designing structured tight frames via an alternating projection method tight frames also known as general welch bound equality sequences generalize orthonormal systems numerous applications including communications coding and sparse approximation require finite dimensional tight frames that possess additional structural properties this paper proposes an alternating projection method that is versatile enough to solve a huge class of inverse eigenvalue problems ieps which includes the frame design problem to apply this method one needs only to solve a matrix nearness problem that arises naturally from the design specifications therefore it is the fast and easy to develop versions of the algorithm that target new design problems alternating projection will often succeed even if algebraic constructions are unavailable to demonstrate that alternating projection is an effective tool for frame design the paper studies some important structural properties in detail first it addresses the most basic design problem constructing tight frames with prescribed vector norms then it discusses equiangular tight frames which are natural dictionaries for sparse approximation finally it examines tight frames whose individual vectors have low peak to average power ratio par which is a valuable property for code division multiple access cdma applications numerical experiments show that the proposed algorithm succeeds in each of these three cases the appendices investigate the convergence properties of the algorithm

2d and 3d elastic wavefield vector decomposition in the wavenumber domain for vti media a pragmatic decomposition of a vector wavefield into p and s waves is based on the helmholtz theory and the christoffel equation it is applicable to vti media when the plane wave polarization is continuous in the vicinity of a given wavenumber and is uniquely defined by that wavenumber except for the kiss singularities on the vti symmetry axis unlike divergence and curl which separate the wavefield into a scalar and a vector field the decomposed p and s wavefields are both vector fields with correct amplitude phase and physical units if the vector components of decomposed wavefields are added they reconstruct those of the original input wavefield wavefield propagation in any portions of a vti medium that have the same polarization distribution i e the same eigenvector in the wavenumber domain have the same decomposition operators and can be recon structed with a single 3d fourier transform for each operator e g one for p waves and one for s waves this applies to isotropic wavefields a

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

adaptive detection of a subspace signal in signal dependent interference this paper deals with the problem of adaptive detection of subspace signals embedded in thermal noise and clutter that depends on the transmitted signal to this end at the design stage we assume that the signal dependent sd clutter shares the same subspace as the target signals as customary a set of secondary data free of signal components is also assumed available two adaptive detectors referred to as the sd rao and sd wald are proposed by resorting to the rao test and wald test design criteria unlike the classical rao and wald tests which are derived by dividing the complex parameter into the real and imaginary parts the proposed detectors treat the complex parameter as a single quantity to reduce the computational burden moreover we derive the theoretical false alarm probabilities and detection probabilities and show that both the two proposed detectors exhibit the constant false alarm rate property numerical results show that the proposed detectors achieve a detection performance improvement over the conventional multidimensional detectors

nonconventional ergodic averages and nilmanifolds we study the l2 convergence of two types of ergodic averages the first is the average of a product of functions evaluated at return times along arithmetic progressions such as the expressions appearing in furstenberg fs proof of szemer ledi fs theorem the second average is taken along cubes whose sizes tend to for each average we show that it is sufficient to prove the convergence for special systems the characteristic factors we build these factors in a general way independent of the type of the average to each of these factors we associate a natural group of transformations and give them the structure of a nilmanifold from the second convergence result we derive a combinatorial interpretation for the arithmetic structure inside a set of integers of positive upper density

a nonlinear conjugate gradient method with a strong global convergence property conjugate gradient methods are widely used for unconstrained optimization especially large scale problems the strong wolfe conditions are usually used in the analyses and implementations of conjugate gradient methods this paper presents a new version of the conjugate gradient method which converges globally provided the line search satisfies the standard wolfe conditions the conditions on the objective function are also weak being similar to those required by the zoutendijk condition

a unified framework for low autocorrelation sequence design via majorization minimization in this paper we consider the low autocorrelation sequence design problem we optimize a unified metric over a general constraint set the unified metric includes the integrated sidelobe level isl and the peak sidelobe level psl as special cases and the general constraint set contains the unimodular constraint peak to average ratio par constraint and similarity constraint to name a few the optimization technique we employ is the majorization minimization mm method which is iterative and enjoys guaranteed convergence to a stationary solution we carry out the mm method in two stages in the majorization stage we propose three majorizing functions two for the unified metric and one for the isl metric in the minimization stage we give closed form solutions for algorithmic updates under different constraints the update step can be implemented with a few fast fourier transformations ffts and or inverse ffts iffts we also show the connections between the mm and gradient projection method under our algorithmic scheme numerical simulations have shown that the proposed mm based algorithms can produce sequences with low autocorrelation and converge faster than the traditional gradient projection method and the state of the art algorithms

doubly constrained robust capon beamformer the standard capon beamformer scb is known to have better resolution and much better interference rejection capability than the standard data independent beamformer when the array steering vector is accurately known however the major problem of the scb is that it lacks robustness in the presence of array steering vector errors in this paper we will first provide a complete analysis of a norm constrained capon beamforming nccb approach which uses a norm constraint on the weight vector to improve the robustness against array steering vector errors and noise our analysis of nccb is thorough and sheds more light on the choice of the norm constraint than what was commonly known we also provide a natural extension of the scb which has been obtained via covariance matrix fitting to the case of uncertain steering vectors by enforcing a double constraint on the array steering vector viz a constant norm constraint and a spherical uncertainty set constraint which we refer to as the doubly constrained robust capon beamformer dcrcb nccb and dcrcb can both be efficiently computed at a comparable cost with that of the scb performance comparisons of nccb dcrcb and several other adaptive beamformers via a number of numerical examples are also presented

on the rank of extreme matrices in semidefinite programs and the multiplicity of optimal eigenvalues we derive some basic results on the geometry of semidefinite programming sdp and eigenvalue optimization i e the minimization of the sum of the k largest eigenvalues of a smooth matrix valued function we provide upper bounds on the rank of extreme matrices in sdps and the first theoretically solid explanation of a phenomenon of intrinsic interest in eigenvalue optimization in the spectrum of an optimal matrix the kth and k 1 st largest eigenvalues tend to be equal and frequently have multiplicity greater than two this clustering is intuitively plausible and has been observed as early as 1975 when the matrix valued function is affine we prove that clustering must occur at extreme points of the set of optimal solutions if the number of variables is sufficiently large we also give a lower bound on the multiplicity of the critical eigenvalue these results generalize to the case of a general matrix valued function under appropriate conditions

scalar reverse time depth migration of prestack elastic seismic data reflected p to p and p to s converted seismic waves in a two component elastic common source gather generated with a p wave source in a two dimensional model can be imaged by two independent scalar reverse time depth migrations the inputs to migration are pure p and s waves that are extracted by divergence and curl calculations during shallow extrapolation of the elastic data recorded at the earth s surface for both p to p and p to s converted reflected waves the imaging time at each point is the p wave traveltime from the source to that point the extracted p wave is reverse time extrapolated and imaged with a p velocity model using a finite difference solution of the scalar wave equation the extracted s wave is reverse time extrapolated and imaged similarly but with an s velocity model converted s wave data requires a polarity correction prior to migration to ensure constructive interference between data from adjacent sources synthetic examples show that the algorithm gives satisfactory resul

a coordinate descent framework to design low psl isl sequences this paper is focused on the design of phase sequences with good aperiodic autocorrelation properties in terms of peak sidelobe level and integrated sidelobe level the problem is formulated as a biobjective pareto optimization forcing either a continuous or a discrete phase constraint at the design stage an iterative procedure based on the coordinate descent method is introduced to deal with the resulting optimization problems that are nonconvex and np hard in general each iteration of the devised method requires the solution of a nonconvex min max problem it is handled either through a novel bisection or an fft based method respectively for the continuous and the discrete phase constraint additionally a heuristic approach to initialize the procedures employing the l p norm minimization technique is proposed simulation results illustrate that the proposed methodologies can outperform some counterparts providing sequences with good autocorrelation features especially in the discrete phase binary case

unified optimization framework for multi static radar code design using information theoretic criteria in this paper we study the problem of code design to improve the detection performance of multi static radar in the presence of clutter i e a signal dependent interference to this end we briefly present a discrete time formulation of the problem as well as the optimal detector in the presence of gaussian clutter due to the lack of analytical expression for receiver operation characteristic roc code design based on roc is not feasible therefore we consider several popular information theoretic criteria including bhattacharyya distance kullback leibler kl divergence j divergence and mutual information mi as design metrics the code optimization problems associated with different information theoretic criteria are obtained and cast under a unified framework we propose two general methods based on majorization minimization to tackle the optimization problems in the framework the first method provides optimal solutions via successive majorizations whereas the second one consists of a majorization step a relaxation and a synthesis stage moreover derivations of the proposed methods are extended to tackle the code design problems with a peak to average ratio power par constraint using numerical investigations a general analysis of the coded system performance computational efficiency of the proposed methods and the behavior of the information theoretic criteria is provided

multifractal analysis of some multiple ergodic averages in linear cookie cutter dynamical systems in this paper we study the multiple ergodic averages of a locally constant real valued function in linear cookie cutter dynamical systems the multifractal spectrum of these multiple ergodic averages is completely determined

information theoretic bounds on target recognition performance based on degraded image data this paper derives bounds on the performance of statistical object recognition systems wherein an image of a target is observed by a remote sensor detection and recognition problems are modeled as composite hypothesis testing problems involving nuisance parameters we develop information theoretic performance bounds on target recognition based on statistical models for sensors and data and examine conditions under which these bounds are tight in particular we examine the validity of asymptotic approximations to probability of error in such imaging problems problems involving gaussian poisson and multiplicative noise and random pixel deletions are considered as well as least favorable gaussian clutter a sixth application involving compressed sensor image data is considered in some detail this study provides a systematic and computationally attractive framework for analytically characterizing target recognition performance under complicated non gaussian models and optimizing system parameters

fast solving of weighted pairing least squares systems this paper presents a generalization of the weighted least squares wls named weighted pairing least squares wpls which uses a rectangular weight matrix and is suitable for data alignment problems two fast solving methods suitable for solving full rank systems as well as rank deficient systems are studied computational experiments clearly show that the best method in terms of speed accuracy and numerical stability is based on a special 1 2 3 inverse whose computation reduces to a very simple generalization of the usual cholesky factorization backward substitution method for solving linear systems

space time code design for mimo detection based on kullback leibler divergence the focus of the paper is on the design of space time codes for a general multiple input multiple output detection problem when multiple observations are available at the receiver the figure of merit used for optimization purposes is the convex combination of the kullback leibler divergences between the densities of the observations under the two hypotheses and different system constraints are considered this approach permits to control the average sample number i e the time for taking a decision in a sequential probability ratio test and to asymptotically minimize the probability of miss in a likelihood ratio test the solutions offer an interesting insight in the optimal transmit policies encapsulated in the rank of the code matrix which rules the amount of diversity to be generated as well as in the power allocation policy along the active eigenmodes a study of the region of achievable divergence pairs whose availability permits optimization of a wide range of merit figures is also undertaken a set of numerical results is finally given in order to analyze and discuss the performance and validate the theoretical results

fast least squares migration with a deblurring filter least squares migration lsm is a linearized waveform inversion for estimating a subsurface reflectivity model that relative to conventional migration improves spatial resolution of migration images the cost however is high because lsm typically requires 10 or more iterations which is at least 20 times more than the cpu cost of conventional migration to alleviate this expense we offer a deblurring filter that can be used in a regularization scheme or a preconditioning scheme to give acceptable lsm images with less than one third the cost of the standard lsm method our results in applying deblurred lsm to synthetic data and field data support this claim in particular a marmousi2 model test shows that the data residual for preconditioned deblurred lsm decreases rapidly in the first iteration which is equivalent to 10 or more iterations of lsm empirical results suggest that regularized deblurred lsm after three iterations is equivalent to about 10 iterations of lsm applying deblurred lsm to 2d marine data gives a higher resolution image compared to those from migration or lsm with three iterations these results suggest that lsm combined with a deblurring filter allows lsm to be a fast practical tool for improved imaging of complicated structures

least squares wave equation migration for avp ava inversion we present an acoustic migration inversion algorithm that uses extended double square root wave equation migration and modeling operators to minimize a constrained least squares data misfit function least squares migration we employ an imaging principle that allows for the extraction of ray parameter domain common image gathers cigs from the propagated seismic wavefield the cigs exhibit amplitude variations as a function of half offset ray parameter avp closely related to the amplitude variation with reflection angle ava our least squares wave equation migration inversion is constrained by a smoothing regularization along the ray parameter this approach is based on the idea that rapid amplitude changes or discontinuities along the ray parameter axis result from noise incomplete wavefield sampling and numerical operator artifacts these discontinuities should therefore be penalized in the inversion the performance of the proposed algorithm is examined with two synthetic examples in the first

adaptive multiple subtraction based on 3d blind separation of convolved mixtures abstractmultiple removal is one of the important preprocessing steps in a seismic data processing sequence for an accurate multiple prediction a full 3d method is required however the application of such methods is often limited by practical and economic constraints therefore in practical situations 2d prediction methods are used such as 2d surface related multiple elimination however the resulting predicted multiples may have significant temporal shift spatial mismatch and amplitude inconsistency compared with true 3d multiples adaptive multiple subtraction based on 2d blind separation of convolved mixtures bscm has been proposed to estimate the 2d matching filter in a single gather to improve the flexibility of the adaptive multiple subtraction for the inconsistencies between the 2d predicted multiples and true 3d multiples we evaluated the adaptive multiple subtraction as a problem of 3d bscm in the proposed method the predicted multiples were modeled as the convolution of the true

fast line searches for the robust solution of linear systems in the hybrid l1 l2 and huber norms linear systems of equations arise in traveltime tomography deconvolution and many other geophysical applications nonlinear problems are often solved by successive linearization leading to a sequence of linear systems overdetermined linear systems are solved by minimizing some measure of the size of the misfit or residual the most commonly used measure is the l2 norm squared leading to least squares problems the advantage of least squares problems for linear systems is that they can be solved by methods for example qr factorization that retain the linear behavior of the problem the disadvantage of least squares solutions is that the solution is sensitive to outliers more robust norms approximating the l1 norm can be used to reduce the sensitivity to outliers unfortunately these more robustnorms lead to nonlinear minimization problems even for linear systems and many efficient algorithms for nonlinear minimiza tion problems require line searches one iterative method for solving linear

optimal transmit receiver design in the presence of signal dependent interference and channel noise optimal detection of a target return contaminated by signal dependent interference as well as additive channel noise requires the design of a transmit pulse f t and a receiver impulse response h t jointly maximizing the output signal to interference plus noise ratio sinr despite the highly nonlinear nature of this problem it has been possible to show that f t may always be chosen minimum phase a full analysis concludes with the construction of an effective numerical procedure for the determination of optimal pairs f h that appears to converge satisfactorily for most values of input sinr extensive simulation reveals that the shape of f t can be a critical factor in particular the performance of a chirp like pulse is often unacceptable especially when clutter and channel noise are low pass dominant and comparable

multifractal analysis of some multiple ergodic averages in this paper we study the multiple ergodic averages on the symbolic space m 0 1 m 1 n where m 2 l 2 q 2 are integers we give a complete solution to the problem of multifractal analysis of the limit of the above multiple ergodic averages actually we develop a non invariant and non linear version of thermodynamic formalism that is of its own interest we study a large class of measures called telescopic product measures the special case of telescopic product measures defined by the fixed points of some non linear transfer operators plays a crucial role in studying the level sets of the limit which are not shift invariant these measures share many properties with gibbs measures in the classical thermodynamic formalism our work also concerns variational principle pressure function and legendre transform in this new setting less

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

design of optimized radar codes with a peak to average power ratio constraint this paper considers the problem of radar waveform design in the presence of colored gaussian disturbance under a peak to average power ratio par and an energy constraint first of all we focus on the selection of the radar signal optimizing the signal to noise ratio snr in correspondence of a given expected target doppler frequency algorithm 1 then through a max min approach we make robust the technique with respect to the received doppler algorithm 2 namely we optimize the worst case snr under the same constraints as in the previous problem since algorithms 1 and 2 do not impose any condition on the waveform phase we also devise their phase quantized versions algorithms 3 and 4 respectively which force the waveform phase to lie within a finite alphabet all the problems are formulated in terms of nonconvex quadratic optimization programs with either a finite or an infinite number of quadratic constraints we prove that these problems are np hard and hence introduce design techniques relying on semidefinite programming sdp relaxation and randomization as well as on the theory of trigonometric polynomials providing high quality suboptimal solutions with a polynomial time computational complexity finally we analyze the performance of the new waveform design algorithms in terms of detection performance and robustness with respect to doppler shifts

relative entropy based waveform design for mimo radar detection in the presence of clutter and interference this paper considers the waveform design problem for multiple input multiple output mimo radars in order to improve the detection performance of the systems we assume that target echoes are embedded in signal dependent clutter as well as colored interference considering the optimal neyman pearson detector obtaining waveforms which maximize the detection probability for a fixed value of the probability of false alarm is intractable therefore we employ relative entropy associated with the detection problem as the figure of merit for the waveform design we devise an iterative method based on minorization maximization mm technique to tackle the nonconvex design problem this method also includes a novel trick for replacing a nonconvex constraint set associated with an equivalent form of the design problem with a convex one iteratively the proposed method increases the design metric monotonically and is guaranteed to converge we extend the devised method for using in design with peak to average power ratio par and similarity constraints the method can be applied to both statistical and colocated mimo radars several numerical examples are included to demonstrate the effectiveness of the proposed method

which data residual norm for robust elastic frequency domain full waveform inversion elastic full waveform inversion is an ill posed data fitting procedure that is sensitive to noise inaccuracies of the starting model definitionofmultiparameterclasses andinaccuratemodeling of wavefield amplitudes we have investigated the performance of different minimization functionals as the least squares norm 2 the least absolute values norm 1 and combinations of both the huber and so called hybrid criteria with reference to twonoisyoffshorevalhallmodelandonshoreoverthrustmodel synthetic data sets the four minimization functionals were implemented in 2d elastic frequency domain full waveform inversion fwi where efficient multiscale strategies were designed by successive inversions of a few increasing frequencies for the offshore and onshore case studies the 1 norm provided the most reliable models for p and s wave velocities vp and vs even when strongly decimated data sets that correspond to fewfrequencieswereusedintheinversionandwhenoutlierspolluted the data the 2 norm can provide reliable results in the presence of uniform white noise for vp and vs if the data redundancyisincreasedbyrefiningthefrequencysamplingintervalin the inversion at the expense of computational efficiency the 1 norm and the huber and hybrid criteria unlike the 2 norm allowforsuccessfulimagingofthevsmodelfromnoisydataina soft seabed environment where the p to s waves have a small footprint in the data however the huber and hybrid criteria are sensitive to a threshold criterion that controls the transition between the criteria and that requires tedious trial and error investigations for reliable estimation the 1 norm provides a robust alternativetothe2 normforinvertingdecimateddatasetsinthe frameworkofefficientfrequency domainfwi

application of the perfectly matched absorbing layer model to the linear elastodynamic problem in anisotropic heterogeneous media we present and analyze a perfectly matched absorbing layer model for the velocity stress formulation of elastodynamics the principal idea of this method consists of introducing an absorbing layer in which we decompose each component of the unknown into two auxiliary components a component orthogonal to the boundary and a component parallel to it a system of equations governing these new unknowns then is constructed a damping term finally is introduced for the component orthogonal to the boundary this layer model has the property of generating no reflection at the interface between the free medium and the artificial absorbing medium in practice both the boundary condition introduced at the outer boundary of the layer and the dispersion resulting from the numerical scheme produce a small reflection which can be controlled even with very thin layers as we will show with several experiments this model gives very satisfactory results namely the reflection coefficient even in the case of heterogeneous anisotropic media is about 1 for a layer thickness of five space discretization steps

an information theoretic approach to robust constrained code design for mimo radars the problem of transmit code design in multiple input multiple output mimo radar systems is addressed in this paper the problem is considered in both colocated and widely separated antenna radars in the presence of signal dependent interference and target mobility due to complexity of exact expressions of the optimal detector in the mimo radars information theoretic criteria are employed as design metrics which results in a general form of nonconvex optimization problems in order to tackle the problem a novel technique based on the minorization maximization algorithm is proposed and solutions are presented under practical constraints on the transmit code namely energy constraint peak to average power ratio constraint and similarity constraint furthermore the devised method is extended to be robust against uncertainties of the clutter and interference statistics finally numerical examples are used to show the performance of the proposed technique in different situations

sequence design to minimize the weighted integrated and peak sidelobe levels sequences with low aperiodic autocorrelation sidelobes are well known to have extensive applications in active sensing and communication systems in this paper we first consider the problem of minimizing the weighted integrated sidelobe level wisl which can be used to design sequences with impulse like autocorrelation and a zero or low correlation zone two algorithms based on the general majorization minimization method are developed to tackle the wisl minimization problem with guaranteed convergence to a stationary point the proposed methods are then extended to optimize the ell p norm of the autocorrelation sidelobes which leads to a way to minimize the peak sidelobe level psl criterion all the proposed algorithms can be implemented via the fast fourier transform fft and thus are computationally efficient an acceleration scheme is considered to further accelerate the algorithms numerical experiments show that the proposed algorithms can efficiently generate sequences with virtually zero autocorrelation sidelobes in a specified lag interval and can also produce very long sequences with much smaller psl compared with some well known analytical sequences

double recurrence and almost sure convergence on repond de facon affirmative a une question posee par furstenberg sur la convergence presque sure de moyennes ergodiques de la forme 1 n n t n f t mn g avec 1 n ou n est un entier fixe t une transformation ergodique et preservant la mesure sur un espace de probabilite et f et g appartenant a l la somme ci dessus est un cas particulier d une recurrence multiple a laquelle peuvent etre facilement generalises les resultats obtenus ici pour la recurrence double

mutual information and minimum mean square error in gaussian channels this paper deals with arbitrarily distributed finite power input signals observed through an additive gaussian noise channel it shows a new formula that connects the input output mutual information and the minimum mean square error mmse achievable by optimal estimation of the input given the output that is the derivative of the mutual information nats with respect to the signal to noise ratio snr is equal to half the mmse regardless of the input statistics this relationship holds for both scalar and vector signals as well as for discrete time and continuous time noncausal mmse estimation this fundamental information theoretic result has an unexpected consequence in continuous time nonlinear estimation for any input signal with finite power the causal filtering mmse achieved at snr is equal to the average value of the noncausal smoothing mmse achieved with a channel whose snr is chosen uniformly distributed between 0 and snr

mimo radar waveform design in colored noise based on information theory in this paper we consider multiple input multiple output mimo radar waveform design in colored noise two information theoretic measures are used as criterions for optimal waveform design under transmitted power constraint the first one is by maximizing the mutual information between target impulse response and target echoes the second one is by maximizing the relative entropy between two hypotheses in the first hypothesis we assume the target is not present in the echoes while in the second hypothesis we assume the target exists in the echoes we derive optimal solutions for both cases interestingly both optimal solutions require that transmitted waveform should match with the target and noise however the optimal solutions of the two problems lead to different power allocation strategies

hybrid l 1 l 2 minimization with applications to tomography least squares or l2 solutions of seismic inversion and tomography problems tend to be very sensitive to data points with large errors the lp minimization for 1 p 2 gives more robust solutions but usually with higher computational cost iteratively reweighted least squares irls gives efficient approximate solutions to these lp problems we apply irls to a hybrid l2 l2 minimization problem that behaves like an l2 fit for small residuals and like an l1 fit for large residuals the smooth transition from l2 to l1 behavior is controlled by a parameter that we choose using an estimate of the standard deviation of the data error for linear problems of full rank the hybrid objective function has a unique minimum and irls can be proven to converge to it we obtain a robust efficient method for nonlinear problems a version of the gauss newton algorithm can be applied synthetic crosswell tomography examples and a field data vsp tomography example demonstrate the improvement of the hybrid method over le

a strategy for nonlinear elastic inversion of seismic reflection data the problem of interpretation of seismic reflection data can be posed with sufficient generality using the concepts of inverse theory in its roughest formulation the inverse problem consists of obtaining the earth model for which the predicted data best fit the observed data if an adequate forward model is used this best model will give the best images of the earth s interior three parameters are needed for describing a perfectly elastic isotropic earth the density x and the lame parameters x and x or the density x and the p wave and s wave velocities x and x the choice of parameters is not neutral in the sense that although theoretically equivalent if they are not adequately chosen the numerical algorithms in the inversion can be inefficient in the long spatial wavelengths of the model adequate parameters are the p wave and s wave velocities while in the short spatial wavelengths p wave impedance s wave impedance and density are adequate the problem of inversion o

elastic full waveform inversion using the second generation wavelet and an adaptive operator length scheme abstractelastic full waveform inversion fwi can generally yield subsurface model parameters of high spatial resolution however the computational and storage burden is tremendous to mitigate this problem we developed the following three strategies first we derived a time space domain adaptive staggered grid finite difference method the size of the calculation was reduced by using smaller operator lengths for high s wave velocities second we evaluated a multiscale elastic fwi scheme based on the second generation wavelet by which scale decompositions of data and model space were implemented with the scale increasing spatial sampling intervals and time steps became larger therefore the minimum computational cost could be achieved by combining the variable operator length scheme with the multiscale scheme third to economize the memory consumption we extended the efficient boundary storage and checkpointing schemes into elastic fwi only wavefields of several parts in the boundary area betwe

on the practical implication of mutual information for statistical decisionmaking a basic mathematical function that conjoins the two key conceptions of mutual information and bayes risk is defined based on that function some asymptotic theorems that verify an important implication of mutual information in the context of practical bayesian decisionmaking are proven

waveform inversion using a back propagation algorithm and a huber function norm waveforminversionfacesdifficultieswhenappliedtoreal seismic data including the existence of many kinds of noise the 1 norm is more robust to noise with outliers than the least squares method nevertheless the least squares method is preferred as an objective function in many algorithms because the gradient of the 1 norm has a singularity when the residual becomes zero we propose a complex valued huber function for frequency domain waveform inversion that combines the 2 norm for small residuals with the 1 norm for large residuals we also derive a discretized formula for the gradient of the huber function through numericaltestsonsimplesyntheticmodelsandmarmousidata we find the huber function is more robust to outliers and coherent noise we apply our waveform inversion algorithm to field data taken from the continental shelf under the east sea in korea in this setting we obtain a velocity model whose syntheticshotprofilesaresimilartotherealseismicdata

diversity integration tradeoffs in mimo detection in this paper a multiple input multiple output mimo detection problem is considered at first we derive the generalized likelihood ratio test glrt for arbitrary transmitted signals and arbitrary time correlation of the disturbance then we investigate design criteria for the transmitted waveforms in both power unlimited and power limited systems and we derive closed form formulas for the probability of false alarm and the detection probability finally we study the interplay among the rank of the optimized space time code i e the number of linearly independent transmitted waveforms the number of transmit diversity paths generated in the signal space and the amount of energy integrated along each path the results confirm that there is an inherent tradeoff between diversity and integration and that no uniformly optimum waveform design strategy exists

the mimo radar and jammer games the interaction between a smart target and a smart mimo radar is investigated from a game theory perspective since the target and the radar form an adversarial system their interaction is modeled as a two person zero sum game the mutual information criterion is used in formulating the utility functions the unilateral hierarchical and symmetric games are studied and the equilibria solutions are derived

elastic least squares reverse time migration with hybrid l1 l2 misfit function abstract we have developed the theory and synthetic tests of elastic least squares reverse time migration elsrtm in this method a least squares reverse time migration algorithm is used to image multicomponent seismic data based on the first order elastic velocity stress wave equation in which the linearized elastic modeling equations are used for forward modeling and its adjoint equations are derived based on the adjoint state method for back propagating the data residuals also we have developed another elsrtm scheme based on the wavefield separation technique in which the p wave image is obtained using p wave forward and adjoint wavefields and the s wave image is obtained using p wave forward and s wave adjoint wavefields in this way the crosstalk artifacts can be minimized to a significant extent in general seismic data inevitably contain noise we apply the hybrid l1 l2 misfit function to the elsrtm algorithm to improve the robustness of our elsrtm to noise numerical tests on synthetic dat

a nonlinear transfer operator theorem in recent papers kenyon et al ergod theory dyn syst 32 1567 1584 2012 and fan et al c r math acad sci paris 349 961 964 2011 adv math 295 271 333 2016 introduced a form of non linear thermodynamic formalism based on solutions to a non linear equation using matrices in this note we consider the more general setting of holder continuous functions

cgg method for robust inversion and its application to velocity stack inversion the modified conjugate gradient cg method called the conjugate guided gradient cgg method is a robust iterative inversion method producing a parsimonious model estimation the cg method for solving least squares ls i e l2 norm minimization problems is modified to solve for different norms or different minimization criteria by guiding the gradient vector appropriately during iteration steps guiding is achieved by iteratively reweighting either the residual vector or the gradient vector during iteration steps like the iteratively reweighted least squares irls method does robustness is achieved by weighting the residual vector and parsimonious model estimation is obtained by weighting the gradient vector unlike the irls method however the cgg method doesn t change the corresponding forward operator of the problem and is implemented in a linear inversion template therefore the cgg method requires less computation than the irls method since the solution in the cgg method is found in a leas

an iterative inversion of back scattered acoustic waves the application of the born approximation to the scattered wave field followed by a wkbj and far field approximation on the propagation green s function for a slowly varying background medium leads to a simple integral relation between the density and bulk modulus anomalies superimposed on the background medium and the scattered wave field an iterative inversion scheme based on successive back projections of the wave field is used to reconstruct the two acoustic parameters the scheme when applied to data generated using the direct integral relation shows that the variations of the parameters can be reconstructed the procedure is readily applicable to actual data since every iterative step is essentially a prestack kirchhoff migration followed by the application of the direct born approximation and far field operator