on nonlinear weighted errors in variables parameter estimation problem in the three parameter weibull model this paper is concerned with the three parameter weibull distribution which is widely used as a model in reliability and lifetime studies in practice the weibull model parameters are not known in advance and must be estimated from a random sample difficulties in applying the method of maximum likelihood to three parameter weibull models have led to a variety of alternative approaches in the literature in this paper we consider the nonlinear weighted errors in variables eiv fitting approach as a main result two theorems on the existence of the eiv estimate are obtained an illustrative example is also included

least squares reverse time migration with an angle dependent weighting factor least squares reverse time migration lsrtm produces higher quality images than conventional rtm however directly using the standard gradient formula the inverted images suffer from low wavenumber noise using a simple high pass filter on the gradient can alleviate the effect of the low wavenumber noise but owing to the illumination issue the amplitudes are not balanced and in the deep part they are often weak these two issues can be mitigated by the iterative approach but it needs more iterations we introduced an angle dependent weighting factor to weight the gradient of lsrtm to suppress the low wavenumber noise and also to emphasize the gradient in the deep part an optimal step length for the l2 norm objective function is also presented to scale the gradient to the right order two numerical examples performed with the data synthesized on the sigsbee2a and marmousi models indicate that when using this weighted gradient combined with the preconditioned l bfgs algorithm with the optimal step length only a few iterations can achieve satisfying results

isotropic angle domain elastic reverse time migration multicomponent data usually are not processed with specifically designed procedures but with procedures analogous to those used for single component data in isotropic media the vertical and horizontal components of the data commonly are taken as proxies for the p and s wave modes which are imaged independently with the acoustic wave equations this procedure works only if the vertical and horizontal components accurately represent p and s wave modes which generally is not true therefore multicomponent images constructed with this procedure exhibit artifacts caused by incorrect wave mode separation at the surface an alternative procedure for elastic imaging uses the full vector fields for wavefield reconstruction and imaging thewavefieldsarereconstructedusingthemulticomponentdata as a boundary condition for a numerical solution to the elastic wave equation the key component for wavefield migration is theimagingcondition whichevaluatesthematchbetweenwavefields reconstructed from sources and receivers for vector wave fields a simple component by component crosscorrelation between two wavefields leads to artifacts caused by crosstalk between the unseparated wave modes we can separate elastic wavefields after reconstruction in the subsurface and implement theimagingconditionascrosscorrelationofpurewavemodesinstead of the cartesian components of the displacement wavefield thisapproachleadstoimagesthatareeasiertointerpretbecause they describe reflectivity of specified wave modes at interfaces of physical properties as for imaging with acoustic wavefields the elastic imaging condition can be formulated conventionally crosscorrelation with zero lag in space and time and extendedtononzerospaceandtimelags theelasticimagesproduced by an extended imaging condition can be used for angle decomposition of primary pp or ss and converted ps or sp reflectivity angle gathers constructed with this procedure have applicationsformigrationvelocityanalysisandamplitude variation with angleanalysis

compensating q effects in viscoelastic media by adjoint based least squares reverse time migration low values of p and s wave quality factors qp and qs result in strong intrinsic seismic attenuation in both seismic modeling and imaging we use a linearized waveform inversion approach by generalizing least squares reverse time migration lsrtm for viscoelastic media q lsrtm to compensate the attenuation loss for both p and s images we use the first order particle velocity stress and memory variable equations with explicit q in the formulations based on the generalized standard linear solid gsls as the forward modeling operator the linearized two way viscoelastic modeling operator is obtained with modulus perturbations introduced for the relaxed p and s moduli the viscoelastic adjoint operator and the p and s imaging conditions for modulus perturbations are derived using the adjoint state method and an augmented lagrangian functional q lsrtm solves the viscoelastic linearized modeling operator for generating synthetic data and the adjoint operator is used for back propagating the data re

brief guaranteed parameter bounding for nonlinear models with uncertain experimental factors in the context of bounded error estimation it is customary to assume that the error between the model output and output data should lie between some known prior bounds in this paper it is also assumed that the factors characterizing the experiments that have been carried out e g measurement times are uncertain with known prior bounds an algorithm based on interval analysis is used to characterize the set of all values of the parameter vector to be estimated that are consistent with these hypotheses this is performed in a guaranteed way even when the model output is a nonlinear function of the parameters and factors characterizing the experiments

algebraic connections between the least squares and total least squares problems in this paper the closeness of the total least squares tls and the classical least squares ls problem is studied algebraically interesting algebraic connections between their solutions their residuals their corrections applied to data fitting and their approximate subspaces are proven all these relationships point out the parameters which mainly determine the equivalences and differences between the two techniques these parameters also lead to a better understanding of the differences in sensitivity between both approaches with respect to perturbations of the data in particular it is shown how the differences between both approaches increase when the equationsax b become less compatible when the length ofb orx is growing or whena tends to be rank deficient they are maximal whenb is parallel with the singular vector ofa associated with its smallest singular value furthermore it is shown how tls leads to a weighted ls problem and assumptions about the underlying perturbation model of both techniques are deduced it is shown that many perturbation models correspond with the same tls solution

on the identification property of a projected gradient method the authors study the convergence properties of a projected gradient algorithm for the general problem min f x x in omega where f r n to r is a mapping continuously differentiable on a closed convex set omega subseteq r n the algorithm which requires only one projection per iteration is a special version of the method of projection of the gradient by demyanov and rubinov approximate methods in optimization problems elsevier new york 1970 where the step choice is made according to a scheme similar to the one used by calamai and more math programming 39 1987 pp 93 116 the authors are mainly interested in analysing the identification property of the algorithm for the case where the set omega is a polyhedron that is the ability to identify in a finite number of steps the face in which the final solution lies the convergence results that are shown are very similar to those shown in 6 for the standard projected gradient method

generalized simulated annealing for function optimization a generalized simulated annealing method has been developed and applied to the optimization of functions possibly constrained having many local extrema the method is illustrated in some difftcult pedagogical examples and used to solve a problem analyzed by bates technometrics 25 pp 373 376 1983 for which we identify an improved optimum the sensitivity of the solution to changes in the constraints and in other specifications of the problem is analyzed and discussed

a limited memory steepest descent method the possibilities inherent in steepest descent methods have been considerably amplified by the introduction of the barzilai borwein choice of step size and other related ideas these methods have proved to be competitive with conjugate gradient methods for the minimization of large dimension unconstrained minimization problems this paper suggests a method which is able to take advantage of the availability of a few additional long vectors of storage to achieve a significant improvement in performance both for quadratic and non quadratic objective functions it makes use of certain ritz values related to the lanczos process lanczos in j res nat bur stand 45 255 282 1950 some underlying theory is provided and numerical evidence is set out showing that the new method provides a competitive and more simple alternative to the state of the art l bfgs limited memory method

existence results for special nonlinear total least squares problem in this paper we prove an existence theorem for a special nonlinear total least squares problem we show that the optimal parameters of the generalized logistic function exist in the sense of total least squares provided the data satisfy the chebyshev s inequality

numerical methods for estimating parameters in nonlinear models with errors in the variables a numerically stable implementation of the gauss newton method for computing least squares estimates of parameters and variables in explicit nonlinear models with errors in the variables is proposed the algorithm uses only orthogonal transformations and exploits the special structure of the problem moreover a partially regularized marquardt like version is described that works with a reasonable overhead of arithmetic operations and storage compared to the error free case

elastic full waveform inversion for vti media a synthetic parameterization study abstractone of the main challenges for full waveform inversion fwi is taking into account both anisotropy and elasticity here we perform elastic fwi for a synthetic 2d vti transversely isotropic with a vertical symmetry axis model based on the geologic section at valhall field in the north sea multicomponent surface data are generated by a finite difference code we apply fwi in the time domain using a multiscale approach with three frequency bands an approximate inverse hessian matrix computed using the l bfgs b algorithm is employed to scale the gradients of the objective function and improve the convergence in the absence of significant diving wave energy in the deeper part of the section the model is updated primarily with reflection data an oblique displacement source which excites sufficiently intensive shear waves in the conventional offset range helps provide more accurate updates in the shear wave vertical velocity especially in the shallow layers we test three model parameteriza

on the regularizing behavior of the sda and sdc gradient methods in the solution of linear ill posed problems we analyze the regularization properties of two recently proposed gradient methods sda and sdc applied to discrete linear inverse problems by studying their filter factors we show that the tendency of these methods to eliminate first the eigencomponents of the gradient corresponding to large singular values allows to reconstruct the most significant part of the solution thus yielding a useful filtering effect this behavior is confirmed by numerical experiments performed on some image restoration problems furthermore the experiments show that for severely ill conditioned problems and high noise levels the sda and sdc methods can be competitive with the conjugate gradient cg method since they are slightly slower than cg but exhibit a better semiconvergence behavior

an approximate inverse to the extended born modeling operator abstractgiven a correct data consistent velocity model reverse time migration rtm correctly positions reflectors but generally with incorrect amplitudes and wavelets iterative least squares migration lsm corrects the amplitude and wavelet by fitting data in the sense of born modeling that is replacing migration by born inversion however lsm also requires a correct velocity model and it may require many migration demigration cycles we modified rtm in the subsurface offset domain to create an asymptotic high frequency approximation to extended lsm this extended born inversion operator outputs extended reflectors depending on the subsurface offset and position in the earth with correct amplitude and phase in the sense that similarly extended born modeling reproduces the data to good accuracy although the theoretical justification of the inversion property relies on ray tracing and stationary phase application of the weight operators does not require any computational ray tracing the co

discrete total lp norm approximation problem for the exponential function in this paper we consider the total l p norm p 0 approximation problem for the exponential function we give sufficient conditions which guarantee the existence of such optimal parameters

algorithms for bound constrained quadratic programming problems we present an algorithm which combines standard active set strategies with the gradient projection method for the solution of quadratic programming problems subject to bounds we show in particular that if the quadratic is bounded below on the feasible set then termination occurs at a stationary point in a finite number of iterations moreover if all stationary points are nondegenerate termination occurs at a local minimizer a numerical comparison of the algorithm based on the gradient projection algorithm with a standard active set strategy shows that on mildly degenerate problems the gradient projection algorithm requires considerable less iterations and time than the active set strategy on nondegenerate problems the number of iterations typically decreases by at least a factor of 10 for strongly degenerate problems the performance of the gradient projection algorithm deteriorates but it still performs better than the active set method

modification of tv rof denoising model based on split bregman iterations abstract minimizing variational models by means of un constrained optimization algorithms is a well known approach for dealing with the image denoising problem in this paper we propose a modification of the widely explored tv rof model named h tv rof in which a penalty term based on higher order derivatives is added a split bregman iterative scheme is used to solve the proposed model and its convergence is proved the performance of the new algorithm is analized and compared with tv rof on a set of numerical experiments

derivation of forward and adjoint operators for least squares shot profile split step migration the forward and adjoint operators for shot profile least squares migration are derived the forward operator is demigration and the adjoint operator is migration the demigration operator is derived from the born approximation the process begins with a green s function that allows for a laterally varying migration velocity model using the split step approximation next the earth is divided into horizontal layers and within each layer the migration velocity model is made to be constant with respect to depth for a given layer 1 the source side wavefield is propagated down to its top using the background wavefield this gives a background wavefield incident at the layer s upper boundary 2 the layer s contribution to the scattered wavefield is computed using the born approximation to the scattered wavefield and the background wavefield 3 next its scattered wavefield is propagated back up to the measurement surface using again the background wavefield the measured wavefield is approximated by the sum of scattered wavefields from each layer in the derivation of the measured wavefield the shot profile migration geometry is used for each shot the resulting wavefield modeling operator takes the form of a fredholm integral equation of the first kind and this is used to write down its adjoint the shot profile migration operator this forward adjoint pair is used for shot profile least squares migration shot profile least squares migration is illustrated with two synthetic examples the first uses data collected over a four layer acoustic model and the second uses data from the sigsbee 2a model

on the steplength selection in gradient methods for unconstrained optimization abstract the seminal paper by barzilai and borwein 1988 has given rise to an extensive investigation leading to the development of effective gradient methods several steplength rules have been first designed for unconstrained quadratic problems and then extended to general nonlinear optimization problems these rules share the common idea of attempting to capture in an inexpensive way some second order information however the convergence theory of the gradient methods using the previous rules does not explain their effectiveness and a full understanding of their practical behaviour is still missing in this work we investigate the relationships between the steplengths of a variety of gradient methods and the spectrum of the hessian of the objective function providing insight into the computational effectiveness of the methods for both quadratic and general unconstrained optimization problems our study also identifies basic principles for designing effective gradient methods

the link of kirchhoff migration and demigration to kirchhoff and born modeling the kirchhoff approximation provides a representation of seismic data as a summation of imaged data along isochron surfaces demigration the asymptotic inversion of this representation provides a migration as a summation of seismic data along diffraction surfaces we replace born inversion techniques with kirchhoff inversion techniques and further show the link between the kirchhoff and born representations after the born linearized reflection coefficient is replaced by the kirchhoff reflection coefficient

prestack scalar reverse time depth migration of 3d elastic seismic data using two independent 3d scalar reverse time depth migrations we migrate the reflected p and s waves in a prestack 3d three component 3 c elastic seismic data volume generated with a p wave source in a 3d model and recorded at the top of the model reflected p and s waves are extracted by divergence a scalar and curl a 3 c vector calculations respectively during shallow downward extrapolation of the elastic seismic data the imaging time for the migrations of both the reflected p and p s converted waves at each point is the one way p wave traveltime from the source to that point the divergence the extracted p waves is reverse time extrapolated using a finite difference solution of the 3d scalar wave equation in a 3d p velocity modeland is imaged to obtain the migrated p image the curl the extracted s waves is first converted into a scalar s wavefield by taking the curl s absolute value as the absolute value of the scalar s wavefield and assigning a positive sign if the curl is counterc

elastic reflection based waveform inversion with a nonlinear approach abstractfull waveform inversion fwi is a highly nonlinear problem due to the complex reflectivity of the earth and this nonlinearity only increases under the more expensive elastic assumption in elastic media we need a good initial p wave velocity and even better initial s wave velocity models with accurate representation of the low model wavenumbers for fwi to converge however inverting for the low wavenumber components of p and s wave velocities using reflection waveform inversion rwi with an objective to fit the reflection shape rather than produce reflections may mitigate the limitations of fwi because fwi performing as a migration operator is preferred of the high wavenumber updates along reflectors we have developed an elastic rwi that inverts for the low wavenumber and perturbation components of the p and s wave velocities to generate the full elastic reflection wavefields we derive an equivalent stress source made up by the inverted model perturbations and incident wavefields w

problems in estimating dynamics from data abstract this paper discusses some difficulties in estimating dynamics from time delay embeddings of experimental data that can be characterized as low dimensional a new procedure is described to reduce noise by exploiting the properties of saddle periodic orbits on the reconstructed attractor

total least squares fitting michaelis menten enzyme kinetic model function the michaelis menten enzyme kinetic model f x a b ax b x a b 0 is widely used in biochemistry pharmacology biology and medical research given the data p i x i y i i 1 m m 3 we consider the total least squares tls problem for the michaelis menten model we show that it is possible that the tls estimate does not exist as the main result we show that the tls estimate exists if the data satisfy some natural conditions some numerical examples are included

air tools a matlab package of algebraic iterative reconstruction methods we present a matlab package with implementations of several algebraic iterative reconstruction methods for discretizations of inverse problems these so called row action methods rely on semi convergence for achieving the necessary regularization of the problem two classes of methods are implemented algebraic reconstruction techniques art and simultaneous iterative reconstruction techniques sirt in addition we provide a few simplified test problems from medical and seismic tomography for each iterative method a number of strategies are available for choosing the relaxation parameter and the stopping rule the relaxation parameter can be fixed or chosen adaptively in each iteration in the former case we provide a new training algorithm that finds the optimal parameter for a given test problem the stopping rules provided are the discrepancy principle the monotone error rule and the ncp criterion for the first two methods training can be used to find the optimal discrepancy parameter

projected barzilai borwein methods for large scale box constrained quadratic programming this paper studies projected barzilai borwein pbb methods for large scale box constrained quadratic programming recent work on this method has modified the pbb method by incorporating the grippo lampariello lucidi gll nonmonotone line search so as to enable global convergence to be proved we show by many numerical experiments that the performance of the pbb method deteriorates if the gll line search is used we have therefore considered the question of whether the unmodified method is globally convergent which we show not to be the case by exhibiting a counter example in which the method cycles a new projected gradient method pabb is then considered that alternately uses the two barzilai borwein steplengths we also give an example in which this method may cycle although its practical performance is seen to be superior to the pbb method with the aim of both ensuring global convergence and preserving the good numerical performance of the unmodified methods we examine other recent work on nonmonotone line searches and propose a new adaptive variant with some attractive features further numerical experiments show that the pabb method with the adaptive line search is the best bb like method in the positive definite case and it compares reasonably well against the gpcg algorithm of more and toraldo in the indefinite case the pbb method with the adaptive line search is shown on some examples to find local minima with better solution values and hence may be preferred for this reason

elastic least squares reverse time migration abstractleast squares migration can produce images with improved resolution and reduced migration artifacts compared with conventional imaging we have developed a method for elastic least squares reverse time migration lsrtm based on a new perturbation imaging condition that yields scalar images of squared p and s velocity perturbations these perturbation images do not suffer from polarity reversals that are common for more conventional elastic imaging methods we use 2d synthetic and field data examples to demonstrate the proposed lsrtm algorithm using the perturbation imaging condition our results show that elastic lsrtm improves the energy focusing and illumination of the elastic images and it attenuates artifacts resulting for instance from sparseness in the wavefield sampling and crosstalk of the p and s modes compared with rtm images the lsrtm images provide more accurate relative amplitude information that is useful for reservoir characterization

on parameter estimation for biaxial mechanical behavior of arteries this article considers the parameter estimation of multi fiber family models for biaxial mechanical behavior of passive arteries in the presence of the measurement errors first the uncertainty propagation due to the errors in variables has been carefully characterized using the constitutive model then the parameter estimation of the artery model has been formulated into nonlinear least squares optimization with an appropriately chosen weight from the uncertainty model the proposed technique is evaluated using multiple sets of synthesized data with fictitious measurement noises the results of the estimation are compared with those of the conventional nonlinear least squares optimization without a proper weight factor the proposed method significantly improves the quality of parameter estimation as the amplitude of the errors in variables becomes larger we also investigate model selection criteria to decide the optimal number of fiber families in the multi fiber family model with respect to the experimental data balancing between variance and bias errors