which is a measure of noise attenuation capability moreover filter design procedures that yield a desired spectral response are detailed finally the proposed wsm filter structure is tested utilizing signal processing applications including low pass bandpass and high pass filtering and image processing applications including image sharpening and denoising evaluating and comparing the wsm filter performance to that of the ws wm and mem filters

rank order operators and the mean absolute error criterion the author shows that among all randomizing stack filters whose output decisions are based on the sum of the bits in the window on each level of the threshold decomposition architecture rank order operators are optimal under an error criterion which is the sum of the absolute error incurred on each level of the threshold decomposition architecture he also shows that if the filtering class being optimized obeys a deterministic stacking property then the traditional multilevel mean absolute error criterion reduces to the sum of the absolute error incurred to each level this leads to an efficient algorithm for choosing the rank order filter which minimizes the multilevel mean absolute error criterion

morphological filters part i their set theoretic analysis and relations to linear shift invariant filters this paper examines the set theoretic interpretation of morphological filters in the framework of mathematical morphology and introduces the representation of classical linear filters in terms of morphological correlations which involve supremum infimum operations and additions binary signals are classified as sets and multilevel signals as functions two set theoretic representations of signals are reviewed filters are classified as set processing sp or function processing fp conditions are provided for certain fp filters that pass binary signals to commute with signal thresholding because then they can be analyzed and implemented as sp filters the basic morphological operations of set erosion dilation opening and closing are related to minkowski set operations and are used to construct fp morphological filters emphasis is then given to analytically and geometrically quantifying the similarities and differences between morphological filtering of signals by sets and functions the latter case allows the definition of morphological convolutions and correlations toward this goal various properties of fp morphological filters are also examined linear shift invariant filters due to their translation invariance are uniquely characterized by their kernel which is a special collection of input signals increasing linear filters are represented as the supremum of erosions by their kernel functions if the filters are also discrete and have a finite extent impulse response they can be represented as the supremum of erosions only by their minimal with respect to a signal ordering kernel functions stable linear filters can be represented as the sum of at most two weighted suprema of erosions these results demonstrate the power of mathematical morphology as a unifying approach to both linear and nonlinear signal shaping strategies

robust image modeling techniques with an image restoration application a robust parameter estimation algorithm for a nonsymmetric half plane nshp autoregressive model where the driving noise is a mixture of a gaussian and an outlier process is presented the convergence of the estimation algorithm is proved an algorithm to estimate parameters and original image intensity simultaneously from the impulse noise corrupted image where the model governing the image is not available is also presented the robustness of the parameter estimates is demonstrated by simulation finally an algorithm to restore realistic images is presented the entire image generally does not obey a simple image model but a small portion e g 8 8 of the image is assumed to obey an nshp model the original image is divided into windows and the robust estimation algorithm is applied for each window the restoration algorithm is tested by comparing it to traditional methods on several different images

no eigenvalues outside the support of the limiting spectral distribution of large dimensional sample covariance matrices let b n 1 n t n 1 2 x n x n t n 1 2 where x n is n times n with i i d complex standardized entries having finite fourth moment and t n 1 2 is a hermitian square root of the nonnegative definite hermitian matrix t n it is known that as n to infty if n n converges to a positive number and the empirical distribution of the eigenvalues of t n converges to a proper probability distribution then the empirical distribution of the eigenvalues of b n converges a s to a nonrandom limit in this paper we prove that under certain conditions on the eigenvalues of t n for any closed interval outside the support of the limit with probability 1 there will be no eigenvalues in this interval for all n sufficiently large

noise reduction of image sequences using motion compensation and signal decomposition in this paper a new spatio temporal filtering method for removing noise from image sequences is proposed this method combines the use of motion compensation and signal decomposition to account for the effects of object motion because of object motion image sequences are temporally nonstationary which requires the use of adaptive filters by motion compensating the sequence prior to filtering nonstationarities i e parts of the signal that are momentarily not stationary can be reduced significantly however since not all nonstationarities can be accounted for by motion a motion compensated signal still contains nonstationarities an adaptive algorithm based on order statistics is described that decomposes the motion compensated signal into a noise free nonstationary part and a noisy stationary part an rls filter is then used to filter the noise from the stationary signal our new method is experimentally compared with various noise filtering approaches from literature

