the shiftable complex directional pyramid part i theoretical aspects this paper presents an over complete multiscale decomposition by combining the laplacian pyramid and the complex directional filter bank dfb the filter bank is constructed in such a way that each complex directional filter is analytical using the dual tree structure of real fan filters necessary and sufficient conditions in order for the resulting multirate filter bank to be shift invariant in energy sense shiftability are derived in terms of the magnitude and phase responses of these filters their connection to 2d hilbert transform relationship is established the proposed transform possesses several desirable properties including multiresolution arbitrarily high directional resolution low redundant ratio and efficient implementation

moving least squares particle hydrodynamics i consistency and stability the smooth particle hydrodynamics sph method is derived in a novel manner by means of a galerkin approximation applied to the lagrangian equations of continuum mechanics as in the finite element method this derivation is modified to replace the sph interpolant with the moving least squares mls interpolant of lancaster and saulkaskas and define a new particle volume which ensures thermodynamic compatibility a variable rank modification of the mls interpolants which retains their desirable summation properties is introduced to remove the singularities that occur when divergent flow reduces the number of neighbours of a particle to less than the minimum required a surprise benefit of the galerkin sph derivation is a theoretical justification of a common ad hoc technique for variable h sph the new mlsph method is conservative if an anti symmetric quadrature rule for the stiffness matrix elements can be supplied in this paper a simple one point collocation rule is used to retain similarity with sph leading to a non conservative method several examples document how mlsph renders dramatic improvements due to the linear consistency of its gradients on three canonical difficulties of the sph method spurious boundary effects erroneous rates of strain and rotation and tension instability two of these examples are non linear lagrangian patch tests with analytic solutions with which mlsph agrees almost exactly the examples also show that mlsph is not absolutely stable if the problems are run to very long times a linear stability analysis explains both why it is more stable than sph and not yet absolutely stable and an argument is made that for realistic dynamic problems mlsph is stable enough the notion of coherent particles for which the numerical stability is identical to the physical stability is introduced the new method is easily retrofitted into a generic sph code and some observations on performance are made copyright 1999 john wiley sons ltd

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

the design of approximate hilbert transform pairs of wavelet bases several authors have demonstrated that significant improvements can be obtained in wavelet based signal processing by utilizing a pair of wavelet transforms where the wavelets form a hilbert transform pair this paper describes design procedures based on spectral factorization for the design of pairs of dyadic wavelet bases where the two wavelets form an approximate hilbert transform pair both orthogonal and biorthogonal fir solutions are presented as well as iir solutions in each case the solution depends on an allpass filter having a flat delay response the design procedure allows for an arbitrary number of vanishing wavelet moments to be specified a matlab program for the procedure is given and examples are also given to illustrate the results

a filter bank for the directional decomposition of images theory and design the authors introduce a directionally oriented 2 d filter bank with the property that the individual channels may be critically sampled without loss of information the passband regions of the component filters are wedge shaped and thus provide directional information it is shown that these filter bank outputs may be maximally decimated to achieve a minimum sample representation in a way that permits the original signal to be exactly reconstructed the authors discuss the theory for directional decomposition and reconstruction in addition implementation issues are addressed where realizations based on both recursive and nonrecursive filters are considered

on the representation of operators in bases of compactly supported wavelets this paper describes exact and explicit representations of the differential operators d n dx n n 1 2 cdots in orthonormal bases of compactly supported wavelets as well as the representations of the hilbert transform and fractional derivatives the method of computing these representations is directly applicable to multidimensional convolution operators also sparse representations of shift operators in orthonormal bases of compactly supported wavelets are discussed and a fast algorithm requiring o n log n operations for computing the wavelet coefficients of all n circulant shifts of a vector of the length n 2 n is constructed as an example of an application of this algorithm it is shown that the storage requirements of the fast algorithm for applying the standard form of a pseudodifferential operator to a vector see g beylkin r r coifman and v rokhlin comm pure appl math 44 1991 pp 141 183 may be reduced from o n to o log 2 n significant entries

analysis synthesis techniques for subband image coding analysis synthesis systems designed for low bit rate image coding their impact on overall system quality and their computational complexity are discussed the investigation focuses on the design of analysis synthesis systems for image coding and the perceptual impact of these systems at low bit rates two objectives are emphasized in developing these systems confining the total size of the subband images to be equal to the original image size and designing the filters so that perceptual distortion is not introduced by the analysis synthesis system methods based on circular convolution and symmetric extensions are developed and discussed in detail the theory design and implementation of both recursive and nonrecursive filtering systems are discussed methods are introduced which display advantages over conventional quadrature mirror filter based approaches

a new shift invariance of discrete time systems and its application to discrete wavelet transform analysis this work is motivated by the search for discrete wavelet transform dwt with near shift invariance after examining the elements of the property we introduce a new notion of shift invariance which is particularly informative for multirate systems that are not shift invariant in the strict sense briefly speaking a discrete time system is mu shift invariant if a shift in input results in the output being shifted as well however the amount of the shift in output is not necessarily identical to that in input a fractional shift is also acceptable and can be properly specified in the fourier domain the mu shift invariance can be interpreted as invariance of magnitude spectrum with linear phase offset of output with respect to shift in input it is stronger than the shiftability in position which is equivalent to insensitivity of energy to shift in input under this generalized notion the expander is always mu shift invariant the m fold decimator is mu shift invariant for input with width of frequency support not more than 2pi m equivalently the output contains no aliasing term in some frequency band with length of 2pi we generalize the transfer function description of linear shift invariant systems for mu shift invariant systems we then perform mu shift invariance analysis of 2 band orthogonal dwt and of the 2 band dual tree complex wavelet transform dt cwt the analysis in each case provides clarifications to early understanding of near shift invariance we show that the dwt is mu shift invariant if and only if the conjugate quadrature filter cqf is analytic or antianalytic for the dt cwt the cqfs must have supports included within 2pi 3 2pi 3 in addition to the well know half sample delay condition at higher levels and the one sample delay condition at the first level

variational and momentum preservation aspects of smooth particle hydrodynamic formulations this paper presents a new variational framework for various existing smooth particle hydrodynamic sph techniques and presents a new corrected sph formulation the linear and angular momentum preserving properties of sph formulations are also discussed the paper will show that in general in order to preserve angular momentum the sph equations must correctly evaluate the gradient of a linear velocity field a corrected algorithm that combines kernel correction with gradient correction is presented the paper will illustrate the theory presented with several examples relating to simple free surface flows

sph simulations of time dependent poiseuille flow at low reynolds numbers a working smoothed particle hydrodynamics sph formalism for solving the equations of motion of a viscous fluid is presented the method is based on a standard symmetrized sph expression for the viscous forces which involves only first order derivatives of the kernel through a direct evaluation of the viscous stress tensor therefore the interpolation can be performed using low order kernels of compact support without compromising the accuracy and stability of the results in principle the scheme is suitable for treating compressible fluids with arbitrary shear and bulk viscosities here we demonstrate that when it is combined with the pressure gradient correction proposed by morris et al the method is also suitable for solving the navier stokes equations for incompressible flows without any further assumptions simulations using the method show close agreement with the analytic series solutions for plane poiseuille and hagen poiseuille flows at very low reynolds numbers at least for these specific tests the results obtained are essentially independent of employing either a cubic or a quintic spline kernel

mild solutions of functional semilinear evolution volterra integrodifferential equations on an unbounded interval abstract in this paper we study the existence of mild solutions for initial value problems for semilinear volterra integrodifferential equations in a banach space the arguments are based on the concept of measure of noncompactness in frechet space and the tikhonov fixed point theorem

development of a finite volume particle method for 3 d fluid flow simulations the finite volume particle method fvpm is a meshless method for simulating fluid flows which includes many of the desirable features of mesh based finite volume methods fvpm benefits from particle interaction vectors to weight conservative fluxes exchanged between particles these vectors are equivalent to the intercell area vectors in mesh based finite volume methods to compute the interaction vectors either numerical or exact integration has been used numerical integration based on quadrature rules is approximate and costly whereas the exact method employing a top hat kernel is precise and fast to date quadrature integration has not been used in 3 d due to its excessive cost and the exact method has been developed only for 2 d computations in this study we develop a new 3 d fvpm formulation which features a rectangular top hat kernel to compute interaction vectors exactly and efficiently we also introduce a new boundary condition enforcement technique based on a single layer of boundary particles in this technique no slip wall boundary conditions with complex geometries are precisely enforced by overlaying a layer of particles on wall surfaces employing ausm for inviscid fluxes weakly compressible fluid flow is studied with the proposed method to achieve more accurate results the solution can be refined near the wall boundary by splitting the fluid particles this formulation is validated for lid driven cavity flow a moving square and jet impingement test cases

an extended validation of the last generation of particle finite element method for free surface flows in this paper a new generation of the particle method known as particle finite element method pfem which combines convective particle movement and a fixed mesh resolution is applied to free surface flows this interesting variant previously described in the literature as pfem 2 is able to use larger time steps when compared to other similar numerical tools which implies shorter computational times while maintaining the accuracy of the computation pfem 2 has already been extended to free surface problems being the main topic of this paper a deep validation of this methodology for a wider range of flows to accomplish this task different improved versions of discontinuous and continuous enriched basis functions for the pressure field have been developed to capture the free surface dynamics without artificial diffusion or undesired numerical effects when different density ratios are involved a collection of problems has been carefully selected such that a wide variety of froude numbers density ratios and dominant dissipative cases are reported with the intention of presenting a general methodology not restricted to a particular range of parameters and capable of using large time steps the results of the different free surface problems solved which include rayleigh taylor instability sloshing problems viscous standing waves and the dam break problem are compared to well validated numerical alternatives or experimental measurements obtaining accurate approximations for such complex flows

high re solutions for incompressible flow using the navier stokes equations and a multigrid method the vorticity stream function formulation of the two dimensional incompressible navierstokes equations is used to study the effectiveness of the coupled strongly implicit multigrid csi mg method in the determination of high re fine mesh flow solutions the driven flow in a square cavity is used as the model problem solutions are obtained for configurations with reynolds number as high as 10 000 and meshes consisting of as many as 257 x 257 points for re 1000 the 129 x 129 grid solution required 1 5 minutes of cpu time on the amdahl 470 v 6 computer because of the appearance of one or more secondary vortices in the flow field uniform mesh refinement was preferred to the use of one dimensional gridclustering coordinate transformations the past decade has witnessed a great deal of progress in the area of computational fluid dynamics developments in computer technology hardware as well as in advanced numerical algorithms have enabled attempts to be made towards analysis and numerical solution of highly complex flow problems for some of these applications the use of simple iterative techniques to solve the navier stokes equations leads to a rather slow convergence rate for the solutions the solution convergence rate can be seriously affected if the coupling among the various governing differential equations is not properly honored either in the interior of the solution domain or at its boundaries the rate of convergence is also generally strongly dependent on such problem parameters as the reynolds number the mesh size and the total number of computational points this has led several researchers to examine carefully the recently emerging multigrid mg technique as a useful means for enhancing the convergence rate of iterative numerical methods for solving discretized equations at a number of computational grid points so large as to be considered impractical previously

simulating free surface flows with sph the sph smoothed particle hydrodynamics method is extended to deal with free surface incompressible flows the method is easy to use and examples will be given of its application to a breaking dam a bore the simulation of a wave maker and the propagation of waves towards a beach arbitrary moving boundaries can be included by modelling the boundaries by particles which repel the fluid particles the method is explicit and the time steps are therefore much shorter than required by other less flexible methods but it is robust and easy to program

adaptive directional lifting based wavelet transform for image coding we present a novel 2 d wavelet transform scheme of adaptive directional lifting adl in image coding instead of alternately applying horizontal and vertical lifting as in present practice adl performs lifting based prediction in local windows in the direction of high pixel correlation hence it adapts far better to the image orientation features in local windows the adl transform is achieved by existing 1 d wavelets and is seamlessly integrated into the global wavelet transform the predicting and updating signals of adl can be derived even at the fractional pixel precision level to achieve high directional resolution while still maintaining perfect reconstruction to enhance the adl performance a rate distortion optimized directional segmentation scheme is also proposed to form and code a hierarchical image partition adapting to local features experimental results show that the proposed adl based image coding technique outperforms jpeg 2000 in both psnr and visual quality with the improvement up to 2 0 db on images with rich orientation features

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

a parametric texture model based on joint statistics of complex wavelet coefficients we present a universal statistical model for texture images in the context of an overcomplete complex wavelet transform the model is parameterized by a set of statistics computed on pairs of coefficients corresponding to basis functions at adjacent spatial locations orientations and scales we develop an efficient algorithm for synthesizing random images subject to these constraints by iteratively projecting onto the set of images satisfying each constraint and we use this to test the perceptual validity of the model in particular we demonstrate the necessity of subgroups of the parameter set by showing examples of texture synthesis that fail when those parameters are removed from the set we also demonstrate the power of our model by successfully synthesizing examples drawn from a diverse collection of artificial and natural textures

construction of hilbert transform pairs of wavelet bases and gabor like transforms we propose a novel method for constructing hilbert transform ht pairs of wavelet bases based on a fundamental approximation theoretic characterization of scaling functions the b spline factorization theorem in particular starting from well localized scaling functions we construct ht pairs of biorthogonal wavelet bases of l2 r by relating the corresponding wavelet filters via a discrete form of the continuous ht filter as a concrete application of this methodology we identify ht pairs of spline wavelets of a specific flavor which are then combined to realize a family of complex wavelets that resemble the optimally localized gabor function for sufficiently large orders analytic wavelets derived from the complexification of ht wavelet pairs exhibit a one sided spectrum based on the tensor product of such analytic wavelets and in effect by appropriately combining four separable biorthogonal wavelet bases of l2 r2 we then discuss a methodology for constructing 2 d directional selective complex wavelets in particular analogous to the ht correspondence between the components of the 1 d counterpart we relate the real and imaginary components of these complex wavelets using a multidimensional extension of the ht the directional ht next we construct a family of complex spline wavelets that resemble the directional gabor functions proposed by daugman finally we present an efficient fast fourier transform fft based filterbank algorithm for implementing the associated complex wavelet transform

extension of the finite volume particle method to viscous flow the finite volume particle method fvpm is a mesh free method for fluid dynamics which allows simple and accurate implementation of boundary conditions and retains the conservation and consistency properties of classical finite volume methods in this article the fvpm is extended to viscous flows using a consistency corrected smoothed particle hydrodynamics sph approximation to evaluate velocity gradients the accuracy of the viscous fvpm is improved by a higher order discretisation of the inviscid flux combined with a second order temporal discretisation the higher order inviscid fvpm is validated for a 1 d shock tube problem in which it demonstrates an enhanced shock capturing ability for two dimensional simulations a small arbitrary lagrange euler correction to fully lagrangian particle motion is beneficial in maintaining a favourable particle distribution over long simulation times the viscous fvpm is validated for two dimensional poiseuille taylor green and lid driven cavity flows and good agreement is achieved with analytic or reference numerical solutions these results establish the viability of fvpm as a tool for mesh free simulation of viscous flows in engineering

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

the monogenic wavelet transform this paper extends the 1 d analytic wavelet transform to the 2 d monogenic wavelet transform the transformation requires care in its specification to ensure suitable transform coefficients are calculated and it is constructed so that the wavelet transform may be considered as both local and monogenic this is consistent with defining the transform as a real wavelet transform of a monogenic signal in analogy with the analytic wavelet transform classes of monogenic wavelets are proposed with suitable local properties it is shown that the monogenic wavelet annihilates anti monogenic signals that the monogenic wavelet transform is phase shift covariant and that the transform magnitude is phase shift invariant a simple form for the magnitude and orientation of the isotropic transform coefficients of a unidirectional signal when observed in a rotated frame of reference is derived the monogenic wavelet ridges of local plane waves are given

an analysis of 1 d smoothed particle hydrodynamics kernels in this paper the smoothed particle hydrodynamics sph kernel is analyzed resulting in measures of merit for one dimensional sph various methods of obtaining an objective measure of the quality and accuracy of the sph kernel are addressed since the kernel is the key element in the sph methodology this should be of primary concern to any user of sph the results of this work are two measures of merit one for smooth data and one near shocks the measure of merit for smooth data is shown to be quite accurate and a useful delineator of better and poorer kernels the measure of merit for non smooth data is not quite as accurate but results indicate the kernel is much less important for these types of problems in addition to the theory 20 kernels are analyzed using the measure of merit demonstrating the general usefulness of the measure of merit and the individual kernels in general it was decided that bell shaped kernels perform better than other shapes

scaling functions robust to translations the discrete wavelet transform dwt is popular in a wide variety of applications its sparse sampling eliminates redundancy in the representation of signals and leads to efficient processing however the dwt lacks translation invariance this makes it ill suited for many problems where the received signal is the superposition of arbitrarily shifted replicas of a transmitted signal as when multipath occurs for example the paper develops algorithms for the design of orthogonal and biorthogonal compact support scaling functions that are robust to translations our approach is to maintain the critical sampling of the dwt while designing multiresolution representations for which the coefficient energy redistributes itself mostly within each subband and not across the entire time scale plane we obtain expedite algorithms by decoupling the optimization from the constraints on the scaling function examples illustrate that the designed scaling function significantly improves the robustness of the representation

the double density dual tree dwt this paper introduces the double density dual tree discrete wavelet transform dwt which is a dwt that combines the double density dwt and the dual tree dwt each of which has its own characteristics and advantages the transform corresponds to a new family of dyadic wavelet tight frames based on two scaling functions and four distinct wavelets one pair of the four wavelets are designed to be offset from the other pair of wavelets so that the integer translates of one wavelet pair fall midway between the integer translates of the other pair simultaneously one pair of wavelets are designed to be approximate hilbert transforms of the other pair of wavelets so that two complex approximately analytic wavelets can be formed therefore they can be used to implement complex and directional wavelet transforms the paper develops a design procedure to obtain finite impulse response fir filters that satisfy the numerous constraints imposed this design procedure employs a fractional delay allpass filter spectral factorization and filterbank completion the solutions have vanishing moments compact support a high degree of smoothness and are nearly shift invariant

a new class of two channel biorthogonal filter banks and wavelet bases proposes a novel framework for a new class of two channel biorthogonal filter banks the framework covers two useful subclasses i causal stable iir filter banks ii linear phase fir filter banks there exists a very efficient structurally perfect reconstruction implementation for such a class filter banks of high frequency selectivity can be achieved by using the proposed framework with low complexity the properties of such a class are discussed in detail the design of the analysis synthesis systems reduces to the design of a single transfer function very simple design methods are given both for fir and iir cases zeros of arbitrary multiplicity at aliasing frequency can be easily imposed for the purpose of generating wavelets with regularity property in the iir case two new classes of iir maximally flat filters different from butterworth filters are introduced the filter coefficients are given in closed form the wavelet bases corresponding to the biorthogonal systems are generated the authors also provide a novel mapping of the proposed 1 d framework into 2 d the mapping preserves the following i perfect reconstruction ii stability in the iir case iii linear phase in the fir case iv zeros at aliasing frequency v frequency characteristic of the filters

shift variance analysis of generalized sampling processes this paper is concerned with quantifying shift variance of linear systems with continuous time input and discrete time output we first introduce a notion of shift invariance for the system it specifies how the system should respond when the input signal is shifted for generalized sampling processes the property is characterized by the sampling kernel and is shown to be equivalent to lack of aliasing and to shiftability we then define a shift variance level which describes how far the system can be possibly away from the set of systems that are shift invariant the level is defined to be the maximum of the induced norms of the commutators of the system and the shift operators both continuous time or discrete time are necessarily involved a shift variance measure is then defined to be the ratio of the shift variance level to the system norm further divided by two so that the measure is between zero and unity for generalized sampling we obtain analytical formulas for the shift variance level and the shift variance measure the results allow us to analyze the shift variance of among others the discrete time wavelet transform dwt and the short time fourier transform stft we obtain a simple relation between the shift variance levels at all scales of the dwt and show that the shift variance measures are identical at all scales we calculate the shift variance level and the shift variance measure of some typical dwts and the stfts

orthonormal bases of compactly supported wavelets we construct orthonormal bases of compactly supported wavelets with arbitrarily high regularity the order of regularity increases linearly with the support width we start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction the construction then follows from a synthesis of these different approaches

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

noise reduction of cdna microarray images using complex wavelets noise reduction is an essential step of cdna microarray image analysis for obtaining better quality gene expression measurements wavelet based denoising methods have shown significant success in traditional image processing the complex wavelet transform cwt is preferred to the classical discrete wavelet transform for denoising of microarray images due to its improved directional selectivity for better representation of the circular edges of spots and near shift invariance property existing cwt based denoising methods are not efficient for microarray image processing because they fail to take into account the signal as well as noise correlations that exist between red and green channel images in this paper two bivariate estimators are developed for the cwt based denoising of microarray images using the standard maximum a posteriori and linear minimum mean squared error estimation criteria the proposed denoising methods are capable of taking into account both the interchannel signal and noise correlations significance of the proposed denoising methods is assessed by examining the effect of noise reduction on the estimation of the log intensity ratio extensive experimentations are carried out to show that the proposed methods provide better noise reduction of microarray images leading to more accurate estimation of the log intensity ratios as compared to the other cwt based denoising methods

wavelets and dilation equations a brief introduction wavelets are new families of basis functions that yield the representation f x sum b jk w 2 j x k their construction begins with the solution phi x to a dilation equation with coefficients c k then w comes from phi and the basis comes by translation and dilation of w it is shown in part 1 how conditions on the c k lead to approximation properties and orthogonality properties of the wavelets part 2 describes the recursive algorithms also based on the c k that decompose and reconstruct f the object of wavelets is to localize as far as possible in both time and frequency with efficient algorithms

incompressible moving boundary flows with the finite volume particle method abstract mesh free methods offer the potential for greatly simplified modeling of flow with moving walls and phase interfaces the finite volume particle method fvpm is a mesh free technique based on interparticle fluxes which are exactly analogous to intercell fluxes in the mesh based finite volume method consequently the method inherits many of the desirable properties of the classical finite volume method including implicit conservation and a natural introduction of boundary conditions via appropriate flux terms in this paper we describe the extension of fvpm to incompressible viscous flow with moving boundaries an arbitrary lagrangian eulerian approach is used in conjunction with the mesh free discretisation to facilitate a straightforward treatment of moving bodies non uniform particle distribution is used to concentrate computational effort in regions of high gradients the underlying method for viscous incompressible flow is validated for a lid driven cavity problem at reynolds numbers of 100 and 1000 to validate the simulation of moving boundaries flow around a translating cylinder at reynolds numbers of 20 40 and 100 is modeled results for pressure distribution surface forces and vortex shedding frequency are in good agreement with reference data from the literature and with fvpm results for an equivalent flow around a stationary cylinder these results establish the capability of fvpm to simulate large wall motions accurately in an entirely mesh free framework

the phaselet transform an integral redundancy nearly shift invariant wavelet transform this paper introduces an approximately shift invariant redundant dyadic wavelet transform the phaselet transform that includes the popular dual tree complex wavelet transform of kingsbury see phil r soc london a sept 1999 as a special case the main idea is to use a finite set of wavelets that are related to each other in a special way and hence called phaselets to achieve approximate shift redundancy the bigger the set the better the approximation a sufficient condition on the associated scaling filters to achieve this is that they are fractional shifts of each other algorithms for the design of phaselets with a fixed number vanishing moments is presented building on the work of selesnick see ieee trans signal processing for the design of wavelet pairs for kingsbury s dual tree complex wavelet transform construction of two dimensional 2 d directional bases from tensor products of one dimensional 1 d phaselets is also described phaselets as a new approach to redundant wavelet transforms and their construction are both novel and should be interesting to the reader independent of the approximate shift invariance property that this paper argues they possess

uniform discrete curvelet transform an implementation of the discrete curvelet transform is proposed in this work the transform is based on and has the same order of complexity as the fast fourier transform fft the discrete curvelet functions are defined by a parameterized family of smooth windowed functions that satisfies two conditions i 2 periodic ii their squares form a partition of unity the transform is named the uniform discrete curvelet transform udct because the centers of the curvelet functions at each resolution are positioned on a uniform lattice the forward and inverse transform form a tight and self dual frame in the sense that they are the exact transpose of each other generalization to m dimensional version of the udct is also presented the novel discrete transform has several advantages over existing transforms such as lower redundancy ratio hierarchical data structure and ease of implementation

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

a hybridized discontinuous galerkin framework for high order particle mesh operator splitting of the incompressible navier stokes equations abstract a generic particle mesh method using a hybridized discontinuous galerkin hdg framework is presented and validated for the solution of the incompressible navier stokes equations building upon particle in cell concepts the method is formulated in terms of an operator splitting technique in which lagrangian particles are used to discretize an advection operator and an eulerian mesh based hdg method is employed for the constitutive modeling to account for the inter particle interactions key to the method is the variational framework provided by the hdg method this allows to formulate the projections between the lagrangian particle space and the eulerian finite element space in terms of local i e cellwise l 2 projections efficiently furthermore exploiting the hdg framework for solving the constitutive equations results in velocity fields which excellently approach the incompressibility constraint in a local sense by advecting the particles through these velocity fields the particle distribution remains uniform over time obviating the need for additional quality control the presented methodology allows for a straightforward extension to arbitrary order spatial accuracy on general meshes a range of numerical examples shows that optimal convergence rates are obtained in space and given the particular time stepping strategy second order accuracy is obtained in time the model capabilities are further demonstrated by presenting results for the flow over a backward facing step and for the flow around a cylinder

modeling low reynolds number incompressible flows using sph the method of smoothed particle hydrodynamics sph is extended to model incompressible flows of low reynolds number for such flows modification of the standard sph formalism is required to minimize errors associated with the use of a quasi incompressible equation of state treatment of viscosity state equation kernel interpolation and boundary conditions are described simulations using the method show close agreement with series solutions for couette and poiseuille flows furthermore comparison with finite element solutions for flow past a regular lattice of cylinders shows close agreement for the velocity and pressure fields the sph results exhibit small pressure fluctuations near curved boundaries further improvements to the boundary conditions may be possible which will reduce these errors a similar method to that used here may permit the simulation of other flows at low reynolds numbers using sph further development will be needed for cases involving free surfaces or substantially different equations of state