identifying codes and covering problems the identifying code problem for a given graph involves finding a minimum set of vertices whose neighborhoods uniquely overlap at any given graph vertex initially introduced in 1998 this problem has demonstrated its fundamental nature through a wide variety of applications such as fault diagnosis location detection and environmental monitoring in addition to deep connections to information theory superimposed and covering codes and tilings this work establishes efficient reductions between the identifying code problem and the well known set covering problem resulting in a tight hardness of approximation result and novel provably tight polynomial time approximations the main results are also extended to r robust identifying codes and analogous set 2r 1 multicover problems finally empirical support is provided for the effectiveness of the proposed approximations including good constructions for well known topologies such as infinite two dimensional grids

second order volterra filtering and its application to nonlinear system identification some recent results on the design and implementation of second order volterra filters are presented the second order volterra filter is a nonlinear filter with the filter structure of second order volterra series a simple minimum mean square error solution for the volterra filter is derived based on the assumption that the filter input is gaussian also we propose an iterative factorization technique to design a subclass of the volterra filters which can alleviate the complexity of the filtering operations considerably furthermore an adaptive algorithm for the volterra filter is investigated along with its mean convergence and asymptotic excess mean square error finally the utility of the volterra filter is demonstrated by utilizing it in studies of nonlinear drift oscillations of moored vessels subject to random sea waves

adaptive noise smoothing filter for images with signal dependent noise in this paper we consider the restoration of images with signal dependent noise the filter is noise smoothing and adapts to local changes in image statistics based on a nonstationary mean nonstationary variance nmnv image model for images degraded by a class of uncorrelated signal dependent noise without blur the adaptive noise smoothing filter becomes a point processor and is similar to lee s local statistics algorithm 16 the filter is able to adapt itself to the nonstationary local image statistics in the presence of different types of signal dependent noise for multiplicative noise the adaptive noise smoothing filter is a systematic derivation of lee s algorithm with some extensions that allow different estimators for the local image variance the advantage of the derivation is its easy extension to deal with various types of signal dependent noise film grain and poisson signal dependent restoration problems are also considered as examples all the nonstationary image statistical parameters needed for the filter can be estimated from the noisy image and no a priori information about the original image is required

a comparison of numerical collocation and variational procedures to the hypersingular acoustic integral operator abstract a major difficulty in implementing many of the more innovative acoustic formulations for the solution of submerged three dimensional thin shells of arbitrary geometry in an unbounded fluid medium has been the difficulty of numerically approximating a hypersingular integral operator a variational approach given by hamdi reduces this hypersingularity cauchy singularity to a weak singularity allowing for its accurate numerical approximation recently mariem and hamdi a new boundary finite element method for fluid structure interaction internat j numer methods engrg 24 1987 1251 1267 presented an acoustic formulation for thin shells where the pressure difference across the shell is related to the shell s normal velocity solely in terms of this integral operator despite its advantage of generating a symmetric fluid matrix a double surface integration is required to form this matrix some researchers have endeavoured to develop a collocation method of approximating this highly singular operator in this paper a novel solution to the numerical approximation of this operator is given in the implementation of both the variational and collocation methodologies quadratic quadrilateral elements are used to interpolate for the acoustic and geometric variables results are then presented for thin shell scattering and radiation problems for both closed and non closed thin shells demonstrating the validity and accuracy of both methods

locating dominating sets of functigraphs abstract a locating dominating set of a graph g is a dominating set of g such that every vertex of g outside the dominating set is uniquely identified by its neighborhood within the dominating set the location domination number of g is the minimum cardinality of a locating dominating set in g let g 1 and g 2 be two disjoint copies of a graph g and f v g 1 v g 2 be a function a functigraph f g f consists of vertex set v g 1 v g 2 and edge set e g 1 e g 2 u v v f u in this paper we study the variation of location domination number in passing from g to f g f and find its sharp lower and upper bounds we also study location domination number of functigraphs of complete graphs for all possible definitions of function f we also obtain location domination number of functigraphs of a family of spanning subgraph of the complete graphs

error probability bounds for nuclear detection a collection of static and mobile radiation sensors is tasked with deciding within a fixed time interval whether a moving target carries radioactive material formally this is a problem of detecting weak time inhomogeneous poisson signals target radiation concealed in another poisson signal naturally occurring background radiation each sensor locally processes its observations to form a likelihood ratio which is transmitted once at the end of the decision interval to a fusion center the latter combines the transmitted information to optimally in the neyman pearson sense decide whether the measurements contain a radiation signal or just noise we provide a set of analytically derived upper bounds for the probabilities of false alarm and missed detection which are used to design threshold tests without the need for computationally intensive monte carlo simulations these analytical bounds couple the physical quantities of interest to facilitate planning the motion of the mobile sensors for minimizing the probability of missed detection the network reconfigures itself in response to the target motion to allow more accurate collective decisions within the given time interval the approach is illustrated in numerical simulations and its effectiveness demonstrated in experiments that emulate the statistics of nuclear emissions using a pulsed laser

stochastic and deterministic networks for texture segmentation several texture segmentation algorithms based on deterministic and stochastic relaxation principles and their implementation on parallel networks are described the segmentation process is posed as an optimization problem and two different optimality criteria are considered the first criterion involves maximizing the posterior distribution of the intensity field given the label field maximum a posteriori estimate the posterior distribution of the texture labels is derived by modeling the textures as gauss markov random fields gmrfs and characterizing the distribution of different texture labels by a discrete multilevel markov model a stochastic learning algorithm is proposed this iterated hill climbing algorithm combines fast convergence of deterministic relaxation with the sustained exploration of the stochastic algorithms but is guaranteed to find only a local minimum the second optimality criterion requires minimizing the expected percentage of misclassification per pixel by maximizing the posterior marginal distribution and the maximum posterior marginal algorithm is used to obtain the corresponding solution all these methods implemented on parallel networks can be easily extended for hierarchical segmentation results of the various schemes in classifying some real textured images are presented

image classification using spectral and spatial information based on mrf models a new criterion for classifying multispectral remote sensing images or textured images by using spectral and spatial information is proposed the images are modeled with a hierarchical markov random field mrf model that consists of the observed intensity process and the hidden class label process the class labels are estimated according to the maximum a posteriori map criterion but some reasonable approximations are used to reduce the computational load a stepwise classification algorithm is derived and is confirmed by simulation and experimental results

end point behaviour of solutions to hypersingular integral equations we consider one dimensional hypersingular integral equations over finite intervals the integral must be interpreted as a finite part integral such equations arise naturally in various physical situations involving thin rigid bodies or cracks examples are given a method is developed for determining the behaviour of the solution to a hypersingular integral equation near the end points of the interval of integration the method uses the mellin transform several examples are worked out in detail

more results on the complexity of identifying problems in graphs we investigate the complexity of several problems linked with identification in graphs for instance given an integer r 1 and a graph g v e the existence of or search for optimal r identifying codes in g or optimal r identifying codes in g containing a subset of vertices x v we locate these problems in the complexity classes of the polynomial hierarchy

on the numerical implementation of a cauchy principal value integral to insure a unique solution for acoustic radiation and scattering in this paper the boundary integral formulation proposed by burton and miller proc r soc london ser a 323 201 210 1971 to insure a unique solution for all frequencies is implemented in an isoparametric element environment a regularized normal derivative integral equation originally derived by maue z phys 126 601 618 1949 is used in the formulation to form a linear combination with the conventional helmholtz integral equation this regularized normal derivative integral equation converges in the cauchy principal value sense rather than only in the finite part sense the cauchy principal value integral can be further transformed into an integral that converges in the normal sense the c continuous isoparametric elements are used in the formulation collocation points are placed inside each element to insure a unique normal direction and continuity of tangential derivatives of the acoustic pressure through a systematic collocation point generation scheme the number of collocation point

connected identifying codes we consider the problem of generating a connected identifying code for an arbitrary graph after a brief motivation we show that the decision problem regarding the existence of such a code is np complete and we propose a novel polynomial time approximation connectid that transforms any identifying code into a connected version of at most twice the size thus leading to an asymptotically optimal approximation bound when the input identifying code to is robust to graph distortions we show that the size of the resulting connected code is related to the best error correcting code of a given minimum distance permitting the use of known coding bounds in addition we show that the size of the input and output codes converge for increasing robustness meaning that highly robust identifying codes are almost connected finally we evaluate the performance connectid of on various random graphs simulations for erdos renyi random graphs show that the connected codes generated are actually at most 25 larger than their unconnected counterparts while simulations with robust input identifying codes confirm that robustness often provides connectivity for free

a generalized em algorithm for 3 d bayesian reconstruction from poisson data using gibbs priors a generalized expectation maximization gem algorithm is developed for bayesian reconstruction based on locally correlated markov random field priors in the form of gibbs functions and on the poisson data model for the m step of the algorithm a form of coordinate gradient ascent is derived the algorithm reduces to the em maximum likelihood algorithm as the markov random field prior tends towards a uniform distribution three different gibbs function priors are examined reconstructions of 3 d images obtained from the poisson model of single photon emission computed tomography are presented

image sequence filtering in quantum limited noise with applications to low dose fluoroscopy clinical angiography requires hundreds of x ray images putting the patients and particularly the medical staff at risk dosage reduction involves an inevitable sacrifice in image quality in this work the latter problem is addressed by first modeling the signal dependent poisson distributed noise that arises as a result of this dosage reduction the commonly utilized noise model for single images is shown to be obtainable from the new model stochastic temporal filtering techniques are proposed to enhance clinical fluoroscopy sequences corrupted by quantum mottle the temporal versions of these filters as developed here are more suitable for filtering image sequences as correlations along the time axis can be utilized for these dynamic sequences the problem of displacement field estimation is treated in conjunction with the filtering stage to ensure that the temporal correlations are taken along the direction of motion to prevent object blur

signal detection under mismatch corresp a binary detection problem of the neymann pearson type in which the probability density functions used are inaccurate versions of the true ones are considered the performance of the above suboptimal detection scheme as the number of observations increases is investigated a necessary and sufficient condition is given for the exponential convergence to zero of the two error probabilities as the number of observations increases the condition is in terms of an inequality between differences of asymptotic per sample informational divergence expressions

identifying codes in line digraphs abstract given an integer l 1 a 1 l identifying code in a digraph is a dominating subset c of vertices such that all distinct subsets of vertices of cardinality at most l have distinct closed in neighborhoods within c in this paper we prove that every line digraph of minimum in degree one does not admit a 1 l identifying code for l 3 then we give a characterization so that a line digraph of a digraph different from a directed cycle of length 4 and minimum in degree one admits a 1 2 identifying code the identifying number of a digraph d i d d is the minimum size of all the identifying codes of d we establish for digraphs without digons with both vertices of in degree one that i d l d is lower bounded by the number of arcs of d minus the number of vertices with out degree at least one then we show that i d l d attains the equality for a digraph having a 1 factor with minimum in degree two and without digons with both vertices of in degree two we finish by giving an algorithm to construct identifying codes in oriented digraphs with minimum in degree at least two and minimum out degree at least one

maximum likelihood image estimation using photon correlated beams a theory is presented addressing the fundamental limits of image estimation in a setup that uses two photon correlated beams these beams have the property that their photon arrivals as a point process are ideally synchronized in time and space the true image represents the spatial distribution of the optical transmittance or reflectance of an object in this setup one beam is used to probe the image while the other is used as a reference providing additional information on the actual number of photons impinging on the object this additional information is exploited to reduce the effect of quantum noise associated with the uncertainty in the number of photons per pixel a stochastic model for the joint statistics of the two observation matrices is developed and used to obtain a local maximum likelihood estimator of the image the model captures the nonideal nature of the correlation between the photons of the beams by means of a simple random translation model the mean square error of the estimator is evaluated and compared to the corresponding conventional techniques conditions for the performance advantage of the proposed estimator are examined in terms of key system parameters the theoretical predictions are demonstrated by means of simulation

identification location domination and metric dimension on interval and permutation graphs i bounds we consider the problems of finding optimal identifying codes open locating dominating sets and resolving sets of an interval or a permutation graph in these problems one asks to find a subset of vertices normally called a solution set using which all vertices of the graph are distinguished the identification can be done by considering the neighborhood within the solution set or by employing the distances to the solution vertices normally the goal is to minimize the size of the solution set then here we study the case of interval graphs unit interval graphs bipartite permutation graphs and cographs for these classes of graphs we give tight lower bounds for the size of such solution sets depending on the order of the input graph while such lower bounds for the general class of graphs are in logarithmic order the improved bounds in these special classes are of the order of either quadratic root or linear in terms of number of vertices moreover the results for cographs lead to linear time algorithms to solve the considered problems on inputs that are cographs

on the robust discrimination of poisson random counting measures corresp statistical decisions are considered between two hypotheses which consist of classes of poisson distributions for random counting measures each poisson distribution is generated by an intensity measure on a general observation space the classes are specified by choquet capacity bounds on the intensity measures this problem was first posed and studied by geraniotis and poor a minimax neyman pearson result for error probability performance is the main contribution recursive computation of the minimax test statistic is also investigated

maximum likelihood reconstruction for emission tomography previous models for emission tomography et do not distinguish the physics of et from that of transmission tomography we give a more accurate general mathematical model for et where an unknown emission density x y z generates and is to be reconstructed from the number of counts n d in each of d detector units d within the model we give an algorithm for determining an estimate of which maximizes the probability p n of observing the actual detector count data n over all possible densities let independent poisson variables n b with unknown means b b 1 b represent the number of unobserved emissions in each of b boxes pixels partitioning an object containing an emitter suppose each emission in box b is detected in detector unit d with probability p b d d 1 d with p b d a one step transition matrix assumed known we observe the total number n n d of emissions in each detector unit d and want to estimate the unknown b b 1 b for each the observed data n has probability or likelihood p n the em algorithm of mathematical statistics starts with an initial estimate 0 and gives the following simple iterative procedure for obtaining a new estimate new from an old estimate old to obtain k k 1 2 new b old b dd 1 n d p b d old b p b d b 1 b

alternative parameterizations of metric dimension abstract a set of vertices w in a graph g is called resolving if for any two distinct x y v g there is v w such that d g v x d g v y where d g u v denotes the length of a shortest path between u and v in the graph g the metric dimension md g of g is the minimum cardinality of a resolving set the metric dimension problem i e deciding whether md g k is np complete even for interval graphs foucaud et al 2017 we study metric dimension for arbitrary graphs from the lens of parameterized complexity the problem parameterized by k was proved to be w 2 hard by hartung and nichterlein 2013 and we study the dual parameterization i e the problem of whether md g n k where n is the order of g we prove that the dual parameterization admits a a kernel with at most 6 k 1 vertices and b a randomized algorithm of runtime o 4 k o k hartung and nichterlein 2013 also observed that metric dimension is fixed parameter tractable when parameterized by the vertex cover number v c g of the input graph we complement this observation by showing that it does not admit a polynomial kernel even when parameterized by v c g k unless np conp poly our reduction also gives evidence for non existence of polynomial turing kernels we also prove that metric dimension parameterized by bandwidth or cutwidth does not admit a polynomial kernel unless np conp poly finally using eppstein s results 2015 we show that metric dimension parameterized by max leaf number does admit a polynomial kernel

bayesian estimation of motion vector fields a stochastic approach to the estimation of 2d motion vector fields from time varying images is presented the formulation involves the specification of a deterministic structural model along with stochastic observation and motion field models two motion models are proposed a globally smooth model based on vector markov random fields and a piecewise smooth model derived from coupled vector binary markov random fields two estimation criteria are studied in the maximum a posteriori probability map estimation the a posteriori probability of motion given data is maximized whereas in the minimum expected cost mec estimation the expectation of a certain cost function is minimized both algorithms generate sample fields by means of stochastic relaxation implemented via the gibbs sampler two versions are developed one for a discrete state space and the other for a continuous state space the map estimation is incorporated into a hierarchical environment to deal efficiently with large displacements

the hardness of decoding linear codes with preprocessing the problem of maximum likelihood decoding of linear block codes is known to be hard the fact that the problem remains hard even if the code is known in advance and can be preprocessed for as long as desired in order to device a decoding algorithm is shown the hardness is based on the fact that existence of a polynomial time algorithm implies that the polynomial hierarchy collapses thus some linear block codes probably do not have an efficient decoder the proof is based on results in complexity theory that relate uniform and nonuniform complexity classes

