solution of inverse problems in image processing by wavelet expansion we describe a wavelet based approach to linear inverse problems in image processing in this approach both the images and the linear operator to be inverted are represented by wavelet expansions leading to a multiresolution sparse matrix representation of the inverse problem the constraints for a regularized solution are enforced through wavelet expansion coefficients a unique feature of the wavelet approach is a general and consistent scheme for representing an operator in different resolutions an important problem in multigrid multiresolution processing this and the sparseness of the representation induce a multigrid algorithm the proposed approach was tested on image restoration problems and produced good results

three term idempotent counterexamples in the hardy littlewood majorant problem the hardy littlewood majorant problem was raised in the 30 s and it can be formulated as the question whether f p g p whenever f g it has a positive answer only for exponents p which are even integers montgomery conjectured that even among the idempotent polynomials there must exist some counterexamples i e there exists some finite set of exponentials and some signs with which the signed exponential sum has larger pth norm than the idempotent obtained with all the signs chosen in the exponential sum that conjecture was proved recently by mockenhaupt and schlag however a natural question is if even the classical 1 e2 ix e2 i k 2 x three term exponential sums used for p 3 and k 1 already by hardy and littlewood should work in this respect that remained unproved as the construction of mockenhaupt and schlag works with four term idempotents we investigate the sharpened question and show that at least in certain cases there indeed exist three term idempotent counterexamples in the hardy littlewood majorant problem that is we have for 0 012 1 e2 ix e2 i p2 2 x p the proof combines delicate calculus with numerical integration and precise error estimates

fuzzy model validation using the local statistical approach the local statistical approach for fault detection and isolation is applied to fuzzy models validation the method detects the inconsistencies between a fuzzy rule base and the modelled system it can also identify which are the faulty parameters of the fuzzy model the fisher information matrix explains the detectability of changes in the parameters of the fuzzy model simulation tests illustrate the method s credibility

on a problem of bourgain concerning the l 1 norm of exponential sums bourgain posed the problem of calculating begin aligned sigma sup n ge 1 sup k 1 cdots k n frac 1 sqrt n left sum j 1 n e 2 pi i k j theta right l 1 0 1 end aligned it is clear that sigma le 1 beyond that determining whether sigma 1 or sigma 1 would have some interesting implications for example concerning the problem whether all rank one transformations have singular maximal spectral type in the present paper we prove sigma ge sqrt pi 2 approx 0 886 by this means improving a result of karatsuba for the proof we use a quantitative two dimensional version of the central limit theorem for lacunary trigonometric series which in its original form is due to salem and zygmund

complemented ideals in the fourier algebra and the radon nikodym property necessary and sufficient conditions are given for an ideal i h of the fourier algebra to be complemented when h is a closed subgroup of g using the radon nikodym property an example of a group g with a normal abelian subgroup h for which i h is not complemented is presented

upper bounds for the number of solutions of a diophantine equation we give upper bound estimates for the number of solutions of a certain diophantine equation our results can be applied to obtain new lower bound estimates for the l 1 norm of certain exponential sums

efficient recursive algorithms for detection of abrupt changes in signals and control systems this paper addresses a number of open problems concerning the generalized likelihood ratio glr rules for online detection of faults and parameter changes in control systems it is shown that with an appropriate choice of the threshold and window size these glr rules are asymptotically optimal the rules are also extended to non likelihood statistics that are widely used in monitoring adaptive algorithms for system identification and control by establishing gaussian approximations to these statistics when the window size is chosen suitably recursive algorithms are developed for practical implementation of the procedure and importance sampling techniques are introduced for determining the threshold of the rule to satisfy prescribed bounds on the false alarm rate

hardy s inequality and the l1 norm of exponential sums in this paper we generalize hardy s inequality 3 for measures of analytic type and obtain a proof of the littlewood conjecture 4 for the l norm of exponential sums as a simple consequence let t be the circle group z the additive group of integers and m t the customary convolution algebra of borel measures on t for pe e m t and n g z put m e ino dp o denote by h t the classical space of all measures e e m t such that j n 0 for all n 0 and let c denote the complex numbers we now state hardy s inequality for measures of analytic type theorem 1 if m c h t then

on global identifiability for arbitrary model parametrizations it is a fundamental problem of identification to be able even before the data have been analyzed to decide if all the free parameters of a model structure can be uniquely recovered from data this is the issue of global identifiability in this contribution we show how global identifiability for an arbitrary model structure basically with analytic non linearities can be analyzed using concepts and algorithms from differential algebra it is shown how the question of global structural identifiability is reduced to the question of whether the given model structure can be rearranged as a linear regression an explicit algorithm to test this is also given furthermore the question of persistent excitation for the input can also be tested explicitly is a similar fashion the algorithms involved are very well suited for implementation in computer algebra one such implementation is also described

