adaptive surface related multiple elimination the major amount of multiple energy in seismic data is related to the large reflectivity of the surface a method is proposed for the elimination of all surface related multiples by means of a process that removes the influence of the surface reflectivity from the data an important property of the proposed multiple elimination process is that no knowledge of the subsurface is required on the other hand the source signature and the surface reflectivity do need to be provided as a consequence the proposed process has been implemented adaptively meaning that multiple elimination is designed as an inversion process where the source and surface reflectivity properties are estimated and where the multiple free data equals the inversion residue results on simulated data and field data show that the proposed multiple elimination process should be considered as one of the key inversion steps in stepwise seismic inversion

multiple subtraction using statistically estimated inverse wavelets surface related multiple elimination srme typically consists of two steps the first step is prediction and the second step is subtraction in subtraction it is important to effectively attenuate multiple events and preserve primary events when multiples cross with or overlap on primaries least square subtraction usually cannot subtract multiples effectively and may also damage the primaries when multiples overlap with primaries least square subtraction cannot always subtract multiples accurately and often damages the primaries to remedy this problem we propose to statistically estimate the inverse source wavelet correct for errors in the estimate of the inverse wavelet and then use the corrected inverse wavelets for multiple subtraction synthetic tests and real data examples show that the proposed method can effectively attenuate multiples while they also preserve the continuity of reflection events and successfully avoid amplitude distortion the proposed method is characterized by low computational costs and ease of implementation

adaptive multiple subtraction with wavelet based complex unary wiener filters abstractadaptive subtraction is a key element in predictive multiple suppression methods it minimizes misalignments and amplitude differences between modeled and actual multiples and thus reduces multiple contamination in the data set after subtraction due to the high crosscorrelation between their waveforms the main challenge resides in attenuating multiples without distorting primaries as they overlap on a wide frequency range we split this wide band problem into a set of more tractable narrow band filter designs using a 1d complex wavelet frame this decomposition enables a single pass adaptive subtraction via complex single sample unary wiener filters consistently estimated on overlapping windows in a complex wavelet transformed domain each unary filter compensates for amplitude differences within its frequency support and can correct small and large misalignment errors through phase and integer delay corrections this approach greatly simplifies the matching filter estimation and despit

adaptive multiple subtraction unification and comparison of matching filters based on the lq norm and statistical independence abstractan adaptive multiple subtraction step is necessary for almost all methods that predict seismic multiple reflected waves we aim at giving a better understanding of matching filters based on lq norms and on statistical independence we found that the formulation of all of these techniques can be gathered in a mutual framework by introducing a space time operator called the primary enhancer acting on the estimated primaries the differences between the considered matching filters become more intuitive because this operator behaves as a simple amplitude compressor in this perspective all the methods tend to uncorrelate the predicted multiples and the enhanced estimated primaries the study of these matching filter methods can be narrowed to the study of the primary enhancer operator because it is the only difference moreover we have emphasized the role of using adjacent traces or windowing approaches in terms of statistics and we show that an adequate windowing strategy may overbear the choice

comparisons of adaptive subtraction methods for multiple attenuation coherent noise may be removed from seismic data by first making an approximate model of the noise then producing an even better estimation of the noise by adaptively matching the modeled noise to the data this modified model of the noise may then be subtracted from the data eliminating most coherent noise the success of this approach depends both on how well the initial model matches the true noise and the success of the adaptive matching in modifying the initial noise prediction to match the true noise the adaptive matching step is complicated by the presence of the signal and other noise in the data in this article the noise of interest is surface related multiples although other types of coherent noise may be removed with this approach

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

switching regression models and fuzzy clustering a family of objective functions called fuzzy c regression models which can be used too fit switching regression models to certain types of mixed data is presented minimization of particular objective functions in the family yields simultaneous estimates for the parameters of c regression models together with a fuzzy c partitioning of the data a general optimization approach for the family of objective functions is given and corresponding theoretical convergence results are discussed the approach is illustrated by two numerical examples that show how it can be used to fit mixed data to coupled linear and nonlinear models

equivalent accuracy at a fraction of the cost overcoming temporal dispersion abstractnumerical dispersion in finite difference fd modeling produces coherent artifacts severely constraining the resolution of advanced imaging and inversion techniques conventionally numerical dispersion is reduced by increasing the order of accuracy of the fd operators and we resign ourselves to paying the high computational cost that is incurred assuming no spatial dispersion we have found that fd time dispersion is independent of the medium velocity and the spatial grid for propagation and only depends on the time stepping scheme and the propagation time based on this observation we have devised postpropagation filters to collapse the time dispersion effect of fd modeling our dispersion correction filters are designed by comparing the input waveform with dispersive waveforms obtained by 1d forward modeling these filters are then applied on multidimensional shot records to eliminate the time dispersion by two schemes 1 stationary filtering plus interpolation and 2 nonstationary fil

general c means clustering model partitional clustering is an important part of cluster analysis based on various theories numerous clustering algorithms have been developed and new clustering algorithms continue to appear in the literature it is known that occam s razor plays a pivotal role in data based models and partitional clustering is categorized as a data based model however no relation had previously been discovered between occam s razor and partitional clustering as we discuss in this paper the three main contributions of this paper can be summarized as follows 1 according to a novel definition of the mean a unifying generative framework for partitional clustering algorithms called a general c means clustering model gcm is presented and studied and 2 based on the local optimality test of the gcm the connection between occam s razor and partitional clustering is established for the first time as its application a comprehensive review of the existing objective function based clustering algorithms is presented based on gcm 3 under a common assumption about partitional clustering a theoretical guide for devising and implementing clustering algorithm is discovered these conclusions are verified by numerical experimental results

amplitude and kinematic corrections of migrated images for nonunitary imaging operators obtaining migrated images with meaningful amplitudes is a challenging problem when the migration operator is not unitary one possible solution to this problem is iterative inversion however inversion is an expensive process that can be rather difficult to apply especially with 3d data in this paper i propose estimating migrated images similar to the least squares inverse images by approximating the inverse hessian thus avoiding the need for iterative inversion the inverse hessian is approximated with a bank of nonstationary matching filters these filters are not exact impulse responses and are limited in their ability to mimic the full effects of least squares inversion tests on two data sets show that this filtering approach gives results similar to iterative least squares inversion at a lower cost this technique is flexible enough to be applied to images migrated from zero offset or angle domain common image point gathers

classification of homogeneous data with large alphabets given training sequences generated by two distinct but unknown distributions on a common alphabet we study the problem of determining whether a third sequence was generated according to the first or second distribution to model sources such as natural language for which the underlying distributions are difficult to learn from realistic amounts of data we allow the alphabet size to grow and therefore the probability distributions to change with the block length our primary focus is the situation in which the underlying probabilities are all of the same order and in this regime we show that consistent classification is possible if and only if the alphabet grows subquadratically with the block length we also show that some commonly used statistical tests are suboptimal in that they are consistent only if the alphabet grows sublinearly

adaptive prediction filtering in t x y domain for random noise attenuation using regularized nonstationary autoregression abstractmany natural phenomena including geologic events and geophysical data are fundamentally nonstationary they may exhibit stationarity on a short timescale but eventually alter their behavior in time and space we developed a 2d t x adaptive prediction filter apf and further extended this to a 3d t x y version for random noise attenuation based on regularized nonstationary autoregression rna instead of patching a popular method for handling nonstationarity we obtained smoothly nonstationary apf coefficients by solving a global regularized least squares problem we used shaping regularization to control the smoothness of the coefficients of apf three dimensional space noncausal t x y apf uses neighboring traces around the target traces in the 3d seismic cube to predict noise free signal so it provided more accurate prediction results than the 2d version in comparison with other denoising methods such as frequency space deconvolution time space prediction filter and frequency space rna

a deterministic algorithm for global optimization we present an algorithm for finding the global maximum of a multimodal multivariate function for which derivatives are available the algorithm assumes a bound on the second derivatives of the function and uses this to construct an upper envelope successive function evaluations lower this envelope until the value of the global maximum is known to the required degree of accuracy the algorithm has been implemented in ratfor and execution times for standard test functions are presented at the end of the paper

possibilistic and probabilistic fuzzy clustering unification within the framework of the non extensive thermostatistics fuzzy clustering algorithms are becoming the major technique in cluster analysis in this paper we consider the fuzzy clustering based on objective functions they can be divided into two categories possibilistic and probabilistic approaches leading to two different function families depending on the conditions required to state that fuzzy clusters are a fuzzy c partition of the input data recently we have presented in menard and eboueya fuzzy sets and systems 27 to be published an axiomatic derivation of the possibilistic and maximum entropy inference mei clustering approaches based upon an unifying principle of physics that of extreme physical information epi defined by frieden physics from fisher information a unification cambridge university press cambridge 1999 here using the same formalism we explicitly give a new criterion in order to provide a theoretical justification of the objective functions constraint terms membership functions and weighting exponent m used in the probabilistic and possibilistic fuzzy clustering moreover we propose an unified framework including the two procedures this approach is inspired by the work of frieden and plastino and plastino and miller physics a 235 577 extending the principle of extremal information in the framework of the non extensive thermostatistics then we show how with the help of epi one can propose extensions of the fcm and possibilistic algorithms

generalized fuzzy c means clustering strategies using l sub p norm distances fuzzy c means fcm is a useful clustering technique modifications of fcm using l sub 1 norm distances increase robustness to outliers object and relational data versions of fcm clustering are defined for the more general case where the l sub p norm p spl ges 1 or semi norm 0 0 in order to facilitate the empirical examination of the object data models both object and relational approaches are included in a numerical study

clustering with evolution strategies tbe applicability of evolution strategies ess population based stochastic optimization techniques to optimize clustering objective functions is explored clustering objective functions are categorized into centroid and non centroid type of functions optimization of the centroid type of objective functions is accomplished by formulating them as functions of real valued parameters using ess both hard and fuzzy clustering objective functions are considered in this study applicability of ess to discrete optimization problems is extended to optimize the non centroid type of objective functions as ess are amenable to parallelization a parallel model master slave model is described in the context of the clustering problem results obtained for selected data sets substantiate the utility of ess in clustering

a fuzzy logic based approach to qualitative modeling this paper discusses a general approach to quali tative modeling based on fuzzy logic the method of qualitative modeling is divided into two parts fuzzy modeling and linguistic approximation it proposes to use a fuzzy clustering method fuzzy c means method to identify the structure of a fuzzy model to clarify the advantages of the proposed method it also shows some examples of modeling among them a model of a dynamical process and a model of a human operator s control action

a contribution to convergence theory of fuzzy c means and derivatives in this paper we revisit the convergence and optimization properties of fuzzy clustering algorithms in general and the fuzzy c means fcm algorithm in particular our investigation includes probabilistic and a slightly modified implementation of possibilistic memberships which will be discussed under a unified view we give a convergence proof for the axis parallel variant of the algorithm by gustafson and kessel that can be generalized to other algorithms more easily than in the usual approach using reformulated fuzzy clustering algorithms we apply banach s classical contraction principle and establish a relationship between saddle points and attractive fixed points for the special case of fcm we derive a sufficient condition for fixed points to be attractive allowing identification of them as local minima of the objective function excluding the possibility of a saddle point

a genetic c means clustering algorithm applied to color image quantization this paper describes a novel data clustering algorithm which is a hybrid approach combining a genetic algorithm with the classical c means clustering algorithm cma the proposed technique is superior to cma in the sense that it converges to a nearby global optimum rather than a local one as an application the problem of color image quantization is elaborated here it is shown that substantial improvement of image quality is obtained by using the genetic approach

multiple subtraction using an expanded multichannel matching filter an expanded multichannel matching emcm filter is proposed for the adaptive subtraction in seismic multiple attenuation for a normal multichannel matching filter where an original seismic trace is matched by a group of multiple model traces the lateral coherency of adjacent traces is likely to be exploited to discriminate the overlapped multiple and primary reflections in the proposed emcm filter a seismic trace is matched by not only a group of the ordinary multiple model traces but also their adjoints generated mathematically the adjoints of a multiple model trace include its first derivative its hilbert transform and the derivative of the hilbert transform the convolutional coefficients associated with the normal multichannel filter can be represented as a 2d operator in the time space domain this 2d operator is expanded with an additional spatial dimension in the emcm filter to improve the robustness of the adaptive subtraction the multiple model traces are generated using moveout equations to afford efficiency in the multiple attenuation application

a methodology for constructing fuzzy algorithms for learning vector quantization this paper presents a general methodology for the development of fuzzy algorithms for learning vector quantization falvq the design of specific falvq algorithms according to existing approaches reduces to the selection of the membership function assigned to the weight vectors of an lvq competitive neural network which represent the prototypes the development of a broad variety of falvq algorithms can be accomplished by selecting the form of the interference function that determines the effect of the nonwinning prototypes on the attraction between the winning prototype and the input of the network the proposed methodology provides the basis for extending the existing falvq 1 falvq 2 and falvq 3 families of algorithms this paper also introduces two quantitative measures which establish a relationship between the formulation that led to falvq algorithms and the competition between the prototypes during the learning process the proposed algorithms and competition measures are tested and evaluated using the iris data set the significance of the proposed competition measure is illustrated using falvq algorithms to perform segmentation of magnetic resonance images of the brain

adaptive fuzzy c shells clustering and detection of ellipses several generalizations of the fuzzy c shells fcs algorithm are presented for characterizing and detecting clusters that are hyperellipsoidal shells an earlier generalization the adaptive fuzzy c shells afcs algorithm is examined in detail and is found to have global convergence problems when the shapes to be detected are partial new formulations are considered wherein the norm inducing matrix in the distance metric is unconstrained in contrast to the afcs algorithm the resulting algorithm called the afcs u algorithm performs better for partial shapes another formulation based on the second order quadrics equation is considered these algorithms can detect ellipses and circles in 2d data they are compared with the hough transform ht based methods for ellipse detection existing ht based methods for ellipse detection are evaluated and a multistage method incorporating the good features of all the methods is used for comparison numerical examples of real image data show that the afcs algorithm requires less memory than the ht based methods and it is at least an order of magnitude faster than the ht approach

convergence of the single pass and online fuzzy c means algorithms scalable versions of the widely used fuzzy c means clustering algorithm called single pass fuzzy c means and online fuzzy c means have been recently introduced both algorithms facilitate scaling to very large numbers of examples while providing partitions that very closely approximate those one would obtain using fuzzy c means both algorithms have been successfully applied to a number of datasets most notably magnetic resonance image volumes of the human brain in this letter we show that weighting examples in the fuzzy c means algorithm does not cause a violation in its convergence proof and we provide a separate proof of convergence that holds for any dataset

random noise attenuation using f x regularized nonstationary autoregression we have developed a novel method for random noise attenuation in seismic data by applying regularized nonstationary autoregression rna in the frequency space f x domain the method adaptively predicts the signal with spatial changes in dip or amplitude using f x rna the key idea is to overcome the assumption of linearity and stationarity of the signal in conventional f x domain prediction technique the conventional f x domain prediction technique uses short temporal and spatial analysis windows to cope with the nonstationary of the seismic data the new method does not require windowing strategies in spatial direction we implement the algorithm by an iterated scheme using the conjugate gradient method we constrain the coefficients of nonstationary autoregression na to be smooth along space and frequency in the f x domain the shaping regularization in least square inversion controls the smoothness of the coefficients of f x rna there are two key parameters in the proposed method filter length

power approximations to multinomial tests of fit abstract multinomial tests for the fit of iid observations x 1 xn to a specified distribution f are based on the counts ni of observations falling in k cells e 1 ek that partition the range of the x j the earliest such test is based on the pearson 1900 chi squared statistic x 2 k i 1 ni npi 2 npi where pi pf xj in ei are the cell probabilities under the null hypothesis a common competing test is the likelihood ratio test based on lr 2 k i 1 ni log ni npi cressie and read 1984 introduced a class of multinomial goodness of fit statistics r based on measures of the divergence between discrete distributions this class includes both x 2 when 1 and lr when 0 all of the r have the same chi squared limiting null distribution the power of the commonly used members of the class is usually approximated from a noncentral chi squared distribution that is also the same for all we propose new approximations to the power that vary with the statistic chosen bot

an integrated approach to fuzzy learning vector quantization and fuzzy c means clustering derives an interpretation for a family of competitive learning algorithms and investigates their relationship to fuzzy c means and fuzzy learning vector quantization these algorithms map a set of feature vectors into a set of prototypes associated with a competitive network that performs unsupervised learning derivation of the new algorithms is accomplished by minimizing an average generalized distance between the feature vectors and prototypes using gradient descent a close relationship between the resulting algorithms and fuzzy c means is revealed by investigating the functionals involved it is also shown that the fuzzy c means and fuzzy learning vector quantization algorithms are related to the proposed algorithms if the learning rate at each iteration is selected to satisfy a certain condition

global optimization in clustering using hyperbolic cross points erich novak and klaus ritter developed in 1996 a global optimization algorithm that uses hyperbolic cross points hcps in this paper we develop a hybrid algorithm for clustering called cmhcp that uses a modified version of this hcp algorithm for global search and the alternating optimization for local search the program has been tested extensively with very promising results and high efficiency this provides a nice addition to the arsenal of global optimization in clustering in the process we also analyze the smoothness of some reformulated objective functions

random noise attenuation using local signal and noise orthogonalization abstractwe have developed a novel approach to attenuate random noise based on local signal and noise orthogonalization in this approach we first removed from a seismic section using one of the conventional denoising operators and then applied a weighting operator to the initially denoised section to predict the signal leakage energy as well as retrieve it from the initial noise section the weighting operator was obtained by solving a least squares minimization problem via shaping regularization with a smoothness constraint next the initially denoised section and the retrieved signal were combined to form the final denoised section the proposed denoising approach corresponded to orthogonalizing the initially denoised signal and noise in a local manner we evaluated the denoising performance using local similarity to test the orthogonalization property of the estimated signal and noise we calculated the local similarity map between the denoised signal section and removed noise section low values o

validity guided re clustering with applications to image segmentation when clustering algorithms are applied to image segmentation the goal is to solve a classification problem however these algorithms do not directly optimize classification duality as a result they are susceptible to two problems 1 the criterion they optimize may not be a good estimator of true classification quality and 2 they often admit many suboptimal solutions this paper introduces an algorithm that uses cluster validity to mitigate problems 1 and 2 the validity guided re clustering vgc algorithm uses cluster validity information to guide a fuzzy re clustering process toward better solutions it starts with a partition generated by a soft or fuzzy clustering algorithm then it iteratively alters the partition by applying novel split and merge operations to the clusters partition modifications that result in improved partition validity are retained vgc is tested on both synthetic and real world data for magnetic resonance image mri segmentation evaluations by radiologists show that vgc outperforms the unsupervised fuzzy c means algorithm and vgc s performance approaches that of the supervised k nearest neighbors algorithm

robust clustering methods a unified view clustering methods need to be robust if they are to be useful in practice in this paper we analyze several popular robust clustering methods and show that they have much in common we also establish a connection between fuzzy set theory and robust statistics and point out the similarities between robust clustering methods and statistical methods such as the weighted least squares technique the m estimator the minimum volume ellipsoid algorithm cooperative robust estimation minimization of probability of randomness and the epsilon contamination model by gleaning the common principles upon which the methods proposed in the literature are based we arrive at a unified view of robust clustering methods we define several general concepts that are useful in robust clustering state the robust clustering problem in terms of the defined concepts and propose generic algorithms and guidelines for clustering noisy data we also discuss why the generalized hough transform is a suboptimal solution to the robust clustering problem

soft learning vector quantization and clustering algorithms based on ordered weighted aggregation operators this paper presents the development and investigates the properties of ordered weighted learning vector quantization lvq and clustering algorithms these algorithms are developed by using gradient descent to minimize reformulation functions based on aggregation operators an axiomatic approach provides conditions for selecting aggregation operators that lead to admissible reformulation functions minimization of admissible reformulation functions based on ordered weighted aggregation operators produces a family of soft lvq and clustering algorithms which includes fuzzy lvq and clustering algorithms as special cases the proposed lvq and clustering algorithms are used to perform segmentation of magnetic resonance mr images of the brain the diagnostic value of the segmented mr images provides the basis for evaluating a variety of ordered weighted lvq and clustering algorithms