regularized estimation of large covariance matrices this paper considers estimating a covariance matrix of p variables from n observations by either banding the sample covariance matrix or estimating a banded version of the inverse of the covariance we show that these estimates are consistent in the operator norm as long as logp 2 n 0 and obtain explicit rates the results are uniform over some fairly natural well conditioned families of covariance matrices we also introduce an analogue of the gaussian white noise model and show that if the population covariance is embeddable in that model and well conditioned then the banded approximations produce consistent estimates of the eigenvalues and associated eigenvectors of the covariance matrix the results can be extended to smooth versions of banding and to non gaussian distributions with su ciently short tails a resampling approach is proposed for choosing the banding parameter in practice this approach is illustrated numerically on both simulated and real data

some statistical properties of alpha trimmed mean and standard type m filters the statistical properties of two classes of filters generalizing the median filter are considered the two classes are the alpha trimmed mean alpha tm filter and the standard type m stm filter both of which are special cases of the l filter results are developed to quantify the white noise suppression and edge preservation characteristics of the filters by considering their output sequence error statistics it is shown that the alpha tm and stm filters perform better than the running mean and median filters in white noise suppression while they can be designed to be comparable to the median filter in edge preservation in the presence of noise

irreducibly inconsistent systems of linear inequalities abstract irreducibly inconsistent systems of linear inequalities are considered from the point of view of applying simplex like methods for investigation we give necessary and sufficient conditions for a system to be irreducibly inconsistent which can be found by applying a simplex algorithm next we consider general inconsistent systems the simplex method can be used to identify irreducibly inconsistent subsystem such subsystems can give structural insight in the inconsistency and are used in trying to make the overall system consistent this can be done in an easy way e g by right hand side manipulations finally the problem of finding a cheapest way of doing this can be formulated and solved as an extended linear program

threshold superposition in morphological image analysis systems it is shown that four composite morphological systems namely morphological edge detection peak valley extraction skeletonization and shape size distributions obey a weak linear superposition called threshold linear superposition the output image signal or measurement from each system is shown to be the sum of outputs due to input binary images that result from thresholding the input gray level image at all levels these results are generalized to a vector space formulation e g to any finite linear combination of simple morphological systems thus many such systems processing gray level images are reduced to corresponding binary image processing systems which are easier to analyze and implement

fir median hybrid filters with predictive fir substructures a class of finite impulse response fir median hybrid fmh filters that contain linear fir substructures to estimate the current signal value using forward and backward prediction is introduced the output of the overall filter is the median of the predicted values and the actual signal value in the middle of the filter window predictors maximizing the signal to noise ratio on signal sections described by an lth order polynominal are derived the ramp enhancement filters are shown to attenuate the noise on a ramp signal better than the standard median sm filters the new predictive fmh filters are shown to have root signals which do not exist for the sm filters e g triangular waves by combining the level and the ramp enhancement fmh filters a filter is obtained which attenuates noise on constant and ramp signals the noise attenuation on ramp signals is better than with the sm filter and the predictive fmh filter has novel and meaningful root structures the number of arithmetic operations needed to implement the predictive fmh filter grows linearly with the length of the filter

on the asymptotic behavior of the sample estimates of eigenvalues and eigenvectors of covariance matrices this paper analyzes the asymptotic behavior of the sample estimators of the eigenvalues and eigenvectors of covariance matrices rather than considering traditional large sample size asymptotics in this paper the focus is on limited sample size situations whereby the number of available observations is comparable in magnitude to the observation dimension using tools from random matrix theory the asymptotic behavior of the traditional sample estimates is investigated under the assumption that both the sample size and the observation dimension tend to infinity while their quotient converges to a positive quantity assuming that an asymptotic eigenvalue splitting condition is fulfilled closed form asymptotic expressions of these estimators are derived proving inconsistency of the traditional sample estimators in these asymptotic conditions the derived expressions are shown to provide a valuable insight into the behavior of the sample estimators in the small sample size regime

multichannel distance filter a nonlinear multichannel digital filter is presented in this correspondence the output is a weighted sum of all samples in the filter window with a single parameter controlling the filter nonlinearity although input data ordering is not required performance can surpass the performance of other ordering based multichannel filters

deterministic properties of analog median filters two key deterministic properties of analog median filters are established the first is that root signals are characterized by a special class of locally monotone functions and the second is that the repeated application of a median filter produces a root signal which retains significant features in the original data both results are extensions of well known facts for discrete median filters in addition it is shown that these properties do not extend to a natural multidimensional version of the median filter

eigen inference for energy estimation of multiple sources in this paper a new method is introduced to blindly estimate the transmit power of multiple signal sources in multiantenna fading channels when the number of sensing devices and the number of available samples are sufficiently large compared to the number of sources recent advances in the field of large dimensional random matrix theory are used that result in a simple and computationally efficient consistent estimator of the power of each source a criterion to determine the minimum number of sensors and the minimum number of samples required to achieve source separation is then introduced simulations are performed that corroborate the theoretical claims and show that the proposed power estimator largely outperforms alternative power inference techniques

a generalization of median filtering using linear combinations of order statistics we consider a class of nonlinear filters whose output is given by a linear combination of the order statistics of the input sequence assuming a constant signal in white noise the coefficients in the linear combination are chosen to minimize the output mse for several noise distributions it is shown that the optimal order statistic filter osf tends toward the median filter as the noise becomes more impulsive the optimal osf is applied to an actual noisy image and is shown to perform well combining properties of both the averaging and median filters a more general design scheme for applications involving nonconstant signals is also given

on the maximum feasible subsystem problem iiss and iis hypergraphs we consider the max fs problem for a given infeasible linear system ax b determine a feasible subsystem containing as many inequalities as possible this problem which is np hard and also difficult to approximate has a number of interesting applications in a wide range of fields in this paper we examine structural and algorithmic properties of max fs and of irreducible infeasible subsystems iiss which are intrinsically related since one must delete at least one constraint from each iis to attain feasibility first we provide a new simplex decomposition characterization of iiss and prove that finding a smallest cardinality iis is very difficult to approximate then we discuss structural properties of iis hypergraphs i e hypergraphs in which each edge corresponds to an iis and show that recognizing iis hypergraphs subsumes the steinitz problem for polytopes and hence is np hard finally we investigate rank facets of the feasible subsystem polytope whose vertices are incidence vectors of feasible subsystems of a given infeasible system in particular using the iis hypergraph structural result we show that only two very specific types of rank inequalities induced by generalized antiwebs which generalize cliques odd holes and antiholes to general independence systems can arise as facets

a new class of detail preserving filters for image processing a new class of median type filters for image processing is proposed in the filters linear fir substructures are used in conjunction with the median operation the root signals and noise attenuation properties of the fir median hybrid filters are analyzed and compared to representative edge preserving filtering operations the concept of multilevel median operation is introduced to improve the detail preserving property of conventional median and the fir median hybrid filters in the multilevel filters there exists a tradeoff between noise attenuation and detail preservation the analysis and examples indicate that fir median hybrid filters preserve details better and are computationally much more efficient than the conventional median and the k nearest neighbor averaging filters

adaptive algorithms for non gaussian noise environments the order statistic least mean square algorithms convergence properties are studied for a class of gradient based adaptive filters known as order statistic least mean square oslms algorithms these algorithms apply an order statistic filtering operation to the gradient estimate of the standard least mean square lms algorithm the order statistic operation in oslms algorithms can reduce the variance of the gradient estimate relative to lms when operating in non gaussian noise environments a consequence is that in steady state the excess mean square error can be reduced it is shown that when the input signals are iid and symmetrically distributed the coefficient estimates for the oslms algorithms converge on average to a small area around their optimal values simulations provide supporting evidence for algorithm convergence as a measurement of performance the mean squared coefficient error of oslms algorithms has been evaluated under a range of noise distributions and os operators guidelines for selection of the os operator are presented based on the expected noise environment

the nearest neighbor median filter some deterministic properties and implementations abstract further analysis of the nearest neighbor median filter nnmf is carried out it is proved that the nnmf has the threshold decomposition property and the stacking property using these properties it is formally shown that the nnmf is a subclass of the weighted median filter wmf and the weight coefficients of the equivalent wmf are derived it is shown that the nnmf is more efficient than the equivalent wmf from the viewpoint of computational complexity two theorems about the effect of repeated operations of nnmf are proved these theorems are described in the style of dealing with local configurations of image moreover hardware implementations of the nnmf are presented

