parametrization of compactly supported orthonormal wavelets the parametrization of two channel reconstruction quadrature mirror filter banks is extended to obtain a single characterization of discrete orthonormal wavelets in particular it is shown that discrete orthonormal wavelets of support less than 2n 1 where n is an even integer are parametrized by n 1 real parameters each taking values in 0 2 pi a parametrization of discrete orthonormal wavelets with a number of vanishing moments greater than one is also given

information measures the curious case of the binary alphabet four problems related to information divergence measures defined on finite alphabets are considered in three of the cases we consider we illustrate a contrast that arises between the binary alphabet and larger alphabet settings this is surprising in some instances since characterizations for the larger alphabet settings do not generalize their binary alphabet counterparts in particular we show that f divergences are not the unique decomposable divergences on binary alphabets that satisfy the data processing inequality thereby clarifying claims that have previously appeared in the literature we also show that kullback leibler kl divergence is the unique bregman divergence which is also an f divergence for any alphabet size we show that kl divergence is the unique bregman divergence which is invariant to statistically sufficient transformations of the data even when nondecomposable divergences are considered like some of the problems we consider this result holds only when the alphabet size is at least three

alpha divergence is unique belonging to both f divergence and bregman divergence classes a divergence measure between two probability distributions or positive arrays positive measures is a useful tool for solving optimization problems in optimization signal processing machine learning and statistical inference the csiszar f divergence is a unique class of divergences having information monotonicity from which the dual alpha geometrical structure with the fisher metric is derived the bregman divergence is another class of divergences that gives a dually flat geometrical structure different from the alpha structure in general csiszar gave an axiomatic characterization of divergences related to inference problems the kullback leibler divergence is proved to belong to both classes and this is the only such one in the space of probability distributions this paper proves that the alpha divergences constitute a unique class belonging to both classes when the space of positive measures or positive arrays is considered they are the canonical divergences derived from the dually flat geometrical structure of the space of positive measures

the power of optimization over randomization in designing experiments involving small samples random assignment typically seen as the standard in controlled trials aims to make experimental groups statistically equivalent before treatment however with a small sample which is a practical reality in many disciplines randomized groups are often too dissimilar to be useful we propose an approach based on discrete linear optimization to create groups whose discrepancy in their means and variances is several orders of magnitude smaller than with randomization we provide theoretical and computational evidence that groups created by optimization have exponentially lower discrepancy than those created by randomization and that this allows for more powerful statistical inference

biorthogonal spline type wavelets let f be an orthonormal scaling function with approximation degree p 1 and let b nbe the b spline of order n then spline type scaling functions defined by n b n n 1 2 possess higher approximation order p n 1 and compact support the corresponding biorthogonal wavelet functions are also constructed this technique is extended to the case of biorthogonal scaling function system as an application of the method supplied in this paper one can easily construct a sequence of pairs of biorthogonal spline type scaling functions from one pair of biorthogonal scaling functions or an orthonormal scaling function in particular if both the method and the lifting scheme of sweldens see 1 are applied then all pairs of biorthogonal spline type scaling functions shown in references 2 and 3 can be constructed from the haar scaling function

nonseparable multidimensional perfect reconstruction filter banks and wavelet bases for r sup n new results on multidimensional filter banks and their connection to multidimensional nonseparable wavelets are presented among the topics discussed are sampling in multiple dimensions multidimensional perfect reconstruction filter banks the two channel case in multiple dimensions the synthesis of multidimensional filter banks and the design of compactly supported wavelets

determination of all semisymmetric recursive information measures of multiplicative type on n positive discrete probability distributions information measures m entropies divergences inaccuracies information improvements etc depending upon n probability distributions which we unite into a vector distribution are recursive of type if m p1 p2 p3 pm m 1 p1 p2 p3 pm p1 p2 2p1p1 p2 p2p1 p2 if also a similar equation holds with three instead of two distinguished vectors then has to be multiplicative except if all m are identically 0 the information measure is semisymmetric if 3 p1 p2 p3 3 p1 p3 p2 we determine all semisymmetric in particular symmetric recursive information measures of multiplicative type allowing first only positive probabilities previously the cases n 3 have been examined mainly for t 1 2 n 1 1 2 2 n n and some probabilities were allowed to be 0 this has made the proofs easier but permitting certain probabilities to be 0 would exclude most information measures important for applications so the description of appropriate domains became complicated however we show how the measures which we determine here can be extended to the old domains and to more general ones

residual analysis for feature detection it is shown that in a very simple form residual analysis achieves results that are at least as good as if not better than those obtained by other techniques there are many ways for extensions of the method for example moving average filters of regularization can be used to obtain the residual images also the strength of the correlation measured by d sub rr o can be used to eliminate noise weak edges etc a more ambitious extension is by considering smoothing filters that leave invariant the function representing the reflectance from smooth surfaces

matching on the fly sequential allocation with higher power and efficiency we propose a dynamic allocation procedure that increases power and efficiency when measuring an average treatment effect in fixed sample randomized trials with sequential allocation subjects arrive iteratively and are either randomized or paired via a matching criterion to a previously randomized subject and administered the alternate treatment we develop estimators for the average treatment effect that combine information from both the matched pairs and unmatched subjects as well as an exact test simulations illustrate the method s higher efficiency and power over several competing allocation procedures in both simulations and in data from a clinical trial

wavelet transforms associated with finite cyclic groups multiresolution analysis via decomposition on wavelet bases has emerged as an important tool in the analysis of signals and images when these objects are viewed as sequences of complex or real numbers an important class of multiresolution decompositions are the laplacian pyramid schemes in which the resolution is successively halved by recursively low pass filtering the signal under analysis and decimating it by a factor of two in general the principal framework within which multiresolution techniques have been studied and applied is the same as that used in the discrete time fourier analysis of sequences of complex numbers an analogous framework is developed for the multiresolution analysis of finite length sequences of elements from arbitrary fields attention is restricted to sequences of length 2 sup n for n a positive integer so that the resolution may be recursively halved to completion as in finite length fourier analysis a cyclic group structure of the index set of such sequences is exploited to characterize the transforms of interest for the particular cases of complex and finite fields

about distances of discrete distributions satisfying the data processing theorem of information theory the distances of discrete probability distributions are considered necessary and sufficient conditions for validity of the data processing theorem of information theory are established these conditions are applied to the burbea rao 1982 divergences and bregman 1967 distances

on the solution of a nonlinear integral equation on the basis of a fixed point technique and cubic b spline scaling functions in this paper we apply the fixed point method to solve some nonlinear functional volterra integral equations which appear in many physical chemical and biological problems in each iteration of this method cubic semi orthogonal compactly supported b spline wavelets are used as basis functions to approximate the solution also the convergence of this numerical method is investigated and some examples are presented to show the accuracy and convergence of the method

asymptotic theory of rerandomization in treatment control experiments although complete randomization ensures covariate balance on average the chance of observing significant differences between treatment and control covariate distributions increases with many covariates rerandomization discards randomizations that do not satisfy a predetermined covariate balance criterion generally resulting in better covariate balance and more precise estimates of causal effects previous theory has derived finite sample theory for rerandomization under the assumptions of equal treatment group sizes gaussian covariate and outcome distributions or additive causal effects but not for the general sampling distribution of the difference in means estimator for the average causal effect we develop asymptotic theory for rerandomization without these assumptions which reveals a non gaussian asymptotic distribution for this estimator specifically a linear combination of a gaussian random variable and truncated gaussian random variables this distribution follows because rerandomization affects only the projection of potential outcomes onto the covariate space but does not affect the corresponding orthogonal residuals we demonstrate that compared with complete randomization rerandomization reduces the asymptotic quantile ranges of the difference in means estimator moreover our work constructs accurate large sample confidence intervals for the average causal effect

rerandomization to improve covariate balance in experiments randomized experiments are the gold standard for estimating causal effects yet often in practice chance imbalances exist in covariate distributions between treatment groups if covariate data are available before units are exposed to treatments these chance imbalances can be mitigated by first checking covariate balance before the physical experiment takes place provided a precise definition of imbalance has been specified in advance unbalanced randomizations can be discarded followed by a rerandomization and this process can continue until a randomization yielding balance according to the definition is achieved by improving covariate balance rerandomization provides more precise and trustworthy estimates of treatment effects

bregman divergence bounds and universality properties of the logarithmic loss a loss function measures the discrepancy between the true values and their estimated fits for a given instance of data in classification problems a loss function is said to be proper if a minimizer of the expected loss is the true underlying probability we show that for binary classification the divergence associated with smooth proper and convex loss functions is upper bounded by the kullback leibler kl divergence to within a normalization constant this implies that by minimizing the logarithmic loss associated with the kl divergence we minimize an upper bound to any choice of loss from this set as such the logarithmic loss is universal in the sense of providing performance guarantees with respect to a broad class of accuracy measures importantly this notion of universality is not problem specific enabling its use in diverse applications including predictive modeling data clustering and sample complexity analysis generalizations to arbitary finite alphabets are also developed the derived inequalities extend several well known f divergence results

adaptive wavelet estimation a block thresholding and oracle inequality approach we study wavelet function estimation via the approach of block thresh olding and ideal adaptation with oracle oracle inequalities are derived and serve as guides for the selection of smoothing parameters based on an oracle inequality and motivated by the data compression and localization properties of wavelets an adaptive wavelet estimator for nonparametric re gression is proposed and the optimality of the procedure is investigated we show that the estimator achieves simultaneously three objectives adaptiv ity spatial adaptivity and computational efficiency specifically it is proved that the estimator attains the exact optimal rates of convergence over a range of besov classes and the estimator achieves adaptive local minimax rate for estimating functions at a point the estimator is easy to imple ment at the computational cost of on simulation shows that the es timator has excellent numerical performance relative to more traditional wavelet estimators 1 introduction wavelet methods have demonstrated considerable suc cess in nonparametric function estimation in terms of spatial adaptivity com putational efficiency and asymptotic optimality in contrast to the traditional linear procedures wavelet methods achieve near optimal convergence rates over large function classes such as besov classes and enjoy excellent mean squared error properties when used to estimate functions that are spatially inhomogeneous for example as shown by donoho and johnstone 1998 wavelet methods can outperform optimal linear methods even at the level of convergence rate over certain besov classes standard wavelet methods achieve adaptivity through term by term thresholding of the empirical wavelet coefficients there each individual empirical wavelet coefficient is compared with a predetermined threshold a wavelet coefficient is retained if its magnitude is above the threshold level and is discarded otherwise a well known example of term by term thresholding is donoho and johnstone s visushrink donoho and johnstone 1994 visushrink is spatially adaptive and the estimator is within a log arithmic factor of the optimal convergence rate over a wide range of besov classes visushrink achieves a degree of tradeoff between variance and bias contributions to the mean squared error however the tradeoff is not optimal visushrink reconstruction is often over smoothed hall kerkyacharian and picard 1999 considered block thresholding for wavelet function estimation which thresholds empirical wavelet coefficients in

wavelet packet division multiplexing and wavelet packet design under timing error effects wavelet packet division multiplexing wpdm is a multiple signal transmission technique in which the message signals are waveform coded onto wavelet packet basis functions for transmission the overlapping nature of such waveforms in time and frequency provides a capacity improvement over the commonly used frequency division multiplexing fdm and time division multiplexing tdm schemes while their orthogonality properties ensure that the overlapping message signals can be separated by a simple correlator receiver the interference caused by timing offset in transmission is examined a design procedure that exploits the inherent degrees of freedom in the wpdm structure to mitigate the effects of timing error is introduced and a waveform that minimizes the energy of the timing error interference is designed an expression for the probability of error due to the presence of gaussian noise and timing error for the transmission of binary data is derived the performance advantages of the designed waveform over standard wavelet packet basis functions are demonstrated by both analytical and simulation methods the capacity improvement of wpdm its simple implementation and the possibility of having optimum waveform designs indicate that wpdm holds considerable promise as a multiple signal transmission technique

wavelet transform inversion with prior scale information the concept of scale is of central importance in all problems related to the interpretation of earth data inversion of geophysical data does not at present however allow the incorporation of scale dependent information directly this article presents an application of the wavelet transform to traveltime inversion where we are specifically concerned with the selection and application of a priori scale information in the wavelet domain to reconstruct tomographic models because of the nature of the problem the wavelet basis chosen for this example is the haar basis the results are compared with the classic damped least squares dls method which is a special case of the wavelet transform approach when all the scales are treated equally we show that with scale dependent prior information most of the artifacts created by the dls technique are diminished considerably

a note on divergences in many areas of neural computation like learning optimization estimation and inference suitable divergences play a key role in this note we study the conjecture presented by amari 2009 and find a counterexample to show that the conjecture does not hold generally moreover we investigate two classes of divergence zhang 2004 weighted f divergence and weighted divergence and prove that if a divergence is a weighted f divergence as well as a bregman divergence then it is a weighted divergence this result reduces in form to the main theorem established by amari 2009 when

on the choice of smoothing parameter threshold and truncation in nonparametric regression by non linear wavelet methods summary concise asymptotic theory is developed for non linear wavelet estimators of regression means in the context of general error distributions general designs general normalizations in the case of stochastic design and non structural assumptions about the mean the influence of the tail weight of the error distribution is addressed in the setting of choosing threshold and truncation parameters mainly the tail weight is described in an extremely simple way by a moment condition previous work on this topic has generally imposed the much more stringent assumption that the error distribution be normal different approaches to correction for stochastic design are suggested these include conventional kernel estimation of the design density in which case the interaction between the smoothing parameters of the non linear wavelet estimator and the linear kernel method is described

detection localization and estimation of edges a method to detect locate and estimate edges in a one dimensional signal is presented it is inherently more accurate than all previous schemes as it explicitly models and corrects interaction between nearby edges the method is iterative with initial estimation of edges provided by the zero crossings of the signal convolved with laplacian of gaussian log filter the necessary computations necessitate knowledge of this convolved output only in a neighborhood around each zero crossing and in most cases could be performed locally by independent parallel processors results on one dimensional slices extracted from real images and on images which have been proposed independently in the row and column directions are shown an analysis of the method is provided including issues of complexity and convergence and directions of future research are outlined

fractional splines and wavelets we extend schoenberg s family of polynomial splines with uniform knots to all fractional degrees alpha 1 these splines which involve linear combinations of the one sided power functions x alpha max 0 x alpha are alpha holder continuous for alpha 0 we construct the corresponding b splines by taking fractional finite differences and provide an explicit characterization in both time and frequency domains we show that these functions satisfy most of the properties of the traditional b splines including the convolution property and a generalized fractional differentiation rule that involves finite differences only we characterize the decay of the b splines that are not compactly supported for nonintegral alpha s their most astonishing feature in reference to the strang fix theory is that they have a fractional order of approximation alpha 1 while they reproduce the polynomials of degree lceil alpha rceil for alpha frac 1 2 they satisfy all the requirements for a multiresolution analysis of ll 2 riesz bounds two scale relation and may therefore be used to build new families of wavelet bases with a continuously varying order parameter our construction also yields symmetrized fractional b splines which provide the connection with duchon s general theory of radial m s splines including thin plate splines in particular we show that the symmetric version of our splines can be obtained as the solution of a variational problem involving the norm of a fractional derivative

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

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

continuous and discrete wavelet transforms this paper is an expository survey of results on integral representations and discrete sum expansions of functions in l 2 bf r in terms of coherent states two types of coherent states are considered weyl heisenberg coherent states which arise from translations and modulations of a single function and affine coherent states called wavelets which arise as translations and dilations of a single function in each case it is shown how to represent any function in l 2 bf r as a sum or integral of these states most of the paper is a survey of literature most notably the work of i daubechies a grossmann and j morlet a few results of the authors are included

