image reconstruction from zero crossings this study is concerned with the information in zero crossings zc of images logan s conditions specifying when a one dimensional signal may be recovered within a multiplicative constant from its zc are extended for various cases of two dimensional signals an algorithm is implemented in reconstruction of context free band pass images it is also successfully applied in reconstruction of contextual images by first dissecting the image into appropriate bandpass band limited two dimensional signals in almost all cases of spectrum confined to less than an octave in one dimension the reconstruction algorithm converges whereas it does not converge for any signal exceeding one octave in bandwidth this paper substantiates the proposition that images are well represented by the partial information confined to zc

wavelet domain blur invariants for image analysis radiometric degradation is a common problem in the image acquisition part of many applications there is much research carried out in an effort to deblur such images however it has been proven that it is not always necessary to go through a burdensome process of deblurring to tackle this problem different blur invariant descriptors have been proposed so far which are either in the spatial domain or based on the properties available in the fourier domain in this paper wavelet domain blur invariants are proposed for the first time for discrete 2 d signals these descriptors which are invariant to centrally symmetric blurs inherit the advantages that this domain provides it is also proven that the spatial domain blur invariants are a special version of the proposed invariants the performance of these invariants will be demonstrated through experiments

discrete time wavelet extrema representation design and consistent reconstruction the paper studies wavelet transform extrema and zero crossings representations within the framework of convex representations in spl lscr z wavelet zero crossings representation of two dimensional signals is introduced as a convex multiscale edge representation as well one appealing property of convex representations is that the reconstruction problem can be solved at least theoretically using the method of alternating projections onto convex sets it turns out that in the case of the wavelet extrema and wavelet zero crossings representations this method yields simple and practical reconstruction algorithms nonsubsampled filter banks that implement the wavelet transform for the two representations are also studied in the paper relevant classes of nonsubsampled perfect reconstruction fir filter banks are characterized this characterization gives a broad class of wavelets for the representations which are derived from those of the filter banks which satisfy a regularity condition

l fuzzy soft sets based on complete boolean lattices in this paper the concept of l fuzzy soft sets based on complete boolean lattices which can be seen as a generalization of fuzzy soft sets is introduced the topological and lattice structure of l fuzzy soft sets are obtained some operations on l fuzzy soft sets are discussed and new types of l fuzzy soft sets such as full keeping intersection and keeping union l fuzzy soft sets are defined and supported by some illustrative examples a pair of l fuzzy soft rough approximations is proposed and their properties are given based on l fuzzy soft rough approximations the concept of l fuzzy soft rough sets is introduced and their structures are studied the fact that every finite l fuzzy topological space is an l fuzzy soft approximation space is revealed in addition we obtain two one to one correspondence relationships associated with l fuzzy soft sets which expounds the broad application prospect of l fuzzy soft sets

zero crossings of a wavelet transform the completeness stability and application to pattern recognition of a multiscale representation based on zero crossings is discussed an alternative projection algorithm is described that reconstructs a signal from a zero crossing representation which is stabilized by keeping the value of the wavelet transform integral between each pair of consecutive zero crossings the reconstruction algorithm has a fast convergence and each iteration requires o n log sup 2 n computation for a signal of n samples the zero crossings of a wavelet transform define a representation which is particularly well adapted for solving pattern recognition problems as an example the implementation and results of a coarse to fine stereo matching algorithm are described

diffusion equation techniques in stochastic monotonicity and positive correlations a diffusion equation approach is investigated for the study of stochastic monotonicity positive correlations and the preservation of lipschitz functions necessary and sufficient conditions are given for diffusion semigroups to be stochastically monotonic and to preserve the class of positively correlated measures applications are given which discuss the shape of the ground state for schrodinger operators v with fkg potentialsv

ergodicity conditions for two dimensional markov chains on the positive quadrant the basic problem considered in this paper is that of determining conditions for recurrence and transience for two dimensional irreducible markov chains whose state space is z 2 z xz assuming bounded jumps and a homogeneity condition malyshev 7 obtained necessary and sufficient conditions for recurrence and transience of two dimensional random walks on the positive quadrant unfortunately his hypothesis that the jumps of the markov chain be bounded rules out for example the poisson arrival process in this paper we generalise malyshev s theorem by means of a method that makes novel use of the solution to laplace s equation in the first quadrant satisfying an oblique derivative condition on the boundaries this method which allows one to replace the very restrictive boundedness condition by a moment condition and a lower boundedness condition is of independent interest

interval algorithms for finding the minimal root in a set of multiextremal one dimensional nondifferentiable functions two problems arising very often in applications are considered the first problem consists of finding the minimal root of an analytic one dimensional function over a given interval it is supposed that the objective function can be multiextremal and nondifferentiable three new algorithms based on interval analysis and branch and bound global optimization approaches are proposed for solving this problem the novelty of the new algorithms is in improving the elimination criteria and the order in which interval and point evaluations are realized the techniques introduced accelerate the search in comparison with interval analysis methods traditionally used for finding roots of equations the second problem considered in the paper is a generalization of the first one and deals with the search for the minimal root in a set of multiextremal and nondifferentiable functions the methods proposed for solving the first problem are generalized for solving the second the main idea is to use the information obtained from any of the functions to reduce the search domain associated with all the functions numerical experiments carried out on a wide set of test functions demonstrate a quite satisfactory performance of the new algorithms in both cases

signal representation in the combined phase spatial space reconstruction and criteria for uniqueness motivated by the major roles of the spectral phase in signal structure and by previous results on the importance of localized representation in images we develop conditions for unique representation of a signal by a combination of its spectral fourier phase and spatial samples methods for signal reconstruction from various combinations of spatial and phase information are introduced it is concluded that most of the previous results in the area of phase only representation and reconstruction are special cases of the general approach presented here

soft sets and soft groups molodtsov introduced the concept of soft set theory which can be used as a generic mathematical tool for dealing with uncertainty in this paper we introduce the basic properties of soft sets and compare soft sets to the related concepts of fuzzy sets and rough sets we then give a definition of soft groups and derive their basic properties using molodtsov s definition of the soft sets

mouvement brownien cones et processus stables letw wt t 0 denote a two dimensional brownian motion starting at 0 and for 0 4 here we construct a measure a local time supported onh for 4 2 the brownian motionw time changed by the inverse of this local time is shown to be a two dimensional stable process with index 2 2 this results extends spitzer s construction of the cauchy process which is recovered by taking 2 a formula which describes the behaviour ofw before a timet h is established and applied to the proof of a conjecture of burdzy we also obtain a two dimensional version of the famous theorem of levy concerning the maximum process of linear brownian motion precisely for 0 2 letst denote the vertex of the smallest wedge of the typez c which contains the path ofw up to timet the processst wt is shown to be a reflected brownian motion in the wedgec with oblique reflection on the sides finally we investigate various extensions of the previous results to brownian motion inrd d 3 letc be the cone associated with an open subset of the spheresd 1 and leth be defined ash above sufficient conditions are given forh to contain nonzero times in terms of the first eigenvalue of the dirichlet laplacian on

subband image coding using watershed and watercourse lines of the wavelet transform reports progress in primitive based image coding using nonorthogonal dyadic wavelets a 3d isotropic wavelet is used to approximate the difference of gaussians d o g operator convolution of the image with dilated versions of the wavelet produces three band pass signals that approximate multiscale smoothed second derivatives an additional convolution of the image with a gaussian shaped low pass wavelet creates a fourth subband signal that preserves low frequency information not described by the three band pass signals the authors show that the original image can be recovered from the watershed and watercourse lines of the three band pass signals plus the lowpass subband signal by thresholding the watershed watercourse representation subsampling the low pass subband and using edge post emphasis the authors achieve data reduction with little loss of fidelity further compression of the watersheds and watercourses is achieved by chain coding their shapes and predictive coding their amplitudes prior to lossless arithmetic coding results are presented for grey level test images at data rates between 0 1 and 0 3 b pixel

analytical footprints compact representation of elementary singularities in wavelet bases we introduce a family of elementary singularities that are point holder regular these singularities are self similar and are the green functions of fractional derivative operators i e by suitable fractional differentiation one retrieves a dirac function at the exact location of the singularity we propose to use fractional operator like wavelets that act as a multiscale version of the derivative in order to characterize and localize singularities in the wavelet domain we show that the characteristic signature when the wavelet interacts with an elementary singularity has an asymptotic closed form expression termed the analytical footprint practically this means that the dictionary of wavelet footprints is embodied in a single analytical form we show that the wavelet coefficients of the nonredundant decomposition can be fitted in a multiscale fashion to retrieve the parameters of the underlying singularity we propose an algorithm based on stepwise parametric fitting and the feasibility of the approach to recover singular signal representations

uniqueness for diffusions with piecewise constant coefficients letl be a second order partial differential operator inrd letrd be the finite union of disjoint polyhedra suppose that the diffusion matrix is everywhere non singular and constant on each polyhedron and that the drift coefficient is bounded and measurable we show that the martingale problem associated withl is well posed

brownian motion in a wedge with variable reflection existence and uniqueness existence and uniqueness in law of reflecting brownian motion in a wedge is proved the direction of reflection along the sides of the wedge varies in a reasonable fashion except perhaps at the corner

reconstructions from zero crossings in scale space in computer vision the one parameter family of images obtained from the laplacian of a gaussian filtered version of the image parameterized by the width of the gaussian has proved to be a useful data structure for the extraction of feature data in particular the zero crossings of this so called scale space data are associated with edges and have been proposed by d marr 1982 and others as the basis of a representation of the image data the question arises as to whether the representation is complete and stable the authors survey some of the studies and results related to these questions as well as several studies that attempt reconstructions based on this or related representations they formulate a novel method for reconstruction from zero crossings in scale space that is based on minimizing equation error and they present results showing that the reconstruction is possible but can be unstable they further show that the method applies when gradient data along the zero crossings are included in the representation and they demonstrate empirically that the reconstruction is then stable

a multiscale edge detection algorithm based on wavelet domain vector hidden markov tree model abstract the wavelet analysis is an efficient tool for the detection of image edges based on the wavelet analysis we present an unsupervised learning algorithm to detect image edges in this paper a wavelet domain vector hidden markov tree wd vhmt is employed in our algorithm to model the statistical properties of multiscale and multidirectional subband wavelet coefficients of an image with this model each wavelet coefficient is viewed as an observation of its hidden state and the hidden state indicates if the wavelet coefficient belongs to an edge the wd vhmt model can be learned by an expectation maximization algorithm after the model is learned we employ an extended viterbi algorithm to uncover the hidden state sequences according to the maximum a posterior estimation the experiment results of the edge detection for several images are provided to evaluate our algorithm

scaling theorems for zero crossings we characterize some properties of the zero crossings of the laplacian of signals in particular images filtered with linear filters as a function of the scale of the filter extending recent work by witkin 16 we prove that in any dimension the only filter that does not create generic zero crossings as the scale increases is the gaussian this result can be generalized to apply to level crossings of any linear differential operator it applies in particular to ridges and ravines in the image intensity in the case of the second derivative along the gradient there is no filter that avoids creation of zero crossings unless the filtering is performed after the derivative is applied

delta ramp encoder for amplitude sampling and its interpretation as time encoding the theoretical basis for conventional acquisition of bandlimited signals typically relies on uniform time sampling and assumes infinite precision amplitude values in this paper we explore signal representation and recovery based on uniform amplitude sampling with assumed infinite precision timing information the approach is based on the delta ramp encoder which consists of applying a one level level crossing detector to the result of adding an appropriate sawtooth like waveform to the input signal the output samples are the time instants of these level crossings thus representing a time encoded version of the input signal for theoretical purposes this system can be equivalently analyzed by reversibly transforming through ramp addition a nonmonotonic input signal into a monotonic one which is then uniformly sampled in amplitude the monotonic function is then represented by the times at which the signal crosses a predefined and equally spaced set of amplitude values we refer to this technique as amplitude sampling the time sequence generated can be interpreted alternatively as nonuniform time sampling of the original source signal we derive duality and frequency domain properties for the functions involved in the transformation iterative algorithms are proposed and implemented for recovery of the original source signal as indicated in the simulations the proposed iterative amplitude sampling algorithm achieves a faster convergence rate than frame based reconstruction for nonuniform sampling the performance can also be improved by appropriate choice of the parameters while maintaining the same sampling density

on the diffusion approximation to two parallel queues with processor sharing a two dimensional queuing model is considered in which the server in the second queue helps the server in the first queue during periods when the second queue is empty the system is analyzed in the heavy traffic limit and explicit approximate solutions are obtained to the resulting diffusion equations using singular perturbation methods approximate asymptotic formulas are obtained for the stationary distribution of the number of customers as well as for some first passage time problems associated with the busy period it is shown that these formulas reduce to the asymptotic expansions of the exact solutions when the latter are available

brownian motion in a wedge with oblique reflection this work is concerned with the existence and uniqueness of a strong markov process that has continuous sample paths and the following additional properties i the state space is an infinite two dimensional wedge and the process behaves in the interior of the wedge like an ordinary brownian motion ii the process reflects instantaneously at the boundary of the wedge the angle of reflection being constant along each side iii the amount of time that the process spends at the comer of the wedge is zero i e the set of times for which the process is at the comer has lebesgue measure zero hereafter let be the angle of the wedge 0 2 let 1 and 2 be the angles of reflection on the two sides of the wedge measured from the inward normals the positive angles being toward the corner 1 2 and set 1 2 the question of existence and uniqueness is recast as a submartingale problem in the style used by stroock and varadhan diffusion processes with boundary conditions comm pure appl math 24 1971 pp 147 225 for diffusions on smooth domains with smooth boundary conditions it is shown that no solution exists if 2 in this case there is a unique continuous strong markov process satisfying i ii above it reaches the corner of the wedge almost surely and it remains there if 2 however then there is a unique continuous strong markov process statisfying i iii it is shown that starting away from the corner this process does not reach the corner of the wedge if 0 and does reach the corner if 0 2 the general theory of multi dimensional diffusions does not apply to the above problem because in general the boundary of the state space is not smooth and there is a discontinuity in the direction of reflection at the corner for some values of the process arises from diffusion approximations to storage systems and queueing networks i the state space is an infinite two dimensional wedge and the process behaves in the interior of the wedge like an ordinary brownian motion ii the process reflects instantaneously at the boundary of the wedge and the angle of reflection being constant along each side iii the amount of time that the process spends at the corner of the wedge is zero i e the set of times for which the process is at the corner has lebesgue measure zero

reconstruction of nonperiodic two dimensional signals from zero crossings in this correspondence we present new results on the reconstruction of two dimensional signals from zero crossing or threshold crossing information specifically we develop new theoretical results which state conditions under which two dimensional bandlimited signals are uniquely specified to within a scale factor with this information unlike previous results in this area our new results do not constrain the signals to be periodic or bandpass

strong solutions of stochastic equations with rank based coefficients we study finite and countably infinite systems of stochastic differential equations in which the drift and diffusion coefficients of each component particle are determined by its rank in the vector of all components of the solution we show that strong existence and uniqueness hold until the first time three particles collide motivated by this result we improve significantly the existing conditions for the absence of such triple collisions in the case of finite dimensional systems and provide the first condition of this type for systems with a countable infinity of particles

the adjoint process of killed reflected brownian motion in a cone and applications let xt be reflected brownian motion rbm in a cone with radially homogeneous reflection killed upon reaching the vertex of the cone we determine the adjoint process and use it to find the martin boundary of the killed rbm together with all the corresponding positive harmonic functions then we can identify and prove uniqueness up to positive scalar multiples of the invariant measure for killed rbm and rbm without killing along the way we prove the strong feller property of the resolvent of rbm no killing 1 introduction denote by s d 1 d 3 the unit sphere in d let s d 1 be a domain such that s d 1 is nonempty and the boundary

geometric and illumination invariants for object recognition we propose invariant formulations that can potentially be combined into a single system in particular we describe a framework for computing invariant features which are insensitive to rigid motion affine transform changes of parameterization and scene illumination perspective transform and view point change this is unlike most current research on image invariants which concentrates on either geometric or illumination invariants exclusively the formulations are widely applicable to many popular basis representations such as wavelets short time fourier analysis and splines exploiting formulations that examine information about shape and color at different resolution levels the new approach is neither strictly global nor local it enables a quasi localized hierarchical shape analysis which is rarely found in other known invariant techniques such as global invariants furthermore it does not require estimating high order derivatives in computing invariants unlike local invariants whence is more robust we provide results of numerous experiments on both synthetic and real data to demonstrate the validity and flexibility of the proposed framework

