continuous time equivalents of welch bound equality sequences the theory developed on the sequence optimization for equal power code division multiple access cdma systems is generalized in this paper unlike previous works where discrete time or vector channel models are predominantly employed the overloaded channels are modeled as strictly band limited continuous time multiple access channels corrupted by additive white gaussian noise awgn after being posed as a multiple input single output miso joint transmitter and receiver optimization problem with the total mean squared error mse as the objective functional to be minimized the variational problem is solved by using a frequency domain approach it is shown that there exist continuous time equivalents of welch bound equality cte wbe sequences as the jointly optimum transmit waveforms and that the matched filters are the jointly optimum receivers the user capacity of the band limited channels is characterized by a necessary and sufficient condition for the admissibility of users into the system in terms of the channel load the received signal to noise ratio and the signal to interference plus noise ratio sinr requirement it is also shown that cte wbe sequences achieve the lower bound on the continuous time equivalent of total squared correlation cte tsc

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

dual gabor frames theory and computational aspects we consider a general method for constructing dual gabor elements different from the canonical dual our approach is based on combining two gabor frames such that the generated frame type operator s sub g spl gamma is nonsingular we provide necessary and sufficient conditions on the gabor window functions g and spl gamma such that s sub g spl gamma is nonsingular for rational oversampling considering both the continuous time and the discrete time settings in contrast to the frame operator the operator s sub g spl gamma is in general not positive therefore all results in gabor analysis that are based on the positivity of the frame operator cannot be applied directly the advantage of the proposed characterization is that the algebraic system for computing the gabor dual elements preserves the high structure of usual gabor frames leading to computationally efficient algorithms in particular we consider examples in which both the condition number and the computational complexity in computing the proposed dual gabor elements decrease in comparison to the canonical dual gabor elements

noncooperative iterative mmse beamforming algorithms for ad hoc networks an asynchronous unicast ad hoc network is considered where each node i is equipped with a receive transmit beam former pair w sub i g sub i designed under a quality of service qos snr constraint it is first shown that the minimum sum power beamformers for the network satisfy a weak duality condition in which the pairs g sub i sup opt w sub i sup opt achieve the same sum power as the primal network however the optimum receive beamformer w sub i sup opt is not in general equal to g sub i sup opt in contrast to the case of cellular and time division duplexing networks iterative minimum mean square error immse beamforming algorithms are then proposed in which w sub i g sub i is enforced these algorithms are shown to be instances of the power algorithm in which gi is the maximizing eigenvector of an snr related objective matrix the immse algorithm can also be viewed as a noncooperative beamforming game in which the payoff includes normalized snr and the tax is related to interference caused at other nodes the existence of fixed points nash equilibria is proved for immse furthermore fixed points of immse are shown to satisfy the first order necessary conditions for optimization using a network lagrangian the immse game is modified to yield a sequential distortionless response beamforming algorithm which is shown to be convergent using a total interference function extensive simulation results illustrate that immse yields better power efficiency than a greedy noncooperative snr maximizing game

rapid development and adjoining of transient finite element models abstract recent advances in high level finite element systems have allowed for the symbolic representation of discretisations and their efficient automated implementation as model source code this allows for the extremely compact implementation of complex non linear models in a handful of lines of high level code in this work we extend the high level finite element fenics system to introduce an abstract representation of the temporal discretisation this enables the similarly rapid development of transient finite element models efficiency is achieved via aggressive optimisations that exploit the temporal structure such as automated pre assembly and caching of forms and the robust re use of matrix factorisations and preconditioner data the resulting models are as fast or faster than hand optimised finite element codes the high level representation of the system remains extremely compact and easily manipulated this structure is exploited to derive the associated discrete adjoint model automatically with the adjoint model inheriting the performance advantages of the forward model combined this provides a system for the rapid development of efficient transient models together with their discrete adjoints

discrete gabor structures and optimal representations the idea of gabor s 1946 signal expansion is to represent a signal in terms of a discrete set of time shifted and frequency modulated signals that are localized in the time frequency or phase space we present detailed descriptions of the block and banded structures for the gabor matrices based on the explicit descriptions of the sparsity of such matrices we can establish the sparse form of the gabor matrix and obtain the dual gabor atom mother wavelet the inverse of the gabor frame operator and carry out the discrete finite gabor transform in a very efficient way some explicit sufficient and also necessary conditions are derived for a gabor atom g to generate a gabor frame with respect to a tf lattice a b

complete discrete 2 d gabor transforms by neural networks for image analysis and compression a three layered neural network is described for transforming two dimensional discrete signals into generalized nonorthogonal 2 d gabor representations for image analysis segmentation and compression these transforms are conjoint spatial spectral representations which provide a complete image description in terms of locally windowed 2 d spectral coordinates embedded within global 2 d spatial coordinates in the present neural network approach based on interlaminar interactions involving two layers with fixed weights and one layer with adjustable weights the network finds coefficients for complete conjoint 2 d gabor transforms without restrictive conditions in wavelet expansions based on a biologically inspired log polar ensemble of dilations rotations and translations of a single underlying 2 d gabor wavelet template image compression is illustrated with ratios up to 20 1 also demonstrated is image segmentation based on the clustering of coefficients in the complete 2 d gabor transform

frame theory based analysis and design of oversampled filter banks direct computational method this paper studies the frames corresponding to oversampled filter banks fbs for this class of fb frames we present a state space parameterization of perfect reconstruction fb frames and explicit and numerically efficient formulas to compute the tightest frame bounds to obtain the dual fb frame and to construct a tight paraunitary fb frame from a given untight nonparaunitary fb frame the derivation uses well developed techniques from modern control theory which results in the unified formulas for generic infinite impulse response iir and finite impulse response fir fbs these formulas involve only algebraic manipulations of real matrices and can be computed efficiently reliably and exactly without the approximation required in the existing methods for generic fbs the results provide a unified framework for frame theory based analysis and systematic design of oversampled filter banks

optimum sequence multisets for synchronous code division multiple access channels it is shown that the sum capacity of the symbol synchronous code division multiple access channel with equal average input energy constraints is maximized precisely by those spreading sequence multisets that meet welch s lower bound on total squared correlation it is further shown that the symmetric capacity of the channel determined by these same sequence multisets is equal to the sum capacity

iterative construction of optimum signature sequence sets in synchronous cdma systems optimum signature sequence sets that maximize the capacity of single cell synchronous code division multiple access cdma systems have been identified optimum signature sequences minimize the total squared correlation tsc they form a set of orthogonal sequences if the number of users is less than or equal to the processing gain and a set of welch 1994 bound equality wbe sequences otherwise we present an algorithm where users update their transmitter signature sequences sequentially in a distributed fashion by using available receiver measurements we show that each update decreases the tsc of the set and produces better signature sequence sets progressively we prove that the algorithm converges to a set of orthogonal signature sequences when the number of users is less than or equal to the processing gain we observe and conjecture that the algorithm converges to a wbe set when the number of users is greater than the processing gain at each step the algorithm replaces one signature sequence from the set with the normalized minimum mean squared error mmse receiver corresponding to that signature sequence since the mmse filter can be obtained by a distributed algorithm for each user the proposed algorithm is amenable to distributed implementation

inversion of block circulant matrices and circular array approach closed form expressions of the inverse of a block circulant matrix bcm are well known such expressions are derived here following two alternative procedures which are based on the discrete fourier transform dft and appear to be simple and brief when compared to previously published procedures in the case of circulant matrices of scalars the formulas of inversion are derived using the theory of circular arrays and this approach suggested an extension of the dft to the bcm case

a unified approach to dual gabor windows in this paper we describe a new method for studying the invertibility of gabor frame operators our approach can be applied to both the continuous on rd and the finite discrete setting in the latter case we obtain algorithms for directly computing the inverse of gabor frame type matrices equivalent to those known in the literature the framework we propose can also be used to derive other known results in gabor theory in a unified way such as the zibulski zeevi representation the approach we suggest is based on an adequate splitting of the twisted convolution which in turn provides another twisted convolution on a finite cyclic group by analogy with the twisted convolution of finite discrete signals we derive a mapping between the sequence space and a matrix algebra which preserves the algebraic structure in this way the invertibility problem reduces to the analysis of finite matrices whose entries are sequences supported on corresponding cosets using cramer s rule and proving wiener s lemma for this special class of matrices we obtain an invertibility criterion that can be applied to a variety of different settings this alternative approach provides further insight into gabor frames as well as a unified framework for gabor analysis

a stochastic newton mcmc method for large scale statistical inverse problems with application to seismic inversion we address the solution of large scale statistical inverse problems in the framework of bayesian inference the markov chain monte carlo mcmc method is the most popular approach for sampling the posterior probability distribution that describes the solution of the statistical inverse problem mcmc methods face two central difficulties when applied to large scale inverse problems first the forward models typically in the form of partial differential equations that map uncertain parameters to observable quantities make the evaluation of the probability density at any point in parameter space very expensive and second the high dimensional parameter spaces that arise upon discretization of infinite dimensional parameter fields make the exploration of the probability density function prohibitive the challenge for mcmc methods is to construct proposal functions that simultaneously provide a good approximation of the target density while being inexpensive to manipulate here we present a so called stoch

rank 2 optimal adaptive design of binary spreading codes over the real complex field the spreading code that maximizes the signal to interference plus noise ratio sinr at the output of the maximum sinr linear filter is the minimum eigenvalue eigenvector of the interference autocovariance matrix in the context of binary spreading codes the maximization problem is np hard with complexity exponential in the code length a new method for the optimization of binary spreading codes under a rank 2 approximation of the inverse interference autocovariance matrix is presented where the rank 2 optimal binary code is obtained in lower than quadratic complexity significant sinr performance improvement is demonstrated over the common binary hard limited eigenvector design which is shown to be equivalent to the rank 1 optimal solution

a hessian based method for uncertainty quantification in global ocean state estimation national science foundation u s collaboration in mathematical geosciences grant 0934404

cdma codeword optimization interference avoidance and convergence via class warfare interference avoidance has been shown to reduce total square correlation tsc for given ensembles of user signature waveforms codewords in a synchronous code division multiple access cdma system in all experiments we have conducted sequential application of interference avoidance produces an optimal codeword set when starting from randomly chosen initial codewords here we provide the first formal proof of convergence to optimal codeword ensembles for greedy interference avoidance algorithms augmented by a technique called class warfare whereby users which reside in more heavily loaded areas of the signal space purposely interfere with attack the reception of users in less crowded areas coordination of deliberate interference by a complete class of aggrieved user is also sometimes necessary such attacks and subsequent codeword adjustment by attacked users are shown to strictly decrease tsc along the way we also show using linear algebra and a variant of stochastic ordering equivalence between minimization of tsc and maximization of sum capacity

optimal signature design for spread spectrum steganography for any given host image or group of host images and any block transform domain of interest we find the signature vector that when used for spread spectrum ss message embedding maximizes the signal to interference plus noise ratio sinr at the output of the corresponding maximum sinr linear filter we establish that under a colored gaussian assumption on the transform domain host data the same derived signature minimizes host distortion for any target message recovery error rate and maximizes the shannon capacity of the covert steganographic link then we derive jointly optimal signature and linear processor designs for ss embedding in linearly modified transform domain host data and demonstrate orders of magnitude improvement over current ss steganographic practices optimized multisignature multimessage embedding in the same host data is studied as well

a bayesian approach to estimate uncertainty for full waveform inversion using a priori information from depth migration abstractfull waveform inversion fwi enables us to obtain high resolution subsurface images however estimating model uncertainties associated with this technique is still a challenging problem we have used a bayesian inference framework to estimate model uncertainties associated with fwi the uncertainties were assessed based on an a posteriori covariance operator evaluated at the maximum a posteriori model for the prior distribution we have used a spatially nonstationary covariance operator based on a plane wave construction with local dips measured from migrated images preconditioned frequency domain fwi was used to estimate the maximum a posteriori model efficient manipulation of the posterior covariance was based on a low rank approximation of the data misfit hessian preconditioned by the prior covariance operator the strong decay of the singular values indicated that data were mostly informative about a low dimensional subspace of model parameters to reduce computational cost of the random

optimal sequences for cdma under colored noise a schur saddle function property we consider direct sequence code division multiple access ds cdma modeling interference from users communicating with neighboring base stations by additive colored noise we consider two types of receiver structures first we consider the information theoretically optimal receiver and use the sum capacity of the channel as our performance measure second we consider the linear minimum mean square error lmmse receiver and use the signal to interference ratio sir of the estimate of the symbol transmitted as our performance measure our main result is a constructive characterization of the possible performance in both these scenarios a central contribution of this characterization is the derivation of a qualitative feature of the optimal performance measure in both the scenarios studied we show that the sum capacity is a saddle function it is convex in the additive noise covariances and concave in the user received powers in the linear receiver case we show that the mini average power required to meet a set of target performance requirements of the users is a saddle function it is convex in the additive noise covariances and concave in the set of performance requirements

representation of the inverse of a frame multiplier certain mathematical objects appear in a lot of scientific disciplines like physics signal processing and naturally mathematics in a general setting they can be described as frame multipliers consisting of analysis multiplication by a fixed sequence called the symbol and synthesis in this paper we show a surprising result about the inverse of such operators if any as well as new results about a core concept of frame theory dual frames we show that for semi normalized symbols the inverse of any invertible frame multiplier can always be represented as a frame multiplier with the reciprocal symbol and dual frames of the given ones furthermore one of those dual frames is uniquely determined and the other one can be arbitrarily chosen we investigate sufficient conditions for the special case when both dual frames can be chosen to be the canonical duals in connection to the above we show that the set of dual frames determines a frame uniquely furthermore for a given frame the union of all coefficients of its dual frames is dense in l2 we also introduce a class of frames called pseudo coherent frames which includes gabor frames and coherent frames and investigate invertible pseudo coherent frame multipliers allowing a classification for frame type operators for these frames finally we give a numerical example for the invertibility of multipliers in the gabor case

a game theoretic framework for interference avoidance various iterative algorithms for interference avoidance ia in networks with co located receivers suitable for distributed implementation have been proposed in the literature in this paper the ia problem is cast in a game theoretic framework and is formulated as a potential game this formulation accommodates previously proposed algorithms and in addition gives us a framework that enables the design of new distributed and convergent algorithms for ia including algorithms with nonidentical utility functions for the users two new convergence results for potential games are then derived the first result establishes the convergence of a class of potential games to the global solution while following best response iterations and when noise is added the second result establishes the convergence of potential games to the nash equilibria of the game while following random better response iterations the first result combined with the potential game formulation allows us to show that for a large class of network scenarios arbitrarily small noise assures the convergence of best response ia algorithms including the eigeniterations to an arbitrarily small neighborhood of the globally optimal signature sequence set the second result enables the design of reduced feedback mechanisms for ia that converge to desirable solutions

noninvertible gabor transforms time frequency analysis such as the gabor transform plays an important role in many signal processing applications the redundancy of such representations is often directly related to the computational load of any algorithm operating in the transform domain to reduce complexity it may be desirable to increase the time and frequency sampling intervals beyond the point where the transform is invertible at the cost of an inevitable recovery error in this paper we initiate the study of recovery procedures for noninvertible gabor representations we propose using fixed analysis and synthesis windows chosen e g according to implementation constraints and to process the gabor coefficients prior to synthesis in order to shape the reconstructed signal we develop three methods for signal recovery the first follows from the consistency requirement namely that the recovered signal has the same gabor representation as the input signal the second is based on minimization of a worst case error last we develop a recovery technique based on the assumption that the input signal lies in some subspace of l2 we show that for each of the criteria the manipulation of the transform coefficients amounts to a 2d twisted convolution which we show how to perform using a filter bank when the undersampling factor is an integer the processing reduces to standard 2d convolution we provide simulation results demonstrating the advantages and weaknesses of each of the algorithms

bayesian inverse problems with l_1 priors a randomize then optimize approach prior distributions for bayesian inference that rely on the l 1 norm of the parameters are of considerable interest in part because they promote parameter fields with less regularity than gaussian priors e g discontinuities and blockiness these l 1 type priors include the total variation tv prior and the besov space b 1 1 s prior and in general yield non gaussian posterior distributions sampling from these posteriors is challenging particularly in the inverse problem setting where the parameter space is high dimensional and the forward problem may be nonlinear this paper extends the randomize then optimize rto method an optimization based sampling algorithm developed for bayesian inverse problems with gaussian priors to inverse problems with l 1 type priors we use a variable transformation to convert an l 1 type prior to a standard gaussian prior such that the posterior distribution of the transformed parameters is amenable to metropolized sampling via rto we demonstrate thi

bounds on the maximum sinr of binary and quaternary code division in code division multiplexing the real complex valued sequence signature that maximizes the pre detection signal to interference plus noise ratio sinr at the output of the maximum sinr filter is simply the minimum eigenvalue eigenvector of the disturbance autocorrelation matrix sinr sequence optimization over a finite alphabet however is np hard in the sequence length in this paper we derive new easy to calculate upper and lower bounds on the sinr of the optimal binary and quaternary sequences that can serve as benchmarking tools for any suggested suboptimal designs

bayesian texture classification from indirect observations using fast sampling a bayesian method for texture model choice from blurred and noisy i e indirect observations is presented the textures are modeled by stationary random fields with various distribution laws either gaussian or scale mixtures of gaussians the power spectral densities of the fields are modeled by parametric functions and the aim is to select the most appropriate model among a set of candidates this is achieved by computing the a posteriori model probabilities through parameter marginalization the marginalization is done by sampling and harmonic mean approach considering separately each model in a within model sampling strategy the highly nonlinear dependency with respect to the parameters imposes the use of the metropolis hastings sampler moreover to achieve efficient sampling the paper proposes a new fast algorithm based on the fisher information matrix the fisher metropolis hastings

varying the time frequency lattice of gabor frames a gabor or weyl heisenberg frame for l 2 r d is generated by time frequency shifts of a square integrable function the gabor atom along a time frequency lattice the dual frame is again a gabor frame generated by the dual atom in general gabor frames are not stable under a perturbation of the lattice constants that is even for arbitrarily small changes of the parameters the frame property can be lost in contrast as a main result we show that this kind of stability does hold for gabor frames generated by a gabor atom from the modulation space m 1 r d which is a dense subspace of l 2 r d moreover in this case the dual atom depends continuously on the lattice constants in fact we prove these results for more general weighted modulation spaces as a consequence we obtain for gabor atoms from the schwartz class that the continuous dependence of the dual atom holds even in the schwartz topology also we complement these main results by corresponding statements for gabor riesz sequences and their biorthogonal system

optimal sequences and sum capacity of synchronous cdma systems the sum capacity of a multiuser synchronous cdma system is completely characterized in the general case of asymmetric user power constraints this solves the open problem posed by rupf and massey see ibid vol 40 p 1261 6 1994 which had solved the equal power constraint case we identify the signature sequences with real components that achieve sum capacity and indicate a simple recursive algorithm to construct them

hessian based adaptive sparse quadrature for infinite dimensional bayesian inverse problems abstract in this work we propose and analyze a hessian based adaptive sparse quadrature to compute infinite dimensional integrals with respect to the posterior distribution in the context of bayesian inverse problems with gaussian prior due to the concentration of the posterior distribution in the domain of the prior distribution a prior based parametrization and sparse quadrature may fail to capture the posterior distribution and lead to erroneous evaluation results by using a parametrization based on the hessian of the negative log posterior the adaptive sparse quadrature can effectively allocate the quadrature points according to the posterior distribution a dimension independent convergence rate of the proposed method is established under certain assumptions on the gaussian prior and the integrands dimension independent and faster convergence than o n 1 2 is demonstrated for a linear as well as a nonlinear inverse problem whose posterior distribution can be effectively approximated by a gaussian distribution at the map point

optimal orthogonal carriers and sum sinr sum capacity of the multiple access vector channel for the general correlated multiple access vector channel we derive algebraically the sum sinr signal to interference plus noise ratio optimal orthonormal set of carriers for any given set of carrier amplitudes if in addition the correlated multiple access channel is assumed gaussian the sum capacity optimal orthonormal carrier set design and the jointly sum capacity optimal orthonormal carrier and power assignment for a given power budget follow readily

maximizing the spectral efficiency of coded cdma under successive decoding we investigate the spectral efficiency achievable by random synchronous code division multiple access cdma with quaternary phase shift keying qpsk modulation and binary error control codes in the large system limit where the number of users the spreading factor and the code block length go to infinity for given codes we maximize spectral efficiency assuming a minimum mean square error mmse successive stripping decoder for the cases of equal rate and equal power users in both cases the maximization of spectral efficiency can be formulated as a linear program and admits a simple closed form solution that can be readily interpreted in terms of power and rate control we provide examples of the proposed optimization methods based on off the shelf low density parity check ldpc codes and we investigate by simulation the performance of practical systems with finite code block length

scalable posterior approximations for large scale bayesian inverse problems via likelihood informed parameter and state reduction two major bottlenecks to the solution of large scale bayesian inverse problems are the scaling of posterior sampling algorithms to high dimensional parameter spaces and the computational cost of forward model evaluations yet incomplete or noisy data the state variation and parameter dependence of the forward model and correlations in the prior collectively provide useful structure that can be exploited for dimension reduction in this setting both in the parameter space of the inverse problem and in the state space of the forward model to this end we show how to jointly construct low dimensional subspaces of the parameter space and the state space in order to accelerate the bayesian solution of the inverse problem as a byproduct of state dimension reduction we also show how to identify low dimensional subspaces of the data in problems with high dimensional observations these subspaces enable approximation of the posterior as a product of two factors i a projection of the posterior onto a low dimensional parameter subspace wherein the original likelihood is replaced by an approximation involving a reduced model and ii the marginal prior distribution on the high dimensional complement of the parameter subspace we present and compare several strategies for constructing these subspaces using only a limited number of forward and adjoint model simulations the resulting posterior approximations can rapidly be characterized using standard sampling techniques e g markov chain monte carlo two numerical examples demonstrate the accuracy and efficiency of our approach inversion of an integral equation in atmospheric remote sensing where the data dimension is very high and the inference of a heterogeneous transmissivity field in a groundwater system which involves a partial differential equation forward model with high dimensional state and parameters

dimension independent likelihood informed mcmc many bayesian inference problems require exploring the posterior distribution of high dimensional parameters that represent the discretization of an underlying function this work introduces a family of markov chain monte carlo mcmc samplers that can adapt to the particular structure of a posterior distribution over functions two distinct lines of research intersect in the methods developed here first we introduce a general class of operator weighted proposal distributions that are well defined on function space such that the performance of the resulting mcmc samplers is independent of the discretization of the function second by exploiting local hessian information and any associated low dimensional structure in the change from prior to posterior distributions we develop an inhomogeneous discretization scheme for the langevin stochastic differential equation that yields operator weighted proposals adapted to the non gaussian structure of the posterior the resulting dimension independent and likelihood informed dili mcmc samplers may be useful for a large class of high dimensional problems where the target probability measure has a density with respect to a gaussian reference measure two nonlinear inverse problems are used to demonstrate the efficiency of these dili samplers an elliptic pde coefficient inverse problem and path reconstruction in a conditioned diffusion

accelerating markov chain monte carlo with active subspaces the markov chain monte carlo mcmc method is the computational workhorse for bayesian inverse problems however mcmc struggles in high dimensional parameter spaces since its iterates must sequentially explore the high dimensional space this struggle is compounded in physical applications when the nonlinear forward model is computationally expensive one approach to accelerate mcmc is to reduce the dimension of the state space active subspaces are part of an emerging set of tools for subspace based dimension reduction an active subspace in a given inverse problem indicates a separation between a low dimensional subspace that is informed by the data and its orthogonal complement that is constrained by the prior with this information one can run the sequential mcmc on the active variables while sampling independently according to the prior on the inactive variables however this approach to increase efficiency may introduce bias we provide a bound on the hellinger distance between the true posterio

blind adaptive multiuser detection the decorrelating detector and the linear minimum mean square error mmse detector are known to be effective strategies to counter the presence of multiuser interference in code division multiple access channels in particular those multiuser detectors provide optimum near far resistance when training data sequences are available the mmse multiuser detector can be implemented adaptively without knowledge of signature waveforms or received amplitudes this paper introduces an adaptive multiuser detector which converges for any initialization to the mmse detector without requiring training sequences this blind multiuser detector requires no more knowledge than does the conventional single user receiver the desired user s signature waveform and its timing the proposed blind multiuser detector is made robust with respect to imprecise knowledge of the received signature waveform of the user of interest

existence conditions for discrete noncanonical multiwindow gabor schemes a class of noncanonical duals for multiwindow gabor mwg schemes encompassing both rational and integer oversampling of the gaborian combined time frequency space is considered using properties of gabor frame matrices gfm block discrete fourier transforms bdfts and results from number theory we use matrix factorization to establish existence conditions for noncanonical duals for both integer and rational oversampling rates in the signal domain for comparison and completeness of the results we also obtain the equivalent results in the finite zak transform fzt domain

ensuring convergence of the mmse iteration for interference avoidance to the global optimum viswanath and anantharam 1999 characterize the sum capacity of multiaccess vector channels for a given number of users received powers spreading gain and noise covariance matrix in a code division multiple access cdma system viswanath and anantharam present a combinatorial algorithm to generate a set of signature sequences that achieves the maximum sum capacity these sets also minimize a performance measure called generalized total square correlation tsc sub g ulukus and yates 2001 propose an iterative algorithm suitable for distributed implementation at each step one signature sequence is replaced by its linear minimum mean square error mmse filter this algorithm results in a decrease of tsc sub g at each step the mmse iteration has fixed points not only at the optimal configurations which attain the global minimum tsc sub g but also at other configurations which are suboptimal the authors of claim that simulations show that when starting with random sequences the algorithm converges to optimum sets of sequences but they give no formal proof we show that the tsc sub g function has no local minima in the sense that given any suboptimal set of sequences there exist arbitrarily close sets with lower tsc sub g therefore only the optimal sets are stable fixed points of the mmse iteration we define a noisy version of the mmse iteration as follows after replacing all the signature sequences one at a time by their linear mmse filter we add a bounded random noise to all the sequences using our observation about the tsc sub g function we can prove that if we choose the bound on the noise adequately making it decrease to zero the noisy mmse iteration converges to the set of optimal configurations with probability one for any initial set of sequences

user capacity of asynchronous cdma systems with matched filter receivers and optimum signature sequences for a symbol asynchronous but chip synchronous single cell code division multiple access cdma system we define a system wide quantity called the total squared asynchronous correlation tsac which for arbitrary signature sets depends on the users delay profile we develop a lower bound for tsac that is independent of the users delays we show that if the signature set achieves this tsac lower bound then the user capacity of the asynchronous cdma system using matched filters becomes the same as that of a single cell synchronous cdma system in this case there is no loss in user capacity due to asynchronism we present iterative signature adaptation algorithms which when executed sequentially by the users appear to converge to these optimum signature sequences however the existence for all user delay profiles of signature sequences achieving this lower bound remains a significant open problem

proposals which speed up function space mcmc abstract inverse problems lend themselves naturally to a bayesian formulation in which the quantity of interest is a posterior distribution of state and or parameters given some uncertain observations for the common case in which the forward operator is smoothing then the inverse problem is ill posed well posedness is imposed via regularization in the form of a prior which is often gaussian under quite general conditions it can be shown that the posterior is absolutely continuous with respect to the prior and it may be well defined on function space in terms of its density with respect to the prior in this case by constructing a proposal for which the prior is invariant one can define metropolis hastings schemes for mcmc which are well defined on function space stuart 2010 1 cotter et al 2 and hence do not degenerate as the dimension of the underlying quantity of interest increases to infinity e g under mesh refinement when approximating pde in finite dimensions however in practice despite the attractive theoretical properties of the currently available schemes they may still suffer from long correlation times particularly if the data is very informative about some of the unknown parameters in fact in this case it may be the directions of the posterior which coincide with the already known prior which decorrelate the slowest the information incorporated into the posterior through the data is often contained within some finite dimensional subspace in an appropriate basis perhaps even one defined by eigenfunctions of the prior we aim to exploit this fact and improve the mixing time of function space mcmc by careful rescaling of the proposal to this end we introduce two new basic methods of increasing complexity involving i characteristic function truncation of high frequencies and ii hessian information to interpolate between low and high frequencies the second more sophisticated version bears some similarities with recent methods which exploit local curvature information for example rmhmc girolami and calderhead 2011 3 and stochastic newton martin et al 2012 4 these ideas are illustrated with numerical experiments on the bayesian inversion of the heat equation and navier stokes equation given noisy observations

unsupervised texture segmentation using gabor filters abstract this paper presents a texture segmentation algorithm inspired by the multi channel filtering theory for visual information processing in the early stages of human visual system the channels are characterized by a bank of gabor filters that nearly uniformly covers the spatial frequency domain and a systematic filter selection scheme is proposed which is based on reconstruction of the input image from the filtered images texture features are obtained by subjecting each selected filtered image to a nonlinear transformation and computing a measure of energy in a window around each pixel a square error clustering algorithm is then used to integrate the feature images and produce a segmentation a simple procedure to incorporate spatial information in the clustering process is proposed a relative index is used to estimate the true number of texture categories

minimum total squared correlation quaternary signature sets new bounds and optimal designs we derive new bounds on the total squared correlation tsc of quaternary quadriphase signature sequence sets for all lengths l and set sizes k then for all k l we design minimum tsc optimal sets that meet the new bounds with equality direct numerical comparison with the tsc value of the recently obtained optimal binary sets shows under what k l realizations gains are materialized by moving from the binary to the quaternary code division multiplexing alphabet on the other hand comparison with the welch tsc value for real complex field sets shows that arguably not much is to be gained by raising the alphabet size above four for any k l the sum capacity as well as the maximum squared correlation and total asymptotic efficiency of minimum tsc quaternary sets is also evaluated in closed form and contrasted against the sum capacity of minimum tsc optimal binary and real complex sets

note on b splines wavelet scaling functions and gabor frames let g be a continuous compactly supported function on such that the integer translates of g constitute a partition of unity we show that the gabor system g a b with window g and time shift and frequency shift parameters a b 0 has no lower frame bound larger than 0 if b 2 3 and a 0 in particular g a b is not a gabor frame if g is a continuous compactly supported wavelet scaling function and if b 2 3 and a 0 we give an example for our result for the case that g b sub 1 the triangle function supported by 1 1 by showing pictures of the canonical dual corresponding to g a b where ab 1 4 and b crosses the lines n 2 3

an operator theory approach to the approximate duality of hilbert space frames abstract the purpose of this paper is to state some properties and applications of approximate duals constructed by bounded operators it is shown that there are close relationships between this kind of approximate duals and some concepts in frame theory such as the closeness of two frames nearly parseval and scalable frames we get some equivalent conditions for a frame to be close to another frame in terms of approximate duals also using approximate duals some conditions for a frame to be nearly parseval or scalable are derived moreover some other properties of approximate duals are obtained in particular some characterizations of them are stated and some of their applications for gabor frames and erasures are given especially the excesses of them are considered

finite step algorithms for constructing optimal cdma signature sequences a description of optimal sequences for direct spread code division multiple access ds cdma is a byproduct of recent characterizations of the sum capacity this paper restates the sequence design problem as an inverse singular value problem and shows that the problem can be solved with finite step algorithms from matrix theory it proposes a new one sided algorithm that is numerically stable and faster than previous methods

implementation of discretized gabor frames and their duals the usefulness of gabor frames depends on the easy computability of a suitable dual window this question is addressed under several aspects several versions of schulz s iterative algorithm for the approximation of the canonical dual window are analyzed for their numerical stability for gabor frames with totally positive windows or with exponential b splines a direct algorithm yields a family of exact dual windows with compact support it is shown that these dual windows converge exponentially fast to the canonical dual window

oversampling in the gabor scheme a method for calculating the coefficients of the gabor expansion in the case of oversampling is presented the method is based on the concept of frames and utilizes the zak transform as such the zak transform highlights the meaning and importance of frames in the context of oversampling and other aspects of signal representation by means of nonorthogonal bases

rms bandwidth constrained signature waveforms that maximize the total capacity of pam synchronous cdma channels optimum time limited signal sets of equal and unequal energies are obtained under root mean square rms bandwidth constraints the total capacity and the total asymptotic efficiency of the pam synchronous gaussian cdma psg cdma channel are considered as the optimality criteria the latter measure is monotonic with the determinant of the correlation matrix r and the former is monotonic with det i spl sigma sup 2 r where spl sigma sup 2 represents the noise level average as well as maximum rms bandwidth constraints are considered in the equal energy case and the energy weighted rms bandwidth constraint is considered for unequal energy signals for the equal energy problem signal sets are found that simultaneously optimize the total asymptotic efficiency under both average and maximum rms bandwidth constraints for the total capacity measure such simultaneously optimal signal sets are also obtained albeit under the restriction that the number of signals n be a hadamard matrix dimension when the hadamard dimension is in particular a power of two we obtain optimum signal sets that are shown to yield equal optimum multiuser detector asymptotic efficiencies for all users of an uncoded psg cdma channel unequal energy signal sets are also found under an energy weighted rms bandwidth constraint for both optimality criteria

multiscale model reduction method for bayesian inverse problems of subsurface flow this work presents a model reduction approach to the inverse problem in the application of subsurface flows one such an application is to estimate models inputs and identify models parameters this is often challenging because the complicated multiscale structures are inherent in the model and the estimated inputs are parameterized in a high dimensional space we often need to estimate the probabilistic distribution of the unknown inputs based on some observations bayesian inference is desirable for this situation and solving the inverse problem for the bayesian inverse problem the forward model needs to be repeatedly computed for a large number of samplers to get a stationary chain this requires large computational efforts to significantly improve the computation efficiency we use generalized multiscale finite element method and least squares stochastic collocation method to construct a reduced computational model to avoid the difficulty of choosing regularization parameter hyperparameters are introduced to build a hierarchical model we use truncated karhunenloeve expansion kle to reduce the dimension of the parameter spaces and decrease the mixed time of markov chains the techniques of hyperparameter and kle are incorporated into the model reduction method the reduced model is constructed offline then it is computed very efficiently in the online sampling stage this strategy can significantly accelerate the evaluation of the markov chain and the resultant posterior distribution converges fast we analyze the convergence for the approximation between the posterior distribution by the reduced model and the reference posterior distribution by the full order model a few numerical examples in subsurface flows are carried out to demonstrate the performance of the presented model reduction method with application of the bayesian inverse problem

sparse grid reduced basis bayesian inversion abstract we analyze reduced basis rb for short short acceleration of recently proposed sparse bayesian inversion algorithms for partial differential equations with uncertain distributed parameter for observation data subject to additive gaussian observation noise specifically bayesian inversion of affine parametric linear operator families on possibly high dimensional parameter spaces we consider high fidelity petrov galerkin pg discretizations of these countably parametric operator families we allow general families of inf sup stable pg finite element methods covering most conforming primal and mixed finite element discretizations of standard problems in mechanics rb acceleration of the high dimensional parametric forward response maps which need to be numerically solved numerous times in bayesian inversion is proposed and convergence rate bounds for the error in the bayesian estimate incurred by the use of rb are derived as consequence of recent theoretical results on dimension independent sparsity of parametric responses and preservation of sparsity for holomorphic parametric problems we establish new convergence rates of greedy rb compressions for both the parametric forward maps as well as for the countably parametric posterior densities which arise in bayesian inversion we show that the convergence rates for the rb compressions of the parametric forward maps as well as of the countably parametric sparse bayesian posterior densities are free from the curse of dimensionality and depend only on the sparsity of the uncertain input data in particular we establish the quadratic convergence of the rb compression for the posterior densities with respect to that for the parametric forward maps numerical experiments for linear elliptic affine parametric model problems in two space dimensions with hundreds of parameters are reported which confirm that the proposed adaptive sparse grid reduced basis algorithms indeed exploit sparsity of both the parametric forward maps as well as the bayesian posterior density

a multiscale method for model order reduction in pde parameter estimation abstract estimating parameters of partial differential equations pdes is of interest in a number of applications such as geophysical and medical imaging parameter estimation is commonly phrased as a pde constrained optimization problem that can be solved iteratively using gradient based optimization a computational bottleneck in such approaches is that the underlying pdes need to be solved numerous times before the model is reconstructed with sufficient accuracy one way to reduce this computational burden is by using model order reduction mor techniques such as the multiscale finite volume method msfv in this paper we apply msfv for solving high dimensional parameter estimation problems given a finite volume discretization of the pde on a fine mesh the msfv method reduces the problem size by computing a parameter dependent projection onto a nested coarse mesh a novelty in our work is the integration of msfv into a pde constrained optimization framework which updates the reduced space in each iteration we present a computationally tractable way of explicitly differentiating the mor solution that acknowledges the change of basis as we demonstrate in our numerical experiments our method leads to computational savings for large scale parameter estimation problems where iterative pde solvers are necessary and offers potential for additional speed ups through parallel implementation

optimally sparse frames frames have established themselves as a means to derive redundant yet stable decompositions of a signal for analysis or transmission while also promoting sparse expansions however when the signal dimension is large the computation of the frame measurements of a signal typically requires a large number of additions and multiplications and this makes a frame decomposition intractable in applications with limited computing budget to address this problem in this paper we focus on frames in finite dimensional hilbert spaces and introduce sparsity for such frames as a new paradigm in our terminology a sparse frame is a frame whose elements have a sparse representation in an orthonormal basis thereby enabling low complexity frame decompositions to introduce a precise meaning of optimality we take the sum of the numbers of vectors needed from this orthonormal basis when expanding each frame vector as sparsity measure we then analyze the recently introduced algorithm spectral tetris for construction of unit norm tight frames and prove that the tight frames generated by this algorithm are in fact optimally sparse with respect to the standard unit vector basis finally we show that even the generalization of spectral tetris for the construction of unit norm frames associated with a given frame operator produces optimally sparse frames

sparse grid reduced basis bayesian inversion we extend the reduced basis rb accelerated bayesian inversion methods for affine parametric linear operator equations which are considered in 16 17 to non affine nonlinear parametric operator equations we generalize the analysis of sparsity of parametric forward solution maps in 20 and of bayesian inversion in 48 49 to the fully discrete setting including petrov galerkin high fidelity hifi discretization of the forward maps we develop adaptive stochastic collocation based reduction methods for the efficient computation of reduced bases on the parametric solution manifold the nonaffinity and nonlinearity with respect to w r t the distributed uncertain parameters and the unknown solution is collocated specifically by the so called empirical interpolation method eim for the corresponding bayesian inversion problems computational efficiency is enhanced in two ways first expectations w r t the posterior are computed by adaptive quadratures with dimension independent convergence rates proposed in 49 the present work generalizes 49 to account for the impact of the pg discretization in the forward maps on the convergence rates of the quantities of interest qoi for short second we propose to perform the bayesian estimation only w r t a parsimonious rb approximation of the posterior density based on the approximation results in 49 the infinite dimensional parametric deterministic forward map and operator admit n term rb and eim approximations which converge at rates which depend only on the sparsity of the parametric forward map in several numerical experiments the proposed algorithms exhibit dimension independent convergence rates which equal at least the currently known rate estimates for n term approximation we propose to accelerate bayesian estimation by first offline construction of reduced basis surrogates of the bayesian posterior density the parsimonious surrogates can then be employed for online data assimilation and for bayesian estimation they also open a perspective for optimal experimental design

a randomized maximum a posteriori method for posterior sampling of high dimensional nonlinear bayesian inverse problems we present a randomized maximum a posteriori rmap method for generating approximate samples of posteriors in high dimensional bayesian inverse problems governed by large scale forward problems we derive the rmap approach by 1 casting the problem of computing the map point as a stochastic optimization problem 2 interchanging optimization and expectation and 3 approximating the expectation with a monte carlo method for a specific randomized data and prior mean rmap reduces to the randomized maximum likelihood rml approach it can also be viewed as an iterative stochastic newton method an analysis of the convergence of the rmap samples is carried out for both linear and nonlinear inverse problems each rmap sample requires solution of a pde constrained optimization problem to solve these problems we employ a state of the art trust region inexact newton conjugate gradient method with sensitivity based warm starts an approximate metropolization approach is presented to reduce the bias in rma

taylor approximation and variance reduction for pde constrained optimal control under uncertainty abstract in this work we develop a scalable computational framework for the solution of pde constrained optimal control problems under high dimensional uncertainty specifically we consider a mean variance formulation of the control objective and employ a taylor expansion with respect to the uncertain parameter field either to directly approximate the control objective or as a control variate for variance reduction the expressions for the mean and variance of the taylor approximation are known analytically although their evaluation requires efficient computation of the trace of the preconditioned hessian of the control objective we propose to estimate this trace by solving a generalized eigenvalue problem using a randomized algorithm that only requires the action of the hessian on a small number of random directions then the computational work does not depend on the nominal dimension of the uncertain parameter but depends only on the effective dimension i e the rank of the preconditioned hessian thus ensuring scalability to high dimensional problems moreover to increase the estimation accuracy of the mean and variance of the control objective by the taylor approximation we use it as a control variate for variance reduction which results in considerable computational savings several orders of magnitude compared to a plain monte carlo method in summary our approach amounts to solving an optimal control problem constrained by the original pde the generalized eigenvalue equations at a small number of eigenfunctions and a set of linearized pdes that arise from the computation of the gradient and hessian of the control objective with respect to the uncertain parameter we use the lagrangian formalism to derive expressions for the gradient with respect to the control and apply a gradient based optimization method to solve the problem we demonstrate the accuracy efficiency and scalability of the proposed computational method for two examples with high dimensional uncertain parameters subsurface flow in a porous medium modeled as an elliptic pde and turbulent jet flow modeled by the reynolds averaged navier stokes equations coupled with a nonlinear advection diffusion equation characterizing model uncertainty in particular for the latter more challenging example we show scalability of our algorithm up to one million parameters resulting from discretization of the uncertain parameter field

sum capacity and tsc bounds in collaborative multibase wireless systems we consider a wireless system with base stations which collaborate and derive bounds on sum capacity and total squared correlation for uniform channels between users and bases the correspondence also investigates structural properties which must be satisfied by user transmit covariance matrices at the optimal sum capacity total squared correlation tsc point and shows that for multibase systems maximizing sum capacity and minimizing tsc are in general not equivalent problems

power minimization for cdma under colored noise rate constrained power minimization pmin over a code division multiple access cdma channel with correlated noise is studied pmin is shown to be an instance of a separable convex optimization problem subject to linear ascending constraints pmin is further reduced to a dual problem of sumrate maximization rmax the results highlight the underlying unity between pmin rmax and a problem closely related to pmin but with linear receiver constraints subsequently conceptually simple sequence design algorithms are proposed to explicitly identify an assignment of sequences and powers that solve pmin the algorithms yield an upper bound of 2n 1 on the number of distinct sequences where n is the processing gain the sequences generated using the proposed algorithms are in general real valued if a rate splitting and multi dimensional cdma approach is allowed the upper bound reduces to n distinct sequences in which case the sequences can form an orthogonal set and be binary plusmn1 valued

bayesian inference with optimal maps we present a new approach to bayesian inference that entirely avoids markov chain simulation by constructing a map that pushes forward the prior measure to the posterior measure existence and uniqueness of a suitable measure preserving map is established by formulating the problem in the context of optimal transport theory we discuss various means of explicitly parameterizing the map and computing it efficiently through solution of an optimization problem exploiting gradient information from the forward model when possible the resulting algorithm overcomes many of the computational bottlenecks associated with markov chain monte carlo advantages of a map based representation of the posterior include analytical expressions for posterior moments and the ability to generate arbitrary numbers of independent posterior samples without additional likelihood evaluations or forward solves the optimization approach also provides clear convergence criteria for posterior approximation and facilitates model selection through automatic evaluation of the marginal likelihood we demonstrate the accuracy and efficiency of the approach on nonlinear inverse problems of varying dimension involving the inference of parameters appearing in ordinary and partial differential equations

on the limitation of generalized welch bound equality signals this correspondence characterizes the performance limitation of the well acclaimed generalized welch bound equality wbe signals under linear minimum mean squared error mmse detection it is analytically proven and experimentally verified that when users in an overloaded but finite size code division multiple access cdma system are allocated such signals the error rate of at least one user floors i e it cannot be driven to zero even in the absence of additive noise independently of the symbol energies if in addition all users are received with equal energy then the error rate of every user floors

adaptive hessian based nonstationary gaussian process response surface method for probability density approximation with application to bayesian solution of large scale inverse problems we develop an adaptive hessian based non stationary gaussian process gp response surface method for approximating a probability density function pdf that exploits its structure particularly the hessian of its negative logarithm of particular interest to us are pdfs that arise from the bayesian solution of large scale inverse problems which imply very expensive to evaluate pdfs the method can be considered as a piecewise adaptive gaussian approximation in which a gaussian tailored to the local hessian of the negative log probability density is constructed for each subregion in high dimensional parameter space the task of efficiently partitioning the parameter space into subregions is done implicitly through hessian informed membership probability functions the gp machinery is then employed to glue all local gaussian approximations into a global analytical response surface that is far cheaper to evaluate than the original expensive probability density the resulting response surface is also equipp

on the ergodic capacity as a function of the correlation properties in systems with multiple transmit antennas without csi at the transmitter in this letter the impact of correlation of the transmit antennas of a multiple input single output miso system with no channel state information csi at the transmitter and perfect csi at the receiver is analyzed we show that the ergodic capacity for the single user miso system is schur concave with respect to the vector with eigenvalues of the channel covariance matrix i e the more correlation that exists between the transmit antennas the less is the achievable capacity furthermore the capacity loss for fully correlated transmit antennas in comparison with the uncorrelated case is derived the results for the ergodic capacity are compared with the impact of correlation on the outage probability the relationship between correlation properties and outage probability is more complicated than the relationship between the correlation properties and the ergodic capacity it is shown that the outage probability is schur convex in the high signal to noise ratio snr regime and schur concave in the low snr regime

x tmcmc adaptive kriging for bayesian inverse modeling abstract the bayesian inference of models associated with large scale simulations is prohibitively expensive even for massively parallel architectures we demonstrate that we can drastically reduce this cost by combining adaptive kriging with the population based transitional markov chain monte carlo tmcmc techniques for uni modal posterior probability distribution functions pdf the proposed hybrid method can reduce the computational cost by an order of magnitude with the same computational resources for complex posterior pdf landscapes we show that it is necessary to further extend the tmcmc by langevin adjusted proposals the proposed hybrid method exhibits high parallel efficiency we demonstrate the capabilities of our method on test bed problems and on high fidelity simulations in structural dynamics

double preconditioning for gabor frames the authors present an application of the general idea of preconditioning in the context of gabor frames while most iterative algorithms aim at a more or less costly exact numerical calculation of the inverse gabor frame matrix we propose here the use of cheap methods to find an approximation for it based on double preconditioning we thereby obtain good approximations of the true dual gabor atom at low computational costs since the gabor frame matrix commutes with certain time frequency shifts it is natural to make use of diagonal and circulant preconditioners sharing this property part of the efficiency of the proposed scheme results from the fact that all the matrices involved share a well known block matrix structure at least for the smooth gabor atoms typically used the combination of these two preconditioners leads consistently to good results these claims are supported by numerical experiments in this paper for numerical evaluations we introduce two new matrix norms which can be calculated efficiently by exploiting the structure of the frame matrix

a linear cost algorithm to compute the discrete gabor transform in this paper we propose an alternative efficient method to calculate the gabor coefficients of a signal given a synthesis window with a support of size much lesser than the length of the signal the algorithm uses the canonical dual of the window which does not need to be calculated beforehand and achieves a computational cost that is linear with the signal length in both analysis and synthesis this is done by exploiting the block structure of the matrices and using an ad hoc cholesky decomposition of the gabor frame matrix

algorithms for kullback leibler approximation of probability measures in infinite dimensions in this paper we study algorithms to find a gaussian approximation to a target measure defined on a hilbert space of functions the target measure itself is defined via its density with respect to a reference gaussian measure we employ the kullback leibler divergence as a distance and find the best gaussian approximation by minimizing this distance it then follows that the approximate gaussian must be equivalent to the gaussian reference measure defining a natural function space setting for the underlying calculus of variations problem we introduce a computational algorithm which is well adapted to the required minimization seeking to find the mean as a function and parameterizing the covariance in two different ways through low rank perturbations of the reference covariance and through schrodinger potential perturbations of the inverse reference covariance two applications are shown to a nonlinear inverse problem in elliptic pdes and to a conditioned diffusion process these gaussian approximations also serve to provide a preconditioned proposal distribution for improved preconditioned crank nicolson monte carlo markov chain sampling of the target distribution this approach is not only well adapted to the high dimensional setting but also behaves well with respect to small observational noise resp small temperatures in the inverse problem resp conditioned diffusion

expectation propagation for nonlinear inverse problems with an application to electrical impedance tomography in this paper we study a fast approximate inference method based on expectation propagation for exploring the posterior probability distribution arising from the bayesian formulation of nonlinear inverse problems it is capable of efficiently delivering reliable estimates of the posterior mean and covariance thereby providing an inverse solution together with quantified uncertainties some theoretical properties of the iterative algorithm are discussed and the efficient implementation for an important class of problems of projection type is described the method is illustrated with one typical nonlinear inverse problem electrical impedance tomography with complete electrode model under sparsity constraints numerical results for real experimental data are presented and compared with that by markov chain monte carlo the results indicate that the method is accurate and computationally very efficient

geometric mcmc for infinite dimensional inverse problems bayesian inverse problems often involve sampling posterior distributions on infinite dimensional function spaces traditional markov chain monte carlo mcmc algorithms are characterized by deteriorating mixing times upon mesh refinement when the finite dimensional approximations become more accurate such methods are typically forced to reduce step sizes as the discretization gets finer and thus are expensive as a function of dimension recently a new class of mcmc methods with mesh independent convergence times has emerged however few of them take into account the geometry of the posterior informed by the data at the same time recently developed geometric mcmc algorithms have been found to be powerful in exploring complicated distributions that deviate significantly from elliptic gaussian laws but are in general computationally intractable for models defined in infinite dimensions in this work we combine geometric methods on a finite dimensional subspace with mesh independent infinite dimensional approaches our objective is to speed up mcmc mixing times without significantly increasing the computational cost per step for instance in comparison with the vanilla preconditioned crank nicolson pcn method this is achieved by using ideas from geometric mcmc to probe the complex structure of an intrinsic finite dimensional subspace where most data information concentrates while retaining robust mixing times as the dimension grows by using pcn like methods in the complementary subspace the resulting algorithms are demonstrated in the context of three challenging inverse problems arising in subsurface flow heat conduction and incompressible flow control the algorithms exhibit up to two orders of magnitude improvement in sampling efficiency when compared with the pcn method

multiuser constrained water pouring for continuous time overloaded gaussian multiple access channels in this paper signature waveforms and signal powers are jointly optimized for multiuser communications over strictly bandlimited continuous time overloaded channels corrupted by additive white gaussian noise awgn the total signal power is minimized subject to general asymmetric signal to interference plus noise ratio sinr constraints at the output of linear minimum mean squared error lmmse receivers using vectorized fourier transform vft technique the optimal solutions as well as a necessary and sufficient condition for the existence of a feasible solution are derived in the frequency domain it turns out that every optimal solution performs the same as the optimal frequency division multiple access fdma system a geometric procedure called multiuser constrained water pouring is developed to construct every possible optimal solution of which profiles of signal power and equivalent bandwidth are respectively the same as those of signal power and physical bandwidth of the optimal fdma system it is shown that orthogonal signature waveforms are assigned to oversized users and continuous time equivalents of generalized welch bound equality cte gwbe sequences are assigned to non oversized users

wiener s lemma for twisted convolution and gabor frames as a consequence ca is invertible and bounded on all p zd for 1 p oo simultaneously in this article we study several non commutative generalizations of wiener s lemma and their application to gabor theory the paper is divided into two parts the first part sections 2 and 3 is devoted to abstract harmonic analysis and extends wiener s lemma to twisted convolution the second part section 4 is devoted to the theory of gabor frames specifically to the design of dual windows with good time frequency localization in particular we solve a conjecture of janssen feichtinger and one of us 17 18 9 these two topics appear to be completely disjoint but they are not the solution of the conjectures about gabor frames is an unexpected application of methods from non commutative harmonic analysis to application oriented mathematics it turns out that the connection between twisted convolution and the heisenberg group and the theory of symmetric group algebras are precisely the tools needed to treat the problem motivated by signal analysis to be more concrete we formulate some of our main results first and will deal with the details and the technical background later

variance reduction using nonreversible langevin samplers a standard approach to computing expectations with respect to a given target measure is to introduce an overdamped langevin equation which is reversible with respect to the target distribution and to approximate the expectation by a time averaging estimator as has been noted in recent papers 30 37 61 72 introducing an appropriately chosen nonreversible component to the dynamics is beneficial both in terms of reducing the asymptotic variance and of speeding up convergence to the target distribution in this paper we present a detailed study of the dependence of the asymptotic variance on the deviation from reversibility our theoretical findings are supported by numerical simulations

on quasi orthogonal signatures for cdma systems sum capacity optimal signatures in synchronous code division multiple access cdma systems are functions of the codebook length as well as the number of active users a new signature set must be assigned every time the number of active users changes this correspondence considers signature sets that are less sensitive to changes in the number of active users equiangular signature sequences are proven to solve a certain max min signal to interference plus noise problem which results from their interference invariance unions of orthonormal bases have subsets that come close to satisfying the welch bound bounds on the maximum number of bases with minimum maximum correlation are derived and a new construction algorithm is provided connections are made between these signature design problems grassmannian line packing frame theory and algebraic geometry

continuity properties of the gabor frame operator abstract for a gabor frame with small lattice it is shown that the frame operator is continuous and invertible on many banach spaces defined by smoothness and decay properties as a consequence it is shown that there exist gabor type frame dual frame pairs and tight frames with good decay and smoothness properties also it is shown that the iteration scheme by which a function can be recovered from its frame coefficients converges robustly e g in lp and sobolev norms also explicit estimates on lattice sizes for which such results hold can be obtained

a framework for the automation of generalized stability theory the traditional approach to investigating the stability of a physical system is to linearize the equations about a steady base solution and to examine the eigenvalues of the linearized operator over the past several decades it has been recognized that this approach only determines the asymptotic stability of the system and neglects the possibility of transient perturbation growth arising due to the nonnormality of the system this observation motivated the development of a more powerful generalized stability theory gst which focuses instead on the singular value decomposition svd of the linearized propagator of the system while gst has had significant successes in understanding the stability of phenomena in geophysical fluid dynamics its more widespread applicability has been hampered by the fact that computing the svd requires both the tangent linear operator and its adjoint deriving the tangent linear and adjoint models is usually a considerable challenge and manually embedding them inside

multirate zero forcing tx rx design for mimo channel under ber constraints this paper is concerned with communicating parallel independent streams of data possibly of different rates through a multiple input multiple output channel each data stream is required to satisfy a bit error rate ber constraint this scenario arises in multimedia communications we find the linear zero forcing transmitter receiver tx rx matrix pair that requires the minimum transmitter power to achieve the ber constraints it is well known that the tx rx pair can be chosen to partition the matrix channel into scalar subchannels corresponding to singular values and different data streams can be transmitted through different subchannels this design is suboptimum in general the optimum design has the following structure the set of input data streams is partitioned into groups called signal groups the set of subchannels is conformably partitioned into subchannel groups each signal group is collectively transmitted through its assigned subchannel group with each signal subchannel group pair is associated a unitary matrix that mixes the signals at the transmitter and unmixes them at the receiver we derive a simple algorithm to determine the optimum signal and subchannel groups we then use a known algorithm from majorization theory to determine the unitary matrices using these we completely specify the optimum tx rx pair

painless nonorthogonal expansions in a hilbert space h discrete families of vectors hj with the property that f j hj f hj for every f in h are considered this expansion formula is obviously true if the family is an orthonormal basis of h but also can hold in situations where the hj are not mutually orthogonal and are overcomplete the two classes of examples studied here are i appropriate sets of weyl heisenberg coherent states based on certain non gaussian fiducial vectors and ii analogous families of affine coherent states it is believed that such quasiorthogonal expansions will be a useful tool in many areas of theoretical physics and applied mathematics

high snr performance analysis of blind minimum output energy receivers for large ds cdma systems high signal to noise ratio snr properties of the minimum output energy moe receiver and the capon channel estimation technique are analyzed in the case of large direct sequence code division multiple access ds cdma systems it is shown that if the noise power tends to zero and the system load is less than one then the signal to interference plus noise ratio sinr of the moe receiver tends to infinity and the capon channel estimate converges to a scaled version of the channel vector of the user of interest for the case when the system load is larger than one an asymptotic sinr expression is obtained furthermore expressions for the efficiency and asymptotic efficiency of the moe receiver are derived simple approximations of and upper lower bounds on these expressions are found and the effects of the system physical parameters on the performance of the moe receiver are discussed