parameter identification of nonlinear aeroelastic system with time delayed feedback control in this paper an enhanced response sensitivity approach is proposed for parameter identification of nonlinear time delay aeroelastic systems two common aeroelastic models are investigated namely

seismic inversion based on proximal objective function optimization algorithm abstractseismic impedance inversion has become a common approach in reservoir prediction at present the critical issue in the application of seismic inversion is its low computational efficiency especially in 3d to improve the computational efficiency we have developed an inversion method derived from the proximal objective function optimization algorithm our inversion method calculates each unknown parameter in the model vector one by one during iteration compared with routine gradient dependent inversion algorithms such as the iteratively reweighted least squares irls algorithm our inversion method has lower computational complexity as well as higher efficiency in addition to obtain a sparse reflectivity series a long tailed cauchy distribution is used as the a priori constraint the weak nonlinear problem owing to the introduction of cauchy sparse constraint is addressed by taking advantage of reweighting strategy results of synthetic and real data tests illustrate that the proposed inv

elastoplastic analysis by active macro zones with linear kinematic hardening and von mises materials in this paper a strategy to perform elastoplastic analysis with linear kinematic hardening for von mises materials under plane strain conditions is shown the proposed approach works with the symmetric galerkin boundary element method applied to multidomain problems using a mixed variables approach to obtain a more stringent solution the elastoplastic analysis is carried out as the response to the loads and the plastic strains the latter evaluated through the self equilibrium stress matrix this matrix is used both in the predictor phase for trial stress evaluation and in the corrector phase for solving a nonlinear global system which provides the elastoplastic solution of the active macro zones i e those zones collecting bem elements where the plastic consistency condition has been violated the simultaneous use of active macro zones gives rise to a nonlocal approach which is characterized by a large decrease in the plastic iteration number although the proposed strategy requires the inversion and updating of jacobian operators generally of big dimensions a strategy developed in order to reduce the computational efforts due to the use of this matrix in a recursive process is shown

relative rock physics a quantitative framework for relative rock physics includes a definition of relative elastic property that is rooted in inverse theory and that can be used practically to compute the properties the framework also includes a set of rules that quantify how operations on absolute properties affect their relative counterparts from these rules a comprehensive table of relative elastic properties can be generated all of which are expressed in terms of relative p velocity s velocity and density finally the framework includes empirical and model based rock physics rules that can be applied directly to the relative properties without reverting to their absolute counterparts that provides a practical route to such interpretation techniques as direct to seismic fluid substitution the framework offers a quantitative alternative to workflows centered on absolute seismic inversion in some cases relative rock physics workflows are preferable to absolute flows because they avoid statistical complications associated with the nonstationarity of the mean of absolute elastic properties

direct numerical identification of boundary values in the laplace equation an inverse boundary value problem for the laplace equation is considered the dirichlet and the neumann data are prescribed on respective part of the boundary while there is the second part of the boundary where no boundary data are given there is the third part of the boundary where the robin condition is prescribed this ill posed problem of finding unknown values along the whole boundary is reformulated in terms of the variational problem which is then recast into primary and adjoint boundary value problems of the laplace equation in conventional forms a direct method for numerical solution of the boundary value problems using the boundary element method is presented

the backus gilbert method and their minimum norm solution abstractthis paper has two objectives one is to review the backus gilbert bg method backus and gilbert investigate continuous inverse problems in a radially symmetric earth using an approach completely different from that of standard inversion methods if m is an earth property of interest the bg method provides average values of m over some radial intervals if an interval w is relatively short and centered near a particular radius r0 the bg average will be a local average of m near r0 with a resolving length of w backus and gilbert also introduce the concept of trade off between resolution and error which is essential in inverse theory regardless of the inversion method in spite of its importance inverse theory texts neither describe the bg method in full nor show how to apply it in all its generality because the three papers that introduce the bg method are mathematically difficult this paper provides background material and a detailed derivation of the method as well as two completely wor

equivalence and normal forms of bilinear forms abstract we present an alternative account of the problem of classifying and finding normal forms for arbitrary bilinear forms beginning from basic results developed by riehm our solution to this problem hinges on the classification of indecomposable forms and in how uniquely they fit together to produce all other forms we emphasize the use of split forms i e those bilinear forms such that the minimal polynomial of the asymmetry of their non degenerate part splits over ground field rather than restricting the field to be algebraically closed in order to obtain the most explicit results without resorting to the classification of hermitian symmetric and quadratic forms we merely require that the underlying field be quadratically closed

