wavelets and filter banks theory and design the wavelet transform is compared with the more classical short time fourier transform approach to signal analysis then the relations between wavelets filter banks and multiresolution signal processing are explored a brief review is given of perfect reconstruction filter banks which can be used both for computing the discrete wavelet transform and for deriving continuous wavelet bases provided that the filters meet a constraint known as regularity given a low pass filter necessary and sufficient conditions for the existence of a complementary high pass filter that will permit perfect reconstruction are derived the perfect reconstruction condition is posed as a bezout identity and it is shown how it is possible to find all higher degree complementary filters based on an analogy with the theory of diophantine equations an alternative approach based on the theory of continued fractions is also given these results are used to design highly regular filter banks which generate biorthogonal continuous wavelet bases with symmetries

feature subset selection by gravitational search algorithm optimization a new method for feature subset selection in machine learning fss mgsa feature subset selection by modified gravitational search algorithm is presented fss mgsa is an evolutionary stochastic search algorithm based on the law of gravity and mass interactions and it can be executed when domain knowledge is not available a wrapper approach over naive bayes id3 k nearest neighbor and support vector machine learning algorithms is used to evaluate the goodness of each visited solution the key to the success of the mgsa is to utilize the piecewise linear chaotic map for increasing its diversity of species and to use sequential quadratic programming for accelerating local exploitation promising results are achieved in a variety of tasks where domain knowledge is not available the experimental results show that the proposed method has the ability of selecting the discriminating input features correctly and can achieve high accuracy of classification which is comparable to or better than well known similar classifier systems furthermore the mgsa is tested on ten functions provided by cec 2005 special session and compared with various modified gravitational search algorithm particle swarm optimization and genetic algorithm the obtained results confirm the high performance of the mgsa in solving various problems in optimization

solving the generalised assignment problem using polyhedral results the generalised assignment problem gap consists of finding a maximal profit assignment of n tasks over m capacity constrained agents whereby each task has to be processed by only one agent we develop an improved implementation of the standard procedure for generating lifted cover inequalities describing an approximation to the convex hull of the knapsack constraints in the gap polytope this improvement yields a good upper bound and closes the gap by an additional 15 on average based on this result we propose two heuristics for finding close to optimal solutions giving us a tight lower bound computational results on a set of 60 representative and highly capacitated problems indicate that these solutions lie within 0 06 of the optimum after applying some pre processing techniques and using the obtained bounds we solve the generated instances to optimality by branch and bound b b within reasonable computing time

two soft thresholding based iterative algorithms for image deblurring iterative regularization algorithms such as the conjugate gradient algorithm for least squares problems cgls and the modified residual norm steepest descent mrnsd algorithm are popular tools for solving large scale linear systems arising from image deblurring problems these algorithms however are hindered by a semi convergence behavior in that the quality of the computed solution first increases and then decreases in this paper in order to overcome the semi convergence behavior we propose two iterative algorithms based on soft thresholding for image deblurring problems one of them combines cgls with a denoising technique like soft thresholding at each iteration and another combines mrnsd with soft thresholding in a similar way we prove the convergence of mrnsd and soft thresholding based algorithm numerical results show that the proposed algorithms overcome the semi convergence behavior and the restoration results are slightly better than those of cgls and mrnsd with their optimal stopping iterations

the lifting factorization of 2d 4 channel nonseparable wavelet transforms abstract one dimensional 1d wavelet transform was lifted successfully using the division with remainder of univariate laurent polynomials however division with remainder does not exist in the case of a bivariate polynomial thus it makes sense that the polyphase matrix of a two dimensional 2d nonseparable wavelet transform cannot be decomposed into the lifting format using the same solution as that of the 1d wavelet transform in this research we present a new lifting factorization method of two dimensional four channel 2d 4 channel nonseparable wavelet filter banks according to the uniform constructing format of high dimensional multivariate wavelet filter banks the general form of 2d 4 channel nonseparable wavelet filter bank is given with these filter banks the polyphase matrix of 2d 4 channel nonseparable wavelet transform is found and proven then we present the lifting factorization of the polyphase matrix and some examples are demonstrated in the factorization procedures finally the lifting performances of the proposed method are analyzed this lifting method factorizes the polyphase matrix into the product of a series of unit lower left triangular numerical matrices unit upper right triangular numerical matrices diagonal numerical matrices and diagonal polynomial matrices whose elements on the diagonal line are 1 x y and xy the original filter banks that all leading principal minors of the numerical matrices are not equal to zero can be factorized into lifting format the proposed method transforms the lifting factorization of the polyphase matrix into the decompositions of the numerical matrices without euclidian division thereby only multiplication and addition operations are performed with no fourier transformation involved when compared with the lifting method of the tensor product lifting wavelet transform and the contourlet transform the proposed lifting method can extract more edge information of images the computational complexity of the original 2d 4 channel nonseparable wavelet transform for image decomposition is n 1 times as much as that of the proposed lifting factorization method and the original wavelet transform is accelerated furthermore the proposed lifting factorization method is faster than the conventional 2d 4 channel nonseparable wavelet transform based on fourier transformation theory and convolution operation when the size of each filter in the latter is greater than 4 n 1 the proposed lifting factorization has better sparsity than that of its original 2d 4 channel nonseparable wavelet transform and other typical 2d 4 channel nonseparable wavelet transforms

