an algorithm for total symmetric obdd detection this paper presents an elegant and efficient algorithm for detection of symmetry in boolean functions represented by ordered binary decision diagrams obdds

detecting inclusions in electrical impedance tomography without reference measurements we develop a new variant of the factorization method that can be used to detect inclusions in electrical impedance tomography from either absolute current to voltage measurements at a single nonzero frequency or from frequency difference measurements this eliminates the need for numerically simulated reference measurements at an inclusion free body and thus greatly improves the method s robustness against forward modeling errors e g in the assumed body s shape

smooth conjugacy and s r b measures for uniformly and non uniformly hyperbolic systems we give a new proof of the fact that the eigenvalues at corresponding periodic orbits forms a complete set of invariants for the smooth conjugacy of low dimensional anosov systems we also show that if a homeomorphism conjugating two smooth low dimensional anosov systems is absolutely continuous then it is as smooth as the maps we furthermore prove generalizations of these facts for non uniformly hyperbolic systems as well as extensions and counterexamples in higher dimensions

a regularized sampling method for solving three dimensional inverse scattering problems the inverse scattering problem under consideration is to determine the shape of an obstacle in re 3 from a knowledge of the time harmonic incident acoustic wave and the far field pattern of the scattered wave with frequency in the resonance region a method for solving this nonlinear and improperly posed problem is presented which is based on solving a linear integral equation of the first kind and avoids the use of nonlinear optimization methods numerical examples are given showing the practicality of this new approach

boundary layer techniques for solving the helmholtz equation in the presence of small inhomogeneities we consider solutions to the helmholtz equation in two and three dimensions based on layer potential techniques we provide for such solutions a rigorous systematic derivation of complete asymptotic expansions of perturbations resulting from the presence of diametrically small inhomogeneities with constitutive parameters different from those of the background medium it is expected that our results will find important applications for developing effective algorithms for reconstructing small dielectric inhomogeneities from boundary measurements

numerical simulation of optimal deconvolution in a shallow water environment a fast technique for deconvolving signals in a dispersive multipath shallow water environment using inverse filters is compared with the more commonly used deconvolution technique of time reversal also known as phase conjugation the objective of such techniques is to improve the accuracy of sound transmission from a source array to some receiving space time reversal provides benefits in this regard but here the additional performance that can be gained from inverse filters is examined several strategies for obtaining a set of inverse filters are discussed each aimed at improving the accuracy of the reconstruction of the desired time signals through inverse techniques it will be shown that an optimal inversion in the sense of achieving a flat system response in the frequency domain does not necessarily achieve a realizable time domain filter a fast field model using oases of the giglio basin shallow water test facility is used as the basis for evaluating the various focusing strategies for single receiver locations it will be seen that inverse filter arrays provide enhanced temporal and spatial focusing when compared to time reversal arrays in addition inverse filtering allows multiple receivers to be used thereby increasing bandwidth or improving redundancy

symmetric minimal covering problem and minimal pla s with symmetric variables this paper first discusses the symmetric property of the minimal covering problem in terms of group theory and then the use of this property in the branch and bound method for solving the problem computational results on solving sample problems are shown to demonstrate the improvement of computational efficiency of the branch and bound method by the utilization of the symmetric property the sample problems contain the minimal sum derivation of symmetric switching functions as an application to the design of minimal programmable logic arrays pla s it is shown that when the minimal covering problem derived for the given switching function has symmetric permutations the given switching function may not be symmetric although when the given switching function is symmetric the minimum covering problem obtained from the function is symmetric the branch and bound method based on the symmetric property can be applied not only to symmetric switching functions but also to switching functions which are not symmetric if the corresponding minimal covering problems have symmetric permutations the method can be also applied to minimal covering problems which arise outside the minimal sum derivation problems for switching functions

music type electromagnetic imaging of a collection of small three dimensional inclusions in this paper we consider the localization of a collection of small three dimensional bounded homogeneous inclusions via time harmonic electromagnetic means typically using arrays of electric or magnetic dipole transmitters and receivers with given polarization s at some distance from the collection possibly also lying in the far field the inclusions somewhat apart or closely spaced are buried within a homogeneous medium and are of arbitrary contrast of permittivity conductivity and permeability vis ag vis this embedding medium the problem is formulated as an inverse scattering problem for the full maxwell equations and it involves a robust asymptotic modeling of the multistatic response matrix no specific application is studied at this stage but characterization of obstacles in subsoils nondestructive evaluation of man made structures and medical imaging are primary fields of application envisaged the proposed approach uses a music multiple signal classification type algorithm and it yields fast numbering accurate localization and estimates of the electromagnetic and geometric parameters polarization tensors of the inclusions the mathematical machinery is detailed first some specific attention being given to triaxial ellipsoidal inclusions and degenerate spherical shapes for the latter known results are retrieved then the viability of this algorithm which would be easily extended to planarly layered environments by introduction of their green s functions is documented by a variety of numerical results from synthetic noiseless and severely noisy field data

an asymptotic factorization method for inverse electromagnetic scattering in layered media we consider the inverse problem to reconstruct the number and the positions of a collection of finitely many small perfectly conducting scatterers buried within the lower halfspace of an unbounded two layered background medium from near field measurements of time harmonic electromagnetic fields for this purpose we first study the direct scattering problem and derive an asymptotic expansion of the scattered field as the size of the scatterers tends to zero integral equation methods and a factorization of the corresponding near field measurement operator are applied to prove this expansion in the second part of this work we use the asymptotic expansion to justify a noniterative reconstruction algorithm which is a combination of factorization methods and music type methods we illustrate the feasibility of this method by a numerical example

logic networks with a minimum number of nor nand gates for parity functions of n variables design of logic networks in single rail input logic with a minimum number of nor gates for parity functions of an arbitrary number of variables is described this is partly based on minimum networks for parity functions of a small number of variables which are designed by the integer programming logic design method although it is generally difficult to design minimum networks for functions of an arbitrarily large number of variables we have previously designed minimum networks for adders of an arbitrary number of variables the minimum networks for parity functions of an arbitrary number of variables discussed in this paper is another case many unique properties of minimum nor networks for parity functions are shown minimum networks with nand gates for parity functions can be easily obtained from those with nor gates because of duality relationship between nand and nor

semantics of dyadic and mixed potential field representation for 3 d current distributions in planar stratified media the full spectral electric dyadic green s function for three dimensional current distributions in planar stratified media can be obtained straight from maxwell s equations by following a physical reasoning analogous with the free space case but using general derivative relations for multilayered green s functions we derive a basic mixed potential form with a simple vector potential kernel but multiple scalar potential kernels and also obtain the well established single scalar potential formulations with a dyadic vector potential kernel mixed potential forms are thus arrived at without the a priori introduction of scalar and vector potential or choice of gauge condition the nonuniqueness of the scalar potential kernel and the dyadic nature of the scalar and or vector potentials are believed to be clarified by the proposed approach a discussion of the different formulations focuses on physical meaning and numerical consequences for the solution of integral equations

analysis of the time reversal operator for a small spherical scatterer in an electromagnetic field the time reversal operator tro for a planar array of crossed dipole elements illuminating a small conducting and or dielectric sphere is investigated in order to determine the general properties of an electromagnetic time reversing array system the behavior of such a system for a given frequency is analyzed by studying the eigenvalues and eigenvectors of the tro each eigenvector specifies a set of complex driving currents for the array elements that produce received voltages that are proportional to the conjugates of the drive currents the proportionality constant is equal to the square root of the associated eigenvalue and is the same for all elements the eigenvalues and eigenvectors can be determined by performing a singular value decomposition svd on the multistatic data matrix of the array the eigenvalues of the tro are the squares of the singular values and the eigenvectors are identical to the singular vectors we have shown that the maximum number of singular vectors associated with the sphere is equal to the number of orthogonal orientations of the dipole moments induced in the sphere when irradiated by the array so there is a maximum of six for a conducting sphere but only three are significant when the conductivity is small and the sphere may be considered being just a dielectric numerical results are presented for linear and circular arrays to show the general behavior of the system

enhanced multilevel linear sampling methods for inverse scattering problems we develop two enhanced techniques for the multilevel linear sampling method mlsm proposed in 32 for inverse scattering problems under some practical situations the mlsm suffers certain undesirable breakage cells problem we propose to avoid the curse of breakage cells by incorporating expanding and searching techniques the new techniques are shown to significantly improve the robustness of the mlsm and meanwhile they possess the same optimal computational complexity as the mlsm numerical experiments are presented to illustrate the promising features of the enhanced mlsms

two numerical methods for recovering small inclusions from the scattering amplitude at a fixed frequency in this paper two noniterative algorithms for locating small electromagnetic inclusions from the scattering amplitude at a fixed frequency are developed in particular a variety of numerical results is presented to highlight their potential and their limitations

the imaging of small perturbations in an anisotropic media abstract in this paper we employ asymptotic analysis to determine information about small volume defects in a known anisotropic scattering medium from far field scattering data the location of the defects is reconstructed via the music algorithm from the range of the multi static response matrix derived from the asymptotic expansion of the far field pattern in the presence of small defects since the same data determines the transmission eigenvalues corresponding to the perturbed media we investigate how the presence of the defects changes the transmission eigenvalues and use this information to recover the strength of the small defects we provide convergence results on transmission eigenvalues as the size of the defects tends to zero as well as derive the first correction term in the asymptotic expansion of the simple transmission eigenvalues numerical examples are presented to show the viability of our imaging method

recent developments in inverse acoustic scattering theory we survey some of the highlights of inverse scattering theory as it has developed over the last 15 years with emphasis on uniqueness theorems and reconstruction algorithms for time harmonic acoustic waves included in our presentation are numerical experiments using real data and numerical examples of the use of inverse scattering methods to detect buried objects

multistatic response matrix of spherical scatterers and the back propagation of singular fields in view of the development of multiple signal classification type non iterative imaging procedures based on the singular value decomposition of the multistatic response msr matrix of a collection of inclusions the full 3 d electromagnetic case with arbitrary contrasts of permeability and permittivity including perfectly electric conducting or perfectly magnetic conducting limit cases is studied the structure of the msr matrix of a single inclusion or a set of well separated ones is analyzed emphasis is on a far field situation in which one considers an electric dipole array operated in the transmit receive mode at a single frequency back propagated electric and magnetic fields associated to the singular vectors of the msr matrix for a single spherical inclusion or again for well separated ones are given in closed form and their leading order values are exhibited numerical illustrations cross sectional maps of back propagated fields computed from a singular value decomposition of the msr matrix are presented for one and two inclusions to illustrate this behavior as a function of the geometric and electromagnetic parameters of the configuration in a possibly noisy case

the iterative time reversal process analysis of the convergence the efficiency of a time reversal acoustic mirror to focus on a reflective target through an inhomogeneous media has been demonstrated in a multitarget media the ability of such a mirror to work in an iterative mode in order to focus selectively on the strongest target was shown c prada f wu and m fink j acoust soc am 90 1119 1991 the theory of how the iterative time reversal process is built is based on a matrix formalism and treats the array of l transducers in a given medium as a linear system of l inputs l outputs the system is characterized at each frequency by its transfer matrix k and the time reversal iterative process is then described by a time reversal operator k k because of the reciprocity principle this operator is hermitian the following result is shown if the scattering medium is a set of well resolved targets of different reflectivities then each eigenvector of the operator k k with nonzero eigenvalue corresponds to one of the targets in the set and provides the opt

reconstructing acoustic obstacles by planar and cylindrical waves in this paper we develop a novel method of reconstructing acoustic obstacles in r2 which follows a similar spirit of the linear sampling method originated by colton and kirsch the reconstruction scheme makes use of the near field measurements encoded into the boundary dirichlet to neumann map or the neumann to dirichlet map both the plane waves and cylindrical waves are shown to meet the reconstruction purpose rigorous mathematical justification of the reconstruction scheme is established the mapping properties of the newly introduced function operators involved in the reconstruction scheme are established these results are of significant mathematical interests for their own sake moreover due to the distinct properties of the function operators the indictor function in the proposed reconstruction scheme exhibits completely different behaviors from those having been established for the indictor function in the original linear sampling method for inverse scattering problems numerical experiments

localizing thin metallic cylinders by a 2 5 d linear distributional approach experimental results the problem of detecting and localizing thin metallic scatterers from electromagnetic scattered field measurements is addressed the scatterers are assumed to be infinitely long and a 2 5 dimensional mathematical model is adopted according to the distributional approach the problem is cast as the inversion of a linear integral operator acting on 6 distributions whose supports are representative of the scatterers locations in this paper we present the experimental validation of such an approach to this end we perform the reconstructions by exploiting experimental scattered field data collected in controlled conditions at the electromagnetic diagnostics laboratory of the second university of naples the experiments are conducted in an anechoic chamber where the scatterers are embedded in a homogenous and lossless background medium the multistatic single view multifrequency and the multistatic multiview multifrequency configurations are both considered

a direct impedance tomography algorithm for locating small inhomogeneities impedance tomography seeks to recover the electrical conductivity distribution inside a body from measurements of current flows and voltages on its surface in its most general form impedance tomography is quite ill posed but when additional a priori information is admitted the situation changes dramatically in this paper we consider the case where the goal is to find a number of small objects inhomogeneities inside an otherwise known conductor taking advantage of the smallness of the inhomogeneities we can use asymptotic analysis to design a direct i e non iterative reconstruction algorithm for the determination of their locations the viability of this direct approach is documented by numerical examples

isometries of lorentz surfaces and convergence groups we study the isometry group of a globally hyperbolic spatially compact lorentz surface such a group acts on the circle and we show that when the isometry group acts non properly the subgroups of mathrm diff mathbb s 1 obtained are semi conjugate to subgroups of finite covers of mathrm psl 2 mathbb r by using convergence groups under an assumption on the conformal boundary we show that we have a conjugacy in mathrm homeo mathbb s 1

music algorithm for location searching of dielectric anomalies from s parameters using microwave imaging abstract motivated by the biomedical engineering used in early stage breast cancer detection we investigated the use of multiple signal classification music algorithm for location searching of small anomalies using s parameters we considered the application of music to functional imaging where a small number of dipole antennas are used our approach is based on the application of born approximation or physical factorization we analyzed cases in which the anomaly is respectively small and large in relation to the wavelength and the structure of the left singular vectors is linked to the nonzero singular values of a multi static response msr matrix whose elements are the s parameters using simulations we demonstrated the strengths and weaknesses of the music algorithm in detecting both small and extended anomalies

locating several small inclusions in impedance tomography from backscatter data this paper investigates backscatter data for the inverse obstacle problem in impedance tomography when the obstacles are small it is shown that under this circumstance the backscatter data are close approximations of a rational function that has second or fourth order poles at the locations of the obstacles furthermore a numerical method is presented to locate the obstacles via the poles of certain laurent pade approximations numerical experiments explore the potential of this algorithm also for extended obstacles taking into consideration that the problem is severely ill posed

detecting interfaces in a parabolic elliptic problem from surface measurements assuming that the heat capacity of a body is negligible outside certain inclusions the heat equation degenerates to a parabolic elliptic interface problem in this work we aim to detect these interfaces from thermal measurements on the surface of the body we deduce an equivalent variational formulation for the parabolic elliptic problem and give a new proof of the unique solvability based on lions s projection lemma for the case that the heat conductivity is higher inside the inclusions we develop an adaptation of the factorization method to this time dependent problem in particular this shows that the locations of the interfaces are uniquely determined by boundary measurements the method also yields to a numerical algorithm to recover the inclusions and thus the interfaces we demonstrate how measurement data can be simulated numerically by a coupling of a finite element method with a boundary element method and finally we present some numerical results for the inverse problem

quasiconformal homeomorphisms and dynamics ii structural stability implies hyperbolicity for kleinian groups sous groupe de psl 2 c familles holomorphes d homeomorphismes de c lemme champs de ligne invariants familles holomorphes de groupes abstraitement isomorphes car finiment genere la stabilite structurelle implique geometriquement fini ou rigide theoreme a avec paraboles stabilite structurelle au sens de la dynamique differentiable

multiple signal classification method for detecting point like scatterers embedded in an inhomogeneous background medium the multiple signal classification music type method has been widely used to detect point like scatterers embedded in a homogeneous background medium this paper extends the music type method to the detection of point like scatterers that are embedded in an inhomogeneous background although the background green s function at each test point is not directly available in inhomogeneous background scenario this paper proposes an approach based on the finite element method to simultaneously obtain the green s function at all test points numerical simulations illustrate the efficacy of the proposed theory and algorithm presented in this paper and some interesting observations which are absent in homogeneous background scenario are highlighted and discussed

identification of small inhomogeneities asymptotic factorization we consider the boundary value problem of calculating the electrostatic potential for a homogeneous conductor containing finitely many small insulating inclusions we give a new proof of the asymptotic expansion of the electrostatic potential in terms of the background potential the location of the inhomogeneities and their geometry as the size of the inhomogeneities tends to zero such asymptotic expansions have already been used to design direct i e noniterative reconstruction algorithms for the determination of the location of the small inclusions from electrostatic measurements on the boundary e g music type methods our derivation of the asymptotic formulas is based on integral equation methods it demonstrates the strong relation between factorization methods and music type methods for the solution of this inverse problem

imaging of location and geometry for extended targets using the response matrix in this paper we study how to image both the location and the shape of extended targets using the response matrix obtained from inter element response of an active array of transducers in particular the time reversal technique is used for efficient initial localization of the target and the level set method is used for shape reconstruction we then show how to couple the location estimation and shape reconstruction in a complementary way to improve accuracy for range estimation resolution analysis for active arrays in remote sensing regime is also presented we illustrate with numerical experiments which show that the method is capable of imaging objects with complicated shapes and that the method is robust with respect to noisy data

discriminating resonant targets from clutter using lanczos iterated single channel time reversal power iterated single channel time reversal is extended to employ lanczos iterations the properties of these algorithms are studied in the presence of varying levels of noise and broadband clutter it is shown the lanczos iterated method possesses superior convergence properties in comparison to the standard power iterated technique results demonstrate that such algorithms provide an efficient means through which to isolate and extract the properties of resonant scatterers in the presence of noise and coherent interference

identification of small inhomogeneities of extreme conductivity by boundary measurements a theorem on continuous dependence we consider an electrostatic problem for a conductor consisting of finitely many small inhomogeneities of extreme conductivity embedded in a spatially varying reference medium firstly we establish an asymptotic formula for the voltage potential in terms of the reference voltage potential the location of the inhomogeneities and their geometry secondly we use this representation formula to prove a lipschitz continuous dependence estimate for the corresponding inverse problem this estimate bounds the difference in the location and in certain geometric properties of two sets of inhomogeneities by the difference in the boundary voltage potentials corresponding to a fixed current distribution

an image reconstruction algorithm using phase conjugation for diffraction limited imaging in an inhomogeneous medium a diffraction limited imaging method in an inhomogeneous medium which uses phase conjugation and multiple reflectors is proposed first several reflectors with frequency dependent reflectivities are put in the observation area second ultrasonic signals are acquired for all combinations of transmitter receiver elements of the array and data acquisition is repeated for each of the frequencies then signal processing is performed in a computer 1 the reflected wave in the mth step is phase conjugated and transmitted to get the reflected wave in the m 1 th step until convergence is attained 2 the converged phase conjugated wave is scanned in bearing to get an image and 3 good image parts obtained for several frequencies are joined together to extend the good image area

the linear sampling method for solving the electromagnetic inverse scattering problem we consider the inverse scattering problem of determining the shape of an obstacle in mathbb r from knowledge of the time harmonic incident electromagnetic wave and the far field pattern of the scattered wave with frequency in the resonance region the approach used is the linear sampling method which does not require a priori knowledge of either the boundary condition or the connectivity of the scattering obstacle numerical examples are given for the case of both a simply connected perfect conductor and multiply connected obstacles satisfying an impedance boundary condition on the boundary of one component and satisfying a perfect conducting boundary condition on the boundary of another component

transducer sensitivity compensation using diagonal preconditioning for time reversal and tikhonov inverse filtering in acoustic systems filters are commonly used in sound reproduction and communication systems as a means of compensating for the response of the electro acoustic plant two commonly used filter designs in the field of acoustics are the time reversal filter and the tikhonov inverse filter in this paper the influence of transducer sensitivities on the performance of these filters is examined it is shown that the sensitivity of the transducers can negatively affect the performance of the resulting filter to compensate for the decrease in performance diagonal preconditioning can be implemented in the system it is shown that by using diagonal matrices which minimize the condition number of the system the loss in performance arising from unbalanced sensitivities is minimized this paper proposes an algorithm to find such a set of diagonal matrices and results are presented showing the improvements in performance arising from the modified filter design

invariants for smooth conjugacy of hyperbolic dynamical systems ii we show that the eigenvalues of the derivatives at periodic points form a complete set of invariants for smooth local conjugacy of anosov diffeomorphisms oft2

source localization using recursively applied and projected rap music a new method for source localization is described that is based on a modification of the well known music algorithm in classical music the array manifold vector is projected onto an estimate of the signal subspace errors in the estimate of the signal subspace can make localization of multiple sources difficult recursively applied and projected rap music uses each successively located source to form an intermediate array gain matrix and projects both the array manifold and the signal subspace estimate into its orthogonal complement the music projection to find the next source is then performed in this reduced subspace special assumptions about the array manifold structure such as vandermonde or shift invariance are not required using the metric of principal angles we describe a general form of the rap music algorithm for the case of diversely polarized sources through a uniform linear array simulation with two highly correlated sources we demonstrate the improved monte carlo error performance of rap music relative to music and two other sequential subspace methods s and ies music we then demonstrate the more general utility of this algorithm for multidimensional array manifolds in a magnetoencephalography meg source localization simulation

differentiable conjugacy for groups of area preserving circle diffeomorphisms we study groups of circle diffeomorphisms whose action on the cylinder c s 1 s 1 preserves a volume form we first show that such a group is topologically conjugate to a subgroup of psl 2 r then discuss the existence of a differentiable conjugacy

experimental subwavelength localization of scatterers by decomposition of the time reversal operator interpreted as a covariance matrix the d o r t method french acronym for decomposition of the time reversal operator is an active remote sensing technique using arrays of antennas for the detection and localization of scatterers prada et al j acoust soc am 99 2067 2076 1996 the analogy between the time reversal operator and the covariance matrix used for classical sources separation in passive remote sensing bienvenu et al ieee trans assp 31 1235 1247 1983 is established then an experiment of subwavelength detection and localization of point like scatterers with a linear array of transducers is presented using classical estimators in reception like maximum likelihood and multiple signal characterization music two point like scatterers separated by 3 and placed at 100 from the array of transducers are resolved in these experiments the role of multiple scattering and the existence of additional eigenvectors associated with dipolar and monopolar radiation of each scatterer is discussed

multistatic response matrix of a 3 d inclusion in half space and music imaging recent work on the retrieval of 3 d bounded dielectric and or magnetic inclusions in free space is extended to burial in a half space though emphasis is on the case of a single inclusion enabling the derivation of closed form mathematical results in illuminating fashion the approach extends to the case of an unknown number of well separated inclusions within an asymptotic field formulation derived from exact contrast source vector integral formulations satisfied by the time harmonic fields and using proper reciprocity relationships of the dyadic green s functions the multistatic response matrix of the inclusion is constructed from the leading order term of the fields its singular value structure is analyzed in detail for a dielectric or a magnetic contrast or both contrasts this is performed in the case of a unique electric dipole array operated in the transmit receive mode at a single frequency a multiple signal classification type algorithm follows from the decomposition yielding a cost functional the magnitude of which peaks at the inclusion center numerical results illustrate the above as a function of the geometric and electromagnetic parameters of the configuration imaging of a spherical inclusion is in particular investigated from severely noisy synthetic data as well as of two inclusions embedded within a non conductive or conductive half space

on the sensitivity of time reversal imaging techniques to model perturbations time reversal tr techniques involve physical or synthetic retransmission of signals acquired by a set of transceivers in a time reversed fashion and can be used for a host of applications including ultrawideband imaging of obscured targets this work investigates the performance of some tr based techniques under non ideal conditions and is divided into three main parts in the first part we investigate the robustness of tr based imaging techniques via the decomposition of tr operator dort algorithm and the multiple signal classification music algorithm under clutter and additive noise in the second part we examine the effect of tr invariance breaking due to losses in the intervening media on the performance of both dort and tr based music in the third part effects of translational perturbations of the tr array are examined as a class of model perturbations these ensuing effects are then exploited in a controlled manner as a means to extract second order spatial statistics of the probed media

high precision identification of an object optimality conditions based concept of imaging a class of inverse problems for the identification of an unknown geometric object from given measurements is considered a concept for object imaging based on optimality conditions and level sets is introduced which provides high resolution properties of the identification problem and stability to discretization and noise errors as a specific case the identification of the center of a test object of arbitrary shape and unknown boundary conditions from d boundary measurements in d spatial dimensions in the context of the helmholtz equation is described in detail for analysis and numerical realization methods from topology optimization generalized singular perturbations endowed with variational techniques and a petrov galerkin enrichment within generalized fem are used

decomposition of the time reversal operator detection and selective focusing on two scatterers the decomposition of the time reversal operator dort method is a selective detection and focusing technique using an array of transmit receive transducers it relies on the theory of iterative time reversal mirrors which was presented by prada et al c prada j l thomas and m fink j acoust soc am 97 62 71 1995 the time reversal operator was defined as k k where is the frequency means complex conjugate and k is the transfer matrix of the array of l transducers insonifying a time invariant scattering medium it was shown that this time reversal operator can be diagonalized and that for ideally resolved scatterers of different reflectivities each of its eigenvectors of nonzero eigenvalue provides the phase law to be applied to the transducers in order to focus on one of the scatterers the dort method consists in determining these eigenvectors and using them for the selective focusing this paper presents a complete analysis of this method in the case of two scatterers the

green s function estimation in speckle using the decomposition of the time reversal operator application to aberration correction in medical imaging the fdort method french acronym for decomposition of the time reversal operator using focused beams is a time reversal based method that can detect point scatterers in a heterogeneous medium and extract their green s function it is particularly useful when focusing in a heterogeneous medium this paper generalizes the theory of the fdort method to random media speckle and shows that it is possible to extract green s functions from the speckle signal using this method therefore it is possible to achieve a good focusing even if no point scatterers are present moreover a link is made between fdort and the van cittert zernike theorem it is deduced from this interpretation that the normalized first eigenvalue of the focused time reversal operator is a well known focusing criterion the concept of an equivalent virtual object is introduced that allows the random problem to be replaced by an equivalent deterministic problem and leads to an intuitive understanding of fdort in speckle applications to aberration correction are presented the reduction of the variance of the green s function estimate is discussed finally it is shown that the method works well in the presence of strong interfering scatterers

electrostatic backscattering by insulating obstacles we introduce and analyze backscattering data for a three dimensional obstacle problem in electrostatics in particular we investigate the asymptotic behavior of these data as i the measurement point goes to infinity and ii the obstacles shrink to individual points we also provide numerical simulations of these data

a phase and space coherent direct imaging method a direct imaging algorithm for point and extended targets is presented the algorithm is based on a physical factorization of the response matrix of a transducer array the factorization is used to transform a passive target problem to an active source problem and to extract principal components tones in a phase consistent way the multitone imaging function can superpose multiple tones spatial diversity aperture of the array and frequencies bandwidth of the probing signal based on phase coherence the method is a direct imaging algorithm that is simple and efficient since no forward solver or iteration is needed robustness of the algorithm with respect to noise is demonstrated via numerical examples