completeness of arbitrarily sampled discrete time wavelet transforms an arbitrarily sampled discrete time wavelet transform is said to be complete if it is uniquely invertible i e if the underlying signal can be uniquely recovered from the available samples of the wavelet transform we develop easy to compute necessary and sufficient conditions and necessary but not sufficient conditions for the completeness of an arbitrarily sampled dyadic discrete time wavelet transform of a periodic signal in particular we provide necessary and sufficient conditions for completeness of the sampled wavelet transform when the lowpass filter associated with the dyadic wavelet filter bank has no unit circle zeros other than those at z 1 we present necessary but not sufficient conditions for completeness when the lowpass filter associated with the dyadic wavelet filter bank has arbitrary unit circle zeros we also provide necessary and sufficient conditions for completeness of a set of samples of both the lowpass approximation to the signal and its wavelet transform all the conditions we derive use only information about the location of the retained samples and the analyzing wavelet filter bank they can easily be checked without explicitly computing of the rank of a matrix finally we present a simple signal reconstruction procedure that can be used once we have determined the arbitrarily sampled discrete time wavelet transform is complete

extraction of shift invariant wavelet features for classification of images with different sizes an effective shift invariant wavelet feature extraction method for classification of images with different sizes is proposed the feature extraction process involves a normalization followed by an adaptive shift invariant wavelet packet transform an energy signature is computed for each subband of these invariant wavelet coefficients a reduced subset of energy signatures is selected as the feature vector for classification of images with different sizes experimental results show that the proposed method can achieve high classification accuracy of 98 5 percent and outperforms the other two image classification methods

principal component filter banks for optimal multiresolution analysis an important issue in multiresolution analysis is that of optimal basis selection an optimal p band perfect reconstruction filter bank prfb is derived in this paper which minimizes the approximation error in the mean square sense between the original signal and its low resolution version the resulting prfb decomposes the input signal into uncorrelated low resolution principal components with decreasing variance optimality issues are further analyzed in the special case of stationary and cyclostationary processes by exploiting the connection between discrete time filter banks and continuous wavelets an optimal multiresolution decomposition of l sub 2 r is obtained analogous results are also derived for deterministic signals some illustrative examples and simulations are presented

on the spectrum of markov semigroups via sample path large deviations the essential spectral radius of a sub markovian process is defined as the infimum of the spectral radiuses of all local perturbations of the process when the family of rescaled processes satisfies sample path large deviation principle the spectral radius and the essential spectral radius are expressed in terms of the rate function the paper is motivated by applications to reflected diffusions and jump markov processes describing stochastic networks for which the sample path large deviation principle has been established and the rate function has been identified while essential spectral radius has not been calculated

oblique derivative boundary conditions and the image method the image method of solving boundary value problems is extended to oblique derivative boundary conditions on plane boundaries for a class of equations including the wave equation the heat equation and laplace s equation this generalizes the recent result of gilbarg and trudinger elliptic partial differential equations of second order springer verlag berlin 1977 for laplace s equation the usefulness of the method is illustrated by solving with it both the wave equation and the heat equation in a half space with an initial point source and an oblique derivative boundary condition in both cases a surface wave is found for the wave equation there is a region near the boundary where the surface wave is the first arrival for the heat equation the surface wave is the largest wave in this region for small values of the time

brownian motion reflected on brownian motion we study brownian motion reflected on an independent brownian path we prove results on the joint distribution of both processes and the support of the parabolic measure in the space time domain bounded by a brownian path we show that there exist two different natural local times for a brownian path reflected on a brownian path

construction and decomposition of reflecting diffusions on lipschitz domains with holder cusps we consider a d dimensional euclidean domain d whose boundary is lipschitz continuous but admits locally finite number of outward or inward holder cusp points using a method of stampacchia and moser for pde we first construct a conservative diffusion process on the euclidean closure of d possessing a strong feller resolvent and associated with a second order uniformly elliptic differential operator of divergence form with measurable coefficients a ij the sample path of the constructed diffusion can be uniquely decomposed as a sum of a martingale additive functional and an additive functional locally of zero energy the second additive functional will be proved to be of bounded variation with a skorohod type expression whenever a ij is weakly differentiable and the holder exponent at each outward cusp boundary point is greater than 1 2 regardless the dimension d

a dyadic wavelet affine invariant function for 2d shape recognition dyadic wavelet transform has been used to derive an affine invariant function first an invariant function using two dyadic levels is derived then this invariant function is used to derive another invariant function using six dyadic levels we introduce the wavelet based conic equation the invariant function is based on analyzing the object boundary using the dyadic wavelet transform experimental results on both synthetic and real data are used to demonstrate the discriminating power of the proposed invariant function it has also been compared with some traditional methods the stability of the proposed invariant function is examined in addition the stability under large perspective transformation is tested

the skorohod oblique reflection problem in domains with corners and application to stochastic differential equations the skorohod oblique reflection problem for d w d a general domain in d x x d a convex cone of directions of reflection w a function ind d is considered it is first proved under a condition on d corresponding to x not being simultaneously too large and too much skewed with respect to d that given a sequence wn of functions converging in the skorohod topology tow any sequence xn n of solutions to the skorohod problem for d wn is relatively compact and any of its limit points is a solution to the skorohod problem for d w next it is shown that if d satisfies the uniform exterior sphere condition and another requirement then solutions to the skorohod problem for d w exist for everyw d d with small enough jump size the requirement is met in the case when d is piecewisecb1 is generated by continuous vector fields on the faces ofd and x makes and angle in a suitable sense of less than 2 with the cone of inward normals atd for everyx d existence of obliquely reflecting brownian motion and of weak solutions to stochastic differential equations with oblique reflection boundary conditions is derived

topological structure of fuzzy soft sets in this paper the concept of fuzzy soft topology is introduced and some of its structural properties such as neighborhood of a fuzzy soft set interior fuzzy soft set fuzzy soft basis fuzzy soft subspace topology are studied

optimal filter banks for signal reconstruction from noisy subband components conventional design techniques for analysis and synthesis filters in subband processing applications guarantee perfect reconstruction of the original signal from its subband components the resulting filters however lose their optimality when additive noise due for example to signal quantization disturbs the subband sequences we propose filter design techniques that minimize the reconstruction mean squared error mse taking into account the second order statistics of signals and noise in the case of either stochastic or deterministic signals a novel recursive pseudo adaptive algorithm is proposed for efficient design of these filters analysis and derivations are extended to 2 d signals and filters using powerful kronecker product notation a prototype application of the proposed ideas in subband coding is presented simulations illustrate the superior performance of the proposed filter banks versus conventional perfect reconstruction filters in the presence of additive subband noise

multidimensional mapping based complex wavelet transforms although the discrete wavelet transform dwt is a powerful tool for signal and image processing it has three serious disadvantages shift sensitivity poor directionality and lack of phase information to overcome these disadvantages we introduce multidimensional mapping based complex wavelet transforms that consist of a mapping onto a complex function space followed by a dwt of the complex mapping unlike other popular transforms that also mitigate dwt shortcomings the decoupled implementation of our transforms has two important advantages first the controllable redundancy of the mapping stage offers a balance between degree of shift sensitivity and transform redundancy this allows us to create a directional nonredundant complex wavelet transform with potential benefits for image coding systems to the best of our knowledge no other complex wavelet transform is simultaneously directional and nonredundant the second advantage of our approach is the flexibility to use any dwt in the transform implementation as an example we exploit this flexibility to create the complex double density dwt a shift insensitive directional complex wavelet transform with a low redundancy of 3 sup m 1 2 sup m 1 in m dimensions no other transform achieves all these properties at a lower redundancy to the best of our knowledge by exploiting the advantages of our multidimensional mapping based complex wavelet transforms in seismic signal processing applications we have demonstrated state of the art results

denoising by singularity detection a new algorithm for noise reduction using the wavelet transform is proposed similar to mallat s 1992 wavelet transform modulus maxima denoising approach we estimate the regularity of a signal from the evolution of its wavelet transform coefficients across scales however we do not perform maxima detection and processing therefore complicated reconstruction is avoided instead the local regularities of a signal are estimated by computing the sum of the modulus of its wavelet coefficients inside the corresponding cone of influence and the coefficients that correspond to the regular part of the signal for reconstruction are selected the algorithm gives an improved denoising result as compared with the previous approaches in terms of mean squared error and visual quality the new denoising algorithm is also invariant to translation it does not introduce spurious oscillations and requires very little a priori information of the signal or noise besides we extend the method to two dimensions to estimate the regularity of an image by computing the sum of the modulus of its wavelet coefficients inside the so called directional cone of influence the denoising technique is applied to tomographic image reconstruction where the improved performance of the new approach can clearly be observed

a stochastic differential game in the orthrant we study a zero sum stochastic differential game in the nonnegative orthrant the state of the system is governed by controlled reflecting diffusions in the nonnegative orthrant we consider discounted and average payoff evaluation criteria we prove the existence of values and optimal strategies for both payoff criteria

reflected brownian motion with skew symmetric data in a polyhedral domain this paper is concerned with the characterization and invariant measures of certain reflected brownian motions rbm s in polyhedral domains the kind of rbm studied here behaves like d dimensional brownian motion with constant drift in the interior of a simple polyhedron and is instantaneously reflected at the boundary in directions that depend on the face that is hit under the assumption that the directions of reflection satisfy a certain skew symmetry condition first introduced in harrison williams 9 it is shown that such an rbm can be characterized in terms of a family of submartingales and that it reaches non smooth parts of the boundary with probability zero in 9 a purely analytic problem associated with such an rbm was solved here the exponential form solution obtained in 9 is shown to be the density of an invariant measure for the rbm furthermore if the density is integrable over the polyhedral state space then it yields the unique stationary distribution for the rbm in the proofs of these results a key role is played by a dual process for the rbm and by results in 9 for reflected brownian motions on smooth approximating domains

reflecting brownian motion in a cusp let c be the cusp x y x 0 x y x where 1 set c 1 x y x 0 y x and c 2 x y x 0 y x we study the existence and uniqueness in law of reflecting brownian motion in c the angle of reflection at c j 0 relative to the inward unit normal is a constant j 2 2 and is positive iff the direction of reflection has a negative first component in all sufficiently small neighborhoods of 0 when 1 2 0 existence and uniqueness in law hold when 1 2 0 existence fails we also obtain results for a large class of asymmetric cusps we make essential use of results of warschawski on the differentiability at the boundary of conformal maps

improved transient signal detection using a wavepacket based detector with an extended translation invariant wavelet transform this paper presents the theory of m band extended translation invariant eti wavelet transforms the eti generalizes the translation invariant wavelet transform of weiss 1933 it is shown that iteration of the eti in a tree structure provides a signal decomposition into an orthonormal wavepacket basis other properties such as translation invariance and invertibility of the transform are proven the theory is then applied to transient signal detection through development of a family of translation invariant wavepacket based detectors this family of detectors provides improved the performance over previously defined wavepacket based detectors a performance analysis is conducted roc curves generated by monte carlo simulation are presented indicating the detector performance the detector performance is demonstrated to be independent of the signal translation

conformal mapping solution of laplace s equation on a polygon with oblique derivative boundary conditions we consider laplace s equation in a polygonal domain together with the boundary conditions that along each side the derivative in the direction at a specified oblique angle from the normal should be zero first we prove that solutions to this problem can always be constructed by taking the real part of an analytic function that maps the domain onto another region with straight sides oriented according to the angles given in the boundary conditions then we show that this procedure can be carried out successfully in practice by the numerical calculation of schwarz christoffel transformations the method is illustrated by application to a hall effect problem in electronics and to a reflected brownian motion problem motivated by queueing theory

