adaptive bayesian wavelet shrinkage abstract when fitting wavelet based models shrinkage of the empirical wavelet coefficients is an effective tool for denoising the data this article outlines a bayesian approach to shrinkage obtained by placing priors on the wavelet coefficients the prior for each coefficient consists of a mixture of two normal distributions with different standard deviations the simple and intuitive form of prior allows us to propose automatic choices of prior parameters these parameters are chosen adaptively according to the resolution level of the coefficients typically shrinking high resolution frequency coefficients more heavily assuming a good estimate of the background noise level we obtain closed form expressions for the posterior means and variances of the unknown wavelet coefficients the latter may be used to assess uncertainty in the reconstruction several examples are used to illustrate the method and comparisons are made with other shrinkage methods

wavelet thresholding via a bayesian approach we discuss a bayesian formalism which gives rise to a type of wavelet threshold estimation in nonparametric regression a prior distribution is imposed on the wavelet coefficients of the unknown response function designed to capture the sparseness of wavelet expansion that is common to most applications for the prior specified the posterior median yields a thresholding procedure our prior model for the underlying function can be adjusted to give functions falling in any specific besov space we establish a relationship between the hyperparameters of the prior model and the parameters of those besov spaces within which realizations from the prior will fall such a relationship gives insight into the meaning of the besov space parameters moreover the relationship established makes it possible in principle to incorporate prior knowledge about the function s regularity properties into the prior model for its wavelet coefficients however prior knowledge about a function s regularity properties might be difficult to elicit with this in mind we propose a standard choice of prior hyperparameters that works well in our examples several simulated examples are used to illustrate our method and comparisons are made with other thresholding methods we also present an application to a data set that was collected in an anaesthesiological study

multiscale methods for data on graphs and irregular multidimensional situations for regularly spaced one dimensional data wavelet shrinkage has proven to be a compelling method for non parametric function estimation we create three new multiscale methods that provide wavelet like transforms both for data arising on graphs and for irregularly spaced spatial data in more than one dimension the concept of scale still exists within these transforms but as a continuous quantity rather than dyadic levels further we adapt recent empirical bayesian shrinkage techniques to enable us to perform multiscale shrinkage for function estimation both on graphs and for irregular spatial data we demonstrate that our methods perform very well when compared with several other methods for spatial regression for both real and simulated data although we concentrate on multiscale shrinkage regression we present our new wavelet transforms as generic tools intended to be the basis of methods that might benefit from a multiscale representation of data either on graphs or for irregular spatial data

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

multiscale modeling and estimation of poisson processes with application to photon limited imaging many important problems in engineering and science are well modeled by poisson processes in many applications it is of great interest to accurately estimate the intensities underlying observed poisson data in particular this work is motivated by photon limited imaging problems this paper studies a new bayesian approach to poisson intensity estimation based on the haar wavelet transform it is shown that the haar transform provides a very natural and powerful framework for this problem using this framework a novel multiscale bayesian prior to model intensity functions is devised the new prior leads to a simple bayesian intensity estimation procedure furthermore we characterize the correlation behavior of the new prior and show that it has 1 f spectral characteristics the new framework is applied to photon limited image estimation and its potential to improve nuclear medicine imaging is examined

ridge regression biased estimation for nonorthogonal problems in multiple regression it is shown that parameter estimates based on minimum residual sum of squares have a high probability of being unsatisfactory if not incorrect if the prediction vectors are not orthogonal proposed is an estimation procedure based on adding small positive quantities to the diagonal of x x introduced is the ridge trace a method for showing in two dimensions the effects of nonorthogonality it is then shown how to augment x x to obtain biased estimates with smaller mean square error

fast unit modulus least squares with applications in beamforming unit modulus least squares uls problems arise in many applications including phase only beamforming sensor network localization synchronization phase retrieval and radar code design uls formulations can always be recast as unit modulus quadratic programs to which semidefinite relaxation sdr can be applied and is often the state of the art approach however sdr lifts the problem dimension i e the number of variables from n to n 2 which drastically increases the memory burden and computational cost when the problem size is already large e g when designing phase only beamformer weights for massive multiple input multiple output systems this paper focuses on scalable first order algorithms for the uls problem and some of its variants it advocates using simple gradient projection gp as a starting point for solving the uls problem establishes global convergence of gp to a karush kuhn tucker point for this np hard problem and bounds its iteration complexity then it proposes uls extensions tailored to reflect practical beamformer design objectives bringing in and exploiting new degrees of freedom to improve the beampattern designs simple variants of gp are proposed to deal with these extended uls problems simulations are used to showcase the effectiveness of the proposed algorithms in both the plain uls problem and in the context of phase only beamforming

heuristics of instability and stabilization in model selection in model selection usually a best predictor is chosen from a collection hat mu cdot s of predictors where hat mu cdot s is the minimum least squares predictor in a collection mathsf u s of predictors here s is a complexity parameter that is the smaller s the lower dimensional smoother the models in mathsf u s if mathsf l is the data used to derive the sequence hat mu cdot s the procedure is called unstable if a small change in mathsf l can cause large changes in hat mu cdot s with a crystal ball one could pick the predictor in hat mu cdot s having minimum prediction error without prescience one uses test sets cross validation and so forth the difference in prediction error between the crystal ball selection and the statistician s choice we call predictive loss for an unstable procedure the predictive loss is large this is shown by some analytics in a simple case and by simulation results in a more complex comparison of four different linear regression methods unstable procedures can be stabilized by perturbing the data getting a new predictor sequence hat mu cdot s and then averaging over many such predictor sequences

a multi model selection framework for unknown and or evolutive misclassification cost problems in this paper we tackle the problem of model selection when misclassification costs are unknown and or may evolve unlike traditional approaches based on a scalar optimization we propose a generic multi model selection framework based on a multi objective approach the idea is to automatically train a pool of classifiers instead of one single classifier each classifier in the pool optimizing a particular trade off between the objectives within the context of two class classification problems we introduce the roc front concept as an alternative to the roc curve representation this strategy is applied to the multi model selection of svm classifiers using an evolutionary multi objective optimization algorithm the comparison with a traditional scalar optimization technique based on an auc criterion shows promising results on uci datasets as well as on a real world classification problem

image denoising in mixed poisson gaussian noise we propose a general methodology pure let to design and optimize a wide class of transform domain thresholding algorithms for denoising images corrupted by mixed poisson gaussian noise we express the denoising process as a linear expansion of thresholds let that we optimize by relying on a purely data adaptive unbiased estimate of the mean squared error mse derived in a non bayesian framework pure poisson gaussian unbiased risk estimate we provide a practical approximation of this theoretical mse estimate for the tractable optimization of arbitrary transform domain thresholