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

two dimensional root structures and convergence properties of the separable median filter the root signals invariant to filtering structures of the two dimensional separable median filter are derived and presented in addition it is proved that with rare exception after repetitive passes of the separable median filter any two dimensional signal will be reduced to a signal containing only root structures

affine order statistic filters medianization of linear fir filters this paper introduces a novel data adaptive filtering framework affine order statistic filters affine order statistic filters operate effectively on a wide range of signal statistics are sensitive to the dispersion of the observed data and are therefore particularly useful in the processing of nonstationary signals these properties result from the introduction of a tunable affinity function that measures the affinity or closeness of observation samples in their natural order to their corresponding order statistics the obtained affinity measures are utilized to control the influence of individual samples in the filtering process depending on the spread of the affinity function which is controlled by a single parameter spl gamma affine order statistic filters operate effectively in various environments ranging from gaussian to impulsive the class of affine order statistic filters subsumes the family of weighted order statistic wos affine filters and the class of fir affine filters we focus on a representative of the wos affine filter class the median affine filter whose behavior can be tuned from that of a linear fir filter to that of a robust median filter by narrowing the affinity function to a process referred to as medianization the superior performance of affine order statistic filters is demonstrated in two applications

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

impulse noise suppression in speech using the stationary wavelet transform an approach for detecting and removing impulse noise from speech using the wavelet transform is proposed the approach utilizes the multi resolution property of the wavelet transform which provides finer time resolution at higher frequencies than the short time fourier transform to effectively identify and remove impulse noise the paper then describes how the impulse detection performance is dependent on certain wavelet features and their relationships with the impulse noise and the underlying speech signal performance comparisons carried out with an existing method show that the wavelet approach yields much better features for detecting the impulses to remove the impulses an algorithm that uses the stationary wavelet transform has been developed the algorithm uses a two step approach where the wavelet coefficients corresponding to the impulses are suppressed in the first step and then substituted by suitable coefficients located within the vicinity of the impulse in the second step performance evaluations with an existing method show that the proposed algorithm gives superior results

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

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

convergence behavior and n roots of stack filters the convergence behavior of two types of stack filters is investigated both types are shown to possess the convergence property and to exhibit nontrivial behavior the first type of stack filter has the erosive property it erodes any input signal to a root after a sufficient number of passes the second type of stack filter has the dilative property it dilates any input signal to a root after a sufficient number of passes for each type of stack filter an algorithm is presented which can determine a filter that has any specific signal or set of signals as roots these two algorithms are efficient in that their execution time is a linear function of the length of the input signal the width of the filter window and the number of signals to be preserved since some stack filters have the phenomenon of oscillations when they filter some input signals successively a partial ordering is defined over the set of stack filters which makes it possible to determine upper and lower bounds for these oscillations

removing the blocking artifacts of block based dct compressed images one of the major drawbacks of the block based dct compression methods is that they may result in visible artifacts at block boundaries due to coarse quantization of the coefficients we propose an adaptive approach which performs blockiness reduction in both the dct and spatial domains to reduce the block to block discontinuities for smooth regions our method takes advantage of the fact that the original pixel levels in the same block provide continuity and we use this property and the correlation between the neighboring blocks to reduce the discontinuity of the pixels across the boundaries for texture and edge regions we apply an edge preserving smoothing filter simulation results show that the proposed algorithm significantly reduces the blocking artifacts of still and video images as judged by both objective and subjective measures

a theoretical analysis of the properties of median filters necessary and sufficient conditions for a signal to be invariant under a specific form of median filtering are derived these conditions state that a signal must be locally monotone to pass through a median filter unchanged it is proven that the form of successive median filtering of a signal i e the filtered output is itself again filtered eventually reduces the original signal to an invariant signal called a root signal for a signal of length l samples a maximum of frac 1 2 l 2 repeated filterings produces a root signal

a generalized gaussian image model for edge preserving map estimation the authors present a markov random field model which allows realistic edge modeling while providing stable maximum a posterior map solutions the model referred to as a generalized gaussian markov random field ggmrf is named for its similarity to the generalized gaussian distribution used in robust detection and estimation the model satisfies several desirable analytical and computational properties for map estimation including continuous dependence of the estimate on the data invariance of the character of solutions to scaling of data and a solution which lies at the unique global minimum of the a posteriori log likelihood function the ggmrf is demonstrated to be useful for image reconstruction in low dosage transmission tomography

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

a smoothing property of the median filter the variation of a discrete signal is defined and used as a measure of roughness it is shown that the median filter does not increase the variation of a signal supporting the perception of the median filter as a smoother signals of both finite and infinite lengths are considered for signals of finite length nonpadding median filters are used

order configuration functions mathematical characterizations and applications to digital signal and image processing we call a function f in n variables an order configuration function if for any x1 xn such that xi1 xin we have f x1 xn xt where t is determined by the n tuple i1 in corresponding to that ordering equivalently it is a function built as a minimum of maxima or a maximum of minima well known examples are the minimum the maximum the median and more generally rank functions or the composition of rank functions such types of functions are often used in nonlinear processing of digital signals or images for example in the median or separable median filter min max filters rank filters etc in this paper we study the mathematical properties of order configuration functions and of a wider class of functions that we call order subconfiguration functions we give several characterization theorems for them we show through various examples how our concepts can be used in the design of digital signal filters or image transformations based on order configuration functions

multilevel nonlinear filters for edge detection and noise suppression two new classes of multilevel nonlinear filters are introduced for simultaneous edge detection and noise suppression which the authors call a nested median filter median averaging filter nmf maf pair and a delayed decision filter embedded median trimmed filter ddf emtf pair median filters and median related filter cause an edge shift in the presence of an impulse near the edge the proposed filters reduce such edge shifting while suppressing impulsive as well as nonimpulsive noise it is shown that at the noisy edge point the nmf and the ddf are substantially superior both theoretically and experimentally to the median filter the spl alpha tm filter and the stm filter in two respects 1 the output bias error and 2 the output mean square error it is also shown that in the noisy homogeneous region nonedge point the bias errors of the maf are zero and the output mean square errors of the maf are substantially close to those of the optimized single level filters the averager the median filter and the min max filter under gaussian laplacian and uniform noise respectively test results confirm that the nmf maf pair and the ddf emtf structure are each robust in preserving sharp edges inhibiting edge shifting and suppressing a wide variety of noise

on the convergence and roots of order statistics filters we propose a comprehensive theory of the convergence and characterization of roots of order statistics filters conditions for the convergence of iterations of order statistics filters are proposed criteria for the morphological characterization of roots of order statistics filters are also proposed

robust estimation approach for blind denoising this work develops a new robust statistical framework for blind image denoising robust statistics addresses the problem of estimation when the idealized assumptions about a system are occasionally violated the contaminating noise in an image is considered as a violation of the assumption of spatial coherence of the image intensities and is treated as an outlier random variable a denoised image is estimated by fitting a spatially coherent stationary image model to the available noisy data using a robust estimator based regression method within an optimal size adaptive window the robust formulation aims at eliminating the noise outliers while preserving the edge structures in the restored image several examples demonstrating the effectiveness of this robust denoising technique are reported and a comparison with other standard denoising filters is presented

stochastic analysis for the recursive median filter process vector probability measure functions density function for recursively median filtered signals are found when the underlying input binary sequences are either independent identically distributed i i d or markov chains the results are parametric in the window size of the filter and in the probability distribution of the input sequence using statistical threshold decomposition the same results are found for discrete alphabet random sequences that are either i i d or markov chains some examples illustrating the efficacy of the recursive median filter relative to the nonrecursive implementation are presented in particular the breakdown probabilities are tabulated for both recursive and nonrecursive median filters

hidden markov processes an overview of statistical and information theoretic aspects of hidden markov processes hmps is presented an hmp is a discrete time finite state homogeneous markov chain observed through a discrete time memoryless invariant channel in recent years the work of baum and petrie 1966 on finite state finite alphabet hmps was expanded to hmps with finite as well as continuous state spaces and a general alphabet in particular statistical properties and ergodic theorems for relative entropy densities of hmps were developed consistency and asymptotic normality of the maximum likelihood ml parameter estimator were proved under some mild conditions similar results were established for switching autoregressive processes these processes generalize hmps new algorithms were developed for estimating the state parameter and order of an hmp for universal coding and classification of hmps and for universal decoding of hidden markov channels these and other related topics are reviewed

a comparative study for the pair creation contact process using series expansions a comparative study between two distinct perturbative series expansions for the pair creation contact process is presented in contrast to the ordinary contact process whose supercritical series expansions provide accurate estimates for its critical behaviour the supercritical approach does not work properly when applied to the pair creation process to circumvent this problem a procedure is introduced in which one site creation is added to the pair creation an alternative method is the generation of subcritical series expansions which works even for the case of the pure pair creation process in contrast to the supercritical case the subcritical series yields estimates that are compatible with numerical simulations

deterministic properties of the recursive separable median filter the recursive separable median filter has been successfully used to extract features from noisy two dimensional signals in many applications it gives better noise suppression and edge preservation than the standard separable median filter in this paper we use a new approach for studying the deterministic properties of separable median filters in particular using threshold decomposition we derive the root structure of the recursive separable median filter where a root is a signal invariant to further filtering it is shown that these root structures differ from those of their nonrecursive counterparts we also show that any two dimensional signal will converge to a root after repeated passes of the recursive separable median filter

the n site approximation for the triplet creation model the nonequilibrium phase transition of the one dimensional triplet creation model is investigated using the n site approximation scheme we find that the phase diagram in the space of parameters d where is the particle decay probability and d is the diffusion probability exhibits a tricritical point for n 4 however the fitting of the tricritical coordinates t dt using data for 4 n 13 predicts that t becomes negative for n 26 indicating thus that the phase transition is always continuous in the limit n however the large discrepancies between the critical parameters obtained in this limit and those obtained by monte carlo simulations as well as a puzzling non monotonic dependence of these parameters on the order of the approximation n argue for the inadequacy of the n site approximation to study the triplet creation model for computationally feasible values of n

a noise filtering method using a local information measure a nonlinear noise filtering method for image processing based on the entropy concept is developed and compared to the well known median filter and to the center weighted median filter cwm the performance of the proposed method is evaluated through subjective and objective criteria it is shown that this method performs better than the classical median for different types of noise and can perform better than the cwm filter in some cases

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

rank conditioned rank selection filters for signal restoration a class of nonlinear filters called rank conditioned rank selection rcrs filters is developed and analyzed in this paper the rcrs filters are developed within the general framework of rank selection rs filters which are filters constrained to output an order statistic from the observation set many previously proposed rank order based filters can be formulated as rs filters the only difference between such filters is in the information used in deciding which order statistic to output the information used by rcrs filters is the ranks of selected input samples hence the name rank conditioned rank selection filters the number of input sample ranks used is referred to as the order of the rcrs filter the order can range from zero to the number of samples in the observation window giving the filters valuable flexibility low order filters can give good performance and are relatively simple to optimize and implement if improved performance is demanded the order can be increased but at the expense of filter simplicity in this paper many statistical and deterministic properties of the rcrs filters are presented a procedure for optimizing over the class of rcrs filters is also presented finally extensive computer simulation results that illustrate the performance of rcrs filters in comparison with other techniques in image restoration applications are presented

phase transition in conservative diffusive contact processes we determine the phase diagrams of conservative diffusive contact processes by means of numerical simulations these models are versions of the ordinary diffusive single creation pair creation and triplet creation contact processes in which the particle number is conserved the transition between the frozen and active states was determined by studying the system in the subcritical regime and the nature of the transition whether continuous or first order was determined by looking at the fractal dimension of the critical cluster for the single creation model the transition remains continuous for any diffusion rate for pair and triplet creation models however the transition becomes first order for high enough diffusion rate our results indicate that in the limit of infinite diffusion rate the jump in density equals 2 3 for the pair creation model and 5 6 for the triplet creation model

state learning and mixing in entropy of hidden markov processes and the gilbert elliott channel hidden markov processes such as the gilbert elliott 1960 channel have an infinite dependency structure therefore entropy and channel capacity calculations require knowledge of the infinite past in practice such calculations are often approximated with a finite past it is commonly assumed that the approximations require an unbounded amount of the past as the memory in the underlying markov chain increases we show that this is not necessarily true we derive an exponentially decreasing upper bound on the accuracy of the finite past approximation that is much tighter than existing upper hounds when the markov chain mixes well we also derive an exponentially decreasing upper bound that applies when the markov chain does not mix at all our methods are demonstrated on the gilbert elliott channel where we prove that a prescribed finite past accuracy is quickly reached independently of the markovian memory we conclude that the past can be used either to learn the channel state when the memory is high or wait until the states mix when the memory is low implications fur computing and achieving capacity on the gilbert elliott channel are discussed