diagnosing infeasibilities in network flow problems we consider the problem of finding a feasible flow in a directed networkg n a in which each nodei n has a supplyb i and each arc i j a has a zero lower bound on flow and an upper bounduij it is well known that this feasibility problem can be transformed into a maximum flow problem it is also well known that there is no feasible flow in the networkg if and only if there is a subsets of nodes such that the net supplies of the nodes ins exceeds the capacity of the arcs emanating froms such a sets is called a witness of infeasibility or simply awitness of the network flow problem in the case that there are many different witnesses for an infeasible problem a small cardinality witness may be preferable in practice because it is generally easier for the user to assimilate and may provide more guidance to the user on how to identify the cause of the infeasibility here we show that the problem of finding a minimum cardinality witness is np hard we also consider the problem of determining aminimal witness that is a witnesss such that no proper subset ofs is also a witness in this paper we show that we can determine a minimal witness by solving a sequence of at mostn maximum flow problems moreover if we use the preflow push algorithm to solve the resulting maximum flow problems and organize computations properly then the total time taken by the algorithm is comparable to that of solving a single maximum flow problem this approach determines a minimal cardinality witness in o n2m1 2 time using simple data structures and in o nm logn time using the standard implementation of the dynamic tree data structures we also show that the recognition version of the minimal witness problem is equivalent to a recognition version of a related problem known as theminimum rooted cut problem 1998 the mathematical programming society inc published by elsevier science b v

edge sensitive image restoration using order constrained least squares methods in this paper we consider a novel technique for the restoration of noise corrupted images using order constrained least squares methods the restoration process uses a moving cross shaped filter window within which two operations are combined the first operation consists of simple hypothesis tests for the presence of an edge of some minimal height crossing the center of the window the second operation computes the window output as the order constrained least squares fit of the windowed values if an edge is deemed to be present or simply the average if no edge is present the new technique is applied to some actual noise corrupted images and the results are compared to the results of applying similarly configured median and averaging filters some computational considerations and comparisons are discussed at the end of the paper

mrl filters a general class of nonlinear systems and their optimal design for image processing a class of morphological rank linear mrl filters is presented as a general nonlinear tool for image processing they consist of a linear combination between a morphological rank filter and a linear filter a gradient steepest descent method is proposed to optimally design these filters using the averaged least mean squares lms algorithm the filter design is viewed as a learning process and convergence issues are theoretically and experimentally investigated a systematic approach is proposed to overcome the problem of nondifferentiability of the nonlinear filter component and to improve the numerical robustness of the training algorithm which results in simple training equations image processing applications in system identification and image restoration are also presented illustrating the simplicity of training mrl filters and their effectiveness for image signal processing

signal detection via spectral theory of large dimensional random matrices results on the spectral behavior of random matrices as the dimension increases are applied to the problem of detecting the number of sources impinging on an array of sensors a common strategy to solve this problem is to estimate the multiplicity of the smallest eigenvalue of the spatial covariance matrix r of the sensed data existing approaches rely on the closeness of the noise eigenvalues of sample covariance matrix to each other and therefore the sample size has to be quite large when the number of sources is large in order to obtain a good estimate the theoretical analysis presented focuses on the splitting of the spectrum of sample covariance matrix into noise and signal eigenvalues it is shown that when the number of sensors is large the number of signals can be estimated with a sample size considerably less than that required by previous approaches

an efficient algorithm for the minimum capacity cut problem given a finite undirected graph with nonnegative edge capacities the minimum capacity cut problem consists of partitioning the graph into two nonempty sets such that the sum of the capacities of edges connecting the two parts is minimum among all possible partitionings the standard algorithm to calculate a minimum capacity cut due to gomory and hu 1961 runs in o n4 time and is difficult to implement we present an alternative algorithm with the same worst case bound which is easier to implement and which was found empirically to be far superior to the standard algorithm we report computational results for graphs with up to 2000 nodes

eigenvalue estimation of parameterized covariance matrices of large dimensional data this article deals with the problem of estimating the covariance matrix of a series of independent multivariate observations in the case where the dimension of each observation is of the same order as the number of observations although such a regime is of interest for many current statistical signal processing and wireless communication issues traditional methods fail to produce consistent estimators and only recently results relying on large random matrix theory have been unveiled in this paper we develop the parametric framework proposed by mestre and consider a model where the covariance matrix to be estimated has a known finite number of eigenvalues each of it with an unknown multiplicity the main contributions of this work are essentially threefold with respect to existing results and in particular to mestre s work to relax the restrictive separability assumption to provide joint consistent estimates for the eigenvalues and their multiplicities and to study the variance error by means of a central limit theorem

optimal rates of convergence for covariance matrix estimation covariance matrix plays a central role in multivariate statistical analysis significant advances have been made recently on developing both theory and methodology for estimating large covariance matrices however a minimax theory has yet been developed in this paper we establish the optimal rates of convergence for estimating the covariance matrix under both the operator norm and frobenius norm it is shown that optimal procedures under the two norms are different and consequently matrix estimation under the operator norm is fundamentally different from vector estimation the minimax upper bound is obtained by constructing a special class of tapering estimators and by studying their risk properties a key step in obtaining the optimal rate of convergence is the derivation of the minimax lower bound the technical analysis requires new ideas that are quite different from those used in the more conventional function sequence estimation problems

an edge gradient enhancing adaptive order statistic filter we consider an adaptive order statistic os filter that can enhance gradients of edges while suppressing impulsive and some nonimpulsive noise components in particular comparison and selection cs filters are introduced in which the output is determined by comparing the sample mean and median values inside each window it is shown theoretically that cs filters can enhance gradients of a variety of edges including noisy blurred ones some root properties of cs filters are also shown finally experimental results are presented to illustrate the performance characteristics of these filters

lum filters a class of rank order based filters for smoothing and sharpening a new class of rank order based filters called lower upper middle lum filters is introduced the output of these filters is determined by comparing a lower and an upper order statistic to the middle sample in the filter window these filters can be designed for smoothing and sharpening or outlier rejection the level of smoothing done by the filter can range from no smoothing to that of the median filter this flexibility allows the lum filter to be designed to best balance the tradeoffs between noise smoothing and signal detail preservation lum filters for enhancing edge gradients can be designed to be insensitive to low levels of additive noise and to remove impulsive noise furthermore lum filters do not cause overshoot or undershoot some statistical and deterministic properties of the lum filters are developed and a number of experimental results are presented to illustrate the performance these experiments include applications to 1d signals and to images

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

an adaptative nonlinear edge preserving filter an adaptative filter whose main feature is to preserve edges and impulses present in the signal is analyzed by the computation of the mean square error mse of its output sequence the filter in its more general form is highly nonlinear resembling the m type estimators used in robust statistics a simplified form used here allows the exact computation of the mse when the filter length is finite this mse can be compared to the ones obtained for a median filter and a mean filter it is shown that for a wide range of the filter and signal parameters such as filter length edge heights and impulse width the performance of the filter proposed in this paper is superior to the other filters mentioned above an additional advantage of the simplified version of the filter is that in most cases its computation amounts to a linear adaptative averaging this contrasts with the amount of calculation required to implement the median filter and any other filter based on the order statistics of the measured samples

a robust running window detector and estimator for step signals in contaminated gaussian noise an n point window is applied to noisy data to recover stepped signals in non gaussian noise robust measures of signal step level and noise distribution spread are used to detect sequential clusters of data points which are statistically significantly different thereby detecting the step using conventional analysis of variance methods but with robust parameter estimates false alarm probabilities are set reasonably accurately and miss probabilities and signal level estimates are shown by simulation to yield good results applications to kalman filtering seismic and well log data and image processing are indicated

exact separation of eigenvalues of large dimensional sample covariance matrices let b n 1 n t n 1 2 x n x n t n 1 2 where x n is n times n with i i d complex standardized entries having finite fourth moment and t n 1 2 is a hermitian square root of the nonnegative definite hermitian matrix t n it was shown in an earlier paper by the authors that under certain conditions on the eigenvalues of t n with probability 1 no eigenvalues lie in any interval which is outside the support of the limiting empirical distribution known to exist for all large n for these n the interval corresponds to one that separates the eigenvalues of t n the aim of the present paper is to prove exact separation of eigenvalues that is with probability 1 the number of eigenvalues of b n and t n lying on one side of their respective intervals are identical for all large n

