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

variational approximations and mean field scaling theory it is shown that mean field finite size scaling theory can be adjusted and applied to sequences of approximations that do not obey the well known power laws of finite size scaling the proposed modification of the theory seems to be well directed to the sequence of baxter s variational approximations this sequence of approximations shows a novel feature according to which exponential laws appear in places where power laws should be expected but the modified scaling theory still yields relations from which non classical critical exponents can be estimated thus two techniques for the estimation of the critical exponent beta are suggested from the finite order variational approximations these techniques are applied to the zero field ising model on the square lattice using the systematic series of the baxter tsang systems and excellent estimates of beta are obtained correct up to 13 significant figures

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

sliding mode control of a discrete system abstract conventional sliding mode control designed on the basis of a continuous system is known to be robust to the plant uncertainties a realized digital system however not only yields chattering but also may become unstable by a long sampling interval this paper presents a stable discrete sliding mode control insensitive to the choice of sampling interval and not yielding chattering the control system is designed on the basis of a discrete lyapunov function and a sufficient condition of the control gain to make the system stable is given contrary to the continuous case the derived switching plane of the control law is different from the sliding mode and in its neighborhood the control law is given by the linear state feedback simulations show the effectiveness of the proposed method

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

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

an approach to critical phenomena from one subsystem based on the cam analysis two systematic series of multi body effective field approximations are constructed and the cam analyses are performed for the ising mode on the two dimensional square lattice in the first series a two body effective field is introduced in addition to the usual one body one and a set of strips are used the critical temperature and the critical index of the susceptibility are estimated as t c approximately 2 2697 j kb and gamma approximately 1 749 in the second series only a three line strip is used and applied with increasing numbers of multi body effective fields the expected cam scaling behaviour has also been observed

series of effective field approximations and coherent anomaly in kosterlitz thouless transitions a series of effective field approximations are formulated for the kosterlitz thouless transition in the sine gordon model by means of the cumulant expansion and the variational method effective field essential singularities xi approximately exp xi n kc n k 1 are obtained for the correlation length as first derived by saito in a single approximation however a systematic variance of the effective field critical coefficient xi n approximately 2ln j 2y0 n 1 pi is found when the order of approximation n increases the true critical exponent nu of the kosterlitz thouless transition is thus revealed to be less than the effective field exponent nu 0 nu nu 0 1 from suzuki s coherent anomaly method the phase transition in the two dimensional xy model is studied from its relation to the sine gordon model the critical exponent eta c of the spin spin correlation function at the critical point is found to be eta c 1 4 1 pi 2

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

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

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

discrete time output feedback sliding mode control design for uncertain systems using linear matrix inequalities an output feedback based sliding mode control design methodology for discrete time systems is considered in this article in previous work it has been shown that by identifying a minimal set of current and past outputs an augmented system can be obtained which permits the design of a sliding surface based upon output information only if the invariant zeros of this augmented system are stable in this work a procedure for realising discrete time controllers via a particular set of extended outputs is presented for non square systems with uncertainties this method is applicable when unstable invariant zeros are present in the original system the conditions for existence of a sliding manifold guaranteeing a stable sliding motion are given a procedure to obtain a lyapunov matrix which simultaneously satisfies both a riccati inequality and a structural constraint is used to formulate the corresponding control to solve the reachability problem a numerical method using linear matrix inequalities is suggested to obtain the lyapunov matrix finally the design approach given in this article is applied to an aircraft problem and the use of the method as a reconfigurable control strategy in the presence of sensor failure is demonstrated

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

multi effective field theory applications to the cam analysis of the two dimensional ising model abstract a multi effective field theory is formulated and applied to the two dimensional ising model from the viewpoint of the coherent anomaly method cam two necessary conditions to construct the cam canonical series are shown two series of approximations are derived on 3 3 and 4 4 clusters and with the use of the cam we estimate the critical exponent of the susceptibility within an error of 0 37 and 0 45 percent respectively for the exact value 1 75 where the exact t c is assumed this accuracy of the estimation shows the effectiveness of this theory it is generally proved that certain kinds of approximations with different combinations of effective fields yield exactly the same approximate critical temperature and mean field coefficient

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

sliding surface design for discrete vss using lqr technique with a preset real eigenvalue abstract this paper presents an lqr based sliding surface design procedure that allows one to specify a desired weighting matrix and a desired real eigenvalue which is important in discrete vss the procedure computes a weighting matrix that simultaneously stays closest to the desired one and yields the desired eigenvalue sliding surface is then determined from the lqr gain matrix and the desired eigenvalue it is shown that feasible weighting matrices almost always exist and are not unique moreover the underlying constrained optimization problem is convex and least squares method may be used to simplify or solve the problem the paper ends with two numerical examples that illustrate the design procedure

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

constructing discontinuity surfaces for variable structure systems a lyapunov approach the problem of constructing discontinuity surfaces in variable structure systems is studied from a lyapunov point of view a switching surface determined by the control coefficient matrix and the associated lyapunov function is able to ensure asymptotic stability for the system in sliding mode the proposed method may also be used for systems with nonlinear dynamics and for linear systems with delays

coherent anomaly method applied to the eight vertex model abstract the coherent anomaly method cam in terms of the multi effective field theory is applied to the eight vertex model in which critical exponents depend on interaction energies of the hamiltonian and vary continuously with them series of approximations are constructed by the rule which we have already proposed and the critical exponent is estimated using the exact critical temperature t c the results that are obtained lie within an error of 1 2 percent for the exact value in a region of interaction energies and this shows that the cam is applicable to a model which does not satisfy the ordinary universality hypothesis

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

coherent anomaly method with a new mean field type approximation abstract in the present paper we propose a new mean field type approximation based on multispin effective fields determined from self consistency conditions for some correlation functions of a cluster using the transfer matrix method we investigate finite width strips of spins for square honeycomb and triangle lattices the results obtained exhibit good scaling properties and can be analyzed with suzuki s coherent anomaly method yielding a very accurate estimation of the critical temperature and the critical exponent

cam approach to the ground state phase transition in the two dimensional transverse ising model the double cluster approximation dca and the multi effective field approximation mefa are formulated for the two dimensional s 1 2 transverse ising model on a square lattice in the ground state these two cluster effective field approximations expand the sizes of clusters effectively combining some suitable series of these approximations with the coherent anomaly method cam the authors have analysed the critical phenomenon of this model they have obtained g c 1 528 or 0 016 and gamma 1 25 or 0 08 using the dca and gamma 1 26 or 0 10 using the mefa these estimates are consistent with the other results g c approximately 1 52 and gamma approximately 1 24 their scheme is expected to be useful in the study of frustrated systems because various shapes of clusters can be used in their calculations

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

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

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