on the diffusion approximation to a fork and join queueing model the use of singular perturbation methods to obtain approximate analytic solutions to the types of diffusion equations that are used to model queueing networks is shown as an example a two dimensional fork and join model is considered approximations to the stationary distribution of the number of customers in the system as well as the residual busy period are computed the formulas obtained clearly show the dependence of the solution on the variables and the parameters of the model

complex wavelet bases steerability and the marr like pyramid our aim in this paper is to tighten the link between wavelets some classical image processing operators and david marr s theory of early vision the cornerstone of our approach is a new complex wavelet basis that behaves like a smoothed version of the gradient laplace operator starting from first principles we show that a single generator wavelet can be defined analytically and that it yields a semi orthogonal complex basis of l 2 r2 irrespective of the dilation matrix used we also provide an efficient fft based filterbank implementation we then propose a slightly redundant version of the transform that is nearly translation invariant and that is optimized for better steerability gaussian like smoothing kernel we call it the marr like wavelet pyramid because it essentially replicates the processing steps in marr s theory of early vision we use it to derive a primal wavelet sketch which is a compact description of the image by a multiscale subsampled edge map finally we provide an efficient iterative algorithm for the reconstruction of an image from its primal wavelet sketch

signal recovery from wavelet transform maxima the paper presents an iterative algorithm for signal recovery from discrete time wavelet transform maxima the signal recovery algorithm is developed by using the method of projections onto convex sets convergence of the algorithm is assured

efficient design of orthonormal wavelet bases for signal representation the efficient representation of a signal as a linear combination of elementary atoms or building blocks is central to much signal processing theory and many applications wavelets provide a powerful flexible and efficiently implementable class of such atoms in this paper we develop an efficient method for selecting an orthonormal wavelet that is matched to a given signal in the sense that the squared error between the signal and some finite resolution wavelet representation of it is minimized since the squared error is not an explicit function of the design parameters some form of approximation of this objective is required if conventional optimization techniques are to be used previous approximations have resulted in nonconvex optimization problems which require delicate management of local minima in this paper we employ an approximation that results in a design problem that can be transformed into a convex optimization problem and efficiently solved constraints on the smoothness of the wavelet can be efficiently incorporated into the design we show that the error incurred in our approximation is bounded by a function that decays to zero as the number of vanishing moments of the wavelet grows in our examples we demonstrate that our method provides wavelet bases that yield substantially better performance than members of standard wavelet families and are competitive with those designed by more intricate nonconvex optimization methods

combination of interval valued fuzzy set and soft set the soft set theory proposed by molodtsov can be used as a general mathematical tool for dealing with uncertainty by combining the interval valued fuzzy set and soft set models the purpose of this paper is to introduce the concept of the interval valued fuzzy soft set the complement and and or operations are defined on the interval valued fuzzy soft sets the demorgan s associative and distribution laws of the interval valued fuzzy soft sets are then proved finally a decision problem is analyzed by the interval valued fuzzy soft set some numerical examples are employed to substantiate the conceptual arguments

an effective and fast iris recognition system based on a combined multiscale feature extraction technique the randomness of iris pattern makes it one of the most reliable biometric traits on the other hand the complex iris image structure and the various sources of intra class variations result in the difficulty of iris representation although a number of iris recognition methods have been proposed it has been found that several accurate iris recognition algorithms use multiscale techniques which provide a well suited representation for iris recognition in this paper and after a thorough analysis and summarization a multiscale edge detection approach has been employed as a pre processing step to efficiently localize the iris followed by a new feature extraction technique which is based on a combination of some multiscale feature extraction techniques this combination uses special gabor filters and wavelet maxima components finally a promising feature vector representation using moment invariants is proposed this has resulted in a compact and efficient feature vector in addition a fast matching scheme based on exclusive or operation to compute bits similarity is proposed where the result experimentation was carryout out using casia database the experimental results have shown that the proposed system yields attractive performances and could be used for personal identification in an efficient and effective manner and comparable to the best iris recognition algorithm found in the current literature

shiftable multiscale transforms one of the major drawbacks of orthogonal wavelet transforms is their lack of translation invariance the content of wavelet subbands is unstable under translations of the input signal wavelet transforms are also unstable with respect to dilations of the input signal and in two dimensions rotations of the input signal the authors formalize these problems by defining a type of translation invariance called shiftability in the spatial domain shiftability corresponds to a lack of aliasing thus the conditions under which the property holds are specified by the sampling theorem shiftability may also be applied in the context of other domains particularly orientation and scale jointly shiftable transforms that are simultaneously shiftable in more than one domain are explored two examples of jointly shiftable transforms are designed and implemented a 1 d transform that is jointly shiftable in position and scale and a 2 d transform that is jointly shiftable in position and orientation the usefulness of these image representations for scale space analysis stereo disparity measurement and image enhancement is demonstrated

a translation invariant wavelet representation algorithm with applications we address the time varying problem of wavelet transforms and a new translation invariant wavelet representation algorithm is proposed using the algorithm introduced by beylkin see siam j numer anal vol 29 p 1716 1740 1992 we compute the wavelet transform for all the circular time shifts of a length n signal in o n log n operations the wavelet coefficients of the time shift with minimal cost are selected as the best representation of the signal using a binary tree search algorithm with an appropriate cost function we apply the translation invariant representation algorithm to a geoacoustic data compression application the results show that the new algorithm can reduce the distortion the squared error in our case substantially if the input signals are transients that are sensitive to time shifts