adaptive stack filtering under the mean absolute error criterion an adaptive filter algorithm is developed for the class of stack filters which is a class of nonlinear filters obeying a weak superposition property the adaptation algorithm can be interpreted as a learning algorithm for a group of decision making units the decisions of which are subject to a set of constraints called the stacking constraints under a rather weak statistical assumption on the training inputs the decision strategy adopted by the group which evolves according to the proposed learning algorithm is shown to converge to an optimal strategy in the sense that it corresponds to an optimal stack filter under the mean absolute error criterion this adaptive algorithm requires only increment decrement and comparison operations and only local interconnections between the learning units implementation of the algorithm in hardware is therefore very feasible an example is provided to show how the adaptive stack filtering algorithm can be used in an application in image processing

the effect of median filtering on edge estimation and detection in this paper we consider the effect of median prefiltering on the subsequent estimation and detection of edges in digital images where possible a quantitative statistical comparison is made for a number of filters defined with two dimensional geometries in some cases one dimensional analyses are required to illustrate certain points noise images prefiltered by median filters defined with a variety of windowing geometries are used to support the analysis and it is found that median prefiltering improves the performance of both thresholding and zero crossing based edge detectors

an optimal nonlinear extension of linear filters based on distributed arithmetic distributed arithmetic da based implementation of linear filters relies on the linear nature of this operation and has been suggested as a multiplication free solution in this work we introduce a nonlinear extension of linear filters optimizing under mean square error criterion the memory function mf multivariate boolean function with not only binary output which is in the core of da based implementation such an extension will improve the filtering of noise which may contain non gaussian components without increasing the complexity of implementation experiments on real images have shown the superiority of the proposed filters over the optimal linear filters different versions of these filters are also considered for an impulsive noise removal faster processing and filtering using large input data windows

streaking in median filtered images this paper presents a probabilistic analysis of the streaking or blotching effect commonly observed in median filtered signals in both one and two dimensions the effcts are identified as runs of equal or nearly equal values which create visual impressions that have no visual correlate for one dimensional discrete iid random signals with continuous input probability densities the probability of a streak of length l occurring is computed and shown to be independent of the input probability distribution expressions for the first and second moments of the streak length are also derived and certain asymptotic results are given as the analysis and definition of the analogous effect in two dimensions is less tractable the probability that medians taken from distinct overlapping windows will take the same value is derived for various filter geometries the analytic results are supported by examples using both one and two dimensional signals

a class of order statistic lms algorithms conventional gradient based adaptive filters as typified by the well known lms algorithm use an instantaneous estimate of the error surface gradient to update the filter coefficients such a strategy leaves the algorithm extremely vulnerable to impulsive interference a class of adaptive algorithms employing order statistic filtering of the sampled gradient estimates is presented these algorithms dubbed order statistic least mean squares oslms are designed to facilitate adaptive filter performance close to the least squares optimum across a wide range of input environments from gaussian to highly impulsive three specific oslms filters are defined the median lms the average lms and the trimmed mean lms the properties of these algorithms are investigated and the potential for improvement demonstrated finally a general adaptive oslms scheme in which the nature of the order statistic operator is also adapted in response to the statistics of the input signal is presented it is shown that this can facilitate performance gains over a wide range of input data types

ber and outage probability approximations for lmmse detectors on correlated mimo channels this paper is devoted to the study of the performance of the linear minimum mean square error lmmse receiver for receive correlated multiple input multiple output mimo systems by the random matrix theory it is well known that the signal to noise ratio snr at the output of this receiver behaves asymptotically like a gaussian random variable as the number of receive and transmit antennas converge to infin at the same rate however this approximation being inaccurate for the estimation of some performance metrics such as the bit error rate ber and the outage probability especially for small system dimensions li proposed convincingly to assume that the snr follows a generalized gamma distribution which parameters are tuned by computing the first three asymptotic moments of the snr in this paper this technique is generalized to receive correlated channels and closed form expressions for the first three asymptotic moments of the snr are provided to obtain these results a random matrix theory technique adapted to matrices with gaussian elements is used this technique is believed to be simple efficient and of broad interest in wireless communications simulations are provided and show that the proposed technique yields in general a good accuracy even for small system dimensions

