mismatch in high rate entropy constrained vector quantization bucklew s 1984 high rate vector quantizer mismatch result is extended from fixed rate coding to variable rate coding using a lagrangian formulation it is shown that if an asymptotically high rate optimal sequence of variable rate codes is designed for a k dimensional probability density function pdf g and then applied to another pdf f for which f g is bounded then the resulting mismatch or loss of performance from the optimal possible is given by the relative entropy or kullback leibler 1968 divergence i f spl par g it is also shown that under the same assumptions an asymptotically optimal code sequence for g can be converted to an asymptotically optimal code sequence for a mismatched source f by modifying only the lossless component of the code applications to quantizer design using uniform and gaussian densities are described including a high rate analog to the shannon rate distortion result of sakrison 1975 and lapidoth 1997 showing that the gaussian is the worst case for lossy compression of a source with known covariance by coupling the mismatch result with composite quantizers the worst case properties of uniform and gaussian densities are extended to conditionally uniform and gaussian densities which provides a lloyd clustering algorithm for fitting mixtures to general densities

on the use of coifman intervallic wavelets in the method of moments for fast construction of wavelet sparsified matrices orthonormal wavelets have been successfully used as basis and testing functions for the integral equations and extremely sparse impedance matrices have been obtained however in many practical problems the solution domain is confined in a bounded interval while the wavelets are originally defined on the entire real line to overcome this problem periodic wavelets have been described in the literature nonetheless the unknown functions must take on equal values at the endpoints of the bounded interval in order to apply periodic wavelets as the basis functions we present the intervallic coifman wavelets coiflets for the method of moments mom the intervallic wavelets release the endpoints restrictions imposed on the periodic wavelets the intervallic wavelets form an orthonormal basis and preserve the same multiresolution analysis mra of other usual unbounded wavelets the coiflets possesses a special property that their scaling functions have many vanishing moments as a result the zero entries of the matrices are identified directly without using a truncation scheme with an artificially established threshold further the majority of matrix elements are evaluated directly without performing numerical integration procedures such as gaussian quadrature for an n spl times n matrix the number of actual numerical integrations is reduced from n sup 2 to the order of 3n 2l 1 when the coiflets of order l is employed the construction of intervallic wavelets is presented numerical examples of scattering problems are discussed and the relative error of this method is studied analytically

a modified fuzzy c means algorithm for bias field estimation and segmentation of mri data we present a novel algorithm for fuzzy segmentation of magnetic resonance imaging mri data and estimation of intensity inhomogeneities using fuzzy logic mri intensity inhomogeneities can be attributed to imperfections in the radio frequency coils or to problems associated with the acquisition sequences the result is a slowly varying shading artifact over the image that can produce errors with conventional intensity based classification our algorithm is formulated by modifying the objective function of the standard fuzzy c means fcm algorithm to compensate for such inhomogeneities and to allow the labeling of a pixel voxel to be influenced by the labels in its immediate neighborhood the neighborhood effect acts as a regularizer and biases the solution toward piecewise homogeneous labelings such a regularization is useful in segmenting scans corrupted by salt and pepper noise experimental results on both synthetic images and mr data are given to demonstrate the effectiveness and efficiency of the proposed algorithm

a large k asymptotics of witten s invariant of seifert manifolds we calculate a largek asymptotic expansion of the exact surgery formula for witten ssu 2 invariant of some seifert manifolds the contributions of all flat connections are identified an agreement with the 1 loop formula is checked a contribution of the irreducible connections appears to contain only a finite number of terms in the asymptotic series a 2 loop correction to the contribution of the trivial connection is found to be proportional to casson s invariant

blind deconvolution using a variational approach to parameter image and blur estimation following the hierarchical bayesian framework for blind deconvolution problems in this paper we propose the use of simultaneous autoregressions as prior distributions for both the image and blur and gamma distributions for the unknown parameters hyperparameters of the priors and the image formation noise we show how the gamma distributions on the unknown hyperparameters can be used to prevent the proposed blind deconvolution method from converging to undesirable image and blur estimates and also how these distributions can be inferred in realistic situations we apply variational methods to approximate the posterior probability of the unknown image blur and hyperparameters and propose two different approximations of the posterior distribution one of these approximations coincides with a classical blind deconvolution method the proposed algorithms are tested experimentally and compared with existing blind deconvolution methods

n 2 topological gauge theory the euler characteristic of moduli spaces and the casson invariant we discuss gauge theory with a topologicaln 2 symmetry this theory captures the de rham complex and riemannian geometry of some underlying moduli space and the partition function equals the euler number of we explicitly deal with moduli spaces of instantons and of flat connections in two and three dimensions to motivate our constructions we explain the relation between the mathai quillen formalism and supersymmetric quantum mechanics and introduce a new kind of supersymmetric quantum mechanics based on the gauss codazzi equations we interpret the gauge theory actions from the atiyah jeffrey point of view and relate them to supersymmetric quantum mechanics on spaces of connections as a consequence of these considerations we propose the euler number of the moduli space of flat connections as a generalization to arbitrary three manifolds of the casson invariant we also comment on the possibility of constructing a topological version of the penner matrix model

a knot invariant via representation spaces a beautiful construction of a casson on the representation spaces corresponding to a heegard splitting of an oriented homology 3 sphere m gives rise to an integer invariant m of m this invariant generalizes the rohlin invariant and gives stricking corollaries in low dimension al topology defined as an intersection number of appropriate subspaces this invariant m can be roughly thought of as the number of conjugacy classes of irreducible representations of n m into su2 counted with signs a detailed discussion of this invariant can be found in an expose by s akbulut and j mccarthy 1 further works on casson s invariant include the generalizations by k walker as well as s boyer and a nicas to rational homology 3 spheres 14 3 and by s cappell r lee and e miller to representatio ns into sun 4 the works of c taubes 13 and a flore 6 interpret casson s invariant as the euler number of the instanton homology or flore homology of m in this paper analogous to casson s original construction we will define an intersection number of the representation spaces corresponding to a braid representative of a knot k in s this intersection number turns out to be an integer knot invariant see theorem 1 8 the representations of the knot group s k used in our construction seem to be mysterious they are representations of s3 k into su2 such that all meridians of k are represented by trace zero matrices call such a representation of the knot group a trace free representation then roughly speaking our knot invariant h k is the number of conjugacy classes of irreducible trace free representations of s3 k counted with signs our knot invariant h k can be computed via knot diagrams it turns out that our algorithm of computing h k by using the skein model is the same as the algorithm of computing sgn k given by j h conway 5

salt and pepper noise removal by median type noise detectors and detail preserving regularization this paper proposes a two phase scheme for removing salt and pepper impulse noise in the first phase an adaptive median filter is used to identify pixels which are likely to be contaminated by noise noise candidates in the second phase the image is restored using a specialized regularization method that applies only to those selected noise candidates in terms of edge preservation and noise suppression our restored images show a significant improvement compared to those restored by using just nonlinear filters or regularization methods only our scheme can remove salt and pepper noise with a noise level as high as 90

a segmentation model using compound markov random fields based on a boundary model markov random field mrf theory has been widely applied to the challenging problem of image segmentation in this paper we propose a new nontexture segmentation model using compound mrfs in which the original label mrf is coupled with a new boundary mrf to help improve the segmentation performance the boundary model is relatively general and does not need prior training on boundary patterns unlike some existing related work the proposed method offers a more compact interaction between label and boundary mrfs furthermore our boundary model systematically takes into account all the possible scenarios of a single edge existing in a 3times3 neighborhood and thus incorporates sophisticated prior information about the relation between label and boundary it is experimentally shown that the proposed model can segment objects with complex boundaries and at the same time is able to work under noise corruption the new method has been applied to medical image segmentation experiments on synthetic images and real clinical datasets show that the proposed model is able to produce more accurate segmentation results and satisfactorily keep the delicate boundary it is also less sensitive to noise in both high and low signal to noise ratio regions than some of the existing models in common use

on the use of wavelet expansions in the method of moments em scattering an approach which incorporates the theory of wavelet transforms in method of moments solutions for electromagnetic wave interaction problems is presented the unknown field or response is expressed as a twofold summation of shifted and dilated forms of a properly chosen basis function which is often referred to as the mother wavelet the wavelet expansion can adaptively fit itself to the various length scales associated with the scatterer by distributing the localized functions near the discontinuities and the more spatially diffused ones over the smooth expanses of the scatterer the approach is thus best suited for the analysis of scatterers which contain a broad spectrum of length scales ranging from a subwavelength to several wavelengths using a galerkin method and subsequently applying a threshold procedure the moment method matrix is rendered sparsely populated the structure of the matrix reveals the localized scale fitting distribution long before the matrix equation is solved the performance of the proposed discretization scheme is illustrated by a numerical study of electromagnetic coupling through a double slot aperture

the symplectic nature of fundamental groups of surfaces soit 7b g la categorie des groupes de lie g avec une forme bilineaire symetrique non singuliere b sur l algebre de lie soit le groupe fondamental d une surface orientee close de genre 1 et soit 7b s la categorie des out espaces symplectiques alors la correspondance g b hom g g b definit un foncteur 7b g 7b s ou b est la structure symplectique sur hom g g definie par b

fast wavelet transforms and numerical algorithms i a class of algorithms is introduced for the rapid numerical application of a class of linear operators to arbitrary vectors previously published schemes of this type utilize detailed analytical information about the operators being applied and are specific to extremely narrow classes of matrices in contrast the methods presented here are based on the recently developed theory of wavelets and are applicable to all calderon zygmund and pseudo differential operators the algorithms of this paper require order o n or o n log n operations to apply an n n matrix to a vector depending on the particular operator and the version of the algorithm being used and our numerical experiments indicate that many previously intractable problems become manageable with the techniques presented here

quadrature rules for numerical integration based on haar wavelets and hybrid functions in this paper haar wavelets and hybrid functions have been applied for numerical solution of double and triple integrals with variable limits of integration this approach is the generalization and improvement of the methods siraj ul islam et al 2010 9 where the numerical methods are only applicable to the integrals with constant limits apart from generalization of the methods 9 the new approach has two major advantages over the classical methods based on quadrature rule i no need of finding optimum weights as the wavelet and hybrid coefficients serve the purpose of optimal weights automatically ii mesh points of the wavelets algorithm are used as nodal values instead of considering the n nodes as unknown roots of polynomial of degree n the new methods are more efficient the novel methods are compared with existing methods and applied to a number of benchmark problems accuracy of the methods are measured in terms of absolute errors

a robust hidden markov gauss mixture vector quantizer for a noisy source noise is ubiquitous in real life and changes image acquisition communication and processing characteristics in an uncontrolled manner gaussian noise and salt and pepper noise in particular are prevalent in noisy communication channels camera and scanner sensors and medical mri images it is not unusual for highly sophisticated image processing algorithms developed for clean images to malfunction when used on noisy images for example hidden markov gauss mixture models hmgmm have been shown to perform well in image segmentation applications but they are quite sensitive to image noise we propose a modified hmgmm procedure specifically designed to improve performance in the presence of noise the key feature of the proposed procedure is the adjustment of covariance matrices in gauss mixture vector quantizer codebooks to minimize an overall minimum discrimination information distortion mdi in adjusting covariance matrices we expand or shrink their elements based on the noisy image while most results reported in the literature assume a particular noise type we propose a framework without assuming particular noise characteristics without denoising the corrupted source we apply our method directly to the segmentation of noisy sources we apply the proposed procedure to the segmentation of aerial images with salt and pepper noise and with independent gaussian noise and we compare our results with those of the median filter restoration method and the blind deconvolution based method respectively we show that our procedure has better performance than image restoration based techniques and closely matches to the performance of hmgmm for clean images in terms of both visual segmentation results and error rate

a contribution of the trivial connection to the jones polynomial and witten s invariant of 3d manifolds ii we extend the results of our previous paper 1 from knots to links by using a formula for the jones polynomial of a link derived recently by n reshetikhin we establish a relation between the parameters of this formula and the multivariable alexander polynomial this relation is illustrated by an example of a torus link we check that our expression for the alexander polynomial satisfies some of its basic properties finally we derive a link surgery formula for the loop corrections to the trivial connection contribution to witten s invariant of rational homology spheres

a study of vector quantization for noisy channels several issues related to vector quantization for noisy channels are discussed an algorithm based on simulated annealing is developed for assigning binary codewords to the vector quantizer code vectors it is shown that this algorithm could result in dramatic performance improvements as compared to randomly selected codewords a modification of the simulated annealing algorithm for binary codeword assignment is developed for the case where the bits in the codeword are subjected to unequal error probabilities resulting from unequal levels of error protection an algorithm for the design of an optimal vector quantizer for a noisy channel is briefly discussed and its robustness under channel mismatch conditions is studied numerical results for a stationary first order gauss markov source and a binary symmetric channel are provided it is concluded that the channel optimized vector quantizer design algorithm if used carefully can result in a fairly robust system with no additional delay the case in which the communication channel is nonstationary as in mobile radio channels is studied and some preliminary ideas for quantizer design are presented

a tree structured markov random field model for bayesian image segmentation we present a new image segmentation algorithm based on a tree structured binary mrf model the image is recursively segmented in smaller and smaller regions until a stopping condition local to each region is met each elementary binary segmentation is obtained as the solution of a map estimation problem with the region prior modeled as an mrf since only binary fields are used and thanks to the tree structure the algorithm is quite fast and allows one to address the cluster validation problem in a seamless way in addition all field parameters are estimated locally allowing for some spatial adaptivity to improve segmentation accuracy a split and merge procedure is also developed and a spatially adaptive mrf model is used numerical experiments on multispectral images show that the proposed algorithm is much faster than a similar reference algorithm based on flat mrf models and its performance in terms of segmentation accuracy and map smoothness is comparable or even superior

image classification by a two dimensional hidden markov model for block based classification an image is divided into blocks and a feature vector is formed for each block by grouping statistics extracted from the block conventional block based classification algorithms decide the class of a block by examining only the feature vector of this block and ignoring context information in order to improve classification by context an algorithm is proposed that models images by two dimensional 2 d hidden markov models hmms the hmm considers feature vectors statistically dependent through an underlying state process assumed to be a markov mesh which has transition probabilities conditioned on the states of neighboring blocks from both horizontal and vertical directions thus the dependency in two dimensions is reflected simultaneously the hmm parameters are estimated by the em algorithm to classify an image the classes with maximum a posteriori probability are searched jointly for all the blocks applications of the hmm algorithm to document and aerial image segmentation show that the algorithm outperforms cart sup tm lvq and bayes vq

new algorithms for the numerical solution of nonlinear fredholm and volterra integral equations using haar wavelets two new algorithms based on haar wavelets are proposed the first algorithm is proposed for the numerical solution of nonlinear fredholm integral equations of the second kind and the second for the numerical solution of nonlinear volterra integral equations of the second kind these methods are designed to exploit the special characteristics of haar wavelets in both one and two dimensions formulae for calculating haar coefficients without solving the system of equations have been derived these formulae are then used in the proposed numerical methods in contrast to other numerical methods the advantage of our method is that it does not involve any intermediate numerical technique for evaluation of the integral present in integral equations the methods are validated on test problems and numerical results are compared with those from existing methods in the literature

on application of fast and adaptive periodic battle lemarie wavelets to modeling of multiple lossy transmission lines in this paper the continuous operator is discretized into matrix forms by galerkin s procedure using periodic battle lemarie wavelets as basis testing functions the polynomial decomposition of wavelets is applied to the evaluation of matrix elements which makes the computational effort of the matrix elements no more expensive than that of method of moments mom with conventional piecewise basis testing functions a new algorithm is developed employing the fast wavelet transform fwt owing to localization cancellation and orthogonal properties of wavelets very sparse matrices have been obtained which are then solved by the lsqr iterative method this algorithm is also adaptive in that one can add at will finer wavelet bases in the regions where fields vary rapidly without any damage to the system orthogonality of the wavelet basis functions to demonstrate the effectiveness of the new algorithm we applied it to the evaluation of frequency dependent resistance and inductance matrices of multiple lossy transmission lines numerical results agree with previously published data and laboratory measurements the valid frequency range of the boundary integral equation results has been extended two to three decades in comparison with the traditional mom approach the new algorithm has been integrated into the computer aided design tool magicad which is used for the design and simulation of high speed digital systems and multichip modules panet al ieee trans hyb manuf technol 15 4 465 1992

image segmentation using hidden markov gauss mixture models image segmentation is an important tool in image processing and can serve as an efficient front end to sophisticated algorithms and thereby simplify subsequent processing we develop a multiclass image segmentation method using hidden markov gauss mixture models hmgmms and provide examples of segmentation of aerial images and textures hmgmms incorporate supervised learning fitting the observation probability distribution given each class by a gauss mixture estimated using vector quantization with a minimum discrimination information mdi distortion we formulate the image segmentation problem using a maximum a posteriori criteria and find the hidden states that maximize the posterior density given the observation we estimate both the hidden markov parameter and hidden states using a stochastic expectation maximization algorithm our results demonstrate that hmgmm provides better classification in terms of bayes risk and spatial homogeneity of the classified objects than do several popular methods including classification and regression trees learning vector quantization causal hidden markov models hmms and multiresolution hmms the computational load of hmgmm is similar to that of the causal hmm

a unified approach for encoding clean and noisy sources by means of waveform and autoregressive model vector quantization data compression by vector quantization is considered for sources which have been degraded by noise it is shown that by appropriately modifying the given distortion measure the problem becomes a standard quantization problem for the noisy source and the modified distortion measure for the special case of sources corrupted by statistically independent additive noise the authors provide sufficient conditions on the original distortion measure and probability distributions of the source and the noise for convergence of the generalized lloyd algorithm in designing the quantizers the results are specialized to waveform and autoregressive model vector quantization using the weighted quadratic and the itakura saito distortion measures respectively

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