wavelet transforms for detecting microcalcifications in mammograms clusters of fine granular microcalcifications in mammograms may be an early sign of disease individual grains are difficult to detect and segment due to size and shape variability and because the background mammogram texture is typically inhomogeneous the authors develop a 2 stage method based on wavelet transforms for detecting and segmenting calcifications the first stage is based on an undecimated wavelet transform which is simply the conventional filter bank implementation without downsampling so that the low low ll low high lh high low hl and high high hh sub bands remain at full size detection takes place in hh and the combination lh hl four octaves are computed with 2 inter octave voices for finer scale resolution by appropriate selection of the wavelet basis the detection of microcalcifications in the relevant size range can be nearly optimized in fact the filters which transform the input image into hh and lh hl are closely related to prewhitening matched filters for detecting gaussian objects idealized microcalcifications in 2 common forms of markov background noise the second stage is designed to overcome the limitations of the simplistic gaussian assumption and provides an accurate segmentation of calcification boundaries detected pixel sites in hh and lh hl are dilated then weighted before computing the inverse wavelet transform individual microcalcifications are greatly enhanced in the output image to the point where straightforward thresholding can be applied to segment them frog curves are computed from tests using a freely distributed database of digitized mammograms

reflected brownian motion on an orthant we consider a k dimensional diffusion process z whose state space is the nonnegative orthant on the interior of the orthant z behaves like a kdimensional brownian motion with arbitrary covariance matrix and drift vector at each of the k 1 dimensional hyperplanes that form the boundary of the orthant z reflects instantaneously in a direction that is constant over that hyperplane there is no extant theory of multidimensional diffusion that applies to this process because the boundary of its state space is not smooth we adopt an approach that requires a restriction on the directions of reflection but reiman has shown that this restriction is met by all diffusions z arising as heavy traffic limits in open k station queuing networks our process z is defined as a path to path mapping of k dimensional brownian motion from this construction it follows that z is a continuous markov process and a semimartingale using the latter property we obtain a change of variable formula from which one can develop a complete analytical theory for the process z

brownian motion with polar drift on cherche a approfondir la connaissance du comportement des diffusions multidimensionnelles pres des points singuliers

image restoration by the method of convex projections part 1ߞtheory a projection operator onto a closed convex set in hilbert space is one of the few examples of a nonlinear map that can be defined in simple abstract terms moreover it minimizes distance and is nonexpansive and therefore shares two of the more important properties of ordinary linear orthogonal projections onto closed linear manifolds in this paper we exploit the properties of these operators to develop several iterative algorithms for image restoration from partial data which permit any number of nonlinear constraints of a certain type to be subsumed automatically their common conceptual basis is as follows every known property of an original image f is envisaged as restricting it to lie in a well defined closed convex set thus m such properties place f in the intersection e0 ei of the corresponding closed convex sets e1 e2 em given only the projection operators pi onto the individual ei s i 1 m we restore f by recursive means clearly in this approach the realization of the pi s in a hilbert space setting is one of the major synthesis problems section i describes the geometrical significance of the three main theorems in considerable detail and most of the underlying ideas are illustrated with the aid of simple diagrams section ii presents rules for the numerical implementation of 11 specific projection operators which are found to occur frequently in many signal processing applications and the appendix contains proofs of all the major results

reconstruction of finite signal derivatives from multiscale extrema representations application to transient estimation and signal approximation in this correspondence we propose a novel approach to the reconstruction of finite signal derivatives from the extrema of a multiscale representation first introduced by berkner we show that this reconstruction procedure naturally leads to the definition of a signal characteristic scale we also focus on signal approximation from the multiscale extrema representation of one of its derivatives numerical applications involve the use of the signal characteristic scale for transient estimation and also the study of the new signal approximation method we propose

reflected brownian motion in a cone semimartingale property in this paper the object of study is reflected brownian motion in a cone ind dimensions d 3 with nonconstant oblique reflection on each radial line emanating from the vertex of the cone the basic question considered here is when is this process a semimartingale conditions for the existence and uniqueness of the process for which the vertex is an instantaneous state were given by kwon which is resolved in terms of a real parameter depending on the cone and the direction of reflection it is shown that starting from any point of the cone the process is a semimartingale if 1 0 and not a semimartingale if 2

the submartingal problem for brownian motion in a cone with non constant oblique reflection this work is concerned with the existence and uniqueness of a strong markov process that has continuous sample paths and the following additional properties 1 the state space is a cone ind dimensions d 3 and the process behaves in the interior of the cone like ordinary brownian motion 2 the process reflects instantaneously at the boundary of the cone the direction of reflection is continuous except at the vertex and has a limit which is fixed on each radial line emanating from the vertex 3 the amount of time that the process spends at the vertex of the cone is zero i e the set of times for which the process is at the vertex has zero lebesgue measure

the wavelet transform time frequency localization and signal analysis two different procedures for effecting a frequency analysis of a time dependent signal locally in time are studied the first procedure is the short time or windowed fourier transform the second is the wavelet transform in which high frequency components are studied with sharper time resolution than low frequency components the similarities and the differences between these two methods are discussed for both schemes a detailed study is made of the reconstruction method and its stability as a function of the chosen time frequency density finally the notion of time frequency localization is made precise within this framework by two localization theorems

a new framework for reconstruction of images from boundaries the problem of reconstructing images from boundaries has been studied in the literature chiefly as one based on the information from zero crossings in contrast we formulate the problem within the framework of approximation theory and we propose a representation scheme involving i the points arbitrarily near the boundaries and ii the gradient information at these points we show that the representation scheme is complete and stable under reasonable conditions further we develop an efficient reconstruction mechanism using the concept of a regularized solution in which we penalize a candidate solution in proportion to its departure from a model which resembles the original in shape but is simple to construct finally we demonstrate the effectiveness of the cost functional with the help of experimental results using a representation in which the number of data points is much less than the number of pixels in the original image

brownian motion in a wedge with variable skew reflection does planar brownian motion confined to a wedge by skew reflection on the sides approach the vertex of the wedge this question has been answered by varadhan and williams in the case where the direction of reflection is constant on each of the sides but here we address the question when the direction reflected is allowed to vary a necessary condition and a sufficient condition are obtained for the vertex to be reached the conditions are of a geometric nature and the gap between them is quite small

two different approaches for iris recognition using gabor filters and multiscale zero crossing representation abstract importance of biometric user identification is increasing everyday one of the most promising techniques is the one based on the human iris the authors in this work describe different approaches to develop this biometric technique based on the works carried out by daugman the authors have worked using gabor filters and hamming distance but in addition they have also worked in zero crossing representation of the dyadic wavelet transform applied to two different iris signatures one based on a single virtual circle of the iris the other one based on an annular region also other metrics have been applied to be compared with the results obtained with the hamming distance in this work euclidean distance and d z will be shown the last proposed approach is translation rotation and scale invariant results will show a classification success up to 99 6 achieving an equal error rate down to 0 12 and the possibility of having null false acceptance rates with very low false rejection rates

wavelet based affine invariant representation a tool for recognizing planar objects in 3d space a technique is developed to construct a representation of planar objects undergoing a general affine transformation the representation can be used to describe planar or nearly planar objects in a three dimensional space observed by a camera under arbitrary orientations the technique is based upon object contours parameterized by an affine invariant parameter and the dyadic wavelet transform the role of the wavelet transform is the extraction of multiresolution affine invariant features from the affine invariant contour representation a dissimilarity function is also developed and used to distinguish among different object representations this function makes use of the extrema on the representations thus making its computation very efficient a study of the effect of using different wavelet functions and their order or vanishing moments is also carried out experimental results show that the performance of the proposed representation is better than that of other existing methods particularly when objects are heavily corrupted with noise

on the semimartingale representation of reflecting brownian motion in a cusp letc be the symmetric cusp x y 2 x y x x 0 where 1 in this paper we decide whether or not reflecting brownian motion inc has a semimartingale representation here the reflecting brownian motion has directions of reflection that make constant angles with the unit inward normals to the boundary our results carry through for a wide class of asymmetric cusps too

probabilistic computation of poiseuille flow velocity fields velocity fields for poiseuille flow through tubes having general cross section are calculated using a path integral method involving the first passage times of random walks in the interior of the cross sectional domain d of the pipe this method is applied to a number of examples where exact results are available and to more complicated geometries of practical interest these examples include a tube with fractal cross section and open channel flows the calculations demonstrate the feasibility of the probabilistic method for pipe flow and other applications having an equivalent mathematical description e g torsional rigidity of rods membrane deflection the example of flow through a fractal pipe shows an extended region of diminished flow velocity near the rough boundary which is similar to the suppressed vibration observed near the boundaries of fractal drums

a multidimensional process involving local time on presente une approche probabiliste a un probleme pose par mckean 1967 pour la construction d un systeme de n particules sur r avec un generateur formel

a new framework for complex wavelet transforms although the discrete wavelet transform dwt is a powerful tool for signal and image processing it has three serious disadvantages shift sensitivity poor directionality and lack of phase information to overcome these disadvantages we introduce two stage mapping based complex wavelet transforms that consist of a mapping onto a complex function space followed by a dwt of the complex mapping unlike other popular transforms that also mitigate dwt shortcomings the decoupled implementation of our transforms has two important advantages first the controllable redundancy of the mapping stage offers a balance between degree of shift sensitivity and transform redundancy this allows us to create a directional non redundant complex wavelet transform with potential benefits for image coding systems to the best of our knowledge no other complex wavelet transform is simultaneously directional and non redundant the second advantage of our approach is the flexibility to use any dwt in the transform implementation as an example we can exploit this flexibility to create the complex double density dwt cddwt a shift insensitive directional complex wavelet transform with a low redundancy of 3 sup m 1 2 sup m 1 in m dimensions to the best of our knowledge no other transform achieves all these properties at a lower redundancy

portfolio selection with transaction costs in this paper optimal consumption and investment decisions are studied for an investor who has available a bank account paying a fixed rate of interest and a stock whose price is a log normal diffusion this problem was solved by merton and others when transactions between bank and stock are costless here we suppose that there are charges on all transactions equal to a fixed percentage of the amount transacted it is shown that the optimal buying and selling policies are the local times of the two dimensional process of bank and stock holdings at the boundaries of a wedge shaped region which is determined by the solution of a nonlinear free boundary problem an algorithm for solving the free boundary problem is given

geometric properties of 2 dimensional brownian paths let a be the set of all points of the plane visited by 2 dimensional brownian motion before time 1 with probability 1 all points of a are twist points except a set of harmonic measure zero twist points may be continuously approached in a only along a special spiral although negligible in the sense of harmonic measure various classes of cone points are dense in a with probability 1 cone points may be approached in a within suitable wedges

properties of the multiscale maxima and zero crossings representations the analysis of a discrete multiscale edge representation is considered a general signal description called an inherently bounded adaptive quasi linear representation aqlr motivated by two important examples namely the wavelet maxima representation and the wavelet zero crossings representation is introduced this paper mainly addresses the questions of uniqueness and stability it is shown that the dyadic wavelet maxima zero crossings representation is in general nonunique nevertheless using the idea of the inherently bounded aqlr two stability results are proven for a general perturbation a global bibo stability is shown for a special case where perturbations are limited to the continuous part of the representation a lipschitz condition is satisfied

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed