antenna array pattern synthesis via convex optimization we show that a variety of antenna array pattern synthesis problems can be expressed as convex optimization problems which can be numerically solved with great efficiency by recently developed interior point methods the synthesis problems involve arrays with arbitrary geometry and element directivity constraints on far and near field patterns over narrow or broad frequency bandwidth and some important robustness constraints we show several numerical simulations for the particular problem of constraining the beampattern level of a simple array for adaptive and broadband arrays

reactively loaded array pattern synthesis as a quadratically constrained quadratic program the pattern synthesis problem of maximizing the gain at a scanning direction subject to a maximum sidelobe level for a reactively loaded antenna array is formulated as a quadratically constrained quadratic program qcqp this formulation is derived from the scattering matrix and the active element patterns of the array considering both fed and loaded antennas as ports since the resulting qcqp is nonconvex the loads are computed from the solution of the semidefinite relaxation of the problem by forcing the feasibility of the constraints in a meaningful physical sense i e by explicitly imposing passive or purely reactive loads numerical results of dipole arrays with various configurations are presented and compared to previous works

an efficient newton barrier method for minimizing a sum of euclidean norms a new newton barrier method is proposed for minimizing a sum of euclidean norms msn f x sum i 1 k a i t x b i 2 msn is a nonsmooth problem because f is not differentiable at any point x where any of the norms is zero the method used is based on approximating f with a smooth function which in the limit has the same optimal value as f msn is shown to have a dual problem with properties very similar to duality theory in linear programming this is used in the development of the method and to give a proof of when an optimal solution for the smooth approximation is epsilon optimal measured in the duality gap for the original problem an implementation of the algorithm is described for large sparse problems and numerical results are presented for problems with more than 270 000 nonlinear variables these problems arise from plastic collapse analysis

unicast multi antenna relay beamforming with per antenna power control optimization and duality we consider amplify and forward multi antenna relaying between a single pair of source and destination under relay per antenna power constraints we design the optimal relay processing matrix to minimize the maximum per antenna power budget for a received snr target with given transmit and receive beamformers at the source and destination respectively we first focus on the equivalent system with single antenna source and destination although non convex we show that the optimization satisfies strong lagrange duality and can be solved in the lagrangian dual domain we reveal a prominent structure of this problem by establishing its duality with direct simo beamforming system with an uncertain noise this enables us to derive a semi closed form expression for the optimal relay processing matrix that depends on a set of dual variables which can be determined through numerical optimization with a significantly reduced problem space we further show that the dual problem has a semi definite programming form which enables efficient numerical optimization methods to determine the dual variables with polynomial complexity using this result the reverse problem of snr maximization under a set of relay per antenna power constraints is then addressed we then consider the maximum relay beamforming achievable rate under different combinations of antenna setups at source and destination in particular we generalize the duality to mimo relay beamforming vs direct mimo beamforming and establish the dual relation of the two systems for different multi antenna setups at source and destination

shaping regularization in geophysical estimation problems regularization is a required component of geophysical estimation problems that operate with insufficient data the goal of regularization is to impose additional constraints on the estimated model i introduce shaping regularization a general method for imposing constraints by explicit mapping of the estimated model to the space of admissible models shaping regularization is integrated in a conjugate gradient algorithm for iterative least squares estimation it provides the advantage of better control on the estimated model in comparison with traditional regularization methods and in some cases leads to a faster iterative convergence simple data interpolation and seismic velocity estimation examples illustrate the concept

local tensor radiation conditions for elastic waves a local boundary condition is formulated representing radiation of elastic waves from an arbitrary point source the boundary condition takes the form of a tensor relation between the stress at a point on an arbitrarily oriented section and the velocity and displacement vectors at the point the tensor relation generalizes the traditional normal incidence impedance condition by accounting for the angle between wave propagation and the surface normal and by including a generalized stiffness term due to spreading of the waves the effectiveness of the local tensor radiation condition is demonstrated by detailed finite element time and frequency analysis of a concentrated force in infinite three dimensional space and by a time analysis of a pulse load in a two dimensional underground gallery

application of convex relaxation to array synthesis problems a general procedure to solve efficiently non convex array synthesis problems is presented it is based on the semidefinite relaxation sdr technique the way to properly relax the constraints in order to formulate the synthesis of shaped beams phase only arrays and reconfigurable arrays as semidefinite programming problems is detailed these so approximated array synthesis problems are then convex easy to implement and can be efficiently solved using off the shelf numerical routines the conditions under which the relaxed problems provide the optimal solution to the original non convex synthesis problems are specified various representative numerical comparisons with arrays designed by other approaches show the validity of the proposed method and illustrate its potentialities

generalized nonelliptic moveout approximation in τ p domain we have derived a generalized nonelliptic moveout approximation in the p domain that is a companion to the generalized nonhyperbolic moveout approximation in the t x domain approximation requires five parameters three parameters that can be determined from the zero slowness ray and two parameters that can be determined from one additional ray we convert the generalized approximation from the p domain to the t x domain and vice versa the generalized nonelliptic moveout approximation in the p domain admits other moveout approximations as special cases several analytical and numerical tests showed a superior accuracy of the generalized nonelliptic moveout approximation

a note on treating a second order cone program as a special case of a semidefinite program it is well known that a vector is in a second order cone if and only if its arrow matrix is positive semidefinite but much less well known is about the relation between a second order cone program socp and its corresponding semidefinite program sdp the correspondence between the dual problem of socp and sdp is quite direct and the correspondence between the primal problems is much more complicated given a sdp primal optimal solution which is not necessarily arrow shaped we can construct a socp primal optimal solution the mapping from the primal optimal solution of sdp to the primal optimal solution of socp can be shown to be unique conversely given a socp primal optimal solution we can construct a sdp primal optimal solution which is not an arrow matrix indeed in general no primal optimal solutions of the socp related sdp can be an arrow matrix

optimal far field focusing of uniformly spaced arrays subject to arbitrary upper bounds in nontarget directions a new approach providing new theoretical results to the optimal far field focusing of uniformly spaced arrays subject to a completely arbitrary mask for sidelobe bounds is presented and discussed in both cases of linear or planar arrays with rectangular boundaries it is first shown that the problem can be formulated without any loss to performances on the maximum as a linear programming one guaranteeing a globally optimal solution second a sufficient uniqueness criterion for the solution of the overall problem is also developed which shows how the solution may not be unique as is actually the case when planar arrays are considered in addition further globally effective optimization procedures are proposed for the latter case in order to optimize directivity smoothness of excitations or other performance parameters in the set of equivalent solutions last an extension to planar arrays with a nonrectangular boundary is also given a thorough numerical analysis confirms the effectiveness of the approach proposed and of the solution codes developed

velocity independent marchenko focusing in time and depth imaging domains for media with mild lateral heterogeneity abstractthe marchenko method retrieves green s functions between the acquisition surface and any arbitrary point in the medium the process generally involves solving an inversion starting with an initial focusing function e g a direct wave green s function from the desired subsurface position typically obtained using an approximate velocity model we have formulated the marchenko method in the time imaging domain in that domain we recognize that the traveltime of the direct wave green s function is related to the cheop s traveltime pyramid commonly used in time domain processing which in turn can be readily obtained from the local slopes of the common midpoint gathers this observation allows us to substitute the velocity model based initial focusing operator with that from a data driven slope estimation process moreover we found that working in the time imaging domain allows for the specification of the desired subsurface position in terms of vertical time which is connected to the cartesian depth position via the time to depth conversion our results suggest that the prior velocity model is only required when specifying the position in depth but this requirement can be circumvented by making use of the time imaging domain within its usual assumptions e g mild lateral heterogeneity provided that those assumptions are satisfied the estimated green s functions from the proposed method have comparable quality to those obtained with the knowledge of a prior velocity model

a algorithm for convex minimization for convex minimization we introduce an algorithm based on space decomposition the method uses a bundle subroutine to generate a sequence of approximate proximal points when a primal dual track leading to a solution and zero subgradient pair exists these points approximate the primal track points and give the algorithm s or corrector steps the subroutine also approximates dual track points that are gradients needed for the method s newton predictor steps with the inclusion of a simple line search the resulting algorithm is proved to be globally convergent the convergence is superlinear if the primal dual track points and the objective s hessian are approximated well enough

velocity independent time domain seismic imaging using local event slopes by estimating local event slopes in prestack seismic reflection data it is possible to accomplish all common time domain imaging tasks from normal moveout to prestack time migration without the need to estimate seismic velocities or any other attributes local slopes contain complete information about the reflection geometry once they are estimated seismic velocities and all other moveout parameters turn into data attributes and are directly mappable from the prestack data domain into the time migrated image domain i develop an analytical theory which defines the transformation from data and local slopes to the image space for different time domain imaging operators computational experiments with synthetic and field data examples confirm theoretical expectations and demonstrate practical effectiveness of the proposed method

projection matrix method for shaped beam synthesis in phased arrays and reflectors we present the projection matrix method for shaped beam synthesis in a general array of different size elements the method relies on orthogonal projection of the desired far field intensity vector onto the space spanned by the far field intensity vectors of the array elements it is found that for a uniform convergence of the solution the far field sample space must be extended beyond the coverage region otherwise the projection matrix becomes ill conditioned a general guideline for the far field sample space is provided the method with necessary amendments is then employed successfully for a reflector surface synthesis the method is found to be several times faster than the gradient search method commonly used for beam synthesis numerical results for array and shaped reflector syntheses are shown and the advantages discussed

normal moveout revisited inhomogeneous media and curved interfaces the equation of normal moveout t2 t02 x2 va2 is valid for a reflection from the base of a single homogeneous and isotropic bed but is only an approximation in the real world of multilayered inhomogeneous media and curved interfaces using the theory of geometrical optics we can find another second order equation which represents hyperbolas that are also symmetrical about the time axis however the centers of these hyperbolas do not coincide with the center of coordinates but are shifted along the time axis the equation describing this second type of hyperbola is t tp t0 2 tp2 x2 v12 where tp is the time of focusing depth and v1 the velocity of the input medium this equation is not only more accurate than the usual normal moveout but its use is more economical on a vector computer because the traditional dynamic correction is a static correction in the tp analysis this procedure makes it possible to compute velocities for all the samples of all the stacked traces and produces a velocity secti

window length selection for optimum slowness resolution of the local slant stack transform one of the most critical decisions in the design of a local slant stack transform lsst is the selection of its aperture or more precisely the selection of the appropriate number of traces and their weighting coefficients for each slant stack the challenge is to achieve a good compromise between the slowness and the spatial resolution conventionally the window size is chosen in a more intuitive manner by visual inspection and some limited tests we analyzed the lsst to establish rigorous criteria for the window selection to achieve the optimum slowness and spatial resolution in the transformed domain for a given data set for this purpose we estimated the slowness resolution in the lsst domain as a function of the spatial window bandwidth and of the spectral characteristics of the waves for a wave with a given bandpass spectrum the slowness resolution the stopband attenuation and the wavefront tracking capability are determined by the spatial window for narrowband signals the spatial window m

finite element analysis of periodic structures without constrained meshes a finite element analysis is detailed of periodic structures without constrained meshes the infinite periodic analysis domain is reduced to the unit cell analysis by means of the floquet bloch decomposition where an admittance type matrix approach is carried out special emphasis is placed on the admittance type matrix generation in such a way that the constrained meshing problem is no longer required as a result periodic ports are permitted in the unit cell and the floquet bloch periodic conditions are easily applied in the admittance type matrix by means of a connection like handling several infinite periodic antennas are shown to be analyzed appropriately

extension of karmarkar s algorithm onto convex quadratically constrained quadratic problems convex quadratically constrained quadratic problems are considered it is shown that such problems can be transformed to aconic form the feasible set of the conic form is the intersection of a direct product of standard quadratic cones intersected with a hyperplane the analogue of a simplex and a linear subspace for a problem of such form the analogue of karmarkar s projective transformation and logarithmic barrier function are built this allows us to extend word by word the method of karmarkar for lp to qcqp and allows us to obtain a similar polynomial worst case bound for the number of iterations

automatic data extrapolation to zero offset along local slope abstractvelocity independent seismic data processing requires information about the local slope in the data from estimates of local time and space derivatives of the data a total least squares algorithm gives an estimate of the local slope at each data point total least squares minimizes the orthogonal distance from the data points the local time and space derivatives to the fitted straight line defining the local slope this gives a more consistent estimate of the local slope than standard least squares because it takes into account uncertainty in the temporal and spatial derivatives the total least squares slope estimate is the same as the one obtained from using the structure tensor with a rectangular window function the estimate of the local slope field is used to extrapolate all traces in a seismic gather to the smallest recorded offset without using velocity information extrapolation to zero offset is done using a hyperbolic traveltime function in which slope information replaces the knowled

a nonlinear primal dual method for total variation based image restoration we present a new method for solving total variation tv minimization problems in image restoration the main idea is to remove some of the singularity caused by the nondifferentiability of the quantity nabla u in the definition of the tv norm before we apply a linearization technique such as newton s method this is accomplished by introducing an additional variable for the flux quantity appearing in the gradient of the objective function which can be interpreted as the normal vector to the level sets of the image u our method can be viewed as a primal dual method as proposed by conn and overton a primal dual interior point method for minimizing a sum of euclidean norms preprint 1994 and andersen ph d thesis odense university denmark 1995 for the minimization of a sum of euclidean norms in addition to possessing local quadratic convergence experimental results show that the new method seems to be globally convergent

a new method for optimal truss topology design truss topology optimization formulated in terms of displacements and bar volumes results in a large nonconvex optimization problem for the case of maximization of stiffness for a prescribed volume this paper presents a new equivalent an unconstrained and convex minimization problem in displacements only where the function to be minimized is the sum of terms each of which is the maximum of two convex quadratic functions existence of solutions is proved as is the convergence of a nonsmooth steepest descent type algorithm for solving the topology optimization problem the algorithm is computationally attractive and has been tested on a large number of examples some of which are presented

fast and robust common reflection surface parameter estimation abstractthe common reflection surface crs method offers a stack with higher signal to noise ratio at the cost of a time consuming semblance search to obtain the stacking parameters we have developed a fast method for extracting the crs parameters using local slope and curvature we estimate the slope and curvature with the gradient structure tensor and quadratic structure tensor on stacked data this is done under the assumption that a stacking velocity is already available our method was compared with an existing slope based method in which the slope is extracted from prestack data an experiment on synthetic data shows that our method has increased robustness against noise compared with the existing method when applied to two real data sets our method achieves accuracy comparable with the pragmatic and full semblance searches our method has the advantage of being approximately two and four orders of magnitude faster than the semblance searches

automatic time domain velocity estimation based on an accelerated clustering method abstracttime domain velocity and moveout parameters can be directly obtained from local event slopes which are estimated on the prestack seismic gathers in practice there are always some errors in the estimated local slopes especially in low signal to noise ratio s n situations thus subsurface velocity information may be hidden in the image domain spanned by velocity and other moveout parameters we have developed an accelerated clustering algorithm to find cluster centers without prior information about the number of clusters first plane wave destruction is implemented to estimate the local event slopes for every sample in the seismic gathers we obtain the estimations of velocity and its location in the image domain according to the local event slopes these mapped data points in the new domain exhibit the structure of groups we represent these points by a mixture distribution model then the cluster centers of the mixture distribution model are located which correspond to maximum likelih

pattern synthesis with multipoint accurate array response control in this paper the problem of pattern synthesis with antenna arrays is addressed and new approaches based on the recently developed accurate array response control textrm a 2 textrm rc algorithm are presented it is shown that the array weight vector obtained by the textrm a 2 textrm rc algorithm to control the normalized response at a single direction in each step belongs to a specific set thus an appropriate weight vector chosen from the intersection of weight vector sets corresponding to the desired responses at multiple directions is capable of simultaneously controlling those responses this results in the so called multipoint accurate array response control textrm ma 2 textrm rc algorithm moreover in order to avoid possible beam axis shift in pattern synthesis a modified textrm ma 2 textrm rc textrm m 2 textrm a 2 textrm rc algorithm is proposed by imposing a derivative constraint on the direction of beam axis representative numerical examples are provided to demonstrate the effectiveness of the proposed textrm ma 2 textrm rc and textrm m 2 textrm a 2 textrm rc algorithms for multipoint responses control and pattern synthesis

robust convex optimization we study convex optimization problems for which the data is not specified exactly and it is only known to belong to a given uncertainty set u yet the constraints must hold for all possible values of the data from u the ensuing optimization problem is called robust optimization in this paper we lay the foundation of robust convex optimization in the main part of the paper we show that if u is an ellipsoidal uncertainty set then for some of the most important generic convex optimization problems linear programming quadratically constrained programming semidefinite programming and others the corresponding robust convex program is either exactly or approximately a tractable problem which lends itself to efficientalgorithms such as polynomial time interior point methods

an efficient primal dual interior point method for minimizing a sum of euclidean norms the problem of minimizing a sum of euclidean norms dates from the 17th century and may be the earliest example of duality in the mathematical programming literature this nonsmooth optimization problem arises in many different kinds of modern scientific applications we derive a primal dual interior point algorithm for the problem by applying newton s method directly to a system of nonlinear equations characterizing primal and dual feasibility and a perturbed complementarity condition the main work at each step consists of solving a system of linear equations the schur complement equations this schur complement matrix is not symmetric unlike in linear programming we incorporate a mehrotra type predictor corrector scheme and present some experimental results comparing several variations of the algorithm including as one option explicit symmetrization of the schur complement with a skew corrector term we also present results obtained from a code implemented to solve large sparse problems using a symmetrized schur complement this has been applied to problems arising in plastic collapse analysis with hundreds of thousands of variables and millions of nonzeros in the constraint matrix the algorithm typically finds accurate solutions in less than 50 iterations and determines physically meaningful solutions previously unobtainable

a logarithmic barrier function algorithm for quadratically constrained convex quadratic programming an interior point method for quadratically constrained convex quadratic programming is presented that is based on a logarithmic barrier function approach and terminates at a required accuracy of an approximate solution in polynomial time this approach generates a sequence of unconstrained optimization problems each of which is approximately solved by taking a single step in a newton direction

low dimensional sdp formulation for large antenna array synthesis bounding the sidelobe and mainlobe levels of an array with complex weights is attractive in that it allows direct control of the radiation pattern in this paper we propose an efficient beamforming technique for synthesizing the patterns of large arrays with bound constraints on the sidelobe and mainlobe levels it is shown that the pattern synthesis problem can be posed as a convex semi infinite program sip which is then turned into a semi definite program sdp via a novel linear matrix inequality lmi characterization of semi infinite trigonometric polynomial constraints in contrast to existing sdp formulations which require a large number of additional variables our sdp representation only uses a minimal number of additional variables this subsequently enables the design of patterns for arrays with several hundred elements to be efficiently achieved on a standard personal computer using existing sdp solvers

applications of second order cone programming in a second order cone program socp a linear function is minimized over the intersection of an affine set and the product of second order quadratic cones socps are nonlinear convex problems that include linear and convex quadratic programs as special cases but are less general than semidefinite programs sdps several efficient primaldual interior point methods for socp have been developed in the last few years after reviewing the basic theory of socps we describe general families of problems that tan be recast as socps these include robust linear programming and robust leastsquares problems problems involving sums or maxima of norms or with convex hyperbolic constraints we discuss a variety of engineering applications such as filter design antenna array weight design truss design and grasping forte optimization in robotics we describe an efficient primaldual interior point method for solving socps which shares many of the features of primaldual interior point methods for linear program

shaped beam synthesis of real antenna arrays via finite element method floquet modal analysis and convex programming a shaped beam synthesis methodology for planar arrays with control of the ripple amplitude in the shaped region and constraints on the sidelobe and cross polar levels is proposed in this paper a previously developed synthesis formulation for designing finite impulse response fir filters by transforming a nonconvex synthesis problem to a convex optimization scheme enforcing conjugate symmetric excitation weights is extended to real and coupled radiating elements of complex geometry taking into account mutual coupling effects the optimization procedure is integrated with a finite array approach simulating different array environments this approach is based on the infinite array model through a floquet modal and general scattering matrix gsm based analysis where the periodic radiating element is characterized from a hybrid and full wave analysis procedure combining the fem modal analysis and domain decomposition technique numerical results of different synthesized beam patterns are presented for arrays of open ended apertures and microstrip antennas

generalized scattering matrix analysis of a class of finite arrays of coupled antennas by using 3 d fem and spherical mode expansion a rigorous method for characterizing in terms of a multimode scattering matrix a finite array of antennas where each antenna can be described by means of spherical waves is presented in this paper the procedure provides the impedance coupling and radiating characteristics of the arrays and comprises two steps first the generalized scattering matrix gsm of each single antenna is numerically calculated over a wide band of frequencies for this purpose we use a previously developed methodology that combines the domain segmentation technique the three dimensional finite element method 3d fem spherical mode expansion and a reduced order model obtained using a symmetric matrix pade spl acute via lanczos sympvl algorithm second the overall gsm of the finite array is calculated starting from the gsm of each antenna and using rotation and translation of spherical waves a closed form expression for the overall gsm is given and different examples are shown in order to validate the proposed method

direct mapping of seismic data to the domain of intercept time and ray parameter a plane wave decomposition marine seismic data recorded as a function of source receiver offset and traveltime are mapped directly to the domain of intercept or vertical delay time and horizontal ray parameter this is a plane wave decomposition based on beam forming of wide aperture seismic array data to determine automatically the loci of coherent seismic reflection and refraction events in this computation semblance in addition to the required slowness or horizontal ray parameter stack is found for linear x t trajectories across subarrays subsequently semblance is used to derive a windowing filter that is applied to the slowness stack to determine the points of stationary phase and eliminate aliasing the resulting filtered slowness stacks for multiple subarrays can then be linearly transformed and combined according to ray parameter range and time the resulting function of intercept time and horizontal ray parameter offers significant computational and interpretational advantages for the case of horizontal homogeneou

robust solutions to uncertain semidefinite programs in this paper we consider semidefinite programs sdps whose data depend on some unknown but bounded perturbation parameters we seek robust solutions to such programs that is solutions which minimize the worst case objective while satisfying the constraints for every possible value of parameters within the given bounds assuming the data matrices are rational functions of the perturbation parameters we show how to formulate sufficient conditions for a robust solution to exist as sdps when the perturbation is full our conditions are necessary and sufficient in this case we provide sufficient conditions which guarantee that the robust solution is unique and continuous holder stable with respect to the unperturbed problem s data the approach can thus be used to regularize ill conditioned sdps we illustrate our results with examples taken from linear programming maximum norm minimization polynomial interpolation and integer programming

unified formulation of radiation conditions for the wave equation a family of radiation boundary conditions for the wave equation is derived by truncating a rational function approximation of the corresponding plane wave representation and it is demonstrated how these boundary conditions can be formulated in terms of fictitious surface densities governed by second order wave equations on the radiating surface several well established radiation boundary conditions appear as special cases corresponding to different choice of the coefficients in the rational approximation the relation between these choices is established and an explicit formulation in terms of selected directions with ideal transmission is presented a mechanical interpretation of the fictitious surface densities enables identification of suitable conditions at corners and boundaries of the radiating surface numerical examples illustrate excellent results with one or two fictitious layers with suitable corner and boundary conditions

time harmonic and transient scattering by finite periodic flat strip arrays hybrid ray floquet mode mom algorithm a frequency and short pulse sp time domain td study of two dimensional plane wave scattering from a finite periodic array of thin flat coplanar perfectly conducting strips is presented rigorous analytical numerical reference solutions are established by spatial spectral wave number decomposition and the method of moments mom followed by frequency inversion the analytical portion is approximated so as to yield via high frequency asymptotics for a sufficiently large number of strips a hybrid ray floquet mode mom algorithm that not only explains the phenomena in physical terms but is also numerically efficient and reasonably accurate when compared with the reference solution of special interest are the td floquet modes with their space time dependent frequencies and wave numbers by superposition they can synthesize the highly resolved pulse train return under sp conditions attention is given also to direct sp td synthesis and to processing options for sp td data

sparse array quiescent beamformer design combining adaptive and deterministic constraints in this paper we examine sparse array quiescent beamforming for multiple sources in interference free environment to maximize the output signal to noise ratio snr the beamformer design comprises two intertwined stages the determination of beamforming weights and the reconfiguration of array structure the snr maximization may produce high sidelobe levels making the receiver vulnerable to interferences we consider the problem of achieving maximum snr beamforming subject to specified quiescent pattern constraints and as such combine both adaptive and deterministic approaches for sparse array configurations we employ two convex relaxation methods and an iterative linear fractional programming algorithm to solve the nonconvex antenna selection problem for sparse array beamformers simulation examples demonstrate that the array configuration plays a vital role in determining the beamforming performance in interference free scenarios

a truncated floquet wave diffraction method for the full wave analysis of large phased arrays i basic principles and 2 d cases this two part sequence deals with the formulation of an efficient method for the full wave analysis of large phased array antennas this is based on the method of moments mom solution of a fringe integral equation ie in which the unknown function is the difference between the exact solution of the finite array and that of the associated infinite array the unknown currents can be interpreted as produced by the field diffracted at the array edge which is excited by the floquet waves fws pertinent to the infinite configuration following this physical interpretation the unknown in the ie is efficiently represented by a very small number of basis functions with domain on the entire array aperture in order to illustrate the basic concepts the first part of this sequence deals with the two dimensional example of a linearly phased slit array it is shown that the dominant phenomenon fur describing the current perturbation with respect to the infinite array is accurately represented in most cases by only three diffracted ray shaped unknown functions this also permits a simple interpretation of the element by element current oscillation which was described by other authors

an efficient algorithm for minimizing a sum of euclidean norms with applications in recent years rich theories on polynomial time interior point algorithms have been developed these theories and algorithms can be applied to many nonlinear optimization problems to yield better complexity results for various applications in this paper the problem of minimizing a sum of euclidean norms is studied this problem is convex but not everywhere differentiable by transforming the problem into a standard convex programming problem in conic form we show that an epsilon optimal solution can be computed efficiently using interior point algorithms as applications to this problem polynomial time algorithms are derived for the euclidean single facility location problem the euclidean multifacility location problem and the shortest network under a given tree topology in particular by solving the newton equation in linear time using em gaussian elimination on leaves of a tree we present an algorithm which computes an epsilon optimal solution to the shortest network under a given full steiner topology interconnecting n regular points in o n sqrt n log bar c epsilon log n arithmetic operations where bar c is the largest pairwise distance among the given points the previous best known result on this problem is a graphical algorithm which requires o n2 arithmetic operations under certain conditions

beampattern synthesis for linear and planar arrays with antenna selection by convex optimization a convex optimization based beampattern synthesis method with antenna selection is proposed for linear and planar arrays conjugate symmetric beamforming weights are used so that the upper and non convex lower bound constraints on the beampattern can be convex thus a mainlobe of an arbitrary beamwidth and response ripple can be obtained this method can achieve completely arbitrary sidelobe levels by minimizing a re weighted objective function based on the magnitudes of the elements in the beamforming weight vector iteratively the proposed method selects certain antennas in an array to satisfy the prescribed beampattern specifications precisely interestingly a sparse array with fewer antennas compared to other methods is produced this method can design non uniformly spaced arrays with inter element spacings larger than one half wavelength without the appearance of grating lobes in the resulting beampattern simulations are shown using arrays of up to a few hundred antennas to illustrate the practicality of the proposed method

transmitter optimization for per antenna power constrained multi antenna downlinks an slnr maximization methodology in this paper we consider signal to leakage plus noise ratio slnr maximized precoding for multi antenna downlinks under per antenna power constraints papcs in contrast to the conventional sum power constraint the per antenna power constrained slnr precoder design problem no longer admits a simple closed form solution and achieving its optimal solution turns out to be much more challenging to conquer the difficulty we first propose to perform the charnes cooper transformation on the problem of interest which yields a solvable simpler second order cone program socp moving beyond this approach we are then able to obtain a semi closed form solution to the optimal slnr precoder the power allocation among users is also optimized for further performance enhancement for which we devise two numerical methods based on gradient projection and a low complexity approximation finally focusing on the imperfect channel state information csi scenario we develop a robust slnr based precoder to combat the performance degradation caused by random csi errors the superiority of all proposed precoder designs in this work is confirmed by numerical simulations

an ol n 3 potential reduction algorithm for linear programming we describe a primal dual potential function for linear programming phi x s rho ln x t s sum limits j 1 n ln x j s j where n x is the primal variable ands is the dual slack variable as a result we develop an interior point algorithm seeking reductions in the potential function with rho n sqrt n neither tracing the central path nor using the projective transformation the algorithm converges to the optimal solution set in o sqrt n l iterations and uses o n3l total arithmetic operations we also suggest a practical approach to implementing the algorithm

migration velocity analysis using residual diffraction moveout in the poststack depth domain abstractdiffraction events contain more direct information on the medium velocity than reflection events we have developed a method for migration velocity improvement and diffraction localization based on a moveout analysis of over or undermigrated diffraction events in the depth domain the method uses an initial velocity model as input it provides an update to the velocity model and diffraction locations in the depth domain as a result the algorithm is based on the focusing of remigration trajectories from incorrectly migrated diffraction curves these trajectories are constructed by applying a ray tracing like approach to the image wave equation for velocity continuation the starting points of the trajectories are obtained from fitting an ellipse or hyperbola to the picked uncollapsed diffraction events in the depth migrated domain focusing of the remigration trajectories points out the approximate location of the associated diffractor as well as local velocity attributes apart from the migrati

velocity continuation and the anatomy of residual prestack time migration velocity continuation is an imaginary continuous process of seismic image transformation in the postmigration domain it generalizes the concepts of residual and cascaded migrations understanding the laws of velocity continuation is crucially important for a successful application of time migration velocity analysis these laws predict the changes in the geometry and intensity of reflection events on migrated images with the change of the migration velocity in this paper i derive kinematic and dynamic laws for the case of prestack residual migration from simple geometric principles the main theoretical result is a decomposition of prestack velocity continuation into three different components corresponding to residual normal moveout residual dip moveout and residual zero offset migration i analyze the contribution and properties of each of the three components separately this theory forms the basis for constructing efficient finite difference and spectral algorithms for time migration velocity ana

signal and noise separation in prestack seismic data using velocity dependent seislet transform abstractthe seislet transform is a waveletlike transform that analyzes seismic data by following varying slopes of seismic events across different scales and provides a multiscale orthogonal basis for seismic data it generalizes the discrete wavelet transform dwt in the sense that the dwt in the lateral direction is simply the seislet transform with a zero slope our earlier work used plane wave destruction pwd to estimate smoothly varying slopes however the pwd operator can be sensitive to strong noise interference which makes the seislet transform based on pwd pwd seislet transform occasionally fail in providing a sparse multiscale representation for seismic field data we adopted a new velocity dependent vd formulation of the seislet transform in which the normal moveout equation served as a bridge between local slope patterns and conventional moveout parameters in the common midpoint domain the vd slope has better resistance to strong random noise which indicated the potential of vd sei

convex programming design of linear and nonlinear phase wideband blocking filters blocking filters are commonly used in array processing to excise targets from data when suitable target free training data is not available a drawback is the reduction of the effective size of the array by the order of the filter motivating a search for the smallest filter that meets the design specifications common linear phase approaches lead to convex optimization and efficient global solutions but can be inefficient when the phase of the blocking filter is unimportant although direct magnitude response optimization is nonconvex in general for narrowband linear arrays optimal magnitude blocking filters can be found using constrained optimization followed by spectral factorization this approach cannot be directly applied to wideband arrays as finite support spectral factors do not generally exist in higher dimensions instead a procedure is presented in which an approximate multidimensional spectral factor of an optimized spectral density is used as a target response in a second optimization stage linear and nonlinear phase solutions are found and compared for both narrowband and wideband notch filters with the nonlinear phase outperforming the linear phase in both notch width and passband error the various optimizations are performed using second order cone programming an efficient class of convex optimization

a theory of normal moveout three geophysical principles are shown to be sufficient to determine the most general practical normal moveout nmo equation the principles are reciprocity in a common midpoint cmp gather finite slowness and exact constant velocity limit the resulting equation is the shifted hyperbola nmo equation that has three parameters comparisons at both near and far offsets between the shifted hyperbola nmo equation and the results for layered media assign geophysical meaning to the parameters two of the parameters zero offset time and nmo velocity are constants and control the very near offset behavior the third parameter is dimensionless and controls the far offset behavior of the nmo curve but it may be a function of offset so as to exactly fit any traveltime curve the parameters may be found by a linear least squares fit to data the theory applies to all offsets for nonturning wave reflections in an isotropic earth for both p waves and converted p sv waves

complete characterizations of stable farkas lemma and cone convex programming duality we establish necessary and sufficient conditions for a stable farkas lemma we then derive necessary and sufficient conditions for a stable duality of a cone convex optimization problem where strong duality holds for each linear perturbation of a given convex objective function as an application we obtain stable duality results for convex semi definite programs and convex second order cone programs

accelerated plane wave destruction abstractwhen plane wave destruction pwd is implemented by implicit finite differences the local slope is estimated by an iterative algorithm we propose an analytical estimator of the local slope that is based on convergence analysis of the iterative algorithm using the analytical estimator we design a noniterative method to estimate slopes by a three point pwd filter compared with the iterative estimation the proposed method needs only one regularization step which reduces computation time significantly with directional decoupling of the plane wave filter the proposed algorithm is also applicable to 3d slope estimation we present synthetic and field experiments to demonstrate that the proposed algorithm can yield a correct estimation result with shorter computational time

array pattern synthesis with excitation control via norm minimization simple and efficient procedures are presented to synthesize antenna array patterns focused or shaped beams while controlling the excitations this synthesis problem is of great practical interest as it makes active arrays more attractive by reducing their complexity cost and weight with a proper regularization of the array pattern synthesis solution the excitations can be optimized in order to design uniform amplitude sparse arrays arrays whose excitations have a low dynamic range ratio or a smooth amplitude variation more specifically the synthesis procedures are composed of the minimization of a norm mixed ell 1 ell infty norm total variation norm or a combination of the ell 1 and ell infty norms associated with radiation pattern constraints various representative array synthesis problems are considered examples including the coupling between antennas and a comparison with a deterministic approach confirm both the usefulness and effectiveness of the proposed procedures

finite element computation of absorbing boundary conditions for time harmonic wave problems this paper proposes a new method in the frequency domain to define absorbing boundary conditions for general two dimensional problems the main feature of the method is that it can obtain boundary conditions from the discretized equations without much knowledge of the analytical behavior of the solutions and is thus very general it is based on the computation of waves in periodic structures and needs the dynamic stiffness matrix of only one period in the medium which can be obtained by standard finite element software boundary conditions at various orders of accuracy can be obtained in a simple way this is then applied to study some examples for which analytical or numerical results are available good agreements between the present results and analytical solutions allow to check the efficiency and the accuracy of the proposed method