a study of some fuzzy cluster validity indices genetic clustering and application to pixel classification in this article the effectiveness of variable string length genetic algorithm along with a recently developed fuzzy cluster validity index pbmf has been demonstrated for clustering a data set into an unknown number of clusters the flexibility of a variable string length genetic algorithm vga is utilized in conjunction with the fuzzy indices to determine the number of clusters present in a data set as well as a good fuzzy partition of the data for that number of clusters a comparative study has been performed for different validity indices namely pbmf xb pe and pc the results of the fuzzy vga algorithm are compared with those obtained by the well known fcm algorithm which is applicable only when the number of clusters is fixed a priori moreover another genetic clustering scheme that also requires fixing the value of the number of clusters is implemented the effectiveness of the pbmf index as the optimization criterion along with a genetic fuzzy partitioning technique is demonstrated on a number of artificial and real data sets including a remote sensing image of the city of kolkata

adaptive multiple subtraction using independent component analysis surface related multiple attenuation srma can effectively remove multiples from seismic data when other e g radon transform methods have difficulty srma generally includes two steps multiple prediction or multiple modeling and adaptive multiple subtraction ams in some cases adaptive subtraction is the main challenge for the success of srma adaptive subtraction is often posed as a least squares minimization problem that minimizes the energy difference between the original input traces and the modeled multiple traces the minimum output energy approach can be implemented by either single or multichannel matching filters these methods assume orthogonality between the primaries and multiples meaning that the two classes of events are uncorrelated

experiments in projection and clustering by simulated annealing simulated annealing is a stochastic relaxation algorithm which has been used successfully to optimize functions of many variables this paper analyzes the simulated annealing algorithm when applied to the minimization of functions from two common problems encountered in exploratory pattern analysis projection and clustering the projection is a nonlinear mapping of patterns in high dimension to two dimensions the simulated annealing mapping is compared to gradient descent minimization of the same objective function as well as eigenvector projection the simulated annealing clustering is compared to a k means algorithm empirical results show that simulated annealing can produce results as good as those obtained by conventional methods but are impractical for small data sets because of the high computational cost simulated annealing does in the case of the mapping problem yield a better optimization and better retained structure for large data sets containing tight gaussian clusters

reducing the time complexity of the fuzzy c means algorithm in this paper we present an efficient implementation of the fuzzy c means clustering algorithm the original algorithm alternates between estimating centers of the clusters and the fuzzy membership of the data points the size of the membership matrix is on the order of the original data set a prohibitive size if this technique is to be applied to very large data sets with many clusters our implementation eliminates the storage of this data structure by combining the two updates into a single update of the cluster centers this change significantly affects the asymptotic runtime as the new algorithm is linear with respect to the number of clusters while the original is quadratic elimination of the membership matrix also reduces the overhead associated with repeatedly accessing a large data structure empirical evidence is presented to quantify the savings achieved by this new method

theory of nonstationary linear filtering in the fourier domain with application to time variant filtering a general linear theory describes the extension of the convolutional method to nonstationary processes this theory can apply any linear nonstationary filter with arbitrary time and frequency variation in the time fourier or mixed domains the filter application equations and the expressions to move the filter between domains are all ordinary fourier transforms or generalized convolutional integrals nonstationary transforms such as the wavelet transform are not required there are many possible applications of this theory including the one way propagation of waves through complex media time migration normal moveout removal time variant filtering and forward and inverse q filtering two complementary nonstationary filters are developed by generalizing the stationary convolution integral the first called nonstationary convolution corresponds to the linear superposition of scaled impulse responses of a nonstationary filter the second called nonstationary combination does not correspond to such a superposition but is shown to be a linear process capable of achieving arbitrarily abrupt temporal variations in the output frequency spectrum both extensions have stationary convolution as a limiting form and in the discrete case can be formulated as matrix operations fourier transformation shows that both filter types are nonstationary filter integrals in the fourier domain as well this result is a generalization of the convolution theorem for stationary signals because as the filter becomes stationary in one domain the integral in the other domain collapses to a scalar multiplication for discrete signals stationary filters are a matrix multiplication of the input signal spectrum by a diagonal spectral matrix while nonstationary filters require off diagonal terms for quasi stationary filters a computational advantage is obtained by computing only the significant terms near the diagonal unlike stationary theory a mixed domain of time and frequency is also possible in this context the nonstationary filter is applied simultaneously with the transform from time to frequency or the reverse nonstationary convolution becomes a generalized forward fourier integral and nonstationary combination is a generalized inverse fourier integral

seismic data interpolation beyond aliasing using regularized nonstationary autoregression seismic data are often inadequately or irregularly sampled along spatial axes irregular sampling can produce artifacts in seismic imaging results we present a new approach to interpolate aliased seismic data based on adaptive predictionerror ltering pef and regularized nonstationary autoregression instead of cutting data into overlapping windows patching a popular method for handling nonstationarity we obtain smoothly nonstationary pef coecients by solving a global regularized least squares problem we employ shaping regularization to control the smoothness of adaptive pefs finding the interpolated traces can be treated as another linear least squares problem which solves for data values rather than lter coecients compared with existing methods the advantages of the proposed method include an intuitive selection of regularization parameters and fast iteration convergence benchmark synthetic and eld data examples show that the proposed technique can successfully reconstruct data with decimated or missing traces