analytic network process for pattern classification problems using genetic algorithms the analytic network process anp is a useful technique for multi attribute decision analysis mcda that employs a network representation to describe interrelationships between diverse attributes owing to effectiveness of the anp in allowing for complex interrelationships between attributes this paper develops an anp based classifier for pattern classification problems with interdependence or independence among attributes to deal with interdependence this study employs genetic algorithms gas to automatically determine elements in the supermatrix that are not easily user specified to find degrees of importance of respective attributes then with the relative importance for each attribute in the limiting supermatrix the current work determines the class label of a pattern by its synthetic evaluation experimental results obtained by the proposed anp based classifier are comparable to those obtained by other fuzzy or non fuzzy classification methods

a set partitioning heuristic for the generalized assignment problem this paper discusses a heuristic for the generalized assignment problem gap the objective of gap is to minimize the costs of assigning j jobs to m capacity constrained machines such that each job is assigned to exactly one machine the problem is known to be np hard and it is hard from a computational point of view as well the heuristic proposed here is based on column generation techniques and yields both upper and lower bounds on a set of relatively hard test problems the heuristic is able to find solutions that are on average within 0 13 from optimality

a genetic algorithm approach to determine the sample size for attribute control charts determining the sample size for control charts ccs is generally an important problem in the literature in this paper kaya and engin s i kaya o engin a new approach to define sample size at attributes control chart in multistage processes an application in engine piston manufacturing process journal of materials processing technology 183 2007 38 48 model based on minimum cost and maximum acceptance probability to determine the sample size for attribute control charts accs and solved by genetic algorithms gas with linear binary representation structure is handled to solve it by a linear real valued representation a new chromosome structure is also suggested to increase the efficiency of gas the performance of gas depends on mutation and crossover operators and their ratios to determine the most appropriate operators five different mutation and crossover operators are used and they are compared with each other an application in a motor engine factory is illustrated u control charts are constructed with respect to the sample size determined by ga in the model the piston production stages in this factory are monitorized using the obtained control charts

transcale control for a class of discrete stochastic systems based on wavelet packet decomposition abstract in this paper a wavelet packet decomposition wpd based real time transcale linear quadratic gaussian lqg tracking control algorithm is given for a class of discrete stochastic systems which is developed with the state space models of wavelet packet coefficients at the coarsest scale decomposition layer established by haar wpd the wpd based transcale control algorithm provides a compromise between performance index and computational efficiency compared with the conventional lqg tracking control algorithm and it is an improvement of the wavelet transform based algorithm previously proposed simulation results are presented to demonstrate the effectiveness of the proposed algorithm

singularity detection and processing with wavelets the mathematical characterization of singularities with lipschitz exponents is reviewed theorems that estimate local lipschitz exponents of functions from the evolution across scales of their wavelet transform are reviewed it is then proven that the local maxima of the wavelet transform modulus detect the locations of irregular structures and provide numerical procedures to compute their lipschitz exponents the wavelet transform of singularities with fast oscillations has a particular behavior that is studied separately the local frequency of such oscillations is measured from the wavelet transform modulus maxima it has been shown numerically that one and two dimensional signals can be reconstructed with a good approximation from the local maxima of their wavelet transform modulus as an application an algorithm is developed that removes white noises from signals by analyzing the evolution of the wavelet transform maxima across scales in two dimensions the wavelet transform maxima indicate the location of edges in images

