mammographic feature enhancement by multiscale analysis introduces a novel approach for accomplishing mammographic feature analysis by overcomplete multiresolution representations the authors show that efficient representations may be identified within a continuum of scale space and used to enhance features of importance to mammography methods of contrast enhancement are described based on three overcomplete multiscale representations 1 the dyadic wavelet transform separable 2 the spl phi transform nonseparable nonorthogonal and 3 the hexagonal wavelet transform nonseparable multiscale edges identified within distinct levels of transform space provide local support for image enhancement mammograms are reconstructed from wavelet coefficients modified at one or more levels by local and global nonlinear operators in each case edges and gain parameters are identified adaptively by a measure of energy within each level of scale space the authors show quantitatively that transform coefficients modified by adaptive nonlinear operators can make more obvious unseen or barely seen features of mammography without requiring additional radiation the authors results are compared with traditional image enhancement techniques by measuring the local contrast of known mammographic features they demonstrate that features extracted from multiresolution representations can provide an adaptive mechanism for accomplishing local contrast enhancement by improving the visualization of breast pathology one can improve chances of early detection while requiring less time to evaluate mammograms for most patients

hex splines a novel spline family for hexagonal lattices this paper proposes a new family of bivariate nonseparable splines called hex splines especially designed for hexagonal lattices the starting point of the construction is the indicator function of the voronoi cell which is used to define in a natural way the first order hex spline higher order hex splines are obtained by successive convolutions a mathematical analysis of this new bivariate spline family is presented in particular we derive a closed form for a hex spline of arbitrary order we also discuss important properties such as their fourier transform and the fact they form a riesz basis we also highlight the approximation order for conventional rectangular lattices hex splines revert to classical separable tensor product b splines finally some prototypical applications and experimental results demonstrate the usefulness of hex splines for handling hexagonally sampled data

a wavelet or lifting scheme based imputation method summary the paper proposes a new approach to imputation using the expected sparse representation of a surface in a wavelet or lifting scheme basis our method incorporates a bayesian mixture prior for these wavelet coefficients into a gibbs sampler to generate a complete posterior distribution for the variable of interest intuitively the estimator operates by borrowing strength from those observed neighbouring values to impute at the unobserved sites we demonstrate the strong performance of our estimator in both one and two dimensional imputation problems where we also compare its application with the standard imputation techniques of kriging and thin plate splines

sub hexagonal phase correlation for motion estimation we present a novel frequency domain motion estimation technique which operates on hexagonal images and employs the hexagonal fourier transform our method involves image sampling on a hexagonal lattice followed by a normalised hexagonal cross correlation in the frequency domain the term subpixel or subcell is defined on a hexagonal grid in order to achieve floating point registration experiments using both artificially induced motion and actual motion demonstrate that the proposed method outperforms the state of the art in frequency domain motion estimation operating on a square lattice in the shape of phase correlation in terms of subpixel accuracy for a range of test material and motion scenarios

orthogonal and biorthogonal fir hexagonal filter banks with sixfold symmetry recently hexagonal image processing has attracted attention the hexagonal lattice has several advantages in comparison with the rectangular lattice the conventionally used lattice for image sampling and processing for example a hexagonal lattice needs less sampling points it has better consistent connectivity it has higher symmetry and its structure is plausible to human vision systems the multiresolution analysis method has been used for hexagonal image processing since the hexagonal lattice has high degree of symmetry it is desirable that the hexagonal filter banks designed for multiresolution hexagonal image processing also have high order of symmetry which is pertinent to the symmetry structure of the hexagonal lattice the orthogonal or prefect reconstruction pr hexagonal filter banks that are available in the literature have only threefold symmetry in this paper we investigate the construction of orthogonal and pr finite impulse response fir hexagonal filter banks with sixfold symmetry we obtain block structures of 7 size refinement seven channel two dimensional orthogonal and pr fir hexagonal filter banks with sixfold rotational symmetry radic7 refinement orthogonal and biorthogonal wavelets based on these block structures are constructed in this paper we also consider fir hexagonal filter banks with axial line symmetry and we present a block structure of fir hexagonal filter banks with pseudo sixfold axial symmetry

multiresolution moment filters theory and applications we introduce local weighted geometric moments that are computed from an image within a sliding window at multiple scales when the window function satisfies a two scale relation we prove that lower order moments can be computed efficiently at dyadic scales by using a multiresolution wavelet like algorithm we show that b splines are well suited window functions because in addition to being refinable they are positive symmetric separable and very nearly isotropic gaussian shape we present three applications of these multiscale local moments the first is a feature extraction method for detecting and characterizing elongated structures in images the second is a noise reduction method which can be viewed as a multiscale extension of savitzky golay filtering the third is a multiscale optical flow algorithm that uses a local affine model for the motion field extending the lucas kanade optical flow method the results obtained in all cases are promising

texture enhanced histogram equalization using tv rm l 1 image decomposition histogram transformation defines a class of image processing operations that are widely applied in the implementation of data normalization algorithms in this paper we present a new variational approach for image enhancement that is constructed to alleviate the intensity saturation effects that are introduced by standard contrast enhancement ce methods based on histogram equalization in this paper we initially apply total variation tv minimization with a l1 fidelity term to decompose the input image with respect to cartoon and texture components contrary to previous papers that rely solely on the information encompassed in the distribution of the intensity information in this paper the texture information is also employed to emphasize the contribution of the local textural features in the ce process this is achieved by implementing a nonlinear histogram warping ce strategy that is able to maximize the information content in the transformed image our experimental study addresses the ce of a wide variety of image data and comparative evaluations are provided to illustrate that our method produces better results than conventional ce strategies

letter to the editor on the conditions for the coincidence of two cubic bezier curves in a recent article wang et al 2 derive a necessary and sufficient condition for the coincidence of two cubic bezier curves with non collinear control points the condition reads that their control points must be either coincident or in reverse order we point out that this uniqueness of the control points for polynomial cubics is a straightforward consequence of a previous and more general result of barry and patterson namely the uniqueness of the control points for rational bezier curves moreover this uniqueness applies to properly parameterized polynomial curves of arbitrary degree

on techniques for detecting circumscribed masses in mammograms a method for detecting one type of breast tumor circumscribed masses in mammograms is presented it relies on a combination of criteria used by experts including the shape brightness contrast and uniform density of tumor areas the method uses modified median filtering to enhance mammogram images and template matching to detect the tumors in the template matching step suspicious areas are identified by thresholding the cross correlation values and a percentile method is used to determine a threshold for each film in addition two tests are used to remove false alarms from the resulting candidates the results obtained by applying these techniques to a set of test images are described they are judged encouraging

matrix transformations between the sequence spaces w 0 p λ v 0 p λ c 0 p λ 1 p and certain bk spaces in this paper we determine the b duals of the sets w 0 p l v 0 p l and c 0 p l for exponentially bounded email protected furthermore we characterize matrix transformations between the sequence spaces w 0 p l v 0 p l c 0 p l 1

fractal modeling and segmentation for the enhancement of microcalcifications in digital mammograms the objective of this research is to model the mammographic parenchymal and ductal patterns and enhance the microcalcifications using a deterministic fractal approach according to the theory of deterministic fractal geometry images can be modeled by deterministic fractal objects which are attractors of sets of two dimensional 2 d affine transformations the iterated functions systems and the collage theorem are the mathematical foundations of fractal image modeling here a methodology based on fractal image modeling is developed to analyze and model breast background structures the authors show that general mammographic parenchymal and ductal patterns can be well modeled by a set of parameters of affine transformations therefore microcalcifications can be enhanced by taking the difference between the original image and the modeled image the authors results are compared with those of the partial wavelet reconstruction and morphological operation approaches the results demonstrate that the fractal modeling method is an effective way to enhance microcalcifications it may also be able to improve the detection and classification of microcalcifications in a computer aided diagnosis system

the conditions for the coincidence or overlapping of two bezier curves in a recent article chen et al 2013 derive the condition for the coincidence of two quartic bezier curves different from straight lines the condition reads that either their control polygons coincide or the curves are degenerate representations of the same quadratic curve we point out that this uniqueness of the control points for properly parameterized polynomial curves is already well known not only for quartics but for curves of arbitrary degree this is a direct consequence of a previous more general result by berry and patterson namely the uniqueness of the control points for rational bezier curves in addition two conjectures posed in chen et al 2013 also derive as straightforward corollaries finally the condition for overlapping of two properly parameterized curves is also derived unsurprisingly it amounts to the coincidence of the bezier polygons for the overlapping segments of the given curves corresponding to the overlapping portions of their domains

on compact operators and some euler b m difference sequence spaces abstract altay and basar 2005 1 and altay basar and mursaleen 2006 2 introduced the euler sequence spaces e 0 t e c t and e t basarir and kayikci 2009 3 defined the b m difference matrix and studied some topological and geometric properties of some generalized riesz b m difference sequence space in this paper we introduce the euler b m difference sequence spaces e 0 t b m e c t b m and e t b m consisting of all sequences whose b m transforms are in the euler spaces e 0 t e c t and e t respectively moreover we determine the and duals of these spaces and construct the schauder basis of the spaces e 0 t b m and e c t b m finally we characterize some matrix classes concerning the spaces e 0 t b m and e c t b m and give the characterization of some classes of compact operators on the sequence spaces e 0 t b m and e t b m

complexity regularized image denoising we study a new approach to image denoising based on complexity regularization this technique presents a flexible alternative to the more conventional l sup 2 l sup 1 and besov regularization methods different complexity measures are considered in particular those induced by state of the art image coders we focus on a gaussian denoising problem and derive a connection between complexity regularized denoising and operational rate distortion optimization this connection suggests the use of efficient algorithms for computing complexity regularized estimates bounds on denoising performance are derived in terms of an index of resolvability that characterizes the compressibility of the true image comparisons with state of the art denoising algorithms are given

applications of the hausdorff measure of noncompactness in some sequence spaces of weighted means in the present paper we establish some identities or estimates for the operator norms and the hausdorff measures of noncompactness of certain operators on some sequence spaces of weighted means furthermore by using the hausdorff measure of noncompactness we apply our results to characterize some classes of compact operators on those spaces

wavelet methods for pdes some recent developments abstract this paper is concerned with recent developments of wavelet schemes for the numerical treatment of operator equations with special emphasis on two issues adaptive solution concepts and nontrivial domain geometries after describing a general multiresolution framework the key features of wavelet bases are highlighted namely locality norm equivalences and cancellation properties assuming first that wavelet bases with these properties are available on the relevant problem domains the relevance of these features for a wide class of stationary problems is explained in subsequent sections the main issues are preconditioning and the efficient adaptive application of wavelet representations of the involved operators we indicate then how these ingredients combined with concepts from nonlinear or best n term approximation culminate in an adaptive wavelet scheme for elliptic selfadjoint problems covering boundary value problems as well as boundary integral equations these schemes can be shown to exhibit convergence rates that are in a certain sense asymptotically optimal we conclude this section with some brief remarks on data structures and implementation interrelations with regularity in a certain scale of besov spaces and strategies of extending such schemes to unsymmetric or indefinite problems we address then the adaptive evaluation of nonlinear functionals of wavelet expansions as a central task arising in connection with nonlinear problems wavelet bases on nontrivial domains are discussed next the main issues are the development of fourier free construction principles and criteria for the validity of norm equivalences finally we indicate possible combinations of wavelet concepts with conventional discretizations such as finite element or finite volume schemes in connection with convection dominated and hyperbolic problems

the wavelet transform of stochastic processes with stationary increments and its application to fractional brownian motion the wavelet transform of random processes with wide sense stationary increments is shown to be a wide sense stationary process whose correlation function and spectral distribution are determined the second order properties of the coefficients in the wavelet orthonormal series expansion of such processes is obtained applications to the spectral analysis and to the synthesis of fractional brownian motion are given

on the b difference sequence space derived by generalized weighted mean and compact operators abstract in the present paper by using generalized weighted mean and difference matrix b we introduce the paranormed sequence space l u v p b which consist of all sequences whose generalized weighted b difference means are in the linear space l p introduced by i j maddox also we give the basis of this space and compute its and duals further we characterize the classes of matrix mappings from l u v p b to l c and c 0 finally we apply the hausdorff measure of noncompactness to characterize some classes of compact operators given by matrices on the space l p u v b 1 p

orthogonal and biorthogonal sqrt 3 refinement wavelets for hexagonal data processing the hexagonal lattice was proposed as an alternative method for image sampling the hexagonal sampling has certain advantages over the conventionally used square sampling hence the hexagonal lattice has been used in many areas a hexagonal lattice allows radic3 dyadic and radic7 refinements which makes it possible to use the multiresolution multiscale analysis method to process hexagonally sampled data the radic3 refinement is the most appealing refinement for multiresolution data processing due to the fact that it has the slowest progression through scale and hence it provides more resolution levels from which one can choose this fact is the main motivation for the study of radic3 refinement surface subdivision and it is also the main reason for the recommendation to use the radic3 refinement for discrete global grid systems however there is little work on compactly supported radic3 refinement wavelets in this paper we study the construction of compactly supported orthogonal and biorthogonal radic3 refinement wavelets in particular we present a block structure of orthogonal fir filter banks with twofold symmetry and construct the associated orthogonal radic3 refinement wavelets we study the sixfold axial symmetry of perfect reconstruction biorthogonal fir filter banks in addition we obtain a block structure of sixfold symmetric radic3 refinement filter banks and construct the associated biorthogonal wavelets

speckle reduction and contrast enhancement of echocardiograms via multiscale nonlinear processing this paper presents an algorithm for speckle reduction and contrast enhancement of echocardiographic images within a framework of multiscale wavelet analysis the authors apply wavelet shrinkage techniques to eliminate noise while preserving the sharpness of salient features in addition nonlinear processing of feature energy is carried out to enhance contrast within local structures and along object boundaries the authors show that the algorithm is capable of not only reducing speckle but also enhancing features of diagnostic importance such as myocardial walls in two dimensional echocardiograms obtained from the parasternal short axis view shrinkage of wavelet coefficients via soft thresholding within finer levels of scale is carried out on coefficients of logarithmically transformed echocardiograms enhancement of echocardiographic features is accomplished via nonlinear stretching followed by hard thresholding of wavelet coefficients within selected midrange spatial frequency levels of analysis the authors formulate the denoising and enhancement problem introduce a class of dyadic wavelets and describe their implementation of a dyadic wavelet transform their approach for speckle reduction and contrast enhancement was shown to be less affected by pseudo gibbs phenomena the authors show experimentally that this technique produced superior results both qualitatively and quantitatively when compared to results obtained from existing denoising methods alone a study using a database of clinical echocardiographic images suggests that such denoising and enhancement may improve the overall consistency of expert observers to manually defined borders

matrix transformations between sequence spaces of generalized weighted means the main object of this paper is to introduce and study some sequence spaces which arise from concept of weighted means determine their b duals and characterize matrix transformations between them

texture classification by wavelet packet signatures this correspondence introduces a new approach to characterize textures at multiple scales the performance of wavelet packet spaces are measured in terms of sensitivity and selectivity for the classification of twenty five natural textures both energy and entropy metrics were computed for each wavelet packet and incorporated into distinct scale space representations where each wavelet packet channel reflected a specific scale and orientation sensitivity wavelet packet representations for twenty five natural textures were classified without error by a simple two layer network classifier an analyzing function of large regularity d sub 20 was shown to be slightly more efficient in representation and discrimination than a similar function with fewer vanishing moments d sub 6 in addition energy representations computed from the standard wavelet decomposition alone 17 features provided classification without error for the twenty five textures included in our study the reliability exhibited by texture signatures based on wavelet packets analysis suggest that the multiresolution properties of such transforms are beneficial for accomplishing segmentation classification and subtle discrimination of texture

multiresolution expansion approximation order and quasiasymptotic behavior of tempered distributions abstract multiresolution analysis of tempered distributions is studied through multiresolution analysis on the corresponding test function spaces s r r r n 0 for a function h which is smooth enough and of appropriate decay it is shown that the derivatives of its projections to the corresponding spaces v j j z in a regular multiresolution analysis of l 2 r denoted by h j multiplied by a polynomial weight converge in sup norm i e h j h in s r r as j analogous result for tempered distributions is obtained by duality arguments the analysis of the approximation order of the projection operator within the framework of the theory of shift invariant spaces gives a further refinement of the results the order of approximation is measured with respect to the corresponding space of test functions as an application we give abelian and tauberian type theorems concerning the quasiasymptotic behavior of a tempered distribution at infinity

fir filter banks for hexagonal data processing images are conventionally sampled on a rectangular lattice thus traditional image processing is carried out on the rectangular lattice the hexagonal lattice was proposed more than four decades ago as an alternative method for sampling compared with the rectangular lattice the hexagonal lattice has certain advantages which include that it needs less sampling points it has better consistent connectivity and higher symmetry the hexagonal structure is also pertinent to the vision process in this paper we investigate the construction of symmetric fir hexagonal filter banks for multiresolution hexagonal image processing we obtain block structures of fir hexagonal filter banks with 3 fold rotational symmetry and 3 fold axial symmetry these block structures yield families of orthogonal and biorthogonal fir hexagonal filter banks with 3 fold rotational symmetry and 3 fold axial symmetry in this paper we also discuss the construction of orthogonal and biorthogonal fir filter banks with scaling functions and wavelets having optimal smoothness in addition we present a few of such orthogonal and biorthogonal fir filters banks

multiresolution detection of spiculated lesions in digital mammograms we present a novel multiresolution scheme for the detection of spiculated lesions in digital mammograms first a multiresolution representation of the original mammogram is obtained using a linear phase nonseparable two dimensional 2 d wavelet transform a set of features is then extracted at each resolution in the wavelet pyramid for every pixel this approach addresses the difficulty of predetermining the neighborhood size for feature extraction to characterize objects that may appear in different sizes detection is performed from the coarsest resolution to the finest resolution using a binary tree classifier this top down approach requires less computation by starting with the least amount of data and propagating detection results to finer resolutions experimental results using the mias image database have shown that this algorithm is capable of detecting spiculated lesions of very different sizes at low false positive rates

spline prewavelets for non uniform knots in this paper we develop a framework suitable for performing a multiresolution analysis using univariate spline spaces of arbitrary degree and with non uniform knot sequences to this end we show among other things the existence of compactly supported prewavelets and of prewavelets that are globally supported but decay exponentially in each case we obtain a decomposition of a fine spline space as a sum of a coarse spline space plus a spline space spanned by prewavelets

multiresolution statistical analysis of high resolution digital mammograms a multiresolution statistical method for identifying clinically normal tissue in digitized mammograms is used to construct an algorithm for separating normal regions from potentially abnormal regions that is small regions that may contain isolated calcifications this is the initial phase of the development of a general method for the automatic recognition of normal mammograms the first step is to decompose the image with a wavelet expansion that yields a sum of independent images each containing different levels of image detail when calcifications are present there is strong empirical evidence that only some of the image components are necessary for the purpose of detecting a deviation from normal the underlying statistic for each of the selected expansion components can be modeled with a simple parametric probability distribution function this function serves as an instrument for the development of a statistical test that allows for the recognition of normal tissue regions the distribution function depends on only one parameter and this parameter itself has an underlying statistical distribution the values of this parameter define a summary statistic that can be used to set detection error rates once the summary statistic is determined spatial filters that are matched to resolution are applied independently to each selected expansion image regions of the image that correlate with the normal statistical model are discarded and regions in disagreement suspicious areas are flagged these results are combined to produce a detection output image consisting only of suspicious areas this type of detection output is amenable to further processing that may ultimately lead to a fully automated algorithm for the identification of normal mammograms

comparison of multiwavelet wavelet haralick and shape features for microcalcification classification in mammograms we present an evaluation and comparison of the performance of four different texture and shape feature extraction methods for classification of benign and malignant microcalcifications in mammograms for 103 regions containing microcalcification clusters texture and shape features were extracted using four approaches conventional shape quantifiers co occurrence based method of haralick wavelet transformations and multi wavelet transformations for each set of features most discriminating features and their optimal weights were found using real valued and binary genetic algorithms ga utilizing a k nearest neighbor classifier and a malignancy criterion for generating roc curves for measuring the performance the best set of features generated areas under the roc curve ranging from 0 84 to 0 89 when using real valued ga and from 0 83 to 0 88 when using binary ga the multi wavelet method outperformed the other three methods and the conventional shape features were superior to the wavelet and haralick features

lagrange wavelets for signal processing this paper deals with the design of interpolating wavelets based on a variety of lagrange functions combined with novel signal processing techniques for digital imaging halfband lagrange wavelets b spline lagrange wavelets and gaussian lagrange lagrange distributed approximating functional daf wavelets are presented as specific examples of the generalized lagrange wavelets our approach combines the perceptually dependent visual group normalization vgn technique and a softer logic masking slm method these are utilized to rescale the wavelet coefficients remove perceptual redundancy and obtain good visual performance for digital image processing

dynamic multiscale spatiotemporal models for gaussian areal data summary we introduce a new class of dynamic multiscale models for spatiotemporal processes arising from gaussian areal data specifically we use nested geographical structures to decompose the original process into multiscale coefficients which evolve through time following state space equations our approach naturally accommodates data that are observed on irregular grids as well as heteroscedasticity moreover we propose a multiscale spatiotemporal clustering algorithm that facilitates estimation of the nested geographical multiscale structure in addition we present a singular forward filter backward sampler for efficient bayesian estimation our multiscale spatiotemporal methodology decomposes large data analysis problems into many smaller components and thus leads to scalable and highly efficient computational procedures finally we illustrate the utility and flexibility of our dynamic multiscale framework through two spatiotemporal applications the first example considers mortality ratios in the state of missouri whereas the second example examines agricultural production in espirito santo state brazil

quantum field theory in ninety minutes on presente divers aspects de la theorie quantique des champs la theorie p 2 a 2 dimensions la theorie 3 4 a 3 dimensions la theorie de yang mills a 4 dimensions

efficient detection of symmetries of polynomially parametrized curves we present efficient algorithms for detecting central and mirror symmetry for the case of algebraic curves defined by means of polynomial parametrizations the algorithms are based on the existence of a linear relationship between two proper polynomial parametrizations of the curve which leads to a triangular polynomial system with complex unknowns that can be solved in a very fast way in particular curves parametrized by polynomials of serious degrees can be analyzed in a few seconds in our analysis we provide a good number of theoretical results on symmetries of polynomial curves algorithms for detecting rotation and mirror symmetry and closed formulas to determine the symmetry center and the symmetry axis when they exist a complexity analysis of the algorithms is also given

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

a block spin construction of ondelettes part i lemarie functions using block spin assignments we construct anl2 orthonormal basis consisting of dyadic scalings and translates of just a finite number of functions these functions have exponential localization and for even values of a construction parameterm one can make them classcm 1 with vanishing moments up to orderm inclusive such a basis has an important application to phase cell cluster expansions in quantum field theory

refinement of operator valued reproducing kernels this paper studies the construction of a refinement kernel for a given operator valued reproducing kernel such that the vector valued reproducing kernel hilbert space of the refinement kernel contains that of the given kernel as a subspace the study is motivated from the need of updating the current operator valued reproducing kernel in multi task learning when underfitting or overfitting occurs numerical simulations confirm that the established refinement kernel method is able to meet this need various characterizations are provided based on feature maps and vector valued integral representations of operator valued reproducing kernels concrete examples of refining translation invariant and finite hilbert schmidt operator valued reproducing kernels are provided other examples include refinement of hessian of scalar valued translation invariant kernels and transformation kernels existence and properties of operator valued reproducing kernels preserved during the refinement process are also investigated

the effect of median filtering on edge estimation and detection in this paper we consider the effect of median prefiltering on the subsequent estimation and detection of edges in digital images where possible a quantitative statistical comparison is made for a number of filters defined with two dimensional geometries in some cases one dimensional analyses are required to illustrate certain points noise images prefiltered by median filters defined with a variety of windowing geometries are used to support the analysis and it is found that median prefiltering improves the performance of both thresholding and zero crossing based edge detectors

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

steerable pyramids and tight wavelet frames in l_ 2 bbr d we present a functional framework for the design of tight steerable wavelet frames in any number of dimensions the 2 d version of the method can be viewed as a generalization of simoncelli s steerable pyramid that gives access to a larger palette of steerable wavelets via a suitable parametrization the backbone of our construction is a primal isotropic wavelet frame that provides the multiresolution decomposition of the signal the steerable wavelets are obtained by applying a one to many mapping n th order generalized riesz transform to the primal ones the shaping of the steerable wavelets is controlled by an m m unitary matrix where m is the number of wavelet channels that can be selected arbitrarily this allows for a much wider range of solutions than the traditional equiangular configuration steerable pyramid we give a complete functional description of these generalized wavelet transforms and derive their steering equations we describe some concrete examples of transforms including some built around a mallat type multiresolution analysis of l2 rd and provide a fast fourier transform based decomposition algorithm we also propose a principal component based method for signal adapted wavelet design finally we present some illustrative examples together with a comparison of the denoising performance of various brands of steerable transforms the results are in favor of an optimized wavelet design equalized principal component analysis which consistently performs best

matrix transformations and compact operators on some new mth order difference sequences abstract we define some new sets of sequences the m th order differences of which are bounded convergent and convergent to zero and apply the general methods in e malkowsky v rakocevic on matrix domains of triangles appl math comput 189 2 2007 1146 1163 to give schauder bases for the latter two determine their duals and characterize matrix transformations on them our results generalize those in b de malafosse the banach algebra s and applications acta sci math szeged 70 1 2 2004 125 145 and improve those in e malkowsky s d parashar matrix transformations in spaces of bounded and convergent difference sequences of order m analysis 17 1997 87 97 we also establish identities and estimates for the hausdorff measure of non compactness of matrix operators from our spaces into the spaces of bounded convergent and null sequences and characterize the respective classes of compact operators some of these results generalize those in e malkowsky v rakocevic the measure of non compactness of linear operators between spaces of m th order difference sequences stud sci math hungar 33 1999 381 391

conditions for coincidence of two cubic bezier curves abstract this paper presents a necessary and sufficient condition for judging whether two cubic bezier curves are coincident two cubic bezier curves whose control points are not collinear are coincident if and only if their corresponding control points are coincident or one curve is the reversal of the other curve however this is not true for degree higher than 3 this paper provides a set of counterexamples of degree 4

a wavelet perspective on variational perceptually inspired color enhancement the issue of perceptually inspired correction of color and contrast in digital images has been recently analyzed with the help of variational principles these techniques allowed building a general framework in which the action of many already existing algorithms can be more easily understood and compared in terms of intensification of local contrast and control of dispersion around the average intensity value in this paper we analyze this issue from the dual perspective of wavelet theory showing that it is possible to build energy functionals of wavelet coefficients that lead to a multilevel perceptually inspired color correction by computing the euler lagrange equations associated to the wavelet based functionals we were able to find an analytical formula for the modification of wavelet detail coefficients that overcomes the problem of an ad hoc selection based on empirical considerations besides these theoretical results the wavelet perspective provides the computational advantage of generating much faster algorithms in comparison with the spatial variational framework

measure of noncompactness of matrix operators on some difference sequence spaces of weighted means for a sequence x x k we denote the difference sequence by dx x k x k 1 let u u k k 0 and v v k k 0 be the sequences of real numbers such that u k 0 v k 0 for all email protected n the difference sequence spaces of weighted means l u v d are defined as l u v d x x k w x email protected where l c c 0 and and the matrix w w n k is defined by w n k u n v k v k 1 kn in this paper we establish some identities or estimates for the operator norms and the hausdorff measures of noncompactness of certain matrix operators on l u v d further we characterize some classes of compact operators on these spaces by using the hausdorff measure of noncompactness

wavelet transform based adaptive filters analysis and new results in this paper the wavelet transform is used in an adaptive filtering structure the coefficients of the adaptive filter are updated by the help of the least mean square lms algorithm first the wavelet transform based adaptive filter wtaf is described and it is analyzed for its wiener optimal solution then the performance of the wtaf is studied by the help of learning curves for three different convergence factors 1 constant convergence factor 2 time varying convergence factor and 3 exponentially weighted convergence factor the exponentially weighted convergence factor is proposed to introduce scale based variation to the weight update equation it is shown for two different sets of data that the rate of convergence increases significantly for all three wtaf structures as compared to that of time domain lms the high convergence rates of the wtaf give us reason to expect that it will perform well in tracking rapid changes in a signal

applications of measures of noncompactness to the infinite system of differential equations in lp spaces abstract in this paper we apply the technique of measures of noncompactness to the theory of infinite system of differential equations in the banach sequence spaces l p 1 p our aim is to present some existence results for infinite system of differential equations formulated with the help of measures of noncompactness

banach algebras of matrix transformations between some sequence spaces related to λ strong convergence and boundedness we study the spaces c 0 l c l and c l of sequences that are l strongly convergent to zero l strongly convergent and l strongly bounded and the related spaces v 0 l and v l in particular we give the characterizations of several classes of matrix transformations between those spaces furthermore we use our results to prove that the classes of matrix transformations from v l c l and c l into themselves are banach algebras as an application of our results we establish an estimate for the hausdorff measure of noncompactness of matrix operators that map c l into itself give a characterization of the subclass of compact operators and a sufficient condition for those operators to be fredholm

conditions for the coincidence of two quartic bezier curves this paper presents efficient and necessary coincidence conditions for two quartic bezier curves i e either their two control polygons are coincident or the two curves can be reparameterized or degenerated into the same quadratic bezier curve

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