spectrum estimation for large dimensional covariance matrices using random matrix theory estimating the eigenvalues of a population covariance matrix from a sample covariance matrix is a problem of fundamental importance in multivariate statistics the eigenvalues of covariance matrices play a key role in many widely used techniques in particular in principal component analysis pca in many modern data analysis problems statisticians are faced with large datasets where the sample size n is of the same order of magnitude as the number of variables p random matrix theory predicts that in this context the eigenvalues of the sample covariance matrix are not good estimators of the eigenvalues of the population covariance we propose to use a fundamental result in random matrix theory the marcenko pastur equation to better estimate the eigenvalues of large dimensional covariance matrices the marcenko pastur equation holds in very wide generality and under weak assumptions the estimator we obtain can be thought of as shrinking in a nonlinear fashion the eigenvalues of the sample covariance matrix to estimate the population eigenvalues inspired by ideas of random matrix theory we also suggest a change of point of view when thinking about estimation of high dimensional vectors we do not try to estimate directly the vectors but rather a probability measure that describes them we think this is a theoretically more fruitful way to think about these problems our estimator gives fast and good or very good results in extended simulations our algorithmic approach is based on convex optimization we also show that the proposed estimator is consistent

improved subspace estimation for multivariate observations of high dimension the deterministic signals case we consider the problem of subspace estimation in situations where the number of available snapshots and the observation dimension are comparable in magnitude in this context traditional subspace methods tend to fail because the eigenvectors of the sample correlation matrix are heavily biased with respect to the true ones it has recently been suggested that this situation where the sample size is small compared to the observation dimension can be very accurately modeled by considering the asymptotic regime where the observation dimension m and the number of snapshots n converge to at the same rate using large random matrix theory results it can be shown that traditional subspace estimates are not consistent in this asymptotic regime furthermore new consistent subspace estimate can be proposed which outperform the standard subspace methods for realistic values of m and n the work carried out so far in this area has always been based on the assumption that the observations are random independent and identically distributed in the time domain the goal of this paper is to propose new consistent subspace estimators for the case where the source signals are modelled as unknown deterministic signals in practice this allows to use the proposed approach regardless of the statistical properties of the source signals in order to construct the proposed estimators new technical results concerning the almost sure location of the eigenvalues of sample covariance matrices of information plus noise complex gaussian models are established these results are believed to be of independent interest

how to compute least infeasible flows it is well known how to use maximum flow to decide when a flow problem with demands lower bounds and upper bounds is infeasible less well known is how to compute a flow that is least infeasible this paper considers many possible ways to define least infeasible and shows how to compute optimal flows for each definition for each definition it also gives a dual characterization in terms of cuts a polynomial routine for recognizing that type of least infeasible flow and relates that definition to dual cut canceling min cost flow network algorithms

a new approach to the maximum flow problem all previously known efficient maximum flow algorithms work by finding augmenting paths either one path at a time as in the original ford and fulkerson algorithm or all shortest length augmenting paths at once using the layered network approach of dinic an alternative method based on the preflow concept of karzanov is introduced a preflow is like a flow except that the total amount flowing into a vertex is allowed to exceed the total amount flowing out the method maintains a preflow in the original network and pushes local flow excess toward the sink along what are estimated to be shortest paths the algorithm and its analysis are simple and intuitive yet the algorithm runs as fast as any other known method on dense graphs achieving an o n 3 time bound on an n vertex graph by incorporating the dynamic tree data structure of sleator and tarjan we obtain a version of the algorithm running in o nm log n 2 m time on an n vertex m edge graph this is as fast as any known method for any graph density and faster on graphs of moderate density the algorithm also admits efficient distributed and parallel implementations a parallel implementation running in o n 2 log n time using n processors and o m space is obtained this time bound matches that of the shiloach vishkin algorithm which also uses n processors but requires o n 2 space

robust techniques for edge detection in multiplicative weibull image noise abstract recent studies of the approximately multiplicative noise present in images from coherent radar systems suggest that the first order statistics can be broadly modeled by the two parameter weibull probability density function w y y 1 exp y this paper defines and compares some novel techniques for the robust detection of sustained image irradiance changes or edges in images immersed in multiplicative weibull noise it is shown that edge detection in multiplicative noise is accomplished effectively by comparing ratios of locally adjacent image irradiance estimates to an appropriate threshold several such estimates are considered local irradiance averages optimal single order statistics and best linear unbiased estimates using order statistics the results of a statistical monte carlo performance analysis suggest that edge detection using ratios of single order statistics ros detector offers the best compromise among computational convenience edge localization and robust performance while the ratio of blues detector rob detector yields the best overall statistical and empirical noise suppression the ratio of averages detector roa detector while statistically optimal in some cases often yields inferior edge localization relative to the other schemes images corrupted by synthetically generated weibull noise are used to support the analysis