subspace based fault detection robust to changes in the noise covariances the detection of changes in the eigenstructure of a linear time invariant system by means of a subspace based residual function has been proposed previously while enjoying some success in its applicability in particular in the context of vibration monitoring the robustness of this framework against changes in the noise properties has not been properly addressed yet in this paper a new robust residual is proposed and the robustness of its statistics against changes in the noise covariances is shown the complete theory for hypothesis testing for fault detection is derived and a numerical illustration is provided

generalized hardy inequalities abstract we show that the generalized hardy inequality k b k f n k c f h 1 holds for f h1 and certain bk lr 2 q whenever n k k 1 n satisfies appropriate growth conditions dependent on r

a new methodology for observer design and implementation observers are usually formulated as explicit systems of differential equations and implemented using standard ode solvers in this paper we show that there can be advantages in formulating the observer as a differential algebraic equation dae we propose a canonical dae observer and show that it can be implemented using standard dae solvers the dae implementation of the observer can be considered regardless of the design philosophy used we present a simple design strategy for this canonical dae observer based on the extended linearization method

diagnosis of unknown parametric faults in non linear stochastic dynamical systems a new detection and isolation scheme for unknown parametric faults in non linear stochastic systems is presented that is particularly suited for small parametric changes the proposed residual is the moving angle between two stochastic processes the error derived from the reference model and the expected error in case a certain fault has occurred since the fault is unknown fault classes are defined most of the faults that belong to such a fault class can be detected and isolated by just testing one representative of this fault class as the moving angle itself is a stochastic process an estimator is designed and characterised conditions for the detectability and isolability of fault classes are given for this estimator based on hypotheses tests finally the theoretical results are confirmed by simulations and monte carlo tests

multiresolution tomographic reconstruction using wavelets shows how the separable two dimensional wavelet representation leads naturally to an efficient multiresolution tomographic reconstruction algorithm this algorithm is similar to the conventional filtered backprojection algorithm except that the filters are now angle dependent and the backprojection gives the wavelet coefficients of the reconstruction which are then used to synthesize the reconstruction at various resolution levels by reconstructing only a small localized region at high resolution the authors show how radiation exposure and computation can be significantly reduced compared to a standard reconstruction

estimates for the norms of products of sines and cosines abstract in this paper we prove asymptotic formulas for the l p norms of p n k 1 n 1 e i k and q n k 1 n 1 e i k these products can be expressed using k 1 n sin k 2 and k 1 n cos k 2 respectively we prove an estimate for p n at a point near where its maximum occurs finally we give an asymptotic formula for the maximum of the fourier coefficients of q n

a wavelet based method for multiscale tomographic reconstruction the authors represent the standard ramp filter operator of the filtered back projection fbp reconstruction in different bases composed of haar and daubechies compactly supported wavelets the resulting multiscale representation of the ramp filter matrix operator is approximately diagonal the accuracy of this diagonal approximation becomes better as wavelets with larger numbers of vanishing moments are used this wavelet based representation enables the authors to formulate a multiscale tomographic reconstruction technique in which the object is reconstructed at multiple scales or resolutions a complete reconstruction is obtained by combining the reconstructions at different scales the authors multiscale reconstruction technique has the same computational complexity as the fbp reconstruction method it differs from other multiscale reconstruction techniques in that 1 the object is defined through a one dimensional multiscale transformation of the projection domain and 2 the authors explicitly account for noise in the projection data by calculating maximum a posteriori probability map multiscale reconstruction estimates based on a chosen fractal prior on the multiscale object coefficients the computational complexity of this maximum a posteriori probability map solution is also the same as that of the fbp reconstruction this result is in contrast to commonly used methods of statistical regularization which result in computationally intensive optimization algorithms

small animal in vivo x ray tomosynthesis anatomical relevance of the reconstructed images whole body x ray micro digital tomosynthesis micro dt for small animal imaging is introduced in this work such a system allows to deal with geometrical constraints that do not allow to use a micro ct system as well as to reduce the radiological dose compared to a micro ct scan data was simulated using the digimouse anatomical model of the mouse with the designed system an algebraic reconstruction algorithm regularized by total variation norm tv minimization was used to reconstruct images parameters for the reconstruction were optimized and the algorithm performance was evaluated quantitatively high contrast tissues were subsequently segmented by thresholding the image quantitative analysis of the segmented domains indicates that a relevant anatomical information can possibly be extracted from micro dt images indeed the dice s coefficient values are greater than 0 8 for the segmented high contrast tissues compared to the phantom which indicates an important overlap between the domains the volume of the segmented tissues is over estimated for the bones and skin with 1 313 and 1 113 ratios of the estimated over reference volumes respectively and under estimated in the case of the lungs with a 0 762 ratio the mean point to surface distance is inferior to the voxel size of 400 mu rm m for the three segmented tissues these results are very encouraging and let us consider micro dt as an alternative to micro ct to deal with geometrical constraints

a quantitative version of the idempotent theorem in harmonic analysis suppose that g is a locally compact abelian group and write m g for the algebra of bounded regular complex valued measures under convolution a measure g m g is said to be idempotent if x i or alternatively if j5 takes only the values 0 and 1 the cohen helson rudin idempotent theorem states that a measure x is idempotent if and only if the set 7 g g i2 7 1 belongs to the coset ring of g that is to say we may write l i i

wavelet sampling and localization schemes for the radon transform in two dimensions two theorems are presented for wavelet decompositions of the two dimensional radon transform the rst theorem establishes an upper error bound in l 2 norm between the radon transform and its wavelet approximation whose coecients at dierent scales are estimated from radon data acquired at corresponding sampling rates the second theorem gives an estimate of the accuracy of a local image reconstructed from localized radon data at multiple levels these results show how to design a multilevel sampling and localization strategy for parallel beam scanning by using wavelet regularity and vanishing moment characteristics clarify the interaction between the wavelet structure and the essential bandwidth of an object image and provide guidelines for wavelet local tomography

limited data x ray tomography using nonlinear evolution equations a novel approach to the x ray tomography problem with sparse projection data is proposed nonnegativity of the x ray attenuation coefficient is enforced by modelling it as max phi x 0 where phi is a smooth function the function phi is computed as the equilibrium solution of a nonlinear evolution equation analogous to the equations used in level set methods the reconstruction algorithm is applied to a simulated full and limited angle projection data of the shepp logan phantom with sparse angular sampling and b measured limited angle projection data of in vitro dental specimens the results are significantly better than those given by traditional backprojection based approaches and similar in quality but faster to compute compared to the algebraic reconstruction technique

wavelet based multiresolution local tomography we develop an algorithm to reconstruct the wavelet coefficients of an image from the radon transform data the proposed method uses the properties of wavelets to localize the radon transform and can be used to reconstruct a local region of the cross section of a body using almost completely local data that significantly reduces the amount of exposure and computations in x ray tomography the property that distinguishes our algorithm from the previous algorithms is based on the observation that for some wavelet bases with sufficiently many vanishing moments the ramp filtered version of the scaling function as well as the wavelet function has extremely rapid decay we show that the variance of the elements of the null space is negligible in the locally reconstructed image also we find an upper bound for the reconstruction error in terms of the amount of data used in the algorithm to reconstruct a local region 16 pixels in radius in a 256 spl times 256 image we require 22 of full exposure data

nonlinear black box models in system identification mathematical foundations we discuss several aspects of the mathematical foundations of the nonlinear black box identification problem we shall see that the quality of the identification procedure is always a result of a certain trade off between the expressive power of the model we try to identify the larger the number of parameters used to describe the model the more flexible is the approximation and the stochastic error which is proportional to the number of parameters a consequence of this trade off is the simple fact that a good approximation technique can be the basis of a good identification algorithm from this point of view we consider different approximation methods and pay special attention to spatially adaptive approximants we introduce wavelet and neuron approximations and show that they are spatially adaptive then we apply the acquired approximation experience to estimation problems finally we consider some implications of these theoretical developments for the practically implemented versions of the spatially adaptive algorithms

asymptotic optimality of mixture rules for detecting changes in general stochastic models the paper addresses a sequential changepoint detection problem for a general stochastic model assuming that the observed data may be non i i d i e dependent and non identically distributed and prior distribution of the change point is arbitrary tartakovsky and veeravalli 2005 baron and tartakovsky 2006 and more recently tartakovsky 2017 developed a general asymptotic theory of changepoint detection for non i i d stochastic models assuming certain stability of the log likelihood ratio process in the case of simple hypotheses when both pre change and post change models are completely specified however in most applications the post change distribution is not completely known in the present paper we generalize previous results to the case of parametric uncertainty assuming that the parameter of the post change distribution is unknown we introduce two detection rules based on mixtures the mixture shiryaev rule and the mixture shiryaev roberts rule and study their asymptotic properties in the bayesian context in particular we provide sufficient conditions under which these rules are first order asymptotically optimal minimizing moments of the delay to detection as the probability of false alarm approaches zero

the barzilai and borwein gradient method for the large scale unconstrained minimization problem the barzilai and borwein gradient method for the solution of large scale unconstrained minimization problems is considered this method requires few storage locations and very inexpensive computations furthermore it does not guarantee descent in the objective function and no line search is required recently the global convergence for the convex quadratic case has been established however for the nonquadratic case the method needs to be incorporated in a globalization scheme in this work a nonmonotone line search strategy that guarantees global convergence is combined with the barzilai and borwein method this strategy is based on the nonmonotone line search technique proposed by grippo lampariello and lucidi siam j numer anal 23 1986 pp 707 716 numerical results to compare the behavior of this method with recent implementations of the conjugate gradient method are presented these results indicate that the global barzilai and borwein method may allow some significant reduction in the number of line searches and also in the number of gradient evaluations

on the structure of spaces of uniformly convergent fourier series we first give some new examples of translation invariant subspaces of c or u without local unconditional structure in the second part we prove that u and u do not have the gordon lewis property in the third part we show that absolutely summing operators from u to a k convex space are compact as a consequence u and u are not isomorphic at last we prove that u and u do not have the daugavet property

hardy s inequality and fractal measures abstract hardy s inequality and the subsequent improvement by mcgehee pigno and smith are generalized from the positive integers to sets of dimension 0 dimension 1 and in between the asymptotic estimate obtained for the fourier transform of fractal measures is much in the spirit of recent work by strichartz

counting zeros of cosine polynomials on a problem of littlewood abstract we show that if a is a finite set of non negative integers then the number of zeros of the function f a a a cos a in 0 2 is at least log log log a 1 2 e this gives the first unconditional lower bound on a problem of littlewood and solves a conjecture of borwein erdelyi ferguson and lockhart we also prove a result that applies to more general cosine polynomials with few distinct rational coefficients one of the main ingredients in the proof is perhaps of independent interest we show that if f is an exponential polynomial with few distinct integer coefficients and f correlates with a low degree exponential polynomial p then f has a very particular structure this result allows us to prove a structure theorem for trigonometric polynomials with few zeros in 0 2 and restricted coefficients

statistical model based damage detection and localization subspace based residuals and damage to noise sensitivity ratios the vibration based structural health monitoring problem is addressed as the double task of detecting damages modeled as changes in the eigenstructure of a linear dynamic system and localizing the detected damages within a fem of the monitored structure the proposed damage detection algorithm is based on a residual generated from a stochastic subspace based covariance driven identification method and on the statistical local approach to the design of detection algorithms this algorithm basically computes a global test which performs a sensitivity analysis of the residuals to the damages relative to uncertainties and noises how this residual relates to some residuals for damage localization and model updating is discussed damage localization is stated as a detection problem this problem is addressed by plugging aggregated sensitivities of the modes and mode shapes w r t fem structural parameters in the above setting this results in directional tests which perform the same type of damage to noise sensitivity analysis of the residual as for damage detection how the sensitivity aggregation mechanism relates to sub structuring is outlined numerical results obtained on one example are reported

efficient framework for model based tomographic image reconstruction using wavelet packets the use of model based algorithms in tomographic imaging offers many advantages over analytical inversion methods however the relatively high computational complexity of model based approaches often restricts their efficient implementation in practice many modern imaging modalities such as computed tomography positron emission tomography or optoacoustic tomography normally use a very large number of pixels voxels for image reconstruction consequently the size of the forward model matrix hinders the use of many inversion algorithms in this paper we present a new framework for model based tomographic reconstructions which is based on a wavelet packet representation of the imaged object and the acquired projection data the frequency localization property of the wavelet packet base leads to an approximately separable model matrix for which reconstruction at each spatial frequency band is independent and requires only a fraction of the projection data thus the large model matrix is effectively separated into a set of smaller matrices facilitating the use of inversion schemes whose complexity is highly nonlinear with respect to matrix size the performance of the new methodology is demonstrated for the case of 2 d optoacoustic tomography for both numerically generated and experimental data

high level primitives for recursive maximum likelihood estimation this paper proposes a high level language constituted of a small number of primitives and macros for describing recursive maximum likelihood ml estimation algorithms this language is applicable to estimation problems involving linear gaussian models or processes taking values in a finite set the use of high level primitives allows the development of highly modular ml estimation algorithms based on simple numerical building blocks the primitives which correspond to the combination of different measurements the extraction of sufficient statistics and the conversion of the status of a variable from unknown to observed or vice versa are first defined for linear gaussian relations specifying mixed deterministic stochastic information about the system variables these primitives are used to define other macros and are illustrated by deriving new filtering and smoothing algorithms for linear descriptor systems the primitives are then extended to finite state processes and used to implement the viterbi ml state sequence estimator for a hidden markov model

change detection in teletraffic models we propose a likelihood based ratio test to detect distributional changes in common teletraffic models these include traditional models like the markov modulated poisson process and processes exhibiting long range dependency in particular gaussian fractional arima processes a practical approach is also developed for the case where the parameter after the change is unknown it is noticed that the algorithm is robust enough to detect slight perturbations of the parameter value after the change a comprehensive set of numerical results including results for the mean detection delay is provided

on the energy of some circulant graphs we give an explicit construction of circulant graphs of very high energy this construction is based on gauss sums we also show the littlewood conjecture can be used to establish new result for a certain class of circulant graphs

sequential changepoint detection in quality control and dynamical systems after a brief survey of a large variety of sequential detection procedures that are widely scattered in statistical references on quality control and engineering references on fault detection and signal processing we study some open problems concerning these procedures and introduce a unified theory of sequential changepoint detection this theory leads to a class of sequential detection rules which are not too demanding in computational and memory requirements for on line implementation and yet are nearly optimal under several performance criteria

eit imaging regularization based on spectral graph wavelets the objective of electrical impedance tomographic reconstruction is to identify the distribution of tissue conductivity from electrical boundary conditions this is an ill posed inverse problem usually solved under the finite element method framework in previous studies standard sparse regularization was used for difference electrical impedance tomography to achieve a sparse solution however regarding elementwise sparsity standard sparse regularization interferes with the smoothness of conductivity distribution between neighboring elements and is sensitive to noise as an effect the reconstructed images are spiky and depict a lack of smoothness such unexpected artifacts are not realistic and may lead to misinterpretation in clinical applications to eliminate such artifacts we present a novel sparse regularization method that uses spectral graph wavelet transforms single scale or multiscale graph wavelet transforms are employed to introduce local smoothness on different scales into the reconstructed images the proposed approach relies on viewing finite element meshes as undirected graphs and applying wavelet transforms derived from spectral graph theory reconstruction results from simulations a phantom experiment and patient data suggest that our algorithm is more robust to noise and produces more reliable images

a generalized change detection problem the purpose of this paper is to give a new statistical approach to the change diagnosis detection isolation problem the change detection problem has received extensive research attention however the change isolation problem has for the most part been ignored we consider a stochastic dynamical system with abrupt changes and investigate the multiple hypotheses extension of lorden s 1971 results we introduce a joint criterion of optimality for the detection isolation problem and then design a change detection isolation algorithm we also investigate the statistical properties of this algorithm we prove a lower bound for the criterion in a class of sequential change detection isolation algorithms it is shown that the proposed algorithm is asymptotically optimal in this class the theoretical results are applied to the case of additive changes in linear stochastic models

enhancement of robustness in observer based fault detection a prerequisite for the feasibility of the technique of observer based fault detection and isolation fdi in dynamic systems is a satisfactory robustness with respect to modelling uncertainties this paper surveys the most relevant methods to increase the robustness in both the stage of residual generation and residual evaluation among these methods are the generalized observer scheme the robust parity space check the unknown input and h observer scheme the decorrelation filter and the concept of adaptive threshold selection it is pointed out that the unknown input observer concept which provides perfect decoupling from the modelling errors or its optimal approximation with the aid of h techniques constitutes a general framework of robust residual generation that generalizes and unifies numerous other approaches among them the parity space and detection filter approach it is further shown that this fdi method can even be applied to a certain class of nonlinear systems

optimally robust redundancy relations for failure detection in uncertain systems all failure detection methods are based either explicitly or implicitly on the use of redundancy i e on possibly dynamic relations among the measured variables the robustness of the failure detection process consequently depends to a great degree on the reliability of the redundancy relations which in turn is affected by the inevitable presence of model uncertainties in this paper the problem of determining redundancy relations that are optimally robust is addressed in a sense that includes several major issues of importance in practical failure detection and that provides a significant amount of intuition concerning the geometry of robust failure detection a procedure is given involving the construction of a single matrix and its singular value decomposition for the determination of a complete sequence of redundancy relations ordered in terms of their level of robustness this procedure also provides the basis for comparing levels of robustness in redundancy provided by different sets of sensors

optimal sensor location for detecting changes in dynamical behavior we address the problem of optimal sensor location for monitoring the eigenstructure of a multivariable dynamical system the criterions which are optimized are the power of new tests designed for detecting and diagnosing changes in the eigencharacteristics of a system 3 12 the key points are the choice of the parameterization for computing the criterion and the comparison of designs with a different number of sensors the discussion of the numerical results for sensor location includes the analysis of the effect of the geometry of the unknown excitation

alexandrov s inequality and conjectures on some toeplitz matrices abstract we study determinant inequalities for certain toeplitz like matrices over c for fixed n and n 1 let q be the n n n 1 zero one toeplitz matrix with q ij 1 for 0 j i n 1 and q ij 0 otherwise we prove that det qq is the minimum of det rr over all complex matrices r with the same dimensions as q satisfying r ij 1 whenever q ij 1 and r ij 0 otherwise although r has a toeplitz like band structure it is not required to be actually toeplitz our proof involves alexandrov s inequality for polarized determinants and its generalizations this problem is motivated by littlewood s conjecture on the minimum 1 norm of n term exponential sums on the unit circle we also discuss polarized bazin reiss picquet identities some connections with k tree enumeration and analogous conjectured inequalities for the elementary symmetric functions of qq

two strategies in the problem of change detection and isolation the comparison between optimal sequential and nonsequential fixed size sample strategies in the problem of abrupt change detection and isolation is discussed in particular we show that sometimes a simple fixed size sample algorithm is almost as efficient as an optimal sequential algorithm which leads to a burdensome number of arithmetical operations

reconstruction from limited angle projections based on delta u spectrum analysis this paper proposes a sparse representation of an image using discrete u functions a u function is defined as the product of a kronecker delta function and a step function based on the sparse representation we have developed a novel and effective method for reconstructing an image from limited angle projections the method first estimates the parameters of the sparse representation from the incomplete projection data and then directly calculates the image to be reconstructed experiments have shown that the proposed method can effectively recover the missing data and reconstruct images more accurately than the total variation tv regularized reconstruction method

wavelet localization of the radon transform the authors develop an algorithm which significantly reduces radiation exposure in x ray tomography when a local region of the body is to be imaged the algorithm uses the properties of wavelets to essentially localize the radon transform this algorithm differs from previous algorithms for doing local tomography because it recovers an approximation to the original image not the image module the nullspace of the local tomography operator or the lambda transform of the image this is possible because the authors do not truly invert the interior radon transform but rather sample the radon transform sparsely away from the local region of interest much attention in the field has been directed towards localized tomography the authors believe that this technique represents a significant contribution towards this effort

independent sums of hn1 t and hn1 δ abstract we construct a new idempotent fourier multiplier on the hardy space on the bidisc which could not be obtained by applying known one dimensional results the main tool is a new l 1 equivalent of the stein martingale inequality which holds for a special filtration of periodic subsets of t with some restrictions on the functions involved we also identify the isomorphic type of the range of the associated operator as the independent sum of dyadic h n 1 which is known to be a complemented and invariant subspace of dyadic h 1

on the zeros of cosine polynomials solution to a problem of littlewood littlewood in his 1968 monograph some problems in real and complex analysis 12 problem 22 poses the following research problem which appears to be still open problem if the nj are integral and all different what is the lower bound

globally convergent edge preserving regularized reconstruction an application to limited angle tomography we introduce a generalization of a deterministic relaxation algorithm for edge preserving regularization in linear inverse problems this algorithm transforms the original possibly nonconvex optimization problem into a sequence of quadratic optimization problems and has been shown to converge under certain conditions when the original cost functional being minimized is strictly convex we prove that our more general algorithm is globally convergent i e converges to a local minimum from any initialization under less restrictive conditions even when the original cost functional is nonconvex we apply this algorithm to tomographic reconstruction from limited angle data by formulating the problem as one of regularized least squares optimization the results demonstrate that the constraint of piecewise smoothness applied through the use of edge preserving regularization can provide excellent limited angle tomographic reconstructions two edge preserving regularizers one convex the other nonconvex are used in numerous simulations to demonstrate the effectiveness of the algorithm under various limited angle scenarios and to explore how factors such as the choice of error norm angular sampling rate and amount of noise affect the reconstruction quality and algorithm performance these simulation results show that for this application the nonconvex regularizer produces consistently superior results

a fault detection scheme for linear discrete time systems with an integrated online performance evaluation this paper is concerned with the design of the fault detection systems into which a residual generation evaluation and threshold are integrated for linear discrete time varying processes over a finite horizon in the proposed design scheme the residual generation is realised in the context of h fault estimation with a prescribed attenuation level this attenuation level is minimised by using the krein space linear estimation theory and subsequently an h fault estimator with the minimum attenuation level is designed in terms of the solution to a set of riccati like recursions for the residual evaluation and decision making purpose the false alarm rate and fault detection rate indicators are introduced in the norm based framework which is integrated into the decision making procedure for the online computations of the false alarm rate and fault detection rate indicators further estimates delivered by the h fault estimator are applied without additional online computations by means of checki

fault detection and isolation in nonlinear dynamic systems a combined input output and local approach the problem of fault detection and isolation fdi is addressed for nonlinear dynamic systems modeled by polynomial differential algebraic equations ritt s algorithm is used to obtain an input output representation of the monitored system by eliminating unknown variables a local approach to change detection is then applied to the input output representation for fdi residual generation and evaluation simulation results on a microbial growth process are provided which illustrate the relevance of the proposed fdi method

a new structural framework for parity equation based failure detection and isolation abstract the paper describes a new framework for developing parity equations that prevent incorrect isolation decisions under marginal size failures in a decision process that tests each residual independently test thresholds that take the noise conditions into account are set high to reduce the occurrence of false alarms while maintaining the algorithm s ability to detect and isolate larger failures the method is applicable to additive failures on the measured input and output variables and to additive plant disturbances a transformation algorithm provides a multitude of models that satisfy the isolability requirements a search procedure utilizing this model redundancy integrates model robustness considerations into the design

projections onto translation invariant subspaces of recently i klemes has characterized the complemented translation invariant subspaces of hl t in this paper we investigate the case of r the main results are that the hull of a complemented translation invariant sub space is e separated for some e 0 and that an e separated subset of r which is in the ring generated by cosets of closed subgroups of r intersected with r and lacunary sequences is the hull of a complemented ideal

on board component fault detection and isolation using the statistical local approach we describe both the key principles and real application examples of a unified theory which allows us to perform the on board incipient fault detection and isolation tasks involved in monitoring for condition based maintenance this theory is known under the name of local approach and it is especially suited to component faults it aims at transforming complex detection problems concerning a parameterized stochastic process into the universal problem of monitoring the mean of a gaussian vector based on a small deviation assumption the key tools are the first order taylor expansion and the asymptotic gaussianity of a convenient parameter estimating function ml ls iv and subspace identification methods are addressed in this perspective in the case of dynamic processes given in state space form the approach may also call for observer based state estimation or state elimination experiments concerning both simulated and real data for linear and nonlinear dynamical processes are reported how the key principles and features of the local approach compare with those of other approaches is discussed

diversity analysis of symbol by symbol linear equalizers in frequency selective channels linear receivers enjoy significantly reduced complexity compared with maximum likelihood receivers at the cost of performance degradation which can be in the form of a loss of the inherent frequency diversity order or reduced coding gain this paper demonstrates that the minimum mean square error symbol by symbol linear equalizer incurs no diversity loss compared to the maximum likelihood receivers in particular for a channel with memory it achieves the full diversity order of 1 while the zero forcing symbol by symbol linear equalizer always achieves a diversity order of one

single sample modal identification of a nonstationary stochastic process gauss markov processes excited by nonstationary noises are encountered in the modeling of vibrating systems we prove that the classical instrumental variable method as well as the ho kalman realization algorithm for identifying the pole part modal characteristics of the model are consistent when used on a single sample of the nonstationary signal

a sequential procedure for multihypothesis testing the sequential testing of more than two hypotheses has important applications in direct sequence spread spectrum signal acquisition multiple resolution element radar and other areas a useful sequential test which we term the msprt is studied in this paper the test is shown to be a generalization of the sequential probability ratio test under bayesian assumptions it is argued that the msprt approximates the much more complicated optimal test when error probabilities are small and expected stopping times are large bounds on error probabilities are derived and asymptotic expressions for the stopping time and error probabilities are given a design procedure is presented for determining the parameters of the msprt two examples involving gaussian densities are included and comparisons are made between simulation results and asymptotic expressions comparisons with bayesian fixed sample size tests are also made and it is found that the msprt requires two to three times fewer samples on average

image compression via joint statistical characterization in the wavelet domain we develop a probability model for natural images based on empirical observation of their statistics in the wavelet transform domain pairs of wavelet coefficients corresponding to basis functions at adjacent spatial locations orientations and scales are found to be non gaussian in both their marginal and joint statistical properties specifically their marginals are heavy tailed and although they are typically decorrelated their magnitudes are highly correlated we propose a markov model that explains these dependencies using a linear predictor for magnitude coupled with both multiplicative and additive uncertainties and show that it accounts for the statistics of a wide variety of images including photographic images graphical images and medical images in order to directly demonstrate the power of the model we construct an image coder called epwic embedded predictive wavelet image coder in which subband coefficients are encoded one bitplane at a time using a nonadaptive arithmetic encoder that utilizes conditional probabilities calculated from the model bitplanes are ordered using a greedy algorithm that considers the mse reduction per encoded bit the decoder uses the statistical model to predict coefficient values based on the bits it has received despite the simplicity of the model the rate distortion performance of the coder is roughly comparable to the best image coders in the literature

information criteria for residual generation and fault detection and isolation using an information point of view we discuss deterministic versus stochastic tools for residual generation and evaluation for fault detection and isolation fdi in linear time invariant lti state space systems in both types of approaches to off line fdi residual generation can be viewed as the design of a linear transformation of a gaussian vector the finite window input adjusted observations several statistical isolation methods are revisited using both a linear transform formulation and the information content of the corresponding residuals we formally state several multiple fault cases with or without causality assumptions and discuss an optimality criterion for the most general one new information criteria are proposed for investigating the residual optimization problem

an invariance property of some subspace based detection algorithms subspace fitting estimates involve multidimensional parameter estimating functions having a particular product form based on estimating functions the statistical local approach builds detection algorithms that enjoy a simple invariance property this article investigates that invariance property for the detectors built on those two concepts

wavelet based reconstruction for limited angle x ray tomography the aim of x ray tomography is to reconstruct an unknown physical body from a collection of projection images when the projection images are only available from a limited angle of view the reconstruction problem is a severely ill posed inverse problem statistical inversion allows stable solution of the limited angle tomography problem by complementing the measurement data by a priori information in this work the unknown attenuation distribution inside the body is represented as a wavelet expansion and a besov space prior distribution together with positivity constraint is used the wavelet expansion is thresholded before reconstruction to reduce the dimension of the computational problem feasibility of the method is demonstrated by numerical examples using in vitro data from mammography and dental radiology

state space formulation a solution to modal parameter estimation abstract as an alternative to fourier techniques based on transfer function fitting modal parameters identification methods derived from a state space formulation of the dynamic equation have been recently studied and developed this formulation leads to the solution of the modal problem via multi dimensional arma model parameters identification in this paper the transition from the dynamic equation to the arma model is described and the algorithms of identification are explained for the very common case of uncontrolled and unmeasured excitation these techniques the qualities of which have been established during extensive processing of offshore structures measurements have been generalized to more complex excitation models such as those of turbo alternators several examples illustrate these different application domains

wavelet thresholding via a bayesian approach we discuss a bayesian formalism which gives rise to a type of wavelet threshold estimation in nonparametric regression a prior distribution is imposed on the wavelet coefficients of the unknown response function designed to capture the sparseness of wavelet expansion that is common to most applications for the prior specified the posterior median yields a thresholding procedure our prior model for the underlying function can be adjusted to give functions falling in any specific besov space we establish a relationship between the hyperparameters of the prior model and the parameters of those besov spaces within which realizations from the prior will fall such a relationship gives insight into the meaning of the besov space parameters moreover the relationship established makes it possible in principle to incorporate prior knowledge about the function s regularity properties into the prior model for its wavelet coefficients however prior knowledge about a function s regularity properties might be difficult to elicit with this in mind we propose a standard choice of prior hyperparameters that works well in our examples several simulated examples are used to illustrate our method and comparisons are made with other thresholding methods we also present an application to a data set that was collected in an anaesthesiological study

nonlinear black box modeling in system identification a unified overview a nonlinear black box structure for a dynamical system is a model structure that is prepared to describe virtually any nonlinear dynamics there has been considerable recent interest in this area with structures based on neural networks radial basis networks wavelet networks and hinging hyperplanes as well as wavelet transform based methods and models based on fuzzy sets and fuzzy rules this paper describes all these approaches in a common framework from a user s perspective it focuses on what are the common features in the different approaches the choices that have to be made and what considerations are relevant for a successful system identification application of these techniques it is pointed out that the nonlinear structures can be seen as a concatenation of a mapping form observed data to a regression vector and a nonlinear mapping from the regressor space to the output space these mappings are discussed separately the latter mapping is usually formed as a basis function expansion the basis functions are typically formed from one simple scalar function which is modified in terms of scale and location the expansion from the scalar argument to the regressor space is achieved by a radial or a ridge type approach basic techniques for estimating the parameters in the structures are criterion minimization as well as two step procedures where first the relevant basis functions are determined using data and then a linear least squares step to determine the coordinates of the function approximation a particular problem is to deal with the large number of potentially necessary parameters this is handled by making the number of used parameters considerably less than the number of offered parameters by regularization shrinking pruning or regressor selection

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed