seismic data restoration via data driven tight frame restoration interpolation of missing traces plays a crucial role in the seismic data processing pipeline efficient restoration methods have been proposed based on sparse signal representation in a transform domain such as fourier wavelet curvelet and shearlet transforms most existing methods are based on transforms with a fixed basis we considered an adaptive sparse transform for restoration of data with complex structures in particular we evaluated a data driven tight frame based sparse regularization method for seismic data restoration the main idea of the data driven tight frame tf is to adaptively learn a set of framelet filters from the currently interpolated data under which the data can be more sparsely represented hence the sparsity promoting l1 norm spl1 minimization methods can produce better restoration results by using the learned filters a split inexact uzawa algorithm which can be viewed as a generalization of the alternating direction of multiplier method admm was applied to solve the presented spl1 model numerical tests were performed on synthetic and real seismic data for restoration of randomly missing traces over a regular data grid our experiments showed that our proposed method obtains the state of the art restoration results in comparison with the traditional fourier based projection onto convex sets the tight frame based method and the recent shearlet regularization admm method

interpolation and denoising of high dimensional seismic data by learning a tight frame abstractsparse transforms play an important role in seismic signal processing steps such as prestack noise attenuation and data reconstruction analytic sparse transforms so called implicit dictionaries such as the fourier radon and curvelet transforms are often used to represent seismic data there are situations however in which the complexity of the data requires adaptive sparse transform methods whose basis functions are determined via learning methods we studied an application of the data driven tight frame ddtf method to noise suppression and interpolation of high dimensional seismic data rather than choosing a model beforehand for example a family of lines parabolas or curvelets to fit the data the ddtf derives the model from the data itself in an optimum manner the process of estimating the basis function from the data can be summarized as follows first the input data are divided into small blocks to form training sets then the ddtf algorithm is applied on the training set

characterizing contextual equivalence in calculi with passivation we study the problem of characterizing contextual equivalence in higher order languages with passivation to overcome the difficulties arising in the proof of congruence of candidate bisimilarities we introduce a new form of labeled transition semantics together with its associated notion of bisimulation which we call complementary semantics complementary semantics allows to apply the well known howe s method for proving the congruence of bisimilarities in a higher order setting even in the presence of an early form of bisimulation we use complementary semantics to provide a coinductive characterization of contextual equivalence in the ho pp calculus an extension of the higher order p calculus with passivation obtaining the first result of this kind we then study the problem of defining a more effective variant of bisimilarity that still characterizes contextual equivalence along the lines of sangiorgi s notion of normal bisimilarity we provide partial results on this difficult problem we show that a large class of test processes cannot be used to derive a normal bisimilarity in ho pp but we show that a form of normal bisimilarity can be defined for ho pp without restriction

multicomponent f x seismic random noise attenuation via vector autoregressive operators we propose an extension of the traditional frequency space f x random noise attenuation method to three component seismic records for this purpose we develop a three component vector autoregressive var model in the f x domain that is applied to the multicomponent spatial samples of each individual temporal frequency var model parameters are estimated using the least squares minimization of forward and backward prediction errors var modeling effectively identifies the potential coherencies between various components of a multicomponent signal we use the squared coherence spectrum of var models as an indicator to determine these coherencies synthetic and real data examples are provided to show the effectiveness of the proposed method

seislet transform and seislet frame we introduce a digital waveletlike transform which is tailored specifically for representing seismic data the transform provides a multiscale orthogonal basis with basis functions aligned along seismic events in the input data it is defined with the help of the wavelet lifting scheme combined with local plane wave destruction in the 1d case the seislet transform is designed to follow locally sinusoidal components in the 2d case it is designed to follow local plane wave components with smoothly variable slopes if more than one component is present the transform turns into an overcomplete representation or a tight frame in these terms the classic digital wavelet transform is simply a seislet transform for a zero frequency in one dimension or zero slope in two dimensions the main objective of the new transform is an effective seismic data compression for designing efficient data analysis algorithms traditional signal processing tasks such as noise attenuation and trace interpolation become simply defined in the seislet domain when applied in the offset direction on common midpoint or common image point gathers the seislet transform finds an additional application in optimal stacking of seismic records

fast generalized fourier transforms abstract let g be a f inite group then ls g the linear complexity of a suitable wedderburn transform corresponding to g is smaller than 2 g 2 we improve this trivial upper bound by showing that ls g is smaller than min s t l t g 7 q t g 3 2 where the minimum is taken over all towers t g n g n 1 g 0 1 of subgroups of g gn and where q t resp s t is the maximum resp sum of all indices gi 1 gi corresponding to t and l t n is the length of the tower a similar upper bound is valid for the linear complexity of the inverse of such a wedderburn transform for symmetric groups our technique yields the stronger estimate ls sn 0 sn log3 sn

five dimensional interpolation recovering from acquisition constraints although 3d seismic data are being acquired in larger volumes than ever before the spatial sampling of these volumes is not always adequate for certain seismic processes this is especially true of marine and land wide azimuth acquisitions leading to the development of multidimensional data interpolation techniques simultaneous interpolation in all five seismic data dimensions inline crossline offset azimuth and frequency has great utility in predicting missing data with correct amplitude and phase variations although there are many techniques that can be implemented in five dimensions this study focused on sparse fourier reconstruction the success of fourier interpolation methods depends largely on two factors 1 having efficient fourier transform operators that permit the use of large multidimensional data windows and 2 constraining the spatial spectrum along dimensions where seismic amplitudes change slowly so that the sparseness and band limitation assumptions remain valid fourier reconstruction can be performed when enforcing a sparseness constraint on the 4d spatial spectrum obtained from frequency slices of five dimensional windows binning spatial positions into a fine 4d grid facilitates the use of the fft which helps on the convergence of the inversion algorithm this improves the results and computational efficiency the 5d interpolation can successfully interpolate sparse data improve avo analysis and reduce migration artifacts target geometries for optimal interpolation and regularization of land data can be classified in terms of whether they preserve the original data and whether they are designed to achieve surface or subsurface consistency

interpolation with fourier radial adaptive thresholding many interpolation methods are effective with regularly sampled or randomly sampled data whereas the spatial sampling of seismic reflectivity data is typically neither regular nor random fourier radial adaptive thresholding frat is a sparsity promoting method in which the interpolated result is sparse in the frequency wavenumber domain and is coherent in a manner consistent with that of a collection of unaliased plane waves the sparsity and the desired pattern in the f k domain are promoted by iterative soft thresholding and adaptive weighting data in the f k domain are transformed to polar coordinates and then low pass filtered along the radial axis to generate the nonlinear weight frat interpolates data that are randomly sampled and aliased i e where the minimum distance between adjacent traces is greater than the nyquist sampling interval a conventional approach to solving this problem is to apply a cascade of two procedures first a sparsity based method such as projection onto convex sets

wave equation trace interpolation spatial aliasing in multichannel seismic data can be overcome by solving an inversion in which the model is the section that would be recorded in a well sampled zero offset experiment and the data are seismic data after normal moveout nmo the formulation of the linear relation between the data and the model is based on the wave equation and on fourier analysis of aliasing a processing sequence in which one treats missing data as zero data and performs partial migration before stacking is equivalent to application of the transpose of the operator that actually needs to be inverted the inverse of that operator cannot be uniquely determined but it can be estimated using spatial spectral balancing in a conjugate gradient iterative scheme the first iteration is conventional processing including prestack partial migration as shown in a field data example in which severe spatial aliasing was simulated a few more iterations are necessary to achieve significantly better results

simultaneous multitrace impedance inversion with transform domain sparsity promotion abstractthe impedance inversion technique plays a crucial role in seismic reservoir properties prediction however most existing impedance inversion methods often suffer from spatial discontinuities and instability because each vertical profile is processed independently in the inversion we tested a transform domain sparsity promotion simultaneous multitrace impedance inversion method to address this issue the approach was implemented through minimizing a data misfit term and a transform domain sparsity constraint term that incorporates the 2d or 3d structural information into the inversion processing a 2d synthetic data example was applied to mainly explain the roles of the transform domain sparsity constraint we determined that the transform domain sparsity constraint can help in stabilizing the inversion reducing the influence of high wavenumber noise on the inverted result and exploring spatial continuities of structures furthermore a 3d field data example was used to examine the effectiven

fourier reconstruction of nonuniformly sampled aliased seismic data there are numerous methods for interpolating uniformly sampled aliased seismic data but few can handle the combination of nonuniform sampling and aliasing we combine the principles of fourier reconstruction of nonaliased nonuniformly sampled data with the ideas of frequency wavenumber f k interpolation of aliased uniformly sampled data in a new two step algorithm in the first step we estimate the fourier coefficients at the lower nonaliased temporal frequencies from the nonuniformly sampled data the coefficients are then used in the second step as an a priori model to distinguish between aliased and nonaliased energy at the higher aliased temporal frequencies by using a nonquadratic model penalty in the inversion both the artifacts in the fourier domain from nonuniform sampling and the aliased energy are suppressed the underlying assumption is that events are planar therefore the algorithm is applied to seismic data in overlapping spatiotemporal windows

improving multiple removal using least squares dip filters and independent component analysis the suppression of multiple events is a crucial task in seismic data processing and the adaptive subtraction of the predicted multiples is recognized as one of the main challenges for the success of the surface related multiple elimination technique the traditional least squares matching approach can affect the primary events because the estimated multiples tend to adapt to the primaries under the minimum energy condition we investigate two filtering techniques for improving the multiple removal results in the first proposed method we combine the advantages of the least squares and pattern dip based subtraction methods doing so we exploit the separation of primaries and multiples in the dip domain and then we apply the least squares adaptive subtraction in each dip band before recomposing the data to obtain the final subtraction result as a result of the dip decomposition the primary multiple interferences are reduced allowing for a more reliable least squares filtering in the second method w

fourier reconstruction of marine streamer data in four spatial coordinates many methods exist for interpolation of seismic data in one and two spatial dimensions but few can interpolate properly in three or four spatial dimensions marine multi streamer data typically are sampled relatively well in the midpoint and absolute offset coordinates but not in the azimuth because the crossline shot coordinate is significantly under sampled we approach the problem of interpolation of marine streamer data in four spatial dimensions by splitting the problem into a 1d interpolation along the densely sampled streamers and a 3d fourier reconstruction for the remaining spatial coordinates in fourier reconstruction the fourier coefficients that synthesize the nonuniformly sampled seismic data are estimated in a least squares inversion the method is computationally efficient requires no subsurface information and can handle uniform grids with missing data as well as nonuniform grids or random sampling the output grid of the 1d interpolation in the first step is arbitrary when the output grid has uniform inline midpoints spacing the 3d fourier reconstruction in the second step is performed in the crossline midpoint absolute offset and azimuth coordinates when the first step outputs to uniform absolute offset the 3d fourier reconstruction handles the crossline inline midpoint and the azimuth coordinates in both cases the main innovation is the inclusion of the azimuthal coordinate in the fourier reconstruction the azimuth multiplicity must be increased for the method to be successful which means that overlap shooting is required we have tested the algorithm on synthetic streamer data for which the proposed method outperforms an approach where the azimuthal coordinate is ignored potential applications are interpolation of marine streamer data to decrease the crossline source sampling for the benefit of 3d multiple prediction and regularization to reduce sampling related differences in processing of time lapse data

new tight frames of curvelets and optimal representations of objects with piecewise c2 singularities this paper introduces new tight frames of curvelets to address the problem of finding optimally sparse representations of objects with discontinuities along piecewise c 2 edges conceptually the curvelet transform is a multiscale pyramid with many directions and positions at each length scale and needle shaped elements at fine scales these elements have many useful geometric multiscale features that set them apart from classical multiscale representations such as wavelets for instance curvelets obey a parabolic scaling relation which says that at scale 2 j each element has an envelope that is aligned along a ridge of length 2 j 2 and width 2 j we prove that curvelets provide an essentially optimal representation of typical objects f that are c 2 except for discontinuities along piecewise c 2 curves such representations are nearly as sparse as if f were not singular and turn out to be far more sparse than the wavelet decomposition of the object for instance the n term partial reconstruction f c n obtained by selecting the n largest terms in the curvelet series obeys f f c n 2 l2 c n 2 log n 3 n this rate of convergence holds uniformly over a class of functions that are c 2 except for discontinuities along piecewise c 2 curves and is essentially optimal in comparison the squared error of n term wavelet approximations only converges as n 1 as n which is considerably worse than the optimal behavior

kronecker basis representation based tensor sparsity and its applications to tensor recovery as a promising way for analyzing data sparse modeling has achieved great success throughout science and engineering it is well known that the sparsity low rank of a vector matrix can be rationally measured by nonzero entries number l 0 norm nonzero singular values number rank respectively however data from real applications are often generated by the interaction of multiple factors which obviously cannot be sufficiently represented by a vector matrix while a high order tensor is expected to provide more faithful representation to deliver the intrinsic structure underlying such data ensembles unlike the vector matrix case constructing a rational high order sparsity measure for tensor is a relatively harder task to this aim in this paper we propose a measure for tensor sparsity called kronecker basis representation based tensor sparsity measure kbr briefly which encodes both sparsity insights delivered by tucker and candecomp parafac cp low rank decompositions for a general tensor then we study the kbr regularization minimization kbrm problem and design an effective admm algorithm for solving it where each involved parameter can be updated with closed form equations such an efficient solver makes it possible to extend kbr to various tasks like tensor completion and tensor robust principal component analysis a series of experiments including multispectral image msi denoising msi completion and background subtraction substantiate the superiority of the proposed methods beyond state of the arts

a tensor higher order singular value decomposition for prestack seismic data noise reduction and interpolation a patch of prestack data depends on four spatial dimensions x y midpoints and x y offsets and frequency the spatial data at one temporal frequency can be represented by a fourth order tensor in ideal conditions of high signal to noise ratio and complete sampling one can assume that the seismic data can be approximated via a low rank fourth order tensor missing samples were recovered by reinserting data obtained by approximating the original noisy and incomplete data volume with new observations obtained via the rank reduction process the higher order singular value decompostion was used to reduce the rank of the prestack seismic tensor synthetic data demonstrated the ability of the proposed seismic data completion algorithm to reconstruct events with curvature the synthetic example allowed to quantify the quality of the reconstruction for different levels of noise and survey sparsity we also provided a real data example from the western canadian sedimentary basin

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

bisimulation can t be traced in the concurrent language ccs two programs are considered the same if they are bisimilar several years and many researchers have demonstrated that the theory of bisimulation is mathematically appealing and useful in practice however bisimulation makes too many distinctions between programs we consider the problem of adding operations to ccs to make bisimulation fully abstract we define the class of gsos operations generalizing the style and technical advantages of ccs operations we characterize gsos congruence in as a bisimulation like relation called ready simulation bisimulation is strictly finer than ready simulation and hence not a congruence for any gsos language

a general description of linear time frequency transforms and formulation of a fast invertible transform that samples the continuous s transform spectrum nonredundantly examining the frequency content of signals is critical in many applications from neuroscience to astronomy many techniques have been proposed to accomplish this one of these the s transform provides simultaneous time and frequency information similar to the wavelet transform but uses sinusoidal basis functions to produce frequency and globally referenced phase measurements it has shown promise in many medical imaging applications but has high computational requirements this paper presents a general transform that describes fourier family transforms including the fourier short time fourier and s transforms a discrete nonredundant formulation of this transform as well as algorithms for calculating the forward and inverse transforms are also developed these utilize efficient sampling of the time frequency plane and have the same computational complexity as the fast fourier transform when configured appropriately this new algorithm samples the continuous s transform spectrum efficiently and nonredundantly allowing signals to be transformed in milliseconds rather than days as compared to the original s transform algorithm the new and efficient algorithms make practical many existing signal and image processing techniques both in biomedical and other applications

mixed value at risk and its numerical investigation abstract we study an extension of value at risk var measure named as mixed var a weighted sum of multiple vars quantified at different confidence levels classical var or single var computed at a fixed confidence level corresponds to a single percentile of distribution and therefore is unable to reveal much information of risk involved in it as a remedy to this we propose to investigate the role of mixed var and its deviation version in risk management of extreme events in the portfolio selection problem we analyze the computational performance of portfolios from optimization models minimizing single var and mixed var and their deviation variants for different combinations of confidence levels over historical as well as on simulated data in various financial performance parameters including mean value risk measures var and cvar values quantified at multiple confidence levels and risk reward measures sharpe ratio sortino ratio sharpe with var and sharpe with cvar we also study the numerical comparison between mixed var with its most crucial counterpart the mixed conditional value at risk mixed cvar we find that the performance of portfolios from mixed var model is lying between the performance of its single var counterparts and rarely yield any worst value in any of the considered performance parameters a similar observation is concluded for the deviation version of the models further we find that mixed var outperforms mixed cvar with respect to risk reward measures considered in the study on both of the data sets historical as well as on simulated

seismic reflection data interpolation with differential offset and shot continuation i propose a finite difference offset continuation filter for interpolating seismic reflection data the filter is constructed from the offset continuation differential equation and is applied on frequency slices in the log stretch frequency domain synthetic and real data tests demonstrate that the proposed method succeeds in structurally complex situations where more simplistic approaches fail

noise attenuation in a low dimensional manifold abstractwe have found that seismic data can be described in a low dimensional manifold and then we investigated using a low dimensional manifold model ldmm method for extremely strong noise attenuation the ldmm supposes the dimension of the patch manifold of seismic data should be low in other words the degree of freedom of the patches should be low under the linear events assumption on a patch the patch can be parameterized by the intercept and slope of the event if the seismic wavelet is identical everywhere the denoising problem is formed as an optimization problem including a fidelity term and an ldmm regularization term we have tested ldmm on synthetic seismic data with different noise levels ldmm achieves better denoised results in comparison with the fourier curvelet and nonlocal mean filtering methods especially in the presence of strong noise or low signal to noise ratio situations we have also tested ldmm on field records indicating that ldmm is a method for handling relatively

joint removal of random and fixed pattern noise through spatiotemporal video filtering we propose a framework for the denoising of videos jointly corrupted by spatially correlated i e nonwhite random noise and spatially correlated fixed pattern noise our approach is based on motion compensated 3d spatiotemporal volumes i e a sequence of 2d square patches extracted along the motion trajectories of the noisy video first the spatial and temporal correlations within each volume are leveraged to sparsify the data in 3d spatiotemporal transform domain and then the coefficients of the 3d volume spectrum are shrunk using an adaptive 3d threshold array such array depends on the particular motion trajectory of the volume the individual power spectral densities of the random and fixed pattern noise and also the noise variances which are adaptively estimated in transform domain experimental results on both synthetically corrupted data and real infrared videos demonstrate a superior suppression of the random and fixed pattern noise from both an objective and a subjective point of view

nonlocal transform domain filter for volumetric data denoising and reconstruction we present an extension of the bm3d filter to volumetric data the proposed algorithm bm4d implements the grouping and collaborative filtering paradigm where mutually similar d dimensional patches are stacked together in a d 1 dimensional array and jointly filtered in transform domain while in bm3d the basic data patches are blocks of pixels in bm4d we utilize cubes of voxels which are stacked into a 4 d group the 4 d transform applied on the group simultaneously exploits the local correlation present among voxels in each cube and the nonlocal correlation between the corresponding voxels of different cubes thus the spectrum of the group is highly sparse leading to very effective separation of signal and noise through coefficient shrinkage after inverse transformation we obtain estimates of each grouped cube which are then adaptively aggregated at their original locations we evaluate the algorithm on denoising of volumetric data corrupted by gaussian and rician noise as well as on reconstruction of volumetric phantom data with non zero phase from noisy and incomplete fourier domain k space measurements experimental results demonstrate the state of the art denoising performance of bm4d and its effectiveness when exploited as a regularizer in volumetric data reconstruction

multidimensional de aliased cadzow reconstruction of seismic records abstractwe tested a strategy for beyond alias interpolation of seismic data using cadzow reconstruction the strategy enables cadzow reconstruction to be used for interpolation of regularly sampled seismic records first in the frequency space f x domain we generated a hankel matrix from the spatial samples of the low frequencies to perform interpolation at a given frequency the spatial samples were interlaced with zero samples and another hankel matrix was generated from the zero interlaced data next the rank reduced eigen decomposition of the hankel matrix at low frequencies was used for beyond alias preconditioning of the hankel matrix at a given frequency finally antidiagonal averaging of the conditioned hankel matrix produced the final interpolated data in addition the multidimensional extension of the proposed algorithm was explained the proposed method provides a unifying thread between reduced rank cadzow reconstruction and beyond alias f x prediction error interpolation synthetic an

2d and 3d prestack seismic data regularization using an accelerated sparse time invariant radon transform abstractthe time invariant radon transform rt is commonly used to regularize and interpolate sparsely sampled or irregularly acquired prestack seismic data the sparseness of the radon model significantly influences the results of regularization we have developed an effective and efficient method for the regularization and interpolation of 2d as well as 3d prestack seismic data we used an accelerated sparse time invariant rt in the mixed frequency time domain to improve the performance of rt based seismic data regularization this 2d sparse rt incorporated the iterative 2d model shrinkage algorithm instead of the traditional iteratively reweighted least squares irls algorithm in the time domain and we computed the forward and inverse rts in the frequency domain to solve the sparse inverse problem which dramatically reduced the computational cost while obtaining a high resolution result the 2d synthetic and real data examples revealed that our 2d approach can better interpolate beyond aliasing a 2

interpolation of near offsets using multiples and prediction error filters reflection seismic data typically are undersampled missing near offsets can be interpolated in reflection seismic data with pseudoprimaries generated by crosscorrelating multiples and primaries in incomplete recorded data these pseudoprimary data can be generated at the missing near offsets but contain many artifacts so it is undesirable simply to replace the missing data with the pseudoprimaries a nonstationary prediction error filter pef can instead be estimated from the pseudoprimaries and used to interpolate missing data to produce an interpolated output that is superior to direct substitution of the pseudoprimaries into the missing offsets this approach is applied successfully to 2d synthetic and field data limitations in conventional acquisition geometry limit this approach in 3d which can be illustrated using a synthetic data set

multistep autoregressive reconstruction of seismic records linear prediction filters in the f x domain are widely used to interpolate regularly sampled data we study the problem of reconstructing irregularly missing data on a regular grid using linear prediction filters we propose a two stage algorithm first we reconstruct the unaliased part of the data spectrum using a fourier method minimum weighted norm interpolation then prediction filters for all the frequencies are extracted from the reconstructed low frequencies the latter is implemented via a multistep autoregressive msar algorithm finally these prediction filters are used to reconstruct the complete data in the f x domain the applicability of the proposed method is examined using synthetic and field data examples

crossline wavefield reconstruction from multicomponent streamer data part 1 multichannel interpolation by matching pursuit mimap using pressure and its crossline gradient we introduce a technique that uses multicomponent seismic measurements to reconstruct the seismic wavefield at any desired crossline position between towed streamers this method called multichannel interpolation by matching pursuit mimap operates on pressure and crossline particle motion measurements it is based on the matching pursuit technique and iteratively reconstructs the signal as a combination of optimal basis functions being a data dependent technique mimap can interpolate severely aliased data without assumptions about seismic events such as linearity or the model related to the seismic wavefield mimap has the capability to perform well in the presence of irregular sampling and is robust when only a small number of samples are available using synthetic data examples we show that the new method has the potential to interpolate signals that are sampled at realistic crossline streamer spacing and in the presence of noise

beyond alias hierarchical scale curvelet interpolation of regularly and irregularly sampled seismic data we propose a robust interpolation scheme for aliased regularly sampled seismic data that uses the curvelet transform in a first pass the curvelet transform is used to compute the curvelet coefficients of the aliased seismic data the aforementioned coefficients are divided into two groups of scales alias free and alias contaminated scales the alias free curvelet coefficients are upscaled to estimate a mask function that is used to constrain the inversion of the alias contaminated scale coefficients the mask function is incorporated into the inversion via a minimum norm least squares algorithm that determines the curvelet coefficients of the desired alias free data once the alias free coefficients are determined the curvelet synthesis operator is used to reconstruct seismograms at new spatial positions the proposed method can be used to reconstruct regularly and irregularly sampled seismic data we believe that our exposition leads to a clear unifying thread between f x and f k beyond alias interpo

a conservative look at operational semantics with variable binding we set up a formal framework to describe transition system specifications in the style of plotkin this framework has the power to express many sortedness general binding mechanisms and substitutions among other notions such as negative hypotheses and unary predicates on terms the framework is used to present a conservativity format in operational semantics which states sufficient criteria to ensure that the extension of a transition system specification with new transition rules does not affect the semantics of the original terms

seismic data interpolation by greedy local radon transform we propose a greedy inversion method for a spatially localized high resolution radon transform the kernel of the method is based on a conventional iterative algorithm conjugate gradient cg but is utilized adaptively in amplitude prioritized local model spaces the adaptive inversion introduces a coherence oriented mechanism to enhance focusing of significant model parameters and hence increases the model resolution and convergence rate we adopt the idea in a time space domain local linear radon transform for data interpolation we find that the local radon transform involves iteratively applying spatially localized forward and adjoint radon operators to fit the input data optimal local radon panels can be found via a subspace algorithm which promotes sparsity in the model and the missing data can be predicted using the resulting local radon panels the subspacing strategy greatly reduces the cost of computing local radon coefficients thereby reducing the total cost for inversion the method can handle irregular and regular geometries and significant spatial aliasing we compare the performance of our method using three simple synthetic data sets with a popular interpolation method known as minimum weighted norm fourier interpolation and show the advantage of the new algorithm in interpolating spatially aliased data we also test the algorithm on the 2d synthetic data and a field data set both tests show that the algorithm is a robust antialiasing tool although it cannot completely recover missing strongly curved events

interpolation and extrapolation using a high resolution discrete fourier transform we present an iterative nonparametric approach to spectral estimation that is particularly suitable for estimation of line spectra this approach minimizes a cost function derived from bayes theorem the method is suitable for line spectra since a long tailed distribution is used to model the prior distribution of spectral amplitudes since the data themselves are used as constraints phase information can also be recovered and used to extend the data outside the original window the objective function is formulated in terms of hyperparameters that control the degree of fit and spectral resolution noise rejection can also be achieved by truncating the number of iterations spectral resolution and extrapolation length are controlled by a single parameter when this parameter is large compared with the spectral powers the algorithm leads to zero extrapolation of the data and the estimated fourier transform yields the periodogram when the data are sampled at a constant rate the algorithm uses one levinson recursion per iteration for irregular sampling the algorithm uses one cholesky decomposition per iteration the performance of the algorithm is illustrated with three different problems that arise in geophysical data 1 harmonic retrieval from a time series contaminated with noise 2 linear event detection from a finite aperture array of receivers 3 interpolation extrapolation of gapped data the performance of the algorithm as a spectral estimator is tested with the kay and marple 1981 data set

simultaneous seismic data denoising and reconstruction via multichannel singular spectrum analysis we present a rank reduction algorithm that permits simultaneous reconstruction and random noise attenuation of seismic records we based our technique on multichannel singular spectrum analysis mssa the technique entails organizing spatial data at a given temporal frequency into a block hankel matrix that in ideal conditions is a matrix of rank k where k is the number of plane waves in the window of analysis additive noise and missing samples will increase the rank of the block hankel matrix of the data consequently rank reduction is proposed as a means to attenuate noise and recover missing traces we present an iterative algorithm that resembles seismic data reconstruction with the method of projection onto convex sets in addition we propose to adopt a randomized singular value decomposition to accelerate the rank reduction stage of the algorithm we apply mssa reconstruction to synthetic examples and a field data set synthetic examples were used to assess the performance of the method in two

spatial antialias filtering in the slowness frequency domain a rigorous explicit spatial antialias filter is designed and applied to spatially coarsely sampled seismic data by removing all energy above the first nyquist wavenumber and aliased energy that is folded back across the nyquist in the horizontal slowness frequency domain the spatial filtering in the slowness frequency domain is explicit free from any event linearity assumption and does not require any interpolation the spatially aliased energy is dispersive and present at small and large slownesses comparison of the output data after antialias spatial filtering with output data after conventional antialias frequency filtering shows that the filter removes the spatially aliased frequencies selectively at each slowness antialias low pass frequency filtering under or overcorrects for spatial aliasing at all slownesses a seismic gather can be spatially dealiased only at the expense of wavelet spectral changes dealiasing and preservation of amplitude variations with offset are not simultaneously possible

high order sparse radon transform for avo preserving data reconstruction abstractthe sparse radon transform rt represents seismic data by the superposition of a few constant amplitude events and thus it has trouble dealing with amplitude versus offset avo variations we integrated the gradient and curvature parameters of avo into the rt with these additional properties the lateral continuity of the events amplitude was modeled in the transformation and it could be fitted with orthogonal polynomials this resulted in a higher order rt which included avo terms the high order rt is a highly underdetermined problem which was solved by extracting the major model parameters from energy distribution in a high order radon domain and by decreasing the number of inversion parameters thus a high order sparse rt was achieved the proposed method can be used for data interpolation as well as extrapolation the avo preservation performance of the proposed algorithm in data reconstruction was illustrated using both synthetic and field data examples and the results showed the fe

wavelet radon domain dealiasing and interpolation of seismic data spatial aliasing is unavoidable in some seismic data and has serious effects on the performance of multichannel data processing and migration antialias filtering produces distortion of the signal through the removal of high frequency information in contrast dealiasing produces an unaliased estimate of the signal at all frequencies present in the original time series a new dealiasing algorithm is developed by exploiting the properties of seismic wavefields in the wavelet radon transform domain specifically the overlap of information between wavelet scales at the same frequency the effectiveness of the wavelet radon dealiasing algorithm is demonstrated through the processing of both synthetic and field seismic data

on sampling functions and fourier reconstruction methods random sampling can lead to algorithms in which the fourier reconstruction is almost perfect when the underlying spectrum of the signal is sparse or band limited conversely regular sampling often hampers the fourier data recovery methods however 2d signals that are band limited in one spatial dimension can be recovered by designing a regular acquisition grid that minimizes the mixing between the unknown spectrum of the well sampled signal and aliasing artifacts this concept can be easily extended to higher dimensions and used to define potential strategies for acquisition guided fourier reconstruction the wavenumber response of various sampling operators is derived and sampling conditions for optimal fourier reconstruction are investigated using synthetic and real data examples

lapb locally adaptive patch based wavelet domain edge preserving image denoising abstract image denoising is one of the most diversified research areas in the field of image processing and computer vision it is highly desirable for a denoising technique to preserve important image features such as edges corners and other sharp structures of an image after denoising wavelet transforms show excellent proficiency in providing efficient edge preserving image denoising due to their capability of suppressing noisy signals from an image this paper presents a novel edge preserving image denoising technique based on wavelet transforms the multi level decomposition of the noisy image is carried out to transform the data into the wavelet domain a locally adaptive patch based lapb thresholding scheme is used to effectively reduce noise while preserving relevant features of the original image experimental results on benchmark test images demonstrate that the proposed method achieves competitive denoising performance in comparison to various state of the art algorithms

three dimensional irregular seismic data reconstruction via low rank matrix completion abstractwe have developed a new algorithm for the reconstruction of seismic traces randomly missing from a uniform grid of a 3d seismic volume several algorithms have been developed for such reconstructions based on properties of the seismic wavefields and on signal processing concepts such as sparse signal representation in a transform domain we have investigated a novel approach originally introduced for noise removal which is based on the premise that for suitable representation of the seismic data as matrices or tensors the rank of the seismic data computed by singular value decomposition increases with noise or missing traces thus we apply low rank matrix completion mc with a designed texture patch transformation to 3d seismic data reconstruction low rank components capture geometrically meaningful structures in seismic data that encompass conventional local features such as events and dips the low rank mc is based on nuclear norm minimization an efficient l1 norm minimizing algorithm

f x adaptive seismic trace interpolation we use exponentially weighted recursive least squares to estimate adaptive prediction filters for frequency space f x seismic interpolation adaptive prediction filters can model signals where the dominant wavenumbers vary in space this concept leads to an f x interpolation method that does not require windowing strategies for optimal results in other words adaptive prediction filters can be used to interpolate waveforms that have spatially variant dips the interpolation method s performance depends on two parameters filter length and forgetting factor we pay particular attention to selection of the forgetting factor because it controls the algorithm s adaptability to changes in local dip finally we use synthetic and real data examples to illustrate the performance of the proposed adaptive f x interpolation method

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

4dcaf a temporal approach for denoising hyperspectral image sequences abstract as a consequence of the fast development of sensor technology in the last decade it is now possible to acquire sequences of hyperspectral images at reasonable frame rates however these sequences may be significantly corrupted by noise especially when the spectral coverage of the data reaches the thermal domain while there is an abundant literature on denoising of standard video sequences or denoising of still hyperspectral images very little has been published on denoising hyperspectral sequences this paper presents a novel denoising method for actual hyperspectral sequences the approach is based on spatio spectral temporal cellular automata based filtering it presents several advantages especially the fact that the cellular automaton used is able to contemplate information concerning the type of noise present through the use of specific sequences to tune the algorithm it also considers temporal information by means of a spatio temporal neighborhood when processing each pixel of the sequence the proposed method outperforms several state of the art algorithms on both simulated and real sequences

seismic trace interpolation in the f x domain interpolation of seismic traces is an effective means of improving migration when the data set exhibits spatial aliasing a major difficulty of standard interpolation methods is that they depend on the degree of reliability with which the various geological events can be separated in this respect a multichannel interpolation method is described which requires neither a priori knowledge of the directions of lateral coherence of the events nor estimation of these directions the method is based on the fact that linear events present in a section made of equally spaced traces may be interpolated exactly regardless of the original spatial interval without any attempt to determine their true dips the predictability of linear events in the f x domain allows the missing traces to be expressed as the output of a linear system the input of which consists of the recorded traces the interpolation operator is obtained by solving a set of linear equations whose coefficients depend only on the spectrum of the spatial prediction filter defined by the recorded traces synthetic examples show that this method is insensitive to random noise and that it correctly handles curvatures and lateral amplitude variations assessment of the method with a real data set shows that the interpolation yields an improved migrated section

bialgebras for structural operational semantics bialgebras and distributive laws are an abstract categorical framework to study various flavors of structural operational semantics this paper aims to introduce the reader to the basics of bialgebras for operational semantics and to sketch the state of the art in this research area

noncausal spatial prediction filtering for random noise reduction on 3 d poststack data a common practice in random noise reduction for 2 d data is to use pseudononcausal pnc 1 d prediction filters at each temporal frequency a 1 d pnc filter is a filter that is forced to be two sided by placing a conjugate reversed version of a 1 d causal filter in front of itself with a zero between the two for 3 d data a similar practice is to solve for two 2 d causal one quadrant filters at each frequency slice a 2 d pnc filter is formed by putting a conjugate flipped version of each quadrant filter in a quadrant opposite itself the center sample of a 2 d pnc filter is zero this paper suggests the use of 1 d and 2 d noncausal nc prediction filters instead of pnc filters for random noise attenuation where an nc filter is a two sided filter solved from one set of normal equations the number of negative and positive lags in the nc filter is the same the center sample of the filter is zero the nc prediction filters are more center loaded than pnc filters they are conjugate symmetric as pnc fi

fast wavelet transforms and numerical algorithms i a class of algorithms is introduced for the rapid numerical application of a class of linear operators to arbitrary vectors previously published schemes of this type utilize detailed analytical information about the operators being applied and are specific to extremely narrow classes of matrices in contrast the methods presented here are based on the recently developed theory of wavelets and are applicable to all calderon zygmund and pseudo differential operators the algorithms of this paper require order o n or o n log n operations to apply an n n matrix to a vector depending on the particular operator and the version of the algorithm being used and our numerical experiments indicate that many previously intractable problems become manageable with the techniques presented here

tensor completion based on nuclear norm minimization for 5d seismic data reconstruction abstractmany standard seismic data processing and imaging techniques require regularly sampled data prestack seismic data are multidimensional signals that can be represented via low rank fourth order tensors in the frequency space f x domain we propose to adopt tensor completion strategies to recover unrecorded observations and to improve the signal to noise ratio of prestack seismic volumes tensor completion can be posed as an inverse problem and solved by minimizing a convex objective function the objective function contains two terms a data misfit and a nuclear norm the data misfit measures the proximity of the reconstructed seismic data to the observations the nuclear norm constraints the reconstructed data to be a low rank tensor in essence we solve the prestack seismic reconstruction problem via low rank tensor completion the cost function of the problem is minimized using the alternating direction method of multipliers we present synthetic examples to illustrate the behavior of the al

joint image denoising using adaptive principal component analysis and self similarity the non local means nlm has attracted enormous interest in image denoising problem in recent years in this paper we propose an efficient joint denoising algorithm based on adaptive principal component analysis pca and self similarity that improves the predictability of pixel intensities in reconstructed images the proposed algorithm consists of two successive steps without iteration the low rank approximation based on parallel analysis and the collaborative filtering first for a pixel and its nearest neighbors the training samples in a local search window are selected to form the similar patch group by the block matching method next it is factorized by singular value decomposition svd whose left and right orthogonal basis denote local and non local image features respectively the adaptive pca automatically chooses the local signal subspace dimensionality of the noisy similar patch group in the svd domain by the refined parallel analysis with monte carlo simulation thus image features can be well preserved after dimensionality reduction and simultaneously the noise is almost eliminated then after the inverse svd transform the denoised image is reconstructed from the aggregate filtered patches by the weighted average method finally the collaborative wiener filtering is used to further remove the noise the experimental results validate its generality and effectiveness in a wide range of the noisy images the proposed algorithm not only produces very promising denoising results that outperforms the state of the art methods in most cases but also adapts to a variety of noise levels

optimal inequalities in probability theory a convex optimization approach we propose a semidefinite optimization approach to the problem of deriving tight moment inequalities for p x in s for a set s defined by polynomial inequalities and a random vector x defined on omega subseteq cal r n that has a given collection of up to kth order moments in the univariate case we provide optimal bounds on p x in s when the first k moments of x are given as the solution of a semidefinite optimization problem in k 1 dimensions in the multivariate case if the sets s and omega are given by polynomial inequalities we obtain an improving sequence of bounds by solving semidefinite optimization problems of polynomial size in n for fixed k we characterize the complexity of the problem of deriving tight moment inequalities we show that it is np hard to find tight bounds for k geq 4 and omega cal r n and for k geq 2 and omega cal r n when the data in the problem is rational for k 1 and omega cal r n we show that we can find tight upper bounds by solving n convex optimization problems when the set s is convex and we provide a polynomial time algorithm when s and omega are unions of convex sets over which linear functions can be optimized efficiently for the case k 2 and omega cal r n we present an efficient algorithm for finding tight bounds when s is a union of convex sets over which convex quadratic functions can be optimized efficiently

minimum weighted norm interpolation of seismic records in seismic data processing we often need to interpolate and extrapolate data at missing spatial locations the reconstruction problem can be posed as an inverse problem where from inadequate and incomplete data we attempt to reconstruct the seismic wavefield at locations where measurements were not acquired we propose a wavefield reconstruction scheme for spatially band limited signals the method entails solving an inverse problem where a wavenumber domain regularization term is included the regularization term constrains the solution to be spatially band limited and imposes a prior spectral shape the numerical algorithm is quite efficient since the method of conjugate gradients in conjunction with fast matrix vector multiplications implemented via the fast fourier transform fft is adopted the algorithm can be used to perform multidimensional reconstruction in any spatial domain

comparing operational models of name passing process calculi we study three operational models of name passing process calculi coalgebras on pre sheaves indexed labelled transition systems and history dependent automata the coalgebraic model is considered both for presheaves over the category of finite sets and injections and for its subcategory of atomic sheaves known as the schanuel topos each coalgebra induces an indexed labelled transition system such transition systems are characterised relating the coalgebraic approach to an existing model of name passing further we consider internal labelled transition systems within the sheaf topos and axiomatise a class that is in precise correspondence with the coalgebraic and the indexed labelled transition system models by establishing and exploiting the equivalence of the schanuel topos with a category of named sets these internal labelled transition systems are also related to the theory of history dependent automata

denoise diffusion weighted images using higher order singular value decomposition noise usually affects the reliability of quantitative analysis in diffusion weighted dw magnetic resonance imaging mri especially at high b values and or high spatial resolution higher order singular value decomposition hosvd has recently emerged as a simple effective and adaptive transform to exploit sparseness within multidimensional data in particular the patch based hosvd denoising has demonstrated superb performance when applied to t1 t2 and proton density weighted mri data in this study we aim to investigate the feasibility of denoising dw data using the hosvd transform with the low signal to noise ratio in typical dw data the patch based hosvd denoising suffers from stripe artifacts in homogeneous regions because of the hosvd bases learned from the noisy patches to address this problem we propose a novel denoising method it first introduces a global hosvd based denoising as a prefiltering stage to guide the subsequent patch based hosvd denoising stage the hosvd bases from the patch groups in prefiltered images are then used to transform the noisy patch groups in original dw data experiments were performed using simulated and in vivo dw data results show that the proposed method significantly reduces stripe artifacts compared with conventional patch based hosvd denoising methods and outperforms two state of the art denoising methods in terms of denoising quality and diffusion parameters estimation

a fast reduced rank interpolation method for prestack seismic volumes that depend on four spatial dimensions rank reduction strategies can be employed to attenuate noise and for prestack seismic data regularization we present a fast version of cadzow reduced rank reconstruction method cadzow reconstruction is implemented by embedding 4d spatial data into a level four block toeplitz matrix rank reduction of this matrix via the lanczos bidiagonalization algorithm is used to recover missing observations and to attenuate random noise the computational cost of the lanczos bidiagonalization is dominated by the cost of multiplying a level four block toeplitz matrix by a vector this is efficiently implemented via the 4d fast fourier transform the proposed algorithm significantly decreases the computational cost of rank reduction methods for multidimensional seismic data denoising and reconstruction synthetic and field prestack data examples are used to examine the effectiveness of the proposed method

image denoising by sparse 3 d transform domain collaborative filtering we propose a novel image denoising strategy based on an enhanced sparse representation in transform domain the enhancement of the sparsity is achieved by grouping similar 2d image fragments e g blocks into 3d data arrays which we call groups collaborative altering is a special procedure developed to deal with these 3d groups we realize it using the three successive steps 3d transformation of a group shrinkage of the transform spectrum and inverse 3d transformation the result is a 3d estimate that consists of the jointly filtered grouped image blocks by attenuating the noise the collaborative filtering reveals even the finest details shared by grouped blocks and at the same time it preserves the essential unique features of each individual block the filtered blocks are then returned to their original positions because these blocks are overlapping for each pixel we obtain many different estimates which need to be combined aggregation is a particular averaging procedure which is exploited to take advantage of this redundancy a significant improvement is obtained by a specially developed collaborative wiener filtering an algorithm based on this novel denoising strategy and its efficient implementation are presented in full detail an extension to color image denoising is also developed the experimental results demonstrate that this computationally scalable algorithm achieves state of the art denoising performance in terms of both peak signal to noise ratio and subjective visual quality

vines a new graphical model for dependent random variables a new graphical model called a vine for dependent random variables is introduced vines generalize the markov trees often used in modelling high dimensional distributions they differ from markov trees and bayesian belief nets in that the concept of conditional independence is weakened to allow for various forms of conditional dependence

comments on image denoising by sparse 3 d transform domain collaborative filtering in order to resolve the problem that the denoising performance has a sharp drop when noise standard deviation reaches 40 proposed to replace the wavelet transform by the dct in this comment we argue that this replacement is unnecessary and that the problem can be solved by adjusting some numerical parameters we also present this parameter modification approach here experimental results demonstrate that the proposed modification achieves better results in terms of both peak signal to noise ratio and subjective visual quality than the original method for strong noise

a patch based low rank tensor approximation model for multiframe image denoising abstract compared with matrix tensor is a more natural representation for multiframe image such as hyperspectral image and mri image low rankness of tensor is essential to describe the intrinsic geometrical structure of these data patch based low rank models have shown their ability to exploit spatial redundancy of computer vision data especially for natural image denoising however most of the existed patch based matrix models are based on two dimensional low rankness which cannot fully reveal the correlation of every direction in high order multiframe images the existed patch based tensor models either need additional assumptions or need svd in every loop of iteration which is computationally expensive in this paper we propose a novel patch based model to recover a low rank tensor by simultaneously performing low rank matrix factorizations to the all mode matricizations of the underlying low rank tensor an augmented lagrangian alternating minimization algorithm is implemented to solve the model along with two adaptive rank adjusting strategies when the exact rank is unknown we apply the proposed algorithm to multiframe image denoising by exploiting the nonlocal self similarity experimental results show that our algorithm can better preserve the sharpness of important image structures and outperforms several state of the art denoising methods

seismic trace interpolation in the f x y domain seismic trace interpolation is implemented as a 2 d x y spatial prediction performed separately on each frequency f slice this so called f x y domain trace interpolation method is based on the relation that the linear prediction lp operator estimated at a given frequency may be used to predict data at a higher frequency but a smaller trace spacing the relationship originally given for thef x domain trace interpolation is successfully extended to the f x y domain the extension is achieved by masking the data samples selectively from the input frequency slice to design the lp operators two interpolation algorithms using the full step and the fractional step predictions respectively are developed both methods use an all azimuth prediction in the x y domain but the fractional step prediction method is computationally more efficient while the interpolation method can be applied to a common offset cube of 3 d seismic it can also be applied to 2 d seismic traces for prestack data processing sy

seismic data interpolation using a fast generalized fourier transform we have found a fast and efficient method for the interpolation of nonstationary seismic data the method uses the fast generalized fourier transform fgft to identify the space wavenumber evolution of nonstationary spatial signals at each temporal frequency the nonredundant nature of fgft renders a big computational advantage to this interpolation method a least squares fitting scheme is used next to retrieve the optimal fgft coefficients representative of the ideal interpolated data for randomly sampled data on a regular grid we seek a sparse representation of fgft coefficients to retrieve the missing samples in addition to interpolate the regularly sampled seismic data at a given frequency we use a mask function derived from the fgft coefficients of the low frequencies synthetic and real data examples can be used to examine the performance of the method

antileakage least squares spectral analysis for seismic data regularization and random noise attenuation spatial transformation of irregularly sampled data series to regularly sampled data series is a challenging problem in many areas such as seismology the classical fourier analysis is limited to regularly sampled data series on the other hand the least squares spectral analysis lssa can analyze irregularly sampled data series although the lssa method takes into account the correlation among the sinusoidal basis functions of irregularly spaced series it still suffers from the problem of spectral leakage energy leaks from one spectral peak into another we propose an iterative method called antileakage lssa to attenuate the spectral leakage and consequently regularize irregular data series in this method we first search for a spectral peak with the highest energy and then we remove suppress it from the original data series in the next step we search for a new peak with the highest energy in the residual data series and remove the new and the old components simultaneously from the original data

efficient simultaneous wave equation statics and trace regularization by series approximation to address the problems of irregular trace spacing and statics correction simultaneous regularization and wave equation statics we statics are implemented by least squares inversion in general inversion is found to be intractable in three dimensions so series approximation is made to reduce significantly the number of required integrals the resulting operator is suitable for direct inversion or for use with gradient methods real and synthetic data are used to determine the viability of the inversion for synthetic data even for severe velocity variation and topography inversion converges to an acceptable solution and aliasing is reduced significantly similarly for real data inversion is found to return an antialiased regularized result with we statics applied

stochastic subsampling for factorizing huge matrices we present a matrix factorization algorithm that scales to input matrices with both huge number of rows and columns learned factors may be sparse or dense and or nonnegative which makes our algorithm suitable for dictionary learning sparse component analysis and nonnegative matrix factorization our algorithm streams matrix columns while subsampling them to iteratively learn the matrix factors at each iteration the row dimension of a new sample is reduced by subsampling resulting in lower time complexity compared to a simple streaming algorithm our method comes with convergence guarantees to reach a stationary point of the matrix factorization problem we demonstrate its efficiency on massive functional magnetic resonance imaging data 2 tb and on patches extracted from hyperspectral images 103 gb for both problems which involve different penalties on rows and columns we obtain significant speed ups compared to state of the art algorithms

comparisons of interpolation methods the purpose of this article is to illustrate the characteristics of various interpolation methods seismic data need to be interpolated when the spatial sampling of acquired data is coarser than the spatial sampling required for a multichannel process this multichannel process can be as simple as stacking traces to reduce coherent noise or as complex as prestack depth migration interpolation requires some assumptions about the character of the seismic data one assumption in the methods considered for this article is that seismic events are linear in practice the data are not perfectly linear and we will show later the results of violating the assumption of linearity

model based interferometric interpolation method we have proposed a two stage model based interferometric interpolation method for filling in gaps in marine seismic data the first stage is creating virtual traces and the second stage is utilizing modified virtual traces for interpolation there are three steps for creating a virtual trace first set the virtual trace s source and receiver coordinates and retrieve two common receiver gathers crg from existing data at least one crg should be obtained otherwise our method cannot be performed second if only one crg is obtained then a synthetic crg should be generated using known velocity model e g water layer model third the virtual trace is created by summing correlated trace pairs over all identical source positions in two crgs when all virtual traces are created a least squares matching filter or a nonstationary prediction error filter pef should be used together with virtual traces to do the interpolation if the trace gap is small or the subsurface geology is simple the local match

regularized field map estimation in mri in fast magnetic resonance mr imaging with long readout times such as echo planar imaging epi and spiral scans it is important to correct for the effects of field inhomogeneity to reduce image distortion and blurring such corrections require an accurate field map a map of the off resonance frequency at each voxel standard field map estimation methods yield noisy field maps particularly in image regions with low spin density this paper describes regularized methods for field map estimation from two or more mr scans having different echo times these methods exploit the fact that field maps are generally smooth functions the methods use algorithms that decrease monotonically a regularized least squares cost function even though the problem is highly nonlinear results show that the proposed regularized methods significantly improve the quality of field map estimates relative to conventional unregularized methods

multi scale segmentation and surface fitting for measuring 3 d macular holes macular holes are blinding conditions where a hole develops in the central part of retina resulting in reduced central vision the prognosis and treatment options are related to a number of variables including the macular hole size and shape high resolution spectral domain optical coherence tomography allows precise imaging of the macular hole geometry in three dimensions but the measurement of these by human observers is time consuming and prone to high inter and intra observer variability being characteristically measured in 2 d rather than 3 d we introduce several novel techniques to automatically retrieve accurate 3 d measurements of the macular hole including surface area base area base diameter top area top diameter height and minimum diameter specifically we introduce a multi scale 3 d level set segmentation approach based on a state of the art level set method and we introduce novel curvature based cutting and 3 d measurement procedures the algorithm is fully automatic and we validate our extracted measurements both qualitatively and quantitatively where our results show the method to be robust across a variety of scenarios our automated processes are considered a significant contribution for clinical applications

a congruence rule format for name passing process calculi abstract we introduce a gsos like rule format for name passing process calculi specifications in this format correspond to theories in nominal logic the intended models of such specifications arise by initiality from a general categorical model theory for operational semantics given in this rule format a natural behavioural equivalence a form of open bisimilarity is a congruence

compositional sos and beyond a coalgebraic view of open systems in this paper we address the issue of providing a structured coalgebra presentation of transition systems with algebraic structure on states determined by an equational specification more precisely we aim at representing such systems as coalgebras for an endofunctor on the category of algebras the systems we consider are specified by using arbitrary sos rules which in general do not guarantee that bisimilarity is a congruence we first show that the structured coalgebra representation works only for systems where transitions out of complex states can be derived from transitions out of corresponding component states this decomposition property of transitions indeed ensures that bisimilarity is a congruence for a system not satisfying this requirement next we propose a closure construction which adds context transitions i e transitions that spontaneously embed a state into a bigger context or vice versa the notion of bisimulation for the enriched system coincides with the notion of dynamic bisimilarity for the original one i e with the coarsest bisimulation which is a congruence this is sufficient to ensure that the structured coalgebra representation works for the systems obtained as result of the closure construction

3d interpolation of irregular data with a pocs algorithm seismic surveys generally have irregular areas where data cannot be acquired these data should often be interpolated a projection onto convex sets pocs algorithm using fourier transforms allows interpolation of irregularly populated grids of seismic data with a simple iterative method that produces high quality results the original 2d image restoration method the gerchberg saxton algorithm is extended easily to higher dimensions and the 3d version of the process used here produces much better interpolations than typical 2d methods the only parameter that makes a substantial difference in the results is the number of iterations used and this number can be overestimated without degrading the quality of the results this simplicity is a significant advantage because it relieves the user of extensive parameter testing although the cost of the algorithm is several times the cost of typical 2d methods the method is easily parallelized and still completely practical

time migration velocity analysis by velocity continuation time migration velocity analysis can be performed by velocity continuation an incremental process that transforms migrated seismic sections according to changes in the migration velocity velocity continuation enhances residual normal moveout correction by properly taking into account both vertical and lateral movements of events on seismic images finite difference and spectral algorithms provide efficient practical implementations for velocity continuation synthetic and field data examples demonstrate the performance of the method and confirm theoretical expectations

localization of the complex spectrum the s transform the s transform which is introduced in the present correspondence is an extension of the ideas of the continuous wavelet transform cwt and is based on a moving and scalable localizing gaussian window it is shown to have some desirable characteristics that are absent in the continuous wavelet transform the s transform is unique in that it provides frequency dependent resolution while maintaining a direct relationship with the fourier spectrum these advantages of the s transform are due to the fact that the modulating sinusoids are fixed with respect to the time axis whereas the localizing scalable gaussian window dilates and translates