edge preserving filtering by combining nonlinear mean and median filters a very general class of nonlinear filters called mapping order statistics filters mosfs is introduced a subclass of the mosfs called l sub p mean median filters l sub p mmfs is discussed the l sub p mmf shows better properties in preserving edges and attenuating positive and negative impulse noise simultaneously than do the nonlinear mean filters in the analysis of the deterministic properties of the l sub p mmf the concept of a monotonic trend region is introduced a necessary condition for a signal to be a root signal is given this necessary condition is also valid for the known finite impulse response median hybrid filter

a robust approach to image enhancement based on fuzzy logic in this paper we propose a robust approach to image enhancement based on fuzzy logic that addresses the seemingly conflicting goals of image enhancement i removing impulse noise ii smoothing out nonimpulse noise and iii enhancing or preserving edges and certain other salient structures we derive three different filters for each of the above three tasks using the weighted or fuzzy least squares ls method and define the criteria for selecting each of the three filters the criteria are based on the local context and they constitute the antecedent clauses of the fuzzy rules the overall result of the fuzzy rule based system is the combination of the results of the individual filters where each result contributes to the degree that the corresponding antecedent clause is satisfied this approach gives us a powerful and flexible image enhancement paradigm results of the proposed method on several types of images are compared with those of other standard techniques

a random matrix approach to the lack of projections in cred f2 abstract in 1982 pimsner and voiculescu computed the k 0 and k 1 groups of the reduced group c algebra c red f k of the free group f k on k generators and settled thereby a long standing conjecture c red f k has no projections except for the trivial projections 0 and 1 later simpler proofs of this conjecture were found by methods from k theory or from non commutative differential geometry in this paper we provide a new proof of the fact that c red f k is projectionless the new proof is based on random matrices and is obtained by a refinement of the methods recently used by the first and the third named author to show that the semigroup ext c red f k is not a group for k 2 by the same type of methods we also obtain that two phenomena proved by bai and silverstein for certain classes of random matrices no eigenvalues outside a small neighbourhood of the support of the limiting distribution and exact separation of eigenvalues by gaps in the limiting distribution also hold for arbitrary non commutative selfadjoint polynomials of independent gue goe or gse random matrices with matrix coefficients

nonlinear smoothing filters based on rank estimates of location a class of nonlinear filters that are based on the rank estimates r estimates of location parameters in statistical theory is introduced it is shown how moving window rank filters r filters can be defined starting from rank estimates of location these filters utilize the relative ranks of the observations in each window to produce an output value the idea of rank winsorization is extended to that of averaging only observations which lie within small temporal neighborhoods this leads to a definition of the class of generalized wilcoxon gw filters which are parameterized by three parameters namely the degrees of temporal and rank winsorization and the degree of averaging the gw filters can be defined to have desirable characteristics of edge preservation detail retention and impulse rejection in addition to the property of gaussian noise smoothing performance characteristics of these filters are considered through analysis and simulation the filters show that all three well known classes of robust location estimates the l m and r estimates can be applied to nonlinear smoothing of signals

fir median hybrid filters with excellent transient response in noisy conditions two classes of fir median hybrid fmh filters are introduced which are called in place growing fir median hybrid ipg fmh and recursive in place growing fir median hybrid ripg fmh filters this new extended family of filters exhibits a very small bias error in the vicinity of an edge an yet provides good noise attenuation it is shown that the ipg fmh filters can be expressed as weighted fmh wfmh filters

a fast parametric maximum flow algorithm and applications the classical maximum flow problem sometimes occurs in settings in which the arc capacities are not fixed but are functions of a single parameter and the goal is to find the value of the parameter such that the corresponding maximum flow or minimum cut satisfies some side condition finding the desired parameter value requires solving a sequence of related maximum flow problems in this paper it is shown that the recent maximum flow algorithm of goldberg and tarjan can be extended to solve an important class of such parametric maximum flow problems at the cost of only a constant factor in its worst case time bound faster algorithms for a variety of combinatorial optimization problems follow from the result