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

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

median filtering by threshold decomposition median filters are a special class of ranked order filters used for smoothing signals repeated application of the filter on a quantized signal of finite length ultimately results in a sequence termed a root signal which is invariant to further passes of the median filter in this paper it is shown that median filtering an arbitrary level signal to its root is equivalent to decomposing the signal into binary signals filtering each binary signal to a root with a binary median filter and then reversing the decomposition this equivalence allows problems in the analysis and the implementation of median filters for arbitrary level signals to be reduced to the equivalent problems for binary signals since the effects of median filters on binary signals are well understood this technique is a powerful new tool

novel transmit beamforming schemes for time selective fading multiantenna systems transmit beamforming has been widely adopted for wireless systems with multiple transmit antennas for a block fading channel the grassmannian beamformer has been shown to provide very good performance for finite rate feedback however the original grassmannian beamformer does not take the time domain correlation of the channel fading into consideration in this paper based on a first order autoregressive ar1 dynamic fading model we develop two new classes of beamforming algorithms that exploit the interframe correlations in the channel fading we first introduce an algorithm based on a standard predictive vector quantization pvq approach and the resulting pvq beamformer accomplishes superior power delivery at the receiver however the error performance of the pvq beamformer is not satisfactory at high signal to noise ratios and it also has a high implementation complexity to resolve these issues we then develop a novel successive beamforming sbf algorithm the new sbf scheme uses the knowledge of the previous fading blocks to aid the beamforming codebook design of the current fading block the beamforming codebook is constructed based on the successive partition of the surface of a spherical cap the new sbf scheme accomplishes nearly the same performance as that of the pvq beamformer and it has a much simpler implementation through numerical simulations we demonstrate that the proposed beamformers outperform the other previously proposed beamformers at various fading scenarios

some properties of a class of rank order smoothers a class of rank order smoothers which operate by minimizing a piecewise linear objective function is considered nonrecursive versions have many properties similar to repeated median smoothing and most of these properties are relevant with qualifications to recursive versions of the class smoothed values are medians in their neighborhoods a root signal is obtained but advantageously in only one application of the algorithm pulses can be passed or rejected and monotone sequences passed in ways similar to median smoothers bit serial algorithms are applicable to both in similar senses

extended permutation filters and their application to edge enhancement extended permutation ep filters are defined and analyzed in particular we focus on extended permutation rank selection eprs filters these filters are constrained to output an order statistic from an extended observation vector this extended vector includes n observation samples and k statistics that are functions of the observation samples the rank permutations from selected samples in this extended observation vector are used as the basis for selecting an order statistic output we show that by including the sample mean in the extended observation vector the filters exhibit excellent edge enhancement properties we also show that several previously defined classes of rank order based edge enhancers cs lum and wmmr sharpeners can be formulated as subclasses of eprs filters these sharpening subclasses are in addition to the smoothing subclasses which include rank conditioned rank selection permutation stack and weighted order statistic filters thus this novel class of filters provides a broad framework within which many rank order based smoothers and edge enhancers can be unified edge enhancement properties are developed and an l sub n norm eprs filter optimization procedure is presented finally extensive computer simulation results are presented comparing the performance of eprs and other sharpening filters in edge enhancement applications

nonlinear space variant postprocessing of block coded images an important application of spatial filtering techniques is in the postprocessing of images degraded by coding linear space invariant filters are inadequate to reduce the noise produced by block coders the noise in block coded images is correlated with the local characteristics of the signal and such filters are unable to exploit this correlation to reduce the noise we propose a new nonlinear space variant filtering algorithm which smooths jagged edges without blurring them and smooths out abrupt intensity changes in monotone areas edge sharpness is preserved because near edges the filtering of the signal is negligible consequently in band noise is not reduced but the well known masking effect reduces the visibility of this in band noise the algorithm is only slightly more complex to implement than simple linear filtering we present examples of processed images and snr figures to demonstrate that a significant improvement in subjective and objective quality is achieved

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

a recursive variant of mallows filter class mallows 1980 nonlinear fir filter class includes most of the nonlinear digital filters in wide use today this filter class is defined in terms of five axioms and this paper modifies two of these axioms to obtain a class of symmetric recursive nonlinear filters one of the main points considered in this paper is the consequence of mallows location invariance axiom a2 and general prescriptions are given for both mallows original fir filter class and its recursive extension this representation is also extremely useful in discussing the root sequences of both the recursive and nonrecursive structures since recursive filters can exhibit various forms of instability a number of stability results are presented for this class of filters finally some simple examples are considered that illustrate the potential utility of the results presented

a binary communication channel with memory based on a finite queue a model for a binary additive noise communication channel with memory is introduced the channel noise process which is generated according to a ball sampling mechanism involving a queue of finite length m is a stationary ergodic mth order markov source the channel properties are analyzed and several of its statistical and information theoretical quantities e g block transition distribution autocorrelation function acf capacity and error exponent are derived in either closed or easily computable form in terms of its four parameters the capacity of the queue based channel qbc is also analytically and numerically compared for a variety of channel conditions with the capacity of other binary models such as the well known gilbert elliott channel gec the fritchman channel and the finite memory contagion channel we also investigate the modeling of the traditional gec using this qbc model the qbc parameters are estimated by minimizing the kullback leibler divergence rate between the probability of noise sequences generated by the gec and the qbc while maintaining identical bit error rates ber and correlation coefficients the accuracy of fitting the gec via the qbc is evaluated in terms of acf channel capacity and error exponent numerical results indicate that the qbc provides a good approximation of the gec for various channel conditions it thus offers an interesting alternative to the gec while remaining mathematically tractable

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

first order transitions in a two dimensional nonequilibrium replicator model abstract a single component two dimensional lattice model of self replicating entities replicators which exhibits a nonequilibrium first order phase transition into a unique absorbing state is introduced and studied through extensive numerical simulations the basic dynamic processes are auto catalytic replication in which groups of at least k 1 adjacent replicators are required to create a new replicator in a neighboring empty cell and spontaneous decay in contrast to the one dimensional versions known as pair creation k 1 and trimer creation k 2 models which present only continuous transitions into the vacuum we find a discontinuous transition for k 2 provided the replication probability is less than some threshold value beyond which the transition becomes continuous for the k 0 and k 1 models the transitions are continuous and belong to the class of universality of directed percolation regardless of the value of the replication probability using the conserved contact process we show that in the discontinuous case the density of replicators exhibits a non monotonic dependence on the decay probability this steady state analysis is complemented by the spreading analysis which allows the calculation of the dynamic critical exponents associated to the asymptotic behavior of the survival probability of a small colony of replicators in an infinite lattice

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

comparison of algorithms for standard median filtering standard median filtering that is searched repeatedly for a median from a sample set which changes only slightly between the subsequent searches is discussed several well known methods for solving this running median problem are reviewed the asymptotical time complexities of the methods are analyzed and simple variants are proposed which are especially suited for small sample sets a frequent situation although the discussion is restricted to the one dimensional case the ideas are easily extended to higher dimensions

edge preserving image denoising and estimation of discontinuous surfaces in this paper we are interested in the problem of estimating a discontinuous surface from noisy data a novel procedure for this problem is proposed based on local linear kernel smoothing in which local neighborhoods are adapted to the local smoothness of the surface measured by the observed data the procedure can therefore remove noise correctly in continuity regions of the surface and preserve discontinuities at the same time since an image can be regarded as a surface of the image intensity function and such a surface has discontinuities at the outlines of objects this procedure can be applied directly to image denoising numerical studies show that it works well in applications compared to some existing procedures

capacity and coding for the gilbert elliott channels the gilbert elliott channel a varying binary symmetric channel with crossover probabilities determined by a binary state markov process is treated in general such a channel has a memory that depends on the transition probabilities between the states a method of calculating the capacity of this channel is introduced and applied to several examples and the question of coding is addressed in the conventional usage of varying channels a code suitable for memoryless channels is used in conjunction with an interleaver with the decoder considering the deinterleaved symbol stream as the output of a derived memoryless channel the transmission rate is limited by the capacity of this memoryless channel which is often considerably less than the capacity of the original channel a decision feedback decoding algorithm that completely recovers this capacity loss is introduced it is shown that the performance of a system incorporating such an algorithm is determined by an equivalent genie aided channel the capacity of which equals that of the original channel the calculated random coding exponent of the genie aided channel indicates a considerable increase in the cutoff rate over that of the conventionally derived memoryless channel

comments on theoretical analysis of the max median filter by g r arce and m p mclaughlin in the original paper ibid vol assp 35 no 1 p 60 9 jan 1987 an approach the max median filter to remove noise from images without distorting geometrical information was introduced the proposed filter structure due to its asymmetrical nature is able to preserve only the subtle signal structures that are larger in intensity than the local background level the commenters suggest another filter structure that has the ability to preserve both positive and negative geometrical information with respect to the background level