empirical and poisson processes on classes of sets or functions too large for central limit theorems let p be the uniform probability law on the unit cube i d in d dimensions and p n the corresponding empirical measure for various classes of sets a i d upper and lower bounds are found for the probable size of sup p n p a a if is the collection of lower layers in i 2 or of convex sets in i 3 an asymptotic lower bound is left left log n right mathord left vphantom left log n right n right n 1 mathord left vphantom 1 2 right kern nulldelimiterspace 2 right left log log n right delta 1 mathord left vphantom 1 2 right 2 quad rm for rm any delta 0 thus the law of the iterated logarithm fails for these classes if 0 is the greatest integer 0 when d 1 the same lower bound is obtained as for the lower layers in i 2 or convex sets in i 3 for 0 alpha underline le d 1 there is also an upper bound equal to a power of log n times the lower bound so the powers of n are sharp

on the glivenko cantelli problem in stochastic programming linear recourse and extensions integrals of optimal values of random optimization problems depending on a finite dimensional parameter are approximated by using empirical distributions instead of the original measure under fairly broad conditions it is proved that uniform convergence of empirical approximations of the right hand sides of the constraints implies uniform convergence of the optimal values in the linear and convex case

mathematics for demosaicking digital color cameras sample the continuous color spectrum using three or more filters however each pixel represents a sample of only one of the color bands this arrangement is called a mosaic to produce a full resolution color image the recorded image must be processed to estimate the values of the pixels for all the other color bands this restoration process is often called demosaicking this paper uses stacked notation to represent the mosaicked image capture and derives the minimum mean square error mmse estimator for the demosaicked image by making common assumptions the restoration can be computed in a cost effective manner extensions to the linear method are proposed to allow adaptive behavior

the mollification method and the numerical solution of the inverse heat conduction problem by finite differences abstract the inverse heat conduction problem involves the calculation of surface heat flux and or temperature histories from transient measured temperatures inside solids we consider the one dimensional semi infinite linear case and present a new solution algorithm based on a data filtering interpretation of the mollification method that automatically determines the radius of mollification depending on the amount of noise in the data and finite differences a fully explicit and stable space marching scheme is developed we describe several numerical experiments of interest showing that the new procedure is accurate and stable with respect to perturbations in the data even for small dimensionless time steps

the asymptotic value to capacity ratio for the multi class stochastic knapsack problem we consider a stochastic knapsack problem that packs multiple classes of random items the pairs of profit and resource requirement for items of the same class are independent and identically distributed however such pairs for different classes of items are independent but not necessarily identically distributed we investigate convergence and the asymptotic value of the ratio of the knapsack value function to the capacity when the capacity increases we consider two growth models for the multi class stochastic knapsack problem one where the number of available items grows proportionally to the capacity and the other one where the available items are sampled until their total resource requirement does not exceed the capacity by extending the results of meanti et al on a single class of random items we show that for each growth model the ratio converges almost surely to a computable constant for special cases where resource requirements or profit coefficients are deterministic we present simple interpretations on the asymptotic values finally we present an exponential order upperbound on the tail probability of the ratio

a mollified space marching finite differences algorithm for the inverse heat conduction problem with slab symmetry abstract the one dimensional inverse heat conduction problem ihcp for a slab is considered a new solution algorithm based on a data filtering interpretation of the mollification method is presented and a fully explicit space marching finite differences scheme is developed after showing the numerical stability of the algorithm the efficiency of the method is demonstrated by means of several examples the numerical results show the procedure to be very useful in the presence of noisy data even for some nonlinear cases

optimized color filter arrays for sparse representation based demosaicking demosaicking is the problem of reconstructing a color image from the raw image captured by a digital color camera that covers its only imaging sensor with a color filter array cfa sparse representation based demosaicking has been shown to produce superior reconstruction quality however almost all existing algorithms in this category use the cfas which are not specifically optimized for the algorithms in this paper we consider optimally designing cfas for sparse representation based demosaicking where the dictionary is well chosen the fact that cfas correspond to the projection matrices used in compressed sensing inspires us to optimize cfas via minimizing the mutual coherence this is more challenging than that for traditional projection matrices because cfas have physical realizability constraints however most of the existing methods for minimizing the mutual coherence require that the projection matrices should be unconstrained making them inapplicable for designing cfas we consider directly minimizing the mutual coherence with the cfa s physical realizability constraints as a generalized fractional programming problem which needs to find sufficiently accurate solutions to a sequence of nonconvex nonsmooth minimization problems we adapt the redistributed proximal bundle method to address this issue experiments on benchmark images testify to the superiority of the proposed method in particular we show that a simple sparse representation based demosaicking algorithm with our specifically optimized cfa can outperform lssc 1 to the best of our knowledge it is the first sparse representation based demosaicking algorithm that beats lssc in terms of cpsnr

probabilistic properties of the dual structure of the multidimensional knapsack problem and fast statistically efficient algorithms properties of several dual characteristics of the multidimensional knapsack problem such as the probability of existence of optimal and optimal feasible lagrange function generalized saddle points magnitude of relative duality gap etc are investigated for different probabilistic models sufficient conditions of good asymptotic behavior of the dual characteristics are given a fast statistically efficient approximate algorithm with linear running time complexity for problems with random coefficients is presented

geometry based demosaicking demosaicking is a particular case of interpolation problems where from a scalar image in which each pixel has either the red the green or the blue component we want to interpolate the full color image state of the art demosaicking algorithms perform interpolation along edges but these edges are estimated locally we propose a level set based geometric method to estimate image edges inspired by the image in painting literature this method has a time complexity of o s where s is the number of pixels in the image and compares favorably with the state of the art algorithms both visually and in most relevant image quality measures

probability inequalities for empirical processes and a law of the iterated logarithm given a class f of functions on x we can view vn as a stochastic process indexed by f and consider limit theorems for this process to prove such theorems it is often helpful to have bounds on the tail of the r v sup w i n f i see for example dudley 1978 kuelbs and dudley 1980 dudley and phillip 1983 or gine and zinn 1983 our main question of interest is for what classes f can best possible bounds be obtained so first we must ask what are these best possible bounds of course

confidence sets for a multivariate distribution on etudie une version multivariable alternative de la bande de confiance unidimensionnelle de kolmogorov smirnov qui preserve l invariance affine

a generalization of the product limit estimator with an application to censored regression the product limit estimator ple and weighted empirical processes are two important ingredients of almost any censored regression analysis a link between them is provided by the generalized ples introduced in this paper these generalized ples are the product limit integrals of the empirical cumulative hazard function estimators in which weighted empirical processes are used to replace the standard empirical processes the weak convergence and some large sample approximations of the generalized ples are established as an application these generalized ples are used to define some minimum distance estimators which are shown to be asymptotically normal these estimators are qualitatively robust in some submodels an optimal choice of the weight matrix is the covariate matrix and some of these estimators are quite efficient at a few common survival distributions to implement these estimators some computational aspects are discussed and an algorithm is given from a real data example and some preliminary simulation results these estimators seem to be very competitive to and more robust than some more traditional estimators such as the buckley james estimator

optimal random matchings tours and spanning trees in hierarchically separated trees we derive tight bounds on the expected weights of several combinatorial optimization problems for random point sets of size n distributed among the leaves of a balanced hierarchically separated tree we consider monochromatic and bichromatic versions of the minimum matching minimum spanning tree and traveling salesman problems we also present tight concentration results for the monochromatic problems

exact bounds for the stochastic upward matching problem we draw at random independently and according to the uniform distribution two sets of n points of the unit square we consider a maximum matching of points of the first set with points of the second set with the restriction that a point can be matched only with a point located at its upper right then with probability close to one the number of unmatched points is of order nl 2 log n 3 4

color demosaicking via directional linear minimum mean square error estimation digital cameras sample scenes using a color filter array of mosaic pattern e g the bayer pattern the demosaicking of the color samples is critical to the image quality this paper presents a new color demosaicking technique of optimal directional filtering of the green red and green blue difference signals under the assumption that the primary difference signals pds between the green and red blue channels are low pass the missing green samples are adaptively estimated in both horizontal and vertical directions by the linear minimum mean square error estimation lmmse technique these directional estimates are then optimally fused to further improve the green estimates finally guided by the demosaicked full resolution green channel the other two color channels are reconstructed from the lmmse filtered and fused pds the experimental results show that the presented color demosaicking technique outperforms the existing methods both in psnr measure and visual perception

adaptive filtering for color filter array demosaicking most digital still cameras acquire imagery with a color filter array cfa sampling only one color value for each pixel and interpolating the other two color values afterwards the interpolation process is commonly known as demosaicking in general a good demosaicking method should preserve the high frequency information of imagery as much as possible since such information is essential for image visual quality we discuss in this paper two key observations for preserving high frequency information in cfa demosaicking 1 the high frequencies are similar across three color components and 2 the high frequencies along the horizontal and vertical axes are essential for image quality our frequency analysis of cfa samples indicates that filtering a cfa image can better preserve high frequencies than filtering each color component separately this motivates us to design an efficient filter for estimating the luminance at green pixels of the cfa image and devise an adaptive filtering approach to estimating the luminance at red and blue pixels experimental results on simulated cfa images as well as raw cfa data verify that the proposed method outperforms the existing state of the art methods both visually and in terms of peak signal to noise ratio at a notably lower computational cost

multilevel algorithms for ill posed problems in this paper new multilevel algorithms are proposed for the numerical solution of first kind operator equations convergence estimates are established for multilevel algorithms applied to tikhonov type regularization methods our theory relates the convergence rate of these algorithms to the minimal eigenvalue of the discrete version of the operator and the regularization parameter the algorithms and analysis are presented in an abstract setting that can be applied to first kind integral equations

optimal aggregation of classifiers in statistical learning classification can be considered as nonparametric estimation of sets where the risk is defined by means of a specific distance between sets associated with misclassification error it is shown that the rates of convergence of classifiers depend on two parameters the complexity of the class of candidate sets and the margin parameter the dependence is explicitly given indicating that optimal fast rates approaching o n 1 can be attained where n is the sample size and that the proposed classifiers have the property of robustness to the margin the main result of the paper concerns optimal aggregation of classifiers we suggest a classifier that automatically adapts both to the complexity and to the margin and attains the optimal fast rates up to a logarithmic factor

the design and evaluation of a generic method for generating mosaicked multispectral filter arrays the technology of color filter arrays cfa has been widely used in the digital camera industry since it provides several advantages like low cost exact registration and strong robustness the same motivations also drive the design of multispectral filter arrays msfa in which more than three spectral bands are used although considerable research has been reported to optimally reconstruct the full color image using various demosaicking algorithms studies on the intrinsic properties of these filter arrays as well as the underlying design principles have been very limited given a set of representative spectral bands the design of an msfa involves two issues the selection of tessellation mechanisms and the arrangement layout of different spectral bands we develop a generic msfa generation method starting from a checkerboard pattern we show through case studies that most of the cfas currently used by the industry can be derived as special cases of msfas generated using the generic algorithm the performance of different msfas are evaluated based on their intrinsic properties namely the spatial uniformity and the spectral consistency we design two metrics static coefficient and consistency coefficient to measure these two parameters respectively the experimental results demonstrate that the generic algorithm can generate optimal or near optimal msfas in both the rectangular and the hexagonal domains

smooth discrimination analysis ties f and g can be based on the estimation of the set g x fx gx we consider applications where it is appropriate to assume that the region g has a smooth boundary or belongs to another nonparametric class of sets in particular this assumption makes sense if discrimination is used as a data analytic tool decision rules based on minimization of empirical risk over the whole class of sets and over sieves are considered their rates of convergence are obtained we show that these rules achieve optimal rates for estimation of g and optimal rates of convergence for bayes risks an interesting conclusion is that the optimal rates for bayes risks can be very fast in particular faster than the parametric root n rate these fast rates cannot be guaranteed for plug in rules

color filter array demosaicking using high order interpolation techniques with a weighted median filter for sharp color edge preservation demosaicking is an estimation process to determine missing color values when a single sensor digital camera is used for color image capture in this paper we propose a number of new methods based on the application of taylor series and cubic spline interpolation for color filter array demosaicking to avoid the blurring of an edge interpolants are first estimated in four opposite directions so that no interpolation is carried out across an edge a weighted median filter whose filter coefficients are determined by a classifier based on an edge orientation map is then used to produce an output from the four interpolants to preserve edges using the proposed methods the original color can be faithfully reproduced with minimal amount of color artifacts even at edges

on rates of convergence and asymptotic normality in the multiknapsack problem in meanti et al 1990 an almost sure asymptotic characterization has been derived for the optimal solution value as function of the knapsack capacities when the profit and requirement coefficients of items to be selected from are random variables in this paper we establish a rate of convergence for this process using results from the theory of empirical processes

an integral solution for the inverse heat conduction problem after the method of weber abstract we consider the linear inverse heat conduction problem ihcp in the one dimensional semi infinite slab and present a new solution algorithm and error bounds based on the integral representation of weber s hyperbolic approximation and a suitable filtered version of the noisy data we discuss the determination of the hyperbolic parameter and describe several numerical examples of interest showing the accuracy and stability of the method

regularity of gaussian processes on donne la validite de la conjecture de fernique 1974 sur l existence de mesures de majoration pouvant caracteriser la limitation des processus gaussiens

robust color demosaicking with adaptation to varying spectral correlations almost all existing color demosaicking algorithms for digital cameras are designed on the assumption of high correlation between red green blue or some other primary color bands they exploit spectral correlations between the primary color bands to interpolate the missing color samples but in areas of no or weak spectral correlations these algorithms are prone to large interpolation errors such demosaicking errors are visually objectionable because they tend to correlate with object boundaries and edges this paper proposes a remedy to the above problem that has long been overlooked in the literature the main contribution of this work is a hybrid demosaicking approach that supplements an existing color demosaicking algorithm by combining its results with those of adaptive intraband interpolation this is formulated as an optimal data fusion problem and two solutions are proposed one is based on linear minimum mean square estimation and the other based on support vector regression experimental results demonstrate that the new hybrid approach is more robust and eliminates the worst type of color artifacts of existing color demosaicking methods

universal demosaicking of color filter arrays a large number of color filter arrays cfas periodic or aperiodic have been proposed to reconstruct images from all different cfas and compare their imaging quality a universal demosaicking method is needed this paper proposes a new universal demosaicking method based on inter pixel chrominance capture and optimal demosaicking transformation it skips the commonly used step to estimate the luminance component at each pixel and thus avoids the associated estimation error instead we directly use the acquired cfa color intensity at each pixel as an input component two independent chrominance components are estimated at each pixel based on the inter pixel chrominance in the window which is captured with the difference of cfa color values between the pixel of interest and its neighbors two mechanisms are employed for the accurate estimation distance related and edge sensing weighting to reflect the confidence levels of the inter pixel chrominance components and pseudoinverse based estimation from the components in a window then from the acquired cfa color component and two estimated chrominance components the three primary colors are reconstructed by a linear color transform which is optimized for the least transform error our experiments show that the proposed method is much better than other published universal demosaicking methods

a geometric method for optimal design of color filter arrays a color filter array cfa used in a digital camera is a mosaic of spectrally selective filters which allows only one color component to be sensed at each pixel the missing two components of each pixel have to be estimated by methods known as demosaicking the demosaicking algorithm and the cfa design are crucial for the quality of the output images in this paper we present a cfa design methodology in the frequency domain the frequency structure which is shown to be just the symbolic dft of the cfa pattern one period of the cfa is introduced to represent images sampled with any rectangular cfas in the frequency domain based on the frequency structure the cfa design involves the solution of a constrained optimization problem that aims at minimizing the demosaicking error to decrease the number of parameters and speed up the parameter searching the optimization problem is reformulated as the selection of geometric points on the boundary of a convex polygon or the surface of a convex polyhedron using our methodology several new cfa patterns are found which outperform the currently commercialized and published ones experiments demonstrate the effectiveness of our cfa design methodology and the superiority of our new cfa patterns

adaptive homogeneity directed demosaicing algorithm a cost effective digital camera uses a single image sensor applying alternating patterns of red green and blue color filters to each pixel location a way to reconstruct a full three color representation of color images by estimating the missing pixel components in each color plane is called a demosaicing algorithm this paper presents three inherent problems often associated with demosaicing algorithms that incorporate two dimensional 2 d directional interpolation misguidance color artifacts interpolation color artifacts and aliasing the level of misguidance color artifacts present in two images can be compared using metric neighborhood modeling the proposed demosaicing algorithm estimates missing pixels by interpolating in the direction with fewer color artifacts the aliasing problem is addressed by applying filterbank techniques to 2 d directional interpolation the interpolation artifacts are reduced using a nonlinear iterative procedure experimental results using digital images confirm the effectiveness of this approach

on maximum likelihood estimation in infinite dimensional parameter spaces an approximate maximum likelihood estimate is known to be consistent under some compactness and integrability conditions in this paper we study its convergence rate and its asymptotic efficiency in estimating smooth functionals of the parameter we provide conditions under which the rate of convergence can be established this rate is essentially governed by the size of the space of score functions as measured by an entropy index we also show that for a large class of smooth functionals the plug in maximum likelihood estimate is asymptotically efficient that is it achieves the minimal fisher information bound the theory is illustrated by several nonparametric or semiparametric examples

average case analysis of cutting and packing in two dimensions abstract stock cutting and packing in two dimensions is a source of problems of great practical significance much has been written on the subject including several surveys but the focus of the mathematically oriented research has been largely on combinatorial optimization and worst case analysis recently substantial progress has been made in the average case analysis of algorithms for two dimensional packing this paper reviews selected illustrative results in this area of research and discusses desirable extensions and open problems several cutting and packing algorithms are defined and the results of their probabilistic analysis reported from the presentation of this material it is clear that the field is still in early stages of development the algorithms and probability models tend to be simplistic and stimates of performance are far more common that exact measures in spite of these limitations valuable and in some cases unexpected insights have emerged

minimax grid matching and empirical measures in this article we solve the minimax grid matching problem in dimensions greater than two as a by product we settle a long open problem involving the glivenko cantelli convergence of empirical measures

central limit theorems for stochastic processes under random entropy conditions necessary and sufficient conditions are found for the weak convergence of the row sums of an infinitesimal row independent triangular array nj of stochastic processes indexed by a set s to a sample continuous gaussian process when the array satisfies a random entropy condition analogous to one used by gine and zinn 1984 for empirical processes this entropy condition is satisfied when s is a class of sets or functions with the vapnik ervonenkis property and each nj f fd nj is of the form njc for some reasonable random finite signed measure vnj as a result we obtain necessary and sufficient conditions for the weak convergence of possibly non i i d partial sum processes and new sufficient conditions for empirical processes indexed by vapnik ervonenkis classes special cases include prokhorov s 1956 central limit theorem for empirical processes and shorack s 1979 theorems on weighted empirical processes