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

edge detection in bar code signals corrupted by integrated time varying speckle accurate edge localization is of primary importance in bar code decoding in this paper we investigate statistical properties of edge localization error when a bar code signal is corrupted by additive noise which is a weakly stationary random process we derive a first order approximation for the expected value and standard deviation of the error in terms of the power spectral density psd of the noise this result is used to estimate the edge localization error caused by speckle noise we show that the standard deviation of the error is determined by the intensity distribution of a scanning beam and the positions of neighboring edges we discuss how the error analysis determines the detection rates of a scanning system and how it can be used in the system design analytical examples are provided for upca bar code symbols and a scanning beam with gaussian distribution

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

algorithms for designing wavelets to match a specified signal algorithms for designing a mother wavelet spl psi x such that it matches a signal of interest and such that the family of wavelets 2 sup j 2 spl psi 2 sup j x k forms an orthonormal riesz basis of l sup 2 spl rscr are developed the algorithms are based on a closed form solution for finding the scaling function spectrum from the wavelet spectrum many applications require wavelets that are matched to a signal of interest most current design techniques however do not design the wavelet directly they either build a composite wavelet from a library of previously designed wavelets modify the bases in an existing multiresolution analysis or design a scaling function that generates a multiresolution analysis with some desired properties in this paper two sets of equations are developed that allow us to design the wavelet directly from the signal of interest both sets impose bandlimitedness resulting in closed form solutions the first set derives expressions for continuous matched wavelet spectrum amplitudes the second set of equations provides a direct discrete algorithm for calculating close approximations to the optimal complex wavelet spectrum the discrete solution for the matched wavelet spectrum amplitude is identical to that of the continuous solution at the sampled frequencies an interesting byproduct of this work is the result that meyer s spectrum amplitude construction for an orthonormal bandlimited wavelet is not only sufficient but necessary specific examples are given which demonstrate the performance of the wavelet matching algorithms for both known orthonormal wavelets and arbitrary signals

optimal a priori balance in the design of controlled experiments summary we develop a unified theory of designs for controlled experiments that balance baseline covariates a priori before treatment and before randomization using the framework of minimax variance and a new method called kernel allocation we show that any notion of a priori balance must go hand in hand with a notion of structure since with no structure on the dependence of outcomes on baseline covariates complete randomization no special covariate balance is always minimax optimal restricting the structure of dependence either parametrically or non parametrically gives rise to certain covariate imbalance metrics and optimal designs this recovers many popular imbalance metrics and designs previously developed ad hoc including randomized block designs pairwise matched allocation and rerandomization we develop a new design method called kernel allocation based on the optimal design when structure is expressed by using kernels which can be parametric or non parametric relying on modern optimization methods kernel allocation which ensures nearly perfect covariate balance without biasing estimates under model misspecification offers sizable advantages in precision and power as demonstrated in a range of real and synthetic examples we provide strong theoretical guarantees on variance consistency and rates of convergence and develop special algorithms for design and hypothesis testing

strictly proper scoring rules prediction and estimation scoring rules assess the quality of probabilistic forecasts by assigning a numerical score based on the predictive distribution and on the event or value that materializes a scoring rule is proper if the forecaster maximizes the expected score for an observation drawn from the distributionf if he or she issues the probabilistic forecast f rather than g f it is strictly proper if the maximum is unique in prediction problems proper scoring rules encourage the forecaster to make careful assessments and to be honest in estimation problems strictly proper scoring rules provide attractive loss and utility functions that can be tailored to the problem at hand this article reviews and develops the theory of proper scoring rules on general probability spaces and proposes and discusses examples thereof proper scoring rules derive from convex functions and relate to information measures entropy functions and bregman divergences in the case of categorical variables we prove a rigorous version of the

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

feature extraction across individual time series observations with spikes using wavelet principal component analysis clinical studies frequently include repeated measurements of individuals often for long periods we present a methodology for extracting common temporal features across a set of individual time series observations in particular the methodology explores extreme observations within the time series such as spikes as a possible common temporal phenomenon wavelet basis functions are attractive in this sense as they are localized in both time and frequency domains simultaneously allowing for localized feature extraction from a time varying signal we apply wavelet basis function decomposition of individual time series with corresponding wavelet shrinkage to remove noise we then extract common temporal features using linear principal component analysis on the wavelet coefficients before inverse transformation back to the time domain for clinical interpretation we demonstrate the methodology on a subset of a large fetal activity study aiming to identify temporal patterns in fetal movement fm count data in order to explore formal fm counting as a screening tool for identifying fetal compromise and thus preventing adverse birth outcomes copyright 2013 john wiley sons ltd

a joint estimation approach for two tone image deblurring by blind deconvolution a new statistical method is proposed for deblurring two tone images i e images with two unknown grey levels that are blurred by an unknown linear filter the key idea of the proposed method is to adjust a deblurring filter until its output becomes two tone two optimization criteria are proposed for the adjustment of the deblurring filter a three step iterative algorithm tsia is also proposed to minimize the criteria it is proven mathematically that by minimizing either of the criteria the original nonblurred image along with the blur filter will be recovered uniquely only with possible scale shift ambiguities at high snr the recovery is guaranteed not only for i i d images but also for correlated and nonstationary images it does not require a priori knowledge of the statistical parameters or the tone values of the original image neither does it require a priori knowledge of the phase or other special information e g fir symmetry nonnegativity etc about the blur filter numerical experiments are carried out to test the method on synthetic and real images

the root unroot algorithm for density estimation as implemented via wavelet block thresholding we propose and implement a density estimation procedure which begins by turning density estimation into a nonparametric regression problem this regression problem is created by binning the original observations into many small size bins and by then applying a suitable form of root transformation to the binned data counts in principle many common nonparametric regression estimators could then be applied to the transformed data we propose use of a wavelet block thresholding estimator in this paper finally the estimated regression function is un rooted by squaring and normalizing the density estimation procedure achieves simultaneously three objectives computational efficiency adaptivity and spatial adaptivity a numerical example and a practical data example are discussed to illustrate and explain the use of this procedure theoretically it is shown that the estimator simultaneously attains the optimal rate of convergence over a wide range of the besov classes the estimator also automatically adapts to the local smoothness of the underlying function and attains the local adaptive minimax rate for estimating functions at a point there are three key steps in the technical argument poissonization quantile coupling and oracle risk bound for block thresholding in the non gaussian setting some of the technical results may be of independent interest

an introduction to wavelets with applications to andrews plots a brief introduction to wavelets targeted to the statistician is given several types of wavelets are described and compared with the fourier functions it is shown how wavelets might extend the multivariate clustering technique of andrews plots

adaptive learning for event modeling and characterization adaptive learning of specific patterns or events of interest has been an area of significant research for various applications in the last two decades in developing diagnostic evaluation and safety monitoring applications of a propulsion system it is critical to detect characterize and model events of interest it is a challenging task since the detection system should allow adaptive characterization of potential events of interest and correlate them to learn new models for future detection for online health monitoring and diagnostic evaluation in this paper a novel framework is established using a hierarchical adaptive clustering approach with fuzzy membership functions to characterize specific events of interest from the measured and processed features raw engine measurement data is first analyzed using the wavelet transform to provide features for localization of frequency information for use in the classification system a method combining hierarchical and fuzzy k means clustering is then applied to a set of selected measurements and computed features to determine the events of interest during engine operations experimental results have shown that the proposed approach is effective and computationally efficient to detect characterize and model new events of interest from data collected through continuous operations

the covariate adaptive biased coin design for balancing clinical trials in the presence of prognostic factors the present paper deals with sequential designs intended to balance the allocations of two competing treatments in the presence of prognostic factors after giving a theoretical framework on the optimality of balanced designs that can arise when covariates are taken into account we propose a new family of covariate adaptive randomized designs that represents higher order approximation to balance treatments both globally and also across covariates we derive the theoretical properties of the suggested designs in terms of loss of precision and predictability the performance of this proposal is illustrated through a simulation study and compared with those of other procedures suggested in the literature copyright 2011 oxford university press

deblurring of bilevel waveforms an algorithm for processing closely spaced edges and accurately restoring their locations is presented the convolution distortion model is based on interacting edges the restoration algorithm takes three edges as input and forces the effects of two of them to cancel each other thus the third edge appears to be isolated and is located using a traditional edge detector experiments on bar code waveforms reveal that this approach outperforms the current commercial bar code readers

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