a chaotic iterative algorithm based on linearized bregman iteration for image deblurring in this paper we propose a new chaotic iterative algorithm for image deblurring the algorithm is based on generalized inverse iteration and linearized bregman iteration for the basis pursuit problem min u r n u 1 au f numerical experiments show that the chaotic algorithm for image restoration is effective and efficient

high speed vlsi multiplication algorithm with a redundant binary addition tree a high speed vlsi multiplication algorithm internally using redundant binary representation is proposed in n bit binary integer multiplication n partial products are first generated and then added up pairwise by means of a binary tree of redundant binary adders since parallel addition of two n digit redundant binary numbers can be performed in a constant time independent of n without carry propagation n bit multiplication can be performed in a time proportional to log2 n the computation time is almost the same as that by a multiplier with a wallace tree in which three partial products will be converted into two in contrast to our two to one conversion and is much shorter than that by an array multiplier for longer operands the number of computation elements of an n bit multiplier based on the algorithm is proportional to n2 it is almost the same as those of conventional ones furthermore since the multiplier has a regular cellular array structure similar to an array multiplier it is suitable for vlsi implementation thus the multiplier is excellent in both computation speed and regularity in layout it can be implemented on a vlsi chip with an area proportional to n2 log2 n the algorithm can be directly applied to both unsigned and 2 s complement binary integer multiplication

on success runs of a fixed length in bernoulli sequences exact and asymptotic results consider a sequence of n bernoulli success failure or 1 0 trials the exact and limiting distribution of the random variable e n k denoting the number of success runs of a fixed length k email protected email protected n is derived along with its mean and variance an associated waiting time is examined as well the exact distribution is given in terms of binomial coefficients and an extension of it covering exchangeable sequences is also discussed limiting distributions of e n k are obtained using poisson and normal approximations the exact mean and variance of e n k which are given in explicit forms are also used to derive bounds and an additional approximation of the distribution of e n k numbers associated with e n k and related random variables counting binary strings and runs of 1 s useful in applications of computer science are provided the overall study is illustrated by an extensive numerical experimentation

filtering for a class of nonlinear discrete time stochastic systems with state delays in this paper the filtering problem is investigated for a class of nonlinear discrete time stochastic systems with state delays we aim at designing a full order filter such that the dynamics of the estimation error is guaranteed to be stochastically exponentially ultimately bounded in the mean square for all admissible nonlinearities and time delays first an algebraic matrix inequality approach is developed to deal with the filter analysis problem and sufficient conditions are derived for the existence of the desired filters then based on the generalized inverse theory the filter design problem is tackled and a set of the desired filters is explicitly characterized a simulation example is provided to demonstrate the usefulness of the proposed design method

best basis for joint representation the median of marginal best bases for low cost information exchanges in distributed signal representation the paper addresses the selection of the best representations for distributed and or dependent signals given an indexed tree structured library of bases and a semi collaborative distribution scheme associated with minimum information exchange emission and reception of one single index corresponding to a marginal best basis the paper proposes the median basis computed on a set of best marginal bases for joint representation or fusion of distributed dependent signals the paper provides algorithms for computing this median basis with respect to standard tree structured libraries of bases such as wavelet packet bases or cosine trees these algorithms are effective when an additive information cost is under consideration experimental results performed on distributed signal compression confirms worthwhile properties for the median of marginal best bases with respect to the ideal best joint basis the latter being underdetermined in practice except when a full collaboration scheme is under consideration

distribution theory of runs a markov chain approach abstract the statistics of the number of success runs in a sequence of bernoulli trials have been used in many statistical areas for almost a century even in the simplest case of independent and identically distributed bernoulli trials the exact distributions of many run statistics still remain unknown departing from the traditional combinatorial approach in this article we present a simple unified approach for the distribution theory of runs based on a finite markov chain imbedding technique our results cover not only the identical bernoulli trials but also the nonidentical bernoulli trials as a byproduct our results also yield the exact distribution of the waiting time for the mth occurrence of a specific run

on runlength codes several results on binary d k codes are given first a novel derivation for the capacity of these codes based on information theoretic principles is given based on this result the spectrum of a d k code is computed finally the problem of computing the capacity of the binary symmetric channel under the condition that the input sequences satisfy the d k constraint is considered lower bounds on the capacity of such a channel are derived

an optimal image watermarking approach based on a multi objective genetic algorithm in accordance with the multi objective nature of image watermarking an optimal image watermarking approach using a multi objective genetic algorithm is presented in this paper both watermarking parameters and embedding positions are often important factors affecting the performance of watermarking systems the proposed multi objective watermarking method can automatically optimize system parameters and a variable length mechanism is specially designed to search the most suitable positions for embedding watermarks the method can also remove the difficult issue of determining optimal watermarking parameters from previous watermarking algorithms the proposed multi objective watermarking method directly deals with the problem of optimizing watermarking under non dominated meaning thus it can effectively avoid the difficulty of determining the optimally weighted factor in existing single objective watermarking schemes in addition a pareto optimal set generated by multi objective optimization can provide flexibility in selecting the most suitable watermarking parameters according to practical requirements

joint image denoising using adaptive principal component analysis and self similarity the non local means nlm has attracted enormous interest in image denoising problem in recent years in this paper we propose an efficient joint denoising algorithm based on adaptive principal component analysis pca and self similarity that improves the predictability of pixel intensities in reconstructed images the proposed algorithm consists of two successive steps without iteration the low rank approximation based on parallel analysis and the collaborative filtering first for a pixel and its nearest neighbors the training samples in a local search window are selected to form the similar patch group by the block matching method next it is factorized by singular value decomposition svd whose left and right orthogonal basis denote local and non local image features respectively the adaptive pca automatically chooses the local signal subspace dimensionality of the noisy similar patch group in the svd domain by the refined parallel analysis with monte carlo simulation thus image features can be well preserved after dimensionality reduction and simultaneously the noise is almost eliminated then after the inverse svd transform the denoised image is reconstructed from the aggregate filtered patches by the weighted average method finally the collaborative wiener filtering is used to further remove the noise the experimental results validate its generality and effectiveness in a wide range of the noisy images the proposed algorithm not only produces very promising denoising results that outperforms the state of the art methods in most cases but also adapts to a variety of noise levels

a survey of algorithms for the generalized assignment problem abstract this paper surveys algorithms for the well known problem of finding the minimum cost assignment of jobs to agents so that each job is assigned exactly once and agents are not overloaded all approaches seem to be based on branch and bound with bound supplied through heuristics and through relaxations of the primal problem formulation from the survey one can select building blocks for the design of one s own tailor made algorithm the survey also reveals that although just about every mathematical programming technique was tried on this problem there is still a lack of a representative set of test problems on which competing enumeration algorithms can be compared as well as a shortage of effective heuristics

finding the minimum number of elements with sum above a threshold motivated by the wavelet compression techniques and their applications we consider the following problem given an unsorted array of numerical values and a threshold what is the minimum number of elements chosen from the array such that the sum of these elements is not less than the threshold value in this article we first provide two linear time algorithms for the problem we then demonstrate the efficacy of these algorithms through experiments lastly as an application of this research we indicate that the construction of wavelet synopses on a prescribed error bound in l 2 metric can be solved in linear time

self organizing genetic algorithm based tuning of pid controllers this paper proposes a self organizing genetic algorithm soga with good global search properties and a high convergence speed first we introduce a new dominant selection operator that enhances the action of the dominant individuals along with a cyclical mutation operator that periodically varies the mutation probability in accordance with evolution generation found in biological evolutionary processes next the soga is constructed using the two operators mentioned above the results of a nonlinear regression analysis demonstrate that the self organizing genetic algorithm is able to avoid premature convergence with a higher convergence speed and also indicate that it possesses self organization properties finally the new algorithm is used to optimize proportional integral derivative pid controller parameters our simulation results indicate that a suitable set of pid parameters can be calculated by the proposed soga

max plus algebra based wavelet transforms and their fpga implementation for image coding in the present paper we propose new image coding methods based on max plus algebra based wavelet transforms mp wavelets max plus algebra is an algebraic structure on the set of integers endowed with maximum minimum and standard addition as operations the proposed wavelet decomposition schemes are novel classes of morphological wavelets which in contrast to the existing approaches involve only integers and only max min and addition in their computation since they do not involve floating point calculations and multiplications mp wavelets have a very low computational complexity and they are suitable for efficient hardware implementation through image coding experiments using 10 000 images extracted from low resolution web crawled misc database the characteristics of the proposed mp wavelets are presented furthermore we show a computational complexity analysis to compare mp wavelets to one of the fastest wavelet transforms the conventional haar wavelet the applicability of mp wavelets in video coding is also confirmed by image coding experiments using residual frames finally the field programmable gate arrays fpga implementation of mp wavelets is presented to confirm suitability of mp wavelets for hardware implementation

adaptive wavelet thresholding for image denoising and compression the first part of this paper proposes an adaptive data driven threshold for image denoising via wavelet soft thresholding the threshold is derived in a bayesian framework and the prior used on the wavelet coefficients is the generalized gaussian distribution ggd widely used in image processing applications the proposed threshold is simple and closed form and it is adaptive to each subband because it depends on data driven estimates of the parameters experimental results show that the proposed method called bayesshrink is typically within 5 of the mse of the best soft thresholding benchmark with the image assumed known it also outperforms sureshrink donoho and johnstone 1994 1995 donoho 1995 most of the time the second part of the paper attempts to further validate claims that lossy compression can be used for denoising the bayesshrink threshold can aid in the parameter selection of a coder designed with the intention of denoising and thus achieving simultaneous denoising and compression specifically the zero zone in the quantization step of compression is analogous to the threshold value in the thresholding function the remaining coder design parameters are chosen based on a criterion derived from rissanen s minimum description length mdl principle experiments show that this compression method does indeed remove noise significantly especially for large noise power however it introduces quantization noise and should be used only if bitrate were an additional concern to denoising

associating visual textures with human perceptions using genetic algorithms this paper deals with an approach allowing to associate visual textures with given human perceptions hereby based on a forward model associating human perceptions for given visual textures the deduction of an reverse process is presented which is able to associate and characterize visual textures for given human perceptions for doing so we propose a constraint based genetic algorithm approach which is able to minimize a specific optimization problem containing constraints in form of band widths for valid individuals low level features extracted from textures in a population the constraints are determined by relationships between low level features characterizing textures in form of high dimensional approximation models additionally in each iteration step checking for valid individuals is carried out with a texture non texture classifier or by using a convex hull over a set of valid textures the whole approach is evaluated based on a real world texture set used as a start population in the genetic algorithm and by defining various kinds of human perceptions for which textures are sought represented by adjective vectors in the aesthetic space the generated individuals low level feature vectors have a high level of fitness they are quite close to the pre defined adjective vectors and a small distance to the initial population the textures synthesized based on the generated individuals are visualized and compared with textures synthesized by a time intensive direct texture mixing and re combination method based on a real world texture data base

homoclinic and heteroclinic orbits in a modified lorenz system this paper presents a mathematically rigorous proof for the existence of chaos in a modified lorenz system using the theory of shil nikov bifurcations of homoclinic and heteroclinic orbits together with its dynamical behaviors which have been extensively studied the chaotic dynamics of the modified lorenz system are now much better understood providing a rigorous theoretic foundation to support studies and applications of this important class of chaotic systems

type 1 and type 2 fuzzy inference systems as integration methods in modular neural networks for multimodal biometry and its optimization with genetic algorithms we describe in this paper a comparative study between fuzzy inference systems as methods of integration in modular neural networks for multimodal biometry these methods of integration are based on techniques of type 1 fuzzy logic and type 2 fuzzy logic also the fuzzy systems are optimized with simple genetic algorithms with the goal of having optimized versions of both types of fuzzy systems first we considered the use of type 1 fuzzy logic and later the approach with type 2 fuzzy logic the fuzzy systems were developed using genetic algorithms to handle fuzzy inference systems with different membership functions like the triangular trapezoidal and gaussian since these algorithms can generate fuzzy systems automatically then the response integration of the modular neural network was tested with the optimized fuzzy systems of integration the comparative study of the type 1 and type 2 fuzzy inference systems was made to observe the behavior of the two different integration methods for modular neural networks for multimodal biometry

an intelligent noise reduction method for chaotic signals based on genetic algorithms and lifting wavelet transforms time series observed in real world is often nonlinear even chaotic however observed data is often contaminated by noise of various types to effectively extract desired information from observed data it is vital to preprocess data to reduce noise for both the analysis of dynamical systems and many potential applications of these systems in this paper we present a noise reduction approach to the problem of additive source separation characterized by wide band power spectra when one of the sources is chaotic the algorithm is based on a center based genetic algorithm cbga in lifting wavelet framework in which the cbga is used for threshold optimization this method intelligently adapts itself to various types of noise and it weighs preservation of dynamics and denoising through signal to noise ratio snr and root mean square error rmse computer simulations show that the approach is very effective in diminishing different kinds of noise and performs better in terms of visual quality as well as quantitative metrics than existing algorithms

a hybrid genetic algorithm with the baldwin effect here we present a new hybrid genetic algorithm hga with the baldwin effect in the hga a local search is employed to change the fitness of individuals but the acquired improvements do not change the individual itself this local search step exploits the baldwin effect some numerical applications show that this algorithm can yield the global optimum more efficiently than commonly used hgas a theorem is presented that guarantees the convergence in probability of the new hga

on the distribution of runs of ones in binary strings in this paper we derive the number of binary strings which contain for a given i k exactly i k runs of 1 s of length k in all possible binary strings of length n email protected email protected n such a knowledge about the distribution pattern of runs of 1 s in binary strings is useful in many engineering applications for example data compression bus encoding techniques to reduce crosstalk in vlsi chip design computer arithmetic using redundant binary number system and design of energy efficient communication schemes in wireless sensor networks by transformation of runs of 1 s into compressed information patterns among others we present here a generating function based approach to derive a solution to this counting problem our experimental results demonstrate that for most commonly used file formats the observed distributions of exactly i k runs of length k email protected email protected n closely follow the theoretically derived distributions for a given n for n 8 we find that the experimentally obtained values for most file formats agree within 5 of the theoretically obtained values for all i k runs of length k email protected email protected n also the root mean square rms values of these deviations across all file types studied in this paper are less than 5 for n 8 in view of these facts the results presented in this paper could be useful in various application domains like the ones mentioned above

complex system fault diagnosis based on a fuzzy robust wavelet support vector classifier and an adaptive gaussian particle swarm optimization this paper proposes a robust loss function that penalizes hybrid noise i e gaussian noise singularity points and larger magnitude noise in a complex fuzzy fault diagnosis system a mapping relationship between fuzzy numbers and crisp real numbers that allows a fuzzy sample set to be transformed into a crisp real sample set is also presented furthermore the paper proposes a novel fuzzy robust wavelet support vector classifier frwsvc based on a wavelet base function and develops an adaptive gaussian particle swarm optimization agpso algorithm to seek the optimal unknown parameter of the frwsvc the results of experiments that apply the hybrid diagnosis model based on the frwsvc and the agpso algorithm to fault diagnosis demonstrate that it is both feasible and effective tests comparing the method proposed in this paper against other fuzzy support vector classifier fsvc machines show that it outperforms them

iterative two step genetic algorithm based method for efficient polynomial b spline surface reconstruction surface reconstruction is a very challenging problem arising in a wide variety of applications such as cad design data visualization virtual reality medical imaging computer animation reverse engineering and so on given partial information about an unknown surface its goal is to construct to the extent possible a compact representation of the surface model in most cases available information about the surface consists of a dense set of either organized or scattered 3d data points obtained by using scanner devices a today s prevalent technology in many reverse engineering applications in such a case surface reconstruction consists of two main stages 1 surface parameterization and 2 surface fitting both tasks are critical in order to recover surface geometry and topology and to obtain a proper fitting to data points they are also pretty troublesome leading to a high dimensional nonlinear optimization problem in this context present paper introduces a new method for surface reconstruction from clouds of noisy 3d data points our method applies the genetic algorithm paradigm iteratively to fit a given cloud of data points by using strictly polynomial b spline surfaces genetic algorithms are applied in two steps the first one determines the parametric values of data points the later computes surface knot vectors then the fitting surface is calculated by least squares through either svd singular value decomposition or lu methods the method yields very accurate results even for surfaces with singularities concavities complicated shapes or nonzero genus six examples including open semi closed and closed surfaces with singular points illustrate the good performance of our approach our experiments show that our proposal outperforms all previous approaches in terms of accuracy and flexibility

a fractional order adaptive regularization primal dual algorithm for image denoising this paper aims to develop a fractional order model and a primal dual algorithm for image denoising where a regularization parameter can be adjusted adaptively according to morozov discrepancy principle at each iteration to ensure that the denoised image retains in a specific set in the light of saddle point theory the convergence of our proposed algorithm is guaranteed simulations with comparisons are carried out to demonstrate the effectiveness of our proposed algorithm for image denoising

on the mean and extreme distances between failures in markovian binary sequences this paper is concerned with the mean minimum and maximum distances between two successive failures in a binary sequence consisting of markov dependent elements these random variables are potentially useful for the analysis of the frequency of critical events occurring in certain stochastic processes exact distributions of these random variables are derived via combinatorial techniques and illustrative numerical results are presented