a discrepancy based penalty method for extended waveform inversion abstractextended waveform inversion globalizes the convergence of seismic waveform inversion by adding nonphysical degrees of freedom to the model thus permitting it to fit the data well throughout the inversion process these extra degrees of freedom must be curtailed at the solution for example by penalizing them as part of an optimization formulation for separable partly linear models a natural objective function combines a mean square data residual and a quadratic regularization term penalizing the nonphysical linear degrees of freedom the linear variables are eliminated in an inner optimization step leaving a function of the outer nonlinear variables to be optimized this variable projection method is convenient for computation but it requires that the penalty weight be increased as the estimated model tends to the physical solution we describe an algorithm based on discrepancy that is maintaining the data residual at the inner optimum within a prescribed range to control the pena

regularization methods in dynamic mri in this work we consider an inverse ill posed problem coming from the area of dynamic magnetic resonance imaging mri where high resolution images must be reconstructed from incomplete data sets collected in the fourier domain the reduced encoding imaging by generalized series reconstruction rigr method used leads to ill conditioned linear systems with hermitian toeplitz matrix and noisy right hand side we analyze the behavior of some regularization methods such as the truncated singular value decomposition tsvd the lavrent yev regularization method and conjugate gradients cg type iterative methods for what concerns the choice of the regularization parameter we use some known methods and we propose new heuristic criteria for iterative regularization methods the simulations are carried on test problems obtained from real data acquired on a 1 5 t phillips system

structure of isometry group of bilinear spaces abstract we describe the structure of the isometry group g of a finite dimensional bilinear space over an algebraically closed field of characteristic not two if the space has no indecomposable degenerate orthogonal summands of odd dimension it admits a canonical orthogonal decomposition into primary components and g is isomorphic to the direct product of the isometry groups of the primary components each of the latter groups is shown to be isomorphic to the centralizer in some classical group of a nilpotent element in the lie algebra of that group in the general case the description of g is more complicated we show that g is a semidirect product of a normal unipotent subgroup k with another subgroup which in its turn is a direct product of a group of the type described in the previous paragraph and another group h which we can describe explicitly the group h has a levi decomposition whose levi factor is a direct product of several general linear groups of various degrees we obtain simple formulae for the dimensions of h and k

svd compression for magnetic resonance fingerprinting in the time domain magnetic resonance mr fingerprinting is a technique for acquiring and processing mr data that simultaneously provides quantitative maps of different tissue parameters through a pattern recognition algorithm a predefined dictionary models the possible signal evolutions simulated using the bloch equations with different combinations of various mr parameters and pattern recognition is completed by computing the inner product between the observed signal and each of the predicted signals within the dictionary though this matching algorithm has been shown to accurately predict the mr parameters of interest one desires a more efficient method to obtain the quantitative images we propose to compress the dictionary using the singular value decomposition which will provide a low rank approximation by compressing the size of the dictionary in the time domain we are able to speed up the pattern recognition algorithm by a factor of between 3 4 4 8 without sacrificing the high signal to noise ratio of the original scheme presented previously

contrast source inversion methods in elastodynamics in this paper a nonlinear inversion method is presented for determining the mass density of an elastic inclusion from the knowledge of how the inclusion scatters known incident elastic waves the algorithm employed is an extension of the multiplicative regularized contrast source inversion method mr csi to elasticity this method involves alternate determination of the mass density contrast and the contrast sources the product of the contrast and the fields in each iterative step the simple updating schemes of the method allow the introduction of an extra regularization term to the cost functional as a multiplicative constraint this so called mr csi method mr csi has been proven to be very effective for the acoustic and electromagnetic inverse scattering problems numerical examples demonstrate that the mr csi method shows excellent edge preserving properties by robustly handling noisy data very well even for more complicated elastodynamic problems

congruences of a square matrix and its transpose abstract it is known that any square matrix a over any field is congruent to its transpose at stas for some nonsingular s moreover s can be chosen such that s2 i that is s can be chosen to be involutory we show that a and at are congruent over any field f of characteristic not two with involution a a the involution can be the identity a t s t as for some nonsingular s moreover s can be chosen such that s s i that is s can be chosen to be coninvolutory the short and simple proof is based on sergeichuk s canonical form for congruence math ussr izvestiya 31 3 1988 481 it follows that any matrix a over f can be represented as a eb in which e is coninvolutory and b is symmetric

sirt and cg type methods for the iterative solution of sparse linear least squares problems abstract sirt and cg type methods have been successfully employed for the approximate solution of least squares problems arising in tomography in this paper we study and compare their convergence and regularization properties it is pointed out that sirt methods apply an uncontrollable implicit rescaling which affects the statistical characteristics of the system whereas cg type methods do not for a large class of model problems it is shown that virtually the same solutions as obtained by sirt methods can be obtained by applying a cg type method to a properly rescaled system but with an amount of work proportional to the square root of the amount of work with sirt

parameter selection for total variation based image restoration using discrepancy principle there are two key issues in successfully solving the image restoration problem 1 estimation of the regularization parameter that balances data fidelity with the regularity of the solution and 2 development of efficient numerical techniques for computing the solution in this paper we derive a fast algorithm that simultaneously estimates the regularization parameter and restores the image the new approach is based on the total variation tv regularized strategy and morozov s discrepancy principle the tv norm is represented by the dual formulation that changes the minimization problem into a minimax problem a proximal point method is developed to compute the saddle point of the minimax problem by adjusting the regularization parameter adaptively in each iteration the solution is guaranteed to satisfy the discrepancy principle we will give the convergence proof of our algorithm and numerically show that it is better than some state of the art methods in terms of both speed and accuracy

the number of equivalence classes of nondegenerate bilinear and sesquilinear forms over a finite field abstract generating functions in the form of infinite products are given for the number of equivalence classes of nondegenerate sesquilinear forms of rank n over gf q2 and for the number of equivalence or congruence classes of nondegenerate bilinear forms of rank n over gf q

on computing first and second order derivative spectra enhancing resolution in spectral response and an ability to differentiate spectral mixing in delineating the endmembers from the spectral response are central to the spectral data analysis first and higher order derivatives analysis of absorbance and reflectance spectral data is commonly used techniques in differentiating the spectral mixing but high sensitivity of derivative to the noise in data is a major problem in the robust estimation of derivative of spectral data an algorithm of robust estimation of first and second order derivative spectra from evenly spaced noisy normal spectral data is proposed the algorithm is formalized in the framework of an inverse problem where based on the fundamental theorem of calculus a matrix equation is formed using a volterra type integral equation of first kind a regularization technique where the balancing principle is used in selecting a posteriori optimal regularization parameter is designed to solve the inverse problem for robust estimation of first order derivative spectra the higher order derivative spectra are obtained while using the algorithm in sequel the algorithm is tested successfully with synthetically generated spectral data contaminated with additive white gaussian noise and also with real absorbance and reflectance spectral data for fresh and sea water respectively robust and efficient algorithm of computing first and second orders derivative spectra is designed the algorithm is based on the premise of inverse problem where a robust solution is achieved via regularization it couples discrepancy and balancing principles to determine regularization parameter and implement stopping rule respectively numerical experiments on noisy data suggest superiority of the method over finite difference and fourier transform based techniques the proposed method is applied on absorbance and reflectance spectral data for fresh and sea water

a regularization algorithm for matrices of bilinear and sesquilinear forms abstract over a field or skew field f with an involution a a possibly the identity involution each singular square matrix a is congruent to a direct sum s as b j n 1 j n p 1 n 1 n p inwhich s is nonsingular and s s t b is nonsingular and is determined by a up to congruence and the ni by ni singular jordan blocks j n i and their multiplicities are uniquely determined by a we give a regularization algorithm that needs only elementary row operations to construct such a decomposition if f c respectively f r we exhibit a regularization algorithm that uses only unitary respectively real orthogonal transformations and a reduced form that can be achieved via a unitary congruence or congruence respectively a real orthogonal congruence the selfadjoint matrix pencil a a is decomposed by our regularization algorithm into the direct sum s a a s b b j n 1 j n 1 j n p j n p with selfadjoint summands

the 2 norm of random matrices abstract numerical experiments show that it is possible to derive simple estimates for the expected 2 norm of random matrices a with elements from a normal distribution with zero mean and standard deviation and from a poisson distribution with mean value these estimates are max m n 2 max m n and e 2 mn respectively where m and n are the dimensions of a

an analysis of the zero crossing method for choosing regularization parameters solving discrete ill posed problems via tikhonov regularization introduces the problem of determining a regularization parameter there are several methods available for choosing such a parameter yet in general the uniqueness of this choice is an open question two empirical methods for determining a regularization parameter which appear in the biomedical engineering literature are the composite residual and smoothing operator and the zero crossing method an equivalence is established between the zero crossing method and a minimum product criterion which has previously been linked with the l curve method finally the uniqueness of a choice of regularization parameter is established under certain restrictions on the fourier coefficients of the data in the ill posed problem

meshless thin plate spline methods for the modified helmholtz equation in this paper we investigate the application of the meshless radial basis function method for solving the helmholtz equation using thin plate splines we use a meshless method mixed with a boundary and a fundamental solution methods the numerical computation is achieved by using the generalized minimal residual gmres the least square lsqr methods associated with tikhonov regularization

an elementary proof of gabriel s theorem on degenerate bilinear forms and its generalization abstract a theorem due to p gabriel shows that every bilinear space decomposes in a unique manner up to equivalence as the orthogonal direct sum of indecomposable degenerate spaces and a nondegenerate space this has been generalized by c riehm and m a shrader frechette to sesquilinear modules over a semisimple ring with an anti automorphism we give an elementary proof of these facts which avoids the use of kronecker modules

an adaptive greedy technique for inverse boundary determination problem in this paper the method of fundamental solutions mfs is employed for determining an unknown portion of the boundary from the cauchy data specified on parts of the boundary we propose a new numerical method with adaptive placement of source points in the mfs to solve the inverse boundary determination problem since the mfs source points placement here is not trivial due to the unknown boundary we employ an adaptive technique to choose a sub optimal arrangement of source points on various fictitious boundaries afterwards the standard tikhonov regularization method is used to solve ill conditional matrix equation while the regularization parameter is chosen by the l curve criterion the numerical studies of both open and closed fictitious boundaries are considered it is shown that the proposed method is effective and stable even for data with relatively high noise levels

symmetric boundary element method versus finite element method the paper examines the effectiveness of the symmetric boundary element formulation when the continuum body is subdivided into large elements called macro elements the approach proposed combines a strong reduction of variables with an elastic solution close to the real response indeed if the displacement method is used this approach permits one to determine for every macro element a relationship connecting the weighted traction vector defined on the sides of the interface boundary with the node displacement vector of the same boundary and with the external action vector such a strategy is very similar to that followed through the finite element method but with the advantages of having the punctual satisfaction of the equilibrium and compatibility by using the fundamental solution and of employing large elements whose discretization is performed on the boundary only some examples are shown using a general computing programme developed by the present authors

congruence and conjunctivity of matrices to their adjoints abstract every square matrix over a field f is involutorily congruent over f to its transpose and hence each such matrix is the product of a symmetric matrix and an involutory matrix over f in the usual complex case every matrix which is conjunctive with its adjoint conjugate transpose is involutorily conjunctive with its adjoint and hence is the product of a hermitian matrix and an involutory matrix furthermore every such matrix is conjunctive with a real matrix these three conditions on a matrix 1 being conjunctive with its adjoint 2 being involutorily conjunctive with its adjoint and 3 being conjunctive with a real matrix are studied in the more general context of a field f with involution and it is shown in general that 3 implies 2 that 2 implies 3 if char f 2 a 2 2 counterexample exists for each f with char f 2 and that 1 does not in general imply 2 a 2 2 counterexample in the complexification of the rational field is presented the problem of deciding which matrices satisfy 2 is equivalent even in this general context to the problem of deciding which pairs of self adjoint hermitian matrices are involutorily conjunctive for the general 2 2 case the three conditions are characterized in terms of norms

existence uniqueness and stability of solutions of generalized tikhonov phillips functionals abstract the tikhonov phillips method is widely used for regularizing ill posed inverse problems mainly due to the simplicity of its formulation as an optimization problem the use of different penalizers in the functionals associated to the corresponding optimization problems has originated a variety of other methods which can be considered as variants of the traditional tikhonov phillips method of order zero such is the case for instance of the tikhonov phillips method of order one the total variation regularization method etc in this article we find sufficient conditions on the penalizers in generalized tikhonov phillips functionals which guarantee existence uniqueness and stability of the minimizers the particular cases in which the penalizers are given by the bounded variation norm by powers of seminorms and by linear combinations of powers of seminorms associated to closed operators are studied several examples are presented and a few results on image restoration are shown

lie algebras and bilinear forms in characteristic 2 abstract all bilinear forms defined on a finite dimensional vector space over an algebraically closed field of characteristic 2 whose associated lie algebra is reductive are determined

wavelet domain image restoration with adaptive edge preserving regularization in this paper we consider a wavelet based edge preserving regularization scheme for use in linear image restoration problems our efforts build on a collection of mathematical results indicating that wavelets are especially useful for representing functions that contain discontinuities i e edges in two dimensions or jumps in one dimension we interpret the resulting theory in a statistical signal processing framework and obtain a highly flexible framework for adapting the degree of regularization to the local structure of the underlying image in particular we are able to adapt quite easily to scale varying and orientation varying features in the image while simultaneously retaining the edge preservation properties of the regularizer we demonstrate a half quadratic algorithm for obtaining the restorations from observed data

full waveform static corrections using blind channel identification near surface wavefield perturbations can be very complex and completely mask the target reflections despite this complexity conventional methods rely on parameterizations characterized by simple time and amplitude anomalies to compensate for these perturbations determining and compensating for time shifts is generally referred to as residual static corrections whereas surface consistent deconvolution techniques deal with amplitude anomalies we present an approach that uses the full waveform to parameterize near surface perturbations therefore we refer to this method as waveform statics important differences from conventional static corrections are that this approachallowstimeshiftstovarywithfrequencyandtakesamplitudevariationsdirectlyintoaccount furthermore theprocedure is fully automated and does not rely on near surface velocity information the waveform static corrections are obtained using blind channel identification and applied to the recordings using multichannel deconvolution as a result the method implicitly incorporates array forming the developed method is validated onsyntheticdataandappliedtopartofafielddatasetacquiredin an area with significant near surface heterogeneity the source and receiver responses obtained are strongly correlated to the near surfaceconditionsandshowchanges bothinphaseandfrequency content along the spread the application of the waveform statics demonstrates that they not only correct for near surface wavefield perturbations but also strongly reduce coherent noise this results in substantial improvements both in trace totrace coherency and in depth resolution in addition the procedure delineates reflection events that are difficult to detect prior to our proposed correction based on these results we conclude that complex near surface perturbations can be successfully dealt with using the multichannel full waveform static correctionprocedure

analysis of discrete ill posed problems by means of the l curve when discrete ill posed problems are analyzed and solved by various numerical regularization techniques a very convenient way to display information about the regularized solution is to plot the norm or seminorm of the solution versus the norm of the residual vector in particular the graph associated with tikhonov regularization plays a central role the main purpose of this paper is to advocate the use of this graph in the numerical treatment of discrete ill posed problems the graph is characterized quantitatively and several important relations between regularized solutions and the graph are derived it is also demonstrated that several methods for choosing the regularization parameter are related to locating a characteristic l shaped corner of the graph

active macro zone approach for incremental elastoplastic contact analysis summary the symmetric boundary element method based on the galerkin hypotheses has found an application in the nonlinear analysis of plasticity and in contact detachment problems but both dealt with separately in this paper we want to treat these complex phenomena together as a linear complementarity problem a mixed variable multidomain approach is utilized in which the substructures are distinguished into macroelements where elastic behavior is assumed and bem elements where it is possible that plastic strains may occur elasticity equations are written for all the substructures and regularity conditions in weighted weak form on the boundary sides and in the nodes strong between contiguous substructures have to be introduced in order to attain the solving equation system governing the elastoplastic contact detachment problem the elastoplasticity is solved by incremental analysis called for active macro zones and uses the well known concept of self equilibrium stress field here shown in a discrete form through the introduction of the influence matrix self stress matrix the solution of the frictionless contact detachment problem was performed using a strategy based on the consistent formulation of the classical signorini equations rewritten in discrete form by utilizing boundary nodal quantities as check elements in the zones of potential contact or detachment copyright 2013 john wiley sons ltd

recovering the density of a string from only lowest frequency data a classical inverse problem is can you hear the density of a string clamped at both ends the answer as narrowly stated is negative one has to give an additional data sequence such as the energy in each mode norming constants or information on the string slope at the endpoints or alternatively change the boundary conditions and obtain the new frequencies what if neither of these options is possible one solution recently proposed was to add a known mass density and remeasure the dirichlet spectrum w rundell and p e sacks siam j appl math 73 2013 pp 1020 1037 in this work we take a related approach we are able to add any number of known mass densities but we can only measure the fundamental frequency that is the lowest eigenvalue in each case we will show that our problem can be closely approximated by a related problem for which there is uniqueness and we discuss a suite of reconstruction methods

asymptotic theory of filtering for linear operator equations with discrete noisy data on considere les equations integrales de fredholm de premiere espece a noyaux continus avec echantillonnage des donnees et alteration par le bruit blanc on etablit une condition suffisante de convergence des methodes de filtrage

a meshless method for some inverse problems associated with the helmholtz equation in this paper a new numerical scheme based on the method of fundamental solutions is proposed for the numerical solution of some inverse boundary value problems associated with the helmholtz equation including the cauchy problem since the resulting matrix equation is badly ill conditioned a regularized solution is obtained by employing truncated singular value decomposition while the regularization parameter for the regularization method is provided by the l curve method numerical results are presented for problems on smooth and piecewise smooth domains with both exact and noisy data and the convergence and stability of the scheme are investigated these results show that the proposed scheme is highly accurate computationally efficient stable with respect to the noise in the data and convergent with respect to decreasing the amount of data noise and increasing the distance between the physical and fictitious boundaries and could be considered as a competitive alternative to existing methods for these problems

planar crack identification in 3d linear elasticity by the reciprocity gap method abstract we study the reciprocity gap method andrieux et al 1999 for the identification of planar cracks in the framework of three dimensional linear elasticity in order to achieve better accuracy on thick domains we propose to use polynomial test functions instead of fourier series we also propose to improve the solution by various regularization techniques that are tested and compared numerical assessments are provided in 2d and 3d

a state space force identification method based on markov parameters precise computation and regularization technique a time domain force identification approach for linear system is proposed this approach can found a highly precise force identification model within the scope of general computer precision while it does not cost much computing time although the force identification model is accurate the force identification process like other inverse methods is still ill posed due to the inversion process and the white noise in measured structural responses the singular value decomposition is used to reveal the intrinsically matter of the ill posedness of force identification problem and a regularization technique is utilized to deal with this issue finally the proposed method with the aid of regularization technique is successfully applied to identify the input forces in two numerical simulations

using the l curve for determining optimal regularization parameters the l curve is a plot in ordinary or doubly logarithmic scale of the norm of tikhonov regularized solutions of an ill posed problem versus the norm of the residuals we show that the popular criterion of choosing the parameter corresponding to the point with maximal curvature of the l curve does not yield a convergent regularization strategy to solve the ill posed problem nevertheless the l curve can be used to compute the regularization parameters produced by morozov s discrepancy principle and by an order optimal variant of the discrepancy principle proposed by engl and gfrerer in an alternate way

optimally scaled vector regularization method to solve ill posed linear problems instead of the tikhonov regularization method which with a scalar being the regularization parameter liu et al 1 have proposed a novel regularization method with a vector as being the regularization parameter as a continuation we further propose an optimally scaled vector regularization method osvrm to solve the ill posed linear problems which is better than the tikhonov regularization method the presently proposed vector regularization method is shown to be well conditioning to overcome the ill posedness of the linear equations system the osvrm causes a significant improvement of stability and accuracy in the numerical solution of ill posed linear problem and its convergence speed is as fast as by solving the well posed linear problem some tests of the linear inverse problems confirm the efficiency and accuracy of the osvrm

an efficient method for dynamic magnetic resonance imaging many magnetic resonance imaging applications require the acquisition of a time series of images in conventional fourier transform based imaging methods each of these images is acquired independently so that the temporal resolution possible is limited by the number of spatial encodings or data points in the fourier space collected or one has to sacrifice spatial resolution for temporal resolution in this paper a generalized series based imaging technique is proposed to address this problem this technique makes use of the fact that in most time sequential imaging problems the high resolution image morphology does not change from one image to another and it improves imaging efficiency and temporal resolution over the conventional fourier imaging methods by eliminating the repeated encodings of this stationary information additional advantages of the proposed imaging technique include a reduced number of radio frequency rf pulses for data collection and thus lower rf power deposition this method should prove useful for a variety of dynamic imaging applications including dynamic studies of contrast agents and functional brain imaging

boundary identification for a 3d laplace equation using a genetic algorithm in this paper we consider the identification of the geometric structure of the boundary of the solution domain for the three dimensional laplace equation we investigate the determination of the shape of an unknown portion of the boundary of a solution domain from cauchy data on the remaining portion of the boundary this problem arises in the study of quantitative non destructive evaluation of corrosion in materials in which boundary measurements of currents and voltages are used to determine the material loss caused by corrosion the domain identification problem is considered as a variational problem to minimize a defect functional which utilises some additional data on certain known parts of the boundary a real coded genetic algorithm rcga is used in order to minimise the objective functional the unknown boundary is parameterized using b splines the laplace equation is discretised using the method of fundamental solutions mfs numerical results are presented and discussed for several test examples

monte carlo sure a black box optimization of regularization parameters for general denoising algorithms we consider the problem of optimizing the parameters of a given denoising algorithm for restoration of a signal corrupted by white gaussian noise to achieve this we propose to minimize stein s unbiased risk estimate sure which provides a means of assessing the true mean squared error mse purely from the measured data without need for any knowledge about the noise free signal specifically we present a novel monte carlo technique which enables the user to calculate sure for an arbitrary denoising algorithm characterized by some specific parameter setting our method is a black box approach which solely uses the response of the denoising operator to additional input noise and does not ask for any information about its functional form this therefore permits the use of sure for optimization of a wide variety of denoising algorithms we justify our claims by presenting experimental results for sure based optimization of a series of popular image denoising algorithms such as total variation denoising wavelet soft thresholding and wiener filtering smoothing splines in the process we also compare the performance of these methods we demonstrate numerically that sure computed using the new approach accurately predicts the true mse for all the considered algorithms we also show that sure uncovers the optimal values of the parameters in all cases

canonical matrices of bilinear and sesquilinear forms abstract canonical matrices are given for i bilinear forms over an algebraically closed or real closed field ii sesquilinear forms over an algebraically closed field and over real quaternions with any nonidentity involution and iii sesquilinear forms over a field f of characteristic different from 2 with involution possibly the identity up to classification of hermitian forms over finite extensions of f the canonical matrices are based on any given set of canonical matrices for similarity over f a method for reducing the problem of classifying systems of forms and linear mappings to the problem of classifying systems of linear mappings is used to construct the canonical matrices this method has its origins in representation theory and was devised in v v sergeichuk classification problems for systems of forms and linear mappings math ussr izv 31 1988 481 501

improved estimation of subject level functional connectivity using full and partial correlation with empirical bayes shrinkage abstract reliability of subject level resting state functional connectivity fc is determined in part by the statistical techniques employed in its estimation methods that pool information across subjects to inform estimation of subject level effects e g bayesian approaches have been shown to enhance reliability of subject level fc however fully bayesian approaches are computationally demanding while empirical bayesian approaches typically rely on using repeated measures to estimate the variance components in the model here we avoid the need for repeated measures by proposing a novel measurement error model for fc describing the different sources of variance and error which we use to perform empirical bayes shrinkage of subject level fc towards the group average in addition since the traditional intra class correlation coefficient icc is inappropriate for biased estimates we propose a new reliability measure denoted the mean squared error intra class correlation coefficient iccmse to properly assess the reliability of the resulting biased estimates we apply the proposed techniques to test retest resting state fmri data on 461 subjects from the human connectome project to estimate connectivity between 100 regions identified through independent components analysis ica we consider both correlation and partial correlation as the measure of fc and assess the benefit of shrinkage for each measure as well as the effects of scan duration we find that shrinkage estimates of subject level fc exhibit substantially greater reliability than traditional estimates across various scan durations even for the most reliable connections and regardless of connectivity measure additionally we find partial correlation reliability to be highly sensitive to the choice of penalty term and to be generally worse than that of full correlations except for certain connections and a narrow range of penalty values this suggests that the penalty needs to be chosen carefully when using partial correlations

image restoration by cosine transform based iterative regularization we consider an ill posed deconvolution problem with a noise contaminated observation and a known convolution kernel in this paper we consider the use of the neumann boundary condition corresponding to a reflection of the original scene at the boundary the resulting blurring matrices are block toeplitz plus hankel matrices with toeplitz plus hankel blocks we study the application of the preconditioned iterative regularization scheme for solving these linear systems where the blurring matrices are approximated by cosine transform preconditioners we give a simple approach for finding these preconditioners and show how iterations can be effectively and efficiently regularized for solving ill posed problems by using the spectral decomposition of the preconditioner

the symmetric boundary element method for unilateral contact problems abstract on the basis of the boundary integral equation method in its symmetric formulation the frictionless unilateral contact between two elastic bodies has been studied a boundary discretization by boundary elements leads to an algebraic formulation in the form of a linear complementarity problem in this paper the process of contact or detachment is obtained through a step by step analysis by using generalized weighted quantities as the check elements the detachment or the contact phenomenon may happen when the weighted traction or the weighted displacement is greater than the weighted cohesion or weighted minimum reference gap respectively the applications are performed by using the karnak sgbem program made by some of the authors of this paper

relations between svd and gsvd of discrete regularization problems in standard and general form abstract we consider an algorithm due to elden that transforms general discrete regularization problems into standard form we derive a simple relationship between the svd associated with the standard form problem and the gsvd associated with the general problem and we discuss the accuracy of the gsvd computed via this transformation

blind separation of sound sources from the principle of least spatial entropy abstract the aim of the paper is to offer a method for separating incoherent and compact sound sources which may overlap in both the space and frequency domains this is found of interest in acoustical applications involving the identification and ranking of sound sources stemming from different physical origins the principle proceeds in two steps the first one being reminiscent to source reconstruction e g as in near field acoustical holography and the second one to blind source separation specifically the source mixture is first expanded into a linear combination of spatial basis functions whose coefficients are set by backpropagating the pressures measured by an array of microphones to the source domain this leads to a formulation similar but no identical to blind source separation in the second step these coefficients are blindly separated into uncorrelated latent variables assigned to incoherent virtual sources these are shown to be defined up to an arbitrary rotation a unique set of sound sources is finally recovered by searching for that rotation by conjugate gradient descent in the stiefel manifold of unitary matrices which maximizes their spatial compactness as measured either by their spatial variance or their spatial entropy this results in the proposal of two separation criteria coined least spatial variance and least spatial entropy respectively the same concept of spatial entropy which is central to the paper is also exploited in defining a new criterion the entropic l curve dedicated to determining the number of active sound sources the idea consists in considering the number of sources that achieves the best compromise between a low spatial entropy as expected from compact sources and a low statistical entropy as expected from a low residual error the proposed methodology is validated on both laboratory experiments and numerical data and illustrated on an industrial example concerned with the ranking of sound sources on a diesel engine at the same time its robustness to the estimated number of active sources is demonstrated

a regularized inverse approach to ultrasonic pulse echo imaging an inverse theoretic approach to ultrasonic pulse echo imaging based on nonquadratic regularization is presented and its effectiveness is investigated computationally by 1 evaluating the quality of the reconstruction of speckle based images as a function of the transmit receive bandwidth and focal number of the transducer 2 comparing the reconstructed images with those obtained by using conventional b mode imaging the l curve and the generalized cross validation methods were evaluated as automatic regularization parameter selection techniques the inversion using regularization produced better results than conventional b mode imaging for high signal to noise ratios snrs a lower bound of 30 db for the snr was found for this study below which several of the image features were lost during the reconstruction process in order to control the distortion due to the noise

a new method for nmr data inversion based on double parameter regularization nuclear magnetic resonance nmr technology plays a significant role in petroleum exploration nmr data can be processed using inversion methods to reflect the relaxation information of all the components a new double parameter regularization dpr method was proposed for the inversion of nmr data whose regularization terms consist of tikhonov regularization and maximum entropy regularization the objective function for the dpr method was solved using the levenberg marquardt method the proportional coefficient of the regularization parameter was obtained using an iteration procedure the optimum regularization parameter of the dpr method was selected using an s curve the relationship between the optimum regularization parameter and the signal to noise ratio snr of the data was evaluated moreover we compared the results of the nmr inversion obtained from the norm smooth method the maximum entropy method and the dpr method for simulated data we evaluated how the proportional coefficient of the re

structural damping identification based on an iterative regularization method a time domain structural damping identification method is presented in this paper the damping of a structure is assumed to be time invariant rayleigh damping time variant rayleigh damping and modal damping respectively and an iterative regularization method is proposed to identify these three types of damping in turn a sensitivity approach is adopted in the formulation of the ill posed inverse problem a new constraint is imposed on the identified iterative increment as well as on the unknown structural parameters to ensure their physical meaning in the identification process is not lost the proposed method is verified in numerical studies with a space frame structure and laboratory measurements of accelerations with accurate results

regularization parameter selection for nonlinear iterative image restoration and mri reconstruction using gcv and sure based methods regularized iterative reconstruction algorithms for imaging inverse problems require selection of appropriate regularization parameter values we focus on the challenging problem of tuning regularization parameters for nonlinear algorithms for the case of additive possibly complex gaussian noise generalized cross validation gcv and weighted mean squared error mse approaches based on stein s unbiased risk estimate sure need the jacobian matrix of the nonlinear reconstruction operator representative of the iterative algorithm with respect to the data we derive the desired jacobian matrix for two types of nonlinear iterative algorithms a fast variant of the standard iterative reweighted least squares method and the contemporary split bregman algorithm both of which can accommodate a wide variety of analysis and synthesis type regularizers the proposed approach iteratively computes two weighted sure type measures predicted sure and projected sure which require knowledge of noise variance 2 and gcv which does not need 2 for these algorithms we apply the methods to image restoration and to magnetic resonance image mri reconstruction using total variation and an analysis type l1 regularization we demonstrate through simulations and experiments with real data that minimizing predicted sure and projected sure consistently lead to near mse optimal reconstructions we also observe that minimizing gcv yields reconstruction results that are near mse optimal for image restoration and slightly suboptimal for mri theoretical derivations in this paper related to jacobian matrix evaluations can be extended in principle to other types of regularizers and reconstruction algorithms

numerical analysis of a frictionless contact problem for elastic viscoplastic materials abstract we consider a mathematical model which describes the unilateral quasistatic contact of two elastic viscoplastic bodies the contact is without friction and it is modeled by the classical signorini boundary conditions the model consists of an evolution equation coupled with a time dependent variational inequality it has been shown that the variational problem of the model has a unique solution here we consider numerical approximations of the problem we use the finite element method to discretize the spatial domain spatially semi discrete and fully discrete schemes are studied for both schemes we show the existence of a unique solution and derive error estimates under appropriate regularity assumptions of the solution we have the optimal order convergence

regularization in model updating this paper presents the theory of sensitivity based model updating with a special focus on the properties of the solution that result from the combination of optimization of the response prediction with a priori information about the uncertain parameters model updating together with the additional regularization criterion is an optimization with two objective functions and must be linearized to obtain the solution structured solutions are obtained based on the generalized singular value decomposition gsvd and specific features of the parameter and response paths as the regularization parameter varies are explored the four different types of spaces that arise in the solution are discussed together with the characteristics of the regularized solution families these concepts are demonstrated on a simulated discrete example and on an experimental case study copyright 2007 john wiley sons ltd

a regularized sampling algorithm for reconstructing non bandlimited signals in this paper the reconstruction of non bandlimited sampling is discussed and a regularized sampling algorithm for non bandlimited signals is presented the error of the regularized sampling algorithm is presented and compared with the previous algorithm based on shannon s sampling theorem and compared with the tikhonov regularization method in the noisy case