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

separating codes and traffic monitoring this paper studies the problem of traffic monitoring which consists of differentiating a set of walks on a directed graph by placing sensors on as few arcs as possible the problem of characterising a set of individuals by testing as few attributes as possible is already well known but traffic monitoring presents new challenges that the previous models of separation fall short from modelling such as taking into account the multiplicity and order of the arcs in a walk we introduce a new and stronger model of separation based on languages that generalises the traffic monitoring problem we study three subproblems with practical applications and develop methods to solve them by combining integer linear programming separating codes and language theory

on the peak to mean envelope power ratio of phase shifted binary codes the peak to mean envelope power ratio pmepr of a code employed in orthogonal frequency division multiplexing ofdm systems can be reduced by permuting its coordinates and by rotating each coordinate by a fixed phase shift motivated by some previous designs of phase shifts using suboptimal methods the following question is considered in this paper for a given binary code how much pmepr reduction can be achieved when the phase shifts are taken from a 2h ary phase shift keying 2h psk constellation a lower bound on the achievable pmepr is established which is related to the covering radius of the binary code generally speaking the achievable region of the pmepr shrinks as the covering radius of the binary code decreases the bound is then applied to some well understood codes including nonredundant bpsk signaling bch codes and their duals reed muller codes and convolutional codes it is demonstrated that most presumably not optimal phase shift designs from the literature attain or approach our bound

maximum likelihood estimation of time varying delay part i this paper presents for the first time the exact theoretical solution to the problem of maximum likelihood ml estimation of time varying delay d t between a random signal s t received at one point in the presence of uncorrelated noise and the time delayed scaled version s t d t of that signal received at another point in the presence of uncorrelated noise the signal is modeled as a sample function of a nonstationary gaussian random process and the observation interval is arbitrary the analysis of this paper represents a generalization of that of knapp and carter 1 who derived the ml estimator for the case that the delay is constant d t d 0 the signal process is stationary and the received processes are observed over the infinite interval we show that the ml estimator of d t can be implemented in any of four canonical forms which in general are time varying systems we also show that our results reduce to a generalized cross correlator for the special case treated in 1

unique optimal solutions complexity results for identifying and locating dominating codes abstract we investigate the complexity of four decision problems dealing with the uniqueness of a solution in a graph uniqueness of an r locating dominating code with bounded size u ldcr uniqueness of an optimal r locating dominating code u oldcr uniqueness of an r identifying code with bounded size u idcr uniqueness of an optimal r identifying code u oidcr for any fixed integer r 1 in particular we describe a polynomial reduction from unique satisfiability of a boolean formula u sat to u oldcr and from u sat to u oidcr for u ldcr and u idcr we can do even better and prove that their complexity is the same as that of u sat up to polynomials consequently all these problems are np hard and u ldcr and u idcr belong to the class dp

asymptotically optimal estimation of ma and arma parameters of non gaussian processes from high order moments a description is given of an asymptotically minimum variance algorithm for estimating the ma moving average and arma autoregressive moving average parameters of non gaussian processes from sample high order moments the algorithm uses the statistical properties covariances and cross covariances of the sample moments explicitly a simpler alternative algorithm that requires only linear operations is also presented the latter algorithm is asymptotically minimum variance in the class of weighted least squares algorithms

image detection under low level illumination image detection under low light level conditions is treated as a hypothesis testing problem in which the observations are modeled as a shot noise process since computing the likelihood ratio for shot noise processes is not feasible the use of a one dimensional test statistic obtained by filtering and sampling the observations is proposed the filter is chosen to maximize a generalized signal to noise ratio the likelihood ratio for the one dimensional test statistic is evaluated numerically by inverting the corresponding characteristic function under each hypothesis

iterative maximum likelihood displacement field estimation in quantum limited image sequences we develop an algorithm for obtaining the maximum likelihood ml estimate of the displacement vector field dvp from two consecutive image frames of an image sequence acquired under quantum limited conditions the estimation of the dvf has applications in temporal filtering object tracking stereo matching and frame registration in low light level image sequences as well as low dose clinical x ray image sequences in the latter case a controlled x ray dosage reduction may be utilized to lower the radiation exposure to the patient and the medical staff the quantum limited effect is modeled as an undesirable poisson distributed signal dependent noise artifact a fisher bayesian formulation is used to estimate the dvf and a block component search algorithm is employed in obtaining the solution several experiments involving a phantom sequence and a teleconferencing image sequence with realistic motion demonstrate the effectiveness of this estimator in obtaining the dvf under severe quantum noise conditions 20 25 events pixel

identifying and locating dominating codes np completeness results for directed graphs let g v a be a directed asymmetric graph and c a subset of vertices and let b sub r sup v denote the set of all vertices x such that there exists a directed path from x to v with at most r arcs if the sets b sub r sup v spl cap c v spl isin v respectively v spl isin v spl bsol c are all nonempty and different we call c an r identifying code respectively an r locating dominating code of g in other words if c is an r identifying code then one can uniquely identify a vertex v spl isin v only by knowing which codewords belong to b sub r sup v and if c is r locating dominating the same is true for the vertices v in v spl bsol c we prove that given a directed asymmetric graph g and an integer k the decision problem of the existence of an r identifying code or of an r locating dominating code of size at most k in g is np complete for any r spl ges 1 and remains so even when restricted to strongly connected directed asymmetric bipartite graphs or to directed asymmetric bipartite graphs without directed cycles

on the complexity of some coding problems corresp it is shown that the problem of finding a codeword with least weight and whose weight is not a multiple of k in a binary linear code belongs to the class of nondeterministic polynomial np hard problems for any k geq 2 some other related problems are shown to belong to the same class these results were motivated by a conjecture due to berlekamp mceliece and van tilborg that the problem of finding the hamming distance of a code is np hard

estimate maximize algorithms for multichannel time delay and signal estimation computationally efficient iterative algorithms are developed for the joint maximum likelihood estimation of the time delays and the spectral parameters of stationary gaussian signals radiated from a stationary source and observed in the presence of uncorrelated additive noise at two or more spatially distributed receivers the first set of algorithms is based on the estimate maximize approach while the second set achieves superlinear performance by using a modified approach these algorithms decouple the estimation of all the unknowns separately estimating the signal the signal spectral parameters and each channel s delay attenuation and noise power this decoupling considerably simplifies the estimator s structure and computation convergence is guaranteed to the set of stationary points of the likelihood function and each iteration increases the likelihood the convergence rates are analyzed theoretically and the algorithm s performance demonstrated via simulation

lower bounds on estimator performance for energy invariant parameters of multidimensional poisson processes using rate distortion theory lower bounds are developed for the mean square error of estimates of a random parameter of an m dimensional inhomogeneous poisson process with respect to which the energy i e the average number of points is invariant the bounds are derived without stringent assumptions on either the form of the intensity or the prior distribution of the parameter and they can handle random nuisance parameters the derivation makes use of a side information averaging principle applied to the distortion rate function and a maximum entropy property of energy constrained poisson processes under the additional assumption of conditional entropy invariance of the point process with respect to the parameter of interest an explicit bound is given which depends on the information discrimination between the inhomogeneous conditionally poisson process and a nearly homogeneous poisson process the application of the explicit bound is illustrated through a treatment of the problems of time shift estimation and relative time shift estimation for poisson streams

sound source reconstruction using inverse boundary element calculations whereas standard boundary element calculations focus on the forward problem of computing the radiated acoustic field from a vibrating structure the aim in this work is to reverse the process i e to determine vibration from acoustic field data this inverse problem is brought on a form suited for solution by means of an inverse boundary element method since the numerical treatment of the inverse source reconstruction results in a discrete ill posed problem regularization is imposed to avoid unstable solutions dominated by errors in the present work the emphasis is on tikhonov regularization and parameter choice methods not requiring an error norm estimate for choosing the right amount of regularization several parameter choice strategies have been presented lately but it still remains to be seen how well these can handle industrial applications with real measurement data in the present work it is demonstrated that the l curve criterion is robust with respect to the errors in a real measurement situation in particular it is shown that the l curve criterion is superior to the more conventional generalized cross validation gcv approach for the present tire noise studies

a new boundary finite element method for fluid structure interaction problems in order to study problems on fluid structure interaction we have used a mixed formulation which couples the classical functional of the structure with a new variational formulation by integral equations for the fluid this formulation has the advantage over the finite element methods of avoiding the discretization of the fluid domain furthermore unlike collocation methods the explicit calculation of the hadamard finite part of the singular integrals is avoided this leads after discretization by boundary finite elements to a small and symmetrical algebraic system typical examples are presented that demonstrate the efficiency of this variational formulation by studying the sound transmission through a baffled plane structure and through a flexible panel backed by a rigid cavity these include the calculation of the transmission loss factor and the determination of which modes dominate the noise transmission good agreement is obtained between numerical results and analytical results found in the literature

on the statistical analysis of dirty pictures may 7th 1986 professor a f m smith in the chair summary a continuous two dimensional region is partitioned into a fine rectangular array of sites or pixels each pixel having a particular colour belonging to a prescribed finite set the true colouring of the region is unknown but associated with each pixel there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model the aim is to reconstruct the true scene with the additional knowledge that pixels close together tend to have the same or similar colours in this paper it is assumed that the local characteristics of the true scene can be represented by a nondegenerate markov random field such information can be combined with the records by bayes theorem and the true scene can be estimated according to standard criteria however the computational burden is enormous and the reconstruction may reflect undesirable largescale properties of the random field thus a simple iterative method of reconstruction is proposed which does not depend on these large scale characteristics the method is illustrated by computer simulations in which the original scene is not directly related to the assumed random field some complications including parameter estimation are discussed potential applications are mentioned briefly

optimal linear quadratic systems for detection and estimation the problem of linear quadratic systems for detection has long been solved by assuming the deflection criterion and gaussian noise it is shown here that the gaussian assumption can be removed and a complete solution is presented for an arbitrary probability distribution with finite fourth order moments the optimal solution can always be obtained by solving a linear system of equations some properties of the optimal systems are developed for particular examples of nongaussian noise it is shown that there is a strong relationship between linear quadratic optimal detection and optimal estimation which extends results known for the purely linear case

nonuniform image motion estimation from noisy data image motion estimation is viewed as a problem in nonlinear demodulation the motion d x modulates the intensity of the previous frame s x to result in the intensity of the present frame s x d x an iterative algorithm based on the generalized maximum likelihood criterion is developed and implemented to demodulate d x an advantage of this scheme is the incorporation of the covariance function matrix which is specifically useful in the stationary case to determine the integration region alpha sub x simulation demonstrated the ability of the algorithm to deal with cases such as markov 2 motion

maximum likelihood estimation of liner signal parameters for poisson processes the estimation of linear signal parameters is studied under the hypothesis of independently poisson distributed measurements a simple interactive maximum likelihood estimator mle is derived and is optimized for rapid convergence it is shown to be statistically optimal in the sense of providing unbiased and minimum variance estimates experimental conditions are identified where mle results in significant performance improvement when compared to conventional linear least squares lls

set graphs ii complexity of set graph recognition and similar problems a graph g is said to be a set graph if it admits an acyclic orientation that is also extensional in the sense that the out neighborhoods of its vertices are pairwise distinct equivalently a set graph is the underlying graph of the digraph representation of a hereditarily finite set in this paper we continue the study of set graphs and related topics focusing on computational complexity aspects we prove that set graph recognition is np complete even when the input is restricted to bipartite graphs with exactly two leaves the problem remains np complete if in addition we require that the extensional acyclic orientation be also slim that is that the digraph obtained by removing any arc from it is not extensional our approach in fact allows us to also show that the counting variants of the above problems are p complete and prove similar complexity results for problems related to a generalization of extensional acyclic digraphs the so called hyper extensional digraphs which were proposed by aczel to describe hypersets our proofs are based on reductions from variants of the hamiltonian path problem we also consider a variant of the well known notion of a separating code in a digraph the so called open out separating code and show that it is np complete to determine whether an input extensional acyclic digraph contains an open out separating code of given size

linear quadratic noise smoothing filters for quantum limited images we consider the use of nonlinear estimators for the noise smoothing of images obtained under quantum limited imaging conditions a volterra expansion is investigated from which a set of linear quadratic filters is derived using higher order statistics the filters are applicable for single frame and multiple frames of a single scene imaged under low light levels

an acoustic boundary integral formulation for open shells allowing different impedance conditions top and bottom surfaces abstract in the automotive aerospace industries as well as the underwater acoustics defense applications the addition of coatings to modify the response of the vibrating structure is commonplace the formulation developed is an extension of the existing thin body formulation currently found in commercial noise prediction codes such as sysnoise in order to allow problems requiring different boundary condition on both sides of the thin shell to be solved for instance a generalised thin body acoustic formulation would allow for a local impedance boundary condition to be specified on the top surface and a hard neumann boundary condition to be specified on the bottom surface such a formulation would allow for different local impedance coatings to be specified on the top and bottom surfaces due to the lack of analytical solutions for such problems even for the simplest geometries it is difficult to validate such a formulation however three test cases are presented two flat plate examples and a open cylinder with a point monopole source excitation at its centre

iterative reweighted total generalized variation based poisson noise removal model total generalized variation tgv regularization model is one of the most effective methods for denoising and eliminating staircase effect however the tgv regularization model tends to blur edges as the existence of high order derivative in order to avoid the staircase effect while alleviating the edge blurring an iterative reweighted tgv based poisson noise removal model is presented under the assumption that each pixel of noisy image follows a poisson distribution the weight function incorporated in the tgv regularization term is derived from the expectation maximization em algorithm we design a new iterative weighted primal dual algorithm which is an improvement of the classic iterative reweighted algorithm numerical experimental results show the better performance of our model in removing noise effectively while preserving edges and eliminating staircase effect

the complexity of computing the covering radius of a code the problem of finding the covering radius of a binary linear code is shown to be nondeterministic polynomial np hard in fact a problem that is complete for the class prod 2 p in the polynomial hierarchy is shown to be reducible to the covering radius problem so that finding the covering radius is strictly harder than any np complete problem unless the polynomial hierarchy collapses with np prod 2 p

adaptive integration techniques for almost singular functions in the boundary element method abstract three numerical adaptive integration schemes for almost singular functions occurring in the boundary element method which use subdivision of a domain or moving of nodes are discussed some numerical examples show efficiency of the methods

robust matched filters for optical receivers the problem of designing optical receivers that are robust against uncertainty in the statistics of the observation process in photodetection is investigated in particular a modification in the design of the postdetection matched filter is proposed to account for possible uncertainty in the rate function of the incident light the rate of the dark current and in the statistics of the additive noise present at the input to the optical receiver this design is based on a game theoretic approach in which a filter is sought that has the maximum worst case output signal to noise ratio possible over the class of allowable statistics that is the design criterion is maximin signal to noise ratio a general characterization of maximin robust matched filters for observed poisson processes is presented in this context and specific solutions for several useful uncertainty models are obtained numerical results are presented for a specific example to illustrate the performance of the proposed technique

robust hypothesis testing for bounded classes of probability densities corresp least favorable pairs of probability density functions and robust tests are obtained for classes of density functions specified as bands with upper and lower bounds the results are shown to extend huber s solution for the epsilon contaminated classes which is contained as a special case a minimum distance property of the least favorable density pair is also made explicit

a recursive nonstationary map displacement vector field estimation algorithm a recursive model based algorithm for obtaining the maximum a posteriori map estimate of the displacement vector field dvf from successive image frames of an image sequence is presented to model the dvf we develop a nonstationary vector field model called the vector coupled gauss markov vcgm model the vcgm model consists of two levels an upper level which is made up of several submodels with various characteristics and a lower level or line process which governs the transitions between the submodels a detailed line process is proposed the vcgm model is well suited for estimating the dvf since the resulting estimates preserve the boundaries between the differently moving areas in an image sequence a kalman type estimator results followed by a decision criterion for choosing the appropriate line process several experiments demonstrate the superior performance of the proposed algorithm with respect to prediction error interpolation error and robustness to noise

on a new class of codes for identifying vertices in graphs we investigate a new class of codes for the optimal covering of vertices in an undirected graph g such that any vertex in g can be uniquely identified by examining the vertices that cover it we define a ball of radius t centered on a vertex spl upsi to be the set of vertices in g that are at distance at most t from spl upsi the vertex spl upsi is then said to cover itself and every other vertex in the ball with center spl upsi our formal problem statement is as follows given an undirected graph g and an integer t spl ges 1 find a minimal set c of vertices such that every vertex in g belongs to a unique set of balls of radius t centered at the vertices in c the set of vertices thus obtained constitutes a code for vertex identification we first develop topology independent bounds on the size of c we then develop methods for constructing c for several specific topologies such as binary cubes nonbinary cubes and trees we also describe the identification of sets of vertices using covering codes that uniquely identify single vertices we develop methods for constructing optimal topologies that yield identifying codes with a minimum number of codewords finally we describe an application of the theory developed in this paper to fault diagnosis of multiprocessor systems

bayesian filtering of poisson noise using local statistics images recorded at low light levels inherently suffer from poisson noise a filter based on the maximum a posteriori probability map criterion is developed to remove this noise the filter is adaptive it responds to local changes in image statistics and thus removes the noise along the edges without significantly affecting the edge sharpness it does not require any a priori information about the original image because all the parameters needed for the filter are estimated from the noisy image by assuming local stationarity additionally the simple structure of the filter can be easily implemented in hardware

covering radius survey and recent results all known results on covering radius are presented as well as some new results there are a number of upper and lower bounds including asymptotic results a few exact determinations of covering radius some extensive relations with other aspects of coding theory through the reed muller codes and new results on the least covering radius of any linear n k code there is also a recent result on the complexity of computing the covering radius

performance bounds for mismatched decision schemes with poisson process observations abstract this paper develops a framework for analyzing the performance loss in fixed time interval decision algorithms that are based on observations of time inhomogeneous poisson processes when some parameters characterizing the observation process are not known exactly key to the development is the formulation of an analytically computable performance metric which can be used in lieu of the true but intractable error probabilities the proposed metric is obtained by identifying analytical upper bounds on the error probabilities in terms of the uncertain parameters using these tools it is shown that performance degrades gracefully as long as the true values of the parameters remain within a neighborhood of the nominal values used in decision making the results find direct application to problems of detecting illicit nuclear materials in transit

factorization properties of lattices over the integers abstract let a be a nonsingular n n matrix over the integers l l a denotes the lattice whose elements are combinations with integer coefficients of the rows of a l is cyclic if it can be defined in the modular form l x x i a i x i 0 mod d where the a i s and d are integers and 0 a i d let l l 1 l 2 b be lattices over the integers l l 1 l 2 is a factorization of l if every element of l is a combination of the rows of b such that the vector of combination coefficients is in l 1 and b is a nonsingular n n matrix the following results are proved every lattice can be expressed as a product of cyclic factors in polynomial time every cyclic lattice can be factored into simple term explained in the text factors in polynomial time every simple lattice can be factored into prime factors in polynomial time if a prime factorization of the determinant of its basis is given in addition we provide polynomial algorithms for the following problems transform a cyclic lattice given by a basis into a modular form and vice versa find a basis of a finite modular lattice given in modular form

two point correlation properties of stochastic splitting processes we study how the two point density correlation properties of a point particle distribution are modified when each particle is divided by a stochastic process into an equal number of identical daughter particles we consider generically that there may be nontrivial correlations in the displacement fields describing the positions of the different daughters of the same mother particle and then treat separately the cases in which there are or are not correlations also between the displacements of daughters belonging to different mothers for both cases exact formulas are derived relating the structure factor power spectrum of the daughter distribution to that of the mothers an application of these results is that they give explicit algorithms for generating starting from regular lattice arrays stochastic particle distributions with an arbitrarily high degree of large scale uniformity such distributions are of interest in particular in the context of studies of self gravitating systems in cosmology

minimizing the size of an identifying or locating dominating code in a graph is np hard let g v e be an undirected graph and c a subset of vertices if the sets br v c v v respectively v v c are all nonempty and different where br v denotes the set of all points within distance r from v we call c an r identifying code respectively an r locating dominating code we prove that given a graph g and an integer k the decision problem of the existence of an r identifying code or of an r locating dominating code of size at most k in g is np complete for any r

the intractability of computing the minimum distance of a code it is shown that the problem of computing the minimum distance of a binary linear code is np hard and the corresponding decision problem is np complete this result constitutes a proof of the conjecture of berlekamp mceliece and van tilborg 1978 extensions and applications of this result to other problems in coding theory are discussed

solution of elastic scattering problems in linear acoustics using h p boundary element method abstract the work is a continuation of 1 a simplified 3d model problem reduced from the general class of elastic scattering problems is analyzed focusing attention on such practical details of the 3d implementation as a triangles based h p approximation and corresponding data structure integration of singular integrals and its effect on theoretically optimal rates of convergence a posteriori error estimation and sample adaptive strategies

perception of temporally filtered x ray fluoroscopy images for noisy x ray fluoroscopy image sequences the authors quantitatively evaluated image quality after digital temporal filtering to reduce noise using an experimental paradigm called a reference test adaptive forced choice method the authors compared detectability of stationary low contrast disks in filtered and un filtered computer generated image sequences in the first experiment a low pass first order recursive filter used in x ray fluoroscopy was found to be much less effective at enhancing detectability than predicted from the reduction of display noise variance a common measurement of filter effectiveness detectability was reasonably predicted by a nonprewhitening human observer model npw hvs that included an independently determined human temporal contrast sensitivity function in another experiment designed to test models over a range of temporal frequencies the authors used paired high pass and low pass temporal filters that both reduced noise variance by 25 the high pass filter was artificially applied to the noise only and greatly improved detectability while the low pass filter had little effect the human observer model quantitatively described the measurements but classical prewhitening and nonprewhitening signal detectors did not as compared to the nonprewhitening spatio temporal matched filter human observer efficiency was low and variable at 2 1 2 9 and 0 06 for 60 frames of un filtered low pass and high pass noise respectively as compared to this detector humans were not very effective at combining information across frames on the other hand signal to noise ratios snrs from the human observer model were comparable to human performance and efficiencies were reasonably constant at 40 52 and 32 respectively the authors conclude that it is imperative to include human observer models and experiments in the analysis of noise reduction filtering of noisy image sequences such as x ray fluoroscopy

performance bounds for discrimination problems with uncertain statistics corresp decision designs that are insensitive to modeling uncertainty are developed for the chernoff bounds on the performance of binary hypothesis testing problems these designs are based on observations with statistical uncertainty modeled by using general classes generated by 2 alternating capacities the results are illustrated for the two cases of independent identically distributed observations with uncertainty in the probability distribution and discrete time stationary gaussian observations with spectral uncertainty and they are applicable to several other cases as well for the chernoff upper bounds on the error probabilities a robust decision design based on the i kel hood ratio test between a least favorable pair of probability distributions or spectral measures respectively is derived it is then shown that for all elements in the uncertainty class this choice of likelihood ratio guarantees the exponential convergence of the aforementioned chernoff bounds to zero as the number of observations or the length of the observation interval increases

intensity estimation from shot noise data the estimation of the intensity function of a poisson driven shot noise process is addressed using a regularization technique where the data is modeled as a signal term plus a signal dependent noise term a new data based method for selecting a pair of regularization parameters is presented and compared with the minimum unbiased risk method the detail in the intensity function can be recovered by both methods but the new method does a better job at suppressing spurious oscillations

identifying codes in some subgraphs of the square lattice an identifying code of a graph is a subset of vertices c such that the sets b v c are all nonempty and different in this paper we investigate the problem of finding identifying codes of minimum cardinality in strips and finite grids we first give exact values for the strips of height 1 and 2 then we give general bounds for strips and finite grids finally we give a sublinear algorithm which finds the minimum cardinality of an identifying code in a restricted class of graphs which includes the grid

on the complexity of multicovering radii the multicovering radius is a generalization of the covering radius in this correspondence we show that lower bounding the m covering radius of an arbitrary binary code is np complete when m is polynomial in the length of the code lower bounding the m covering radius of a linear code is spl sigma sub 2 sup p complete when m is polynomial in the length of the code if p is not equal to np then the m covering radius of an arbitrary binary code cannot be approximated within a constant factor or within a factor n sup spl epsi where n is the length of the code and spl epsi 1 in polynomial time note that the case when m 1 was also previously unknown if np is not equal to spl sigma sub 2 sup p then the m covering radius of a linear code cannot be approximated within a constant factor or within a factor n sup spl epsi where n is the length of the code and spl epsi 1 in polynomial time

timing estimation for a filtered poisson process in gaussian noise the problem of estimation of time shift of an inhomogeneous casually filtered poisson process in the presence of additive gaussian noise is discussed approximate expressions for the likelihood function the map estimator and the mmse estimator that becomes increasingly accurate as the per unit time density of superimposed filter responses becomes small are obtained the optimal map estimator takes the form of a cascade of linear and memoryless nonlinear components for smooth point process intensities the performance of the map estimator is studied via local bias and local variance a rate distortion type lower bound on the mse of any estimator of time delay is then derived by identification of a communications channel that accounts for the mapping from time delay to observation process results of numerical studies of estimator performance are presented based on the examples considered it is concluded 1 the small error mse of the nonlinear map estimator can be significantly better than the small error mse of the optimal linear estimator 2 the rate distortion lower bound can be significantly tighter than the poisson limited bounds determined in previous studies

determination of the best crc codes with up to 10 bit redundancy all binary polynomials of degree up to 10 which are suitable to be used as generator polynomials of crc codes are classified and all the necessary data for the evaluation of the error control performance of the crc codes generated by the classified polynomials is calculated a procedure based on the computed data for choosing the best crc code is suggested

blind intensity estimation from shot noise data the estimation of the intensity function of an inhomogeneous poisson process is considered when the observable data consists of sampled shot noise that results from passing the poisson process through an unknown linear time invariant system the proposed method consists of first estimating a histogram of the underlying point process the estimated histogram is used to construct a kernel estimate of the intensity function an estimate of the unknown impulse response of the linear time invariant system is constructed via a regularized backsubstitution of a discrete time convolution with the estimated histogram

minimax discrimination for observed poisson processes with uncertain rate functions the problem of robust design is considered in the context of testing hypotheses concerning the rate function of an observed point process designs that are insensitive to uncertainty in the rate functions are developed by applying a minimax formulation to two different measures of signal to noise ratio uncertainty in the rate is modeled by using general classes of rate measures generated by choquet 2 alternating capacities and solutions are characterized for this case by a radon nikodym type derivative between such classes it is shown that for uncertainty within capacity classes the robust decision design developed for the signal to noise ratio is also robust in a weaker sense for the chernoff upper bounds on the error probabilities furthermore the use of such a test guarantees the exponential convergence of these bounds to zero with increasing length of the observation interval for all rates in the uncertainty class