the number of classes in chi squared goodness of fit tests abstract the power of pearson chi squared and likelihood ratio goodness of fit tests based on different partitions is studied by considering families of densities between the null density and fixed alternative densities for sample sizes n local asymptotic theory with respect to the number of classes k is developed for such families simple sufficient and almost necessary conditions are derived under which it is asymptotically optimal to let k tend to infinity with n a numerical study shows that the results of the asymptotic local theory for contamination families agree well with the actual power performance of the tests for heavy tailed alternatives the tests have the best power when k is relatively large unbalanced partitions with some small classes in the tails perform surprisingly well in particular when the alternatives have fairly heavy tails

fuzzy order statistics and their application to fuzzy clustering the median and the median absolute deviation mad are robust statistics based on order statistics order statistics are extended to fuzzy sets to define a fuzzy median and a fuzzy mad the fuzzy c means fcm clustering algorithm is defined for any p norm pfcm including the l sub 1 norm 1fcm the 1fcm clustering algorithm is implemented via the alternating optimization ao method and the clustering centers are shown to be the fuzzy median the resulting ao 1fcm clustering algorithm is called the fuzzy c medians fcmed clustering algorithm an example illustrates the robustness of the fcmed

simultaneous inversion of multiples and primaries inversion versus subtraction in this article we propose an inversion scheme to replace the adaptive subtraction approaches which are widely used in conventional two step prediction subtraction multiple elimination methods this new method named simp simultaneous inversion for multiples and primaries inverts seismic data using constraints e g modeled multiples and or geologic discriminants for multiples and primaries simultaneously simp incorporates pattern recognition and shaping filters into one concise and practically solvable formulation its main advantages are that no orthogonality between multiples and primaries is assumed and that wavelet information is not necessary for the inversion

relational duals of cluster validity functions for the c means family clustering aims to identify groups of similar objects to evaluate the results of cluster algorithms an investigator uses cluster validity indices while the theory of cluster validity is well established for vector object data little effort has been made to extend it to relationship based data as such this paper proposes a theory of reformulation for object data validity indices so that they can be used to rank the results produced by the relational means clustering algorithms more specifically we create a class of relational validity indices which is called dual relational indices that are guaranteed under certain but easily met constraints to produce the same results and hence the same cluster counts as their object data counterparts

internal multiple prediction and removal using marchenko autofocusing and seismic interferometry standard seismic processing steps such as velocity analysis and reverse time migration imaging usually assume that all reflections are primaries multiples represent a source of coherent noise and must be suppressed to avoid imaging artifacts many suppression methods are relatively ineffective for internal multiples we show how to predict and remove internal multiples using marchenko autofocusing and seismic interferometry we first show how internal multiples can theoretically be reconstructed in convolutional interferometry by combining purely reflected up and downgoing green s functions from virtual sources in the subsurface we then generate the relevant up and downgoing wavefields at virtual sources along discrete subsurface boundaries using autofocusing then we convolve purely scattered components of up and downgoing green s functions to reconstruct only the internal multiple field which is adaptively subtracted from the measured data crucially this is all possible without detailed modeled information about the earth s subsurface the method only requires surface reflection data and estimates of direct nonreflected arrivals between subsurface virtual sources and the acquisition surface the method is demostrated on a stratified synclinal model and shown to be particularly robust against errors in the reference velocity model used

optimization of clustering criteria by reformulation various hard fuzzy and possibilistic clustering criteria objective functions are useful as bases for a variety of pattern recognition problems at present many of these criteria have customized individual optimization algorithms because of the specialized nature of these algorithms experimentation with new and existing criteria can be very inconvenient and costly in terms of development and implementation time this paper shows how to reformulate some clustering criteria so that specialized algorithms can be replaced by general optimization routines found in commercially available software we prove that the original and reformulated versions of each criterion are fully equivalent finally two numerical examples are given to illustrate reformulation

diffraction imaging and time migration velocity analysis using oriented velocity continuation abstractwe perform seismic diffraction imaging and time migration velocity analysis by separating diffractions from specular reflections and decomposing them into slope components we image the slope components using migration velocity extrapolation in time space slope coordinates the extrapolation is described by a convection type partial differential equation and implemented in a highly parallel manner in the fourier domain synthetic and field data experiments show that the proposed algorithms are able to detect accurate time migration velocities by measuring the flatness of diffraction events in slope gathers for single and multiple offset data

on the bahadur efficient testing of uniformity by means of the entropy this paper compares the power divergence statistics of orders with the information divergence statistic in the problem of testing the uniformity of a distribution in this problem the information divergence statistic is equivalent to the entropy statistic extending some previously established results about information diagrams it is proved that the information divergence statistic in this problem is more efficient in the bahadur sense than any power divergence statistic of order this means that the entropy provides in this sense the most efficient way of characterizing the uniformity of a distribution

competitive algorithms for the clustering of noisy data abstract in this paper we consider the issue of clustering when outliers exist the outlier set is defined as the complement of the data set following this concept a specially designed fuzzy membership weighted objective function is proposed and the corresponding optimal membership is derived unlike the membership of fuzzy c means the derived fuzzy membership does not reduce with the increase of the cluster number with the suitable redefinition of the distance metric we demonstrate that the objective function could be used to extract c spherical shells a hard clustering algorithm alleviating the prototype under utilization problem is also derived artificially generated data are used for comparisons

adaptive multiple subtraction using regularized nonstationary regression stationary regression is the backbone of seismic data processing algorithms including match filtering which is commonly applied for adaptive multiple subtraction however the assumption of stationarity is not always adequate for describing seismic signals i have developed a general method of nonstationary regression and that applies to nonstationary match filtering the key idea is the use of shaping regularization to constrain the variability of nonstationary regression coefficients simple computational experiments demonstrate advantages of shaping regularization over classic tikhonov s regularization including a more intuitive selection of parameters and a faster iterative convergence using benchmark synthetic data examples i have successfully applied this method to the problem of adaptive subtraction of multiple reflections

on moderate and large deviations in multinomial distributions on presente des theoremes pour les statistiques du rapport de vraisemblance et du khi deux de pearson

change point detection in multinomial data with a large number of categories we consider a sequence of multinomial data for which the probabilities associated with the categories are subject to abrupt changes of unknown magnitudes at unknown locations when the number of categories is comparable to or even larger than the number of subjects allocated to these categories conventional methods such as the classical pearson s chi squared test and the deviance test may not work well motivated by high dimensional homogeneity tests we propose a novel change point detection procedure that allows the number of categories to tend to infinity the null distribution of our test statistic is asymptotically normal and the test performs well with finite samples the number of change points is determined by minimizing a penalized objective function based on segmentation and the locations of the change points are estimated by minimizing the objective function with the dynamic programming algorithm under some mild conditions the consistency of the estimators of multiple change points is established simulation studies show that the proposed method performs satisfactorily for identifying change points in terms of power and estimation accuracy and it is illustrated with an analysis of a real data set

uniformly powerful goodness of fit tests the simple hypothesis is tested that the distribution of independent random variables x1 x2 xn is a given probability measure po let 7r be any sequence of partitions the alternative hypothesis is the set of probability measures p with ea ip a po a i 8 where 8 0 note the dependence of this set of alternatives on the sample size it is shown that if the effective cardinality of the partitions is of the same order as the sample size then sequences of tests exist with uniformly exponentially small probabilities of error conversely if the effective cardinality is of larger order than the sample size then no such sequence of tests exists the effective cardinality is the number of sets in the partition which exhaust all but a negligible portion of the probability under the null hypothesis

reformulated radial basis neural networks trained by gradient descent this paper presents an axiomatic approach for constructing radial basis function rbf neural networks this approach results in a broad variety of admissible rbf models including those employing gaussian rbfs the form of the rbfs is determined by a generator function new rbf models can be developed according to the proposed approach by selecting generator functions other than exponential ones which lead to gaussian rbfs this paper also proposes a supervised learning algorithm based on gradient descent for training reformulated rbf neural networks constructed using the proposed approach a sensitivity analysis of the proposed algorithm relates the properties of rbfs with the convergence of gradient descent learning experiments involving a variety of reformulated rbf networks generated by linear and exponential generator functions indicate that gradient descent learning is simple easily implementable and produces rbf networks that perform considerably better than conventional rbf models trained by existing algorithms

target oriented wave equation inversion a target oriented strategy can be applied to estimate a wave equation least squares inverse lsi image by explicitly computing the wave equation hessian the lsi image is obtained as the solution of a nonstationary least squares inverse filtering problem the rows of the hessian are the nonstationary filters containing information about the acquisition geometry the velocity model and the band limited characteristics of the seismic data by exploiting the sparsity and the structure of the hessian matrix a large number of iterations necessary to achieve convergence can be computed cheaply the results on a structurally complex model show the improvements of the lsi image versus the migrated image

optimality tests for fixed points of the fuzzy c means algorithm abstract the fuzzy c means fcm clustering algorithms are known to converge to either local minima or saddle points of the objective function which defines the fcm method the object of this paper is to derive efficient numerical tests for local extrema of the fcm functional that enable one to identify each candidate as a local minimum or saddle point numerical examples of the theory derived illustrate that the tests proposed cover all possible cases

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

seismic data decomposition into spectral components using regularized nonstationary autoregression summary seismic data can be decomposed into nonstationary spectral components with smoothly variable frequencies and smoothly variable amplitudes to estimate local frequencies i use a nonstationary version of prony s spectral analysis method defined with the help of regularized nonstationary autoregression rnar to estimate local amplitudes of different components i fit their sum to the data using regularized nonstationary regression rnr shaping regularization ensures stability of the estimation process and provides controls on smoothness potential applications of the proposed technique include noise attenuation seismic data compression and seismic data regularization

generalized error exponents for small sample universal hypothesis testing the small sample universal hypothesis testing problem is investigated in this paper in which the number of samples n is smaller than the number of possible outcomes m the goal of this paper is to find an appropriate criterion to analyze statistical tests in this setting a suitable model for analysis is the high dimensional model in which both n and m increase to infinity and n o m a new performance criterion based on large deviations analysis is proposed and it generalizes the classical error exponent applicable for large sample problems in which m o n this generalized error exponent criterion provides insights that are not available from asymptotic consistency or central limit theorem analysis the following results are established for the uniform null distribution 1 the best achievable probability of error pe decays as pe exp n2 m j 1 o 1 for some j 0 2 a class of tests based on separable statistics including the coincidence based test attains the optimal generalized error exponents 3 pearson s chi square test has a zero generalized error exponent and thus its probability of error is asymptotically larger than the optimal test

time frequency analysis of seismic data using local attributes time frequency analysis is an important technology in seismic data processing and interpretation to localize frequency content in time we have developed a novel method for computing a time frequency map for nonstationary signals using an iterative inversion framework we calculated time varying fourier coefficients by solving a least squares problem that uses regularized nonstationary regression we defined the time frequency map as the norm of time varying coefficients time varying average frequency of the seismic data can also be estimated from the time frequency map calculated by our method we tested the method on benchmark synthetic signals and compared it with the well known s transform two field data examples showed applications of the proposed method for delineation of sand channels and for detection of low frequency anomalies

fuzzy j means a new heuristic for fuzzy clustering abstract a fuzzy clustering problem consists of assigning a set of patterns to a given number of clusters with respect to some criteria such that each of them may belong to more than one cluster with different degrees of membership in order to solve it we first propose a new local search heuristic called fuzzy j means where the neighbourhood is defined by all possible centroid to pattern relocations the integer solution is then moved to a continuous one by an alternate step i e by finding centroids and membership degrees for all patterns and clusters to alleviate the difficulty of being stuck in local minima of poor value this local search is then embedded into the variable neighbourhood search metaheuristic results on five standard test problems from the literature are reported and compared with those obtained with the well known fuzzy c means heuristic it appears that solutions of substantially better quality are obtained with the proposed methods than with this former one

adaptive overburden elimination with the multidimensional marchenko equation abstractiterative substitution of the multidimensional marchenko equation has been introduced recently to integrate internal multiple reflections in the seismic imaging process in so called marchenko imaging a macro velocity model of the subsurface is required to meet this objective the model is used to back propagate the data during the first iteration and to truncate integrals in time during all successive iterations in case of an erroneous model the image will be blurred akin to conventional imaging and artifacts may arise from inaccurate integral truncations however the scheme is still successful in removing artifacts from internal multiple reflections inspired by these observations we rewrote the marchenko equation such that it can be applied early in a processing flow without the need of a macro velocity model instead we have required an estimate of the two way traveltime surface of a selected horizon in the subsurface we have introduced an approximation such that adaptive subtracti

signal extraction using randomized order multichannel singular spectrum analysis abstractmultichannel singular spectrum analysis mssa is an effective algorithm for random noise attenuation however it cannot be used to suppress coherent noise this limitation results from the fact that the conventional mssa method cannot distinguish between useful signals and coherent noise in the singular spectrum we have developed a randomization operator to disperse the energy of the coherent noise in the time space domain furthermore we have developed a novel algorithm for the extraction of useful signals i e for simultaneous random and coherent noise attenuation by introducing a randomization operator into the conventional mssa algorithm in this method which we call randomized order mssa the traces along the trajectory of each signal component are randomly rearranged two ways to extract the trajectories of different signal components are investigated the first is based on picking the extrema of the upper envelopes a method that is also constrained by local and global gradients th

building good starting models for full waveform inversion using adaptive matching filtering misfit abstractwe have proposed a misfit function based on adaptive matching filtering amf to tackle challenges associated with cycle skipping and local minima in full waveform inversion fwi this amf is designed to measure time varying phase differences between observations and predictions compared with classical least squares waveform differences our misfit function behaves as a smooth quadratic function with a broad basin of attraction these characters are important because local gradient based optimization approaches used in most fwi schemes cannot guarantee convergence toward true models if misfit functions include local minima or if the starting model is far away from the global minimum the 1d and 2d synthetic experiments illustrate the advantages of the proposed misfit function compared with the classical least squares waveform misfit furthermore we have derived adjoint sources associated with the proposed misfit function and applied them in several 2d time domain acoustic fwi experiments nume

consistent nonparametric tests of independence three simple and explicit procedures for testing the independence of two multi dimensional random variables are described two of the associated test statistics l1 log likelihood are defined when the empirical distribution of the variables is restricted to finite partitions a third test statistic is defined as a kernel based independence measure two kinds of tests are provided distribution free strong consistent tests are derived on the basis of large deviation bounds on the test statistics these tests make almost surely no type i or type ii error after a random sample size asymptotically level tests are obtained from the limiting distribution of the test statistics for the latter tests the type i error converges to a fixed non zero value and the type ii error drops to zero for increasing sample size all tests reject the null hypothesis of independence if the test statistics become large the performance of the tests is evaluated experimentally on benchmark data