censored median regression using weighted empirical survival and hazard functions abstract for median regression models that regress the median of the survival time or a transform thereof on the covariates some semi parametric estimators that include the intercept component are introduced when the survival time may be censored these new median regression estimators do not require estimating the censoring distributions they can be viewed as an extension of the sample median to the censored regression model these estimators are based on some weighted empirical survival and hazard functions and are shown to be consistent and asymptotically normal they performed very well in various numerical studies the proposed procedures are illustrated in some real data examples

an edge sensing generic demosaicing algorithm with application to image resampling in this paper we introduce a new demosaicing algorithm that can be used for various sensor images captured by digital cameras equipped with various red green blue color filter arrays our algorithm enhances the universal demosaicing algorithm of lukac et al by defining a new spectral interpolation model that exploits not only the information on the color of pixels but also the relative distance between neighboring pixels within an image moreover we include an edge detection model that makes our algorithm adaptive and reduces the presence of color shifts and artifacts a series of tests has been made on images of the kodak database and our algorithm performs better than the universal demosaicing algorithm with regard to both subjective and objective evaluation the versatility of our demosaicing algorithm is also highlighted through an application to the issue of color image resampling and we obtain conclusive experimental results

some new estimators for cox regression new estimators for cox regression are considered their asymptotic properties both on and off the model are established corollaries include conditions under which the maximum partial likelihood estimator defines a parameter in the population and the asymptotics of the case cohort estimator robust estimators that minimize the asymptotic variance subject to a bound on the maximal bias on infinitesimal neighborhoods are discussed the estimators are illustrated with medical data

competing risks quantile regression quantile regression has emerged as a significant extension of traditional linear models and its potential in survival applications has recently been recognized in this paper we study quantile regression with competing risks data formulating the model based on conditional quantiles defined using the cumulative incidence function which includes as a special case an analog to the usual accelerated failure time model the proposed competing risks quantile regression model provides meaningful physical interpretations of covariate effects and moreover relaxes the constancy constraint on regression coefficients thereby providing a useful perhaps more flexible alternative to the popular subdistribution proportional hazards model we derive an unbiased monotone estimating equation for regression parameters in the quantile model the uniform consistency and weak convergence of the resulting estimators are established across a quantile continuum we develop inferences including covariance estimation second

wavelet and fourier methods for solving the sideways heat equation we consider an inverse heat conduction problem the sideways heat equation which is a model of a problem where one wants to determine the temperature on both sides of a thick wall but where one side is inaccessible to measurements mathematically it is formulated as a cauchy problem for the heat equation in a quarter plane with data given along the line x 1 where the solution is wanted for 0 leq x 1 the problem is ill posed in the sense that the solution if it exists does not depend continuously on the data we consider stabilizations based on replacing the time derivative in the heat equation by wavelet based approximations or a fourier based approximation the resulting problem is an initial value problem for an ordinary differential equation which can be solved by standard numerical methods e g a runge kutta method we discuss the numerical implementation of fourier and wavelet methods for solving the sideways heat equation theory predicts that the fourier method and a method based on meyer wavelets will give equally good results our numerical experiments indicate that also a method based on daubechies wavelets gives comparable accuracy as test problems we take model equations with constant and variable coefficients we also solve a problem from an industrial application with actual measured data

coupled samples in simulation assume that we wish to generate two samples of n independent identically distributed random variables x1 xn and y1 yn where x1 and y1 have densities f and g respectively if these samples are used in a simulation and f is close to g it is sometimes desirable to have close simulation results this can be achieved by insisting that both samples agree in most of their components that is xi yi for as many i as possible under the given distributional constraints samples with this property are said to be optimally coupled in this paper we propose and study various methods of coupling two samples a sequence of samples and an infinite family of samples

a note on phillips 1991 a constrained maximum likelihood approach to estimating switching regressions abstract phillips phillips r f 1991 a constrained maximum likelihood approach to estimating switching regressions journal of econometrics 48 241 262 proposed a constrained maximum likelihood approach to estimating the parameters in a switching regression model in this note we propose a new approach which leads to a proof of a more general result than phillips s specifically we prove that the constrained mle cmle is still strongly consistent when the constant c decreases to 0 at the rate of exp n 1 2 log n as n increases to with 1 we also suggest a suitable hence c n for practice based on simulation results

a new color filter array with optimal properties for noiseless and noisy color image acquisition digital color cameras acquire color images by means of a sensor on which a color filter array cfa is overlaid the bayer cfa dominates the consumer market but there has recently been a renewed interest for the design of cfas however robustness to noise is often neglected in the design though it is crucial in practice in this paper we present a new 2 3 periodic cfa which provides by construction the optimal tradeoff between robustness to aliasing chrominance noise and luminance noise moreover a simple and efficient linear demosaicking algorithm is described which fully exploits the spectral properties of the cfa practical experiments confirm the superiority of our design both in noiseless and noisy scenarios

the multidimensional 0 1 knapsack problem an overview abstract the multidimensional 0 1 knapsack problem is one of the most well known integer programming problems and has received wide attention from the operational research community during the last four decades although recent advances have made possible the solution of medium size instances solving this np hard problem remains a very interesting challenge especially when the number of constraints increases this paper surveys the main results published in the literature the focus is on the theoretical properties as well as approximate or exact solutions of this special 0 1 program

estimation of extreme risk regions under multivariate regular variation when considering d possibly dependent random variables one is often interested in extreme risk regions with very small probability p we consider risk regions of the form z rd f z where f is the joint density and a small number estimation of such an extreme risk region is difficult since it contains hardly any or no data using extreme value theory we construct a natural estimator of an extreme risk region and prove a refined form of consistency given a random sample of multivariate regularly varying random vectors in a detailed simulation and comparison study the good performance of the procedure is demonstrated we also apply our estimator to financial data

multiscale gradients based color filter array interpolation single sensor digital cameras use color filter arrays to capture a subset of the color data at each pixel coordinate demosaicing or color filter array cfa interpolation is the process of estimating the missing color samples to reconstruct a full color image in this paper we propose a demosaicing method that uses multiscale color gradients to adaptively combine color difference estimates from different directions the proposed solution does not require any thresholds since it does not make any hard decisions and it is noniterative although most suitable for the bayer cfa pattern the method can be extended to other mosaic patterns to demonstrate this we describe its application to the lukac cfa pattern experimental results show that it outperforms other available demosaicing methods by a clear margin in terms of cpsnr and s cielab measures for both mosaic patterns

a stable space marching finite differences algorithm for the inverse heat conduction problem with no initial filtering procedure abstract we consider the one dimensional semi infinite linear inverse heat conduction problem ihcp and present a new solution algorithm based on singular perturbation techniques the new method successfully incorporates the needed initial filtering procedure of the noisy data into the marching scheme the concept of formal stability for the ihcp is analyzed and its relationship with the high frequency components of the measured data funciton is further studied by comparing the new method with the mollification method and the method of weber a fully explicit space marching finite differences scheme is developed and several numerical experiments of interest showing the accuracy and stability properties of the algorithm in the presence of noisy data and for small dimensionless time steps are investigated

on line bin packing with items of random size consider an i i d sequence of random variables x1 xn distributed according to a given distribution on 0 1 let c be the asymptotic optimal packing ratio i e c limn etn n where tn is the minimum number of unit size bins needed to pack x1 xn we prove the existence of an on line algorithm dependent on that packs x1 xn in nc on1 2log n3 4 bins

invariance principles for sums of banach space valued random elements and empirical processes almost sure and probability invariance principles are established for sums of independent not necessarily measurable random elements with values in a not necessarily separable banach space it is then shown that empirical processes readily fit into this general framework thus we bypass the problems of measurability and topology characteristic for the previous theory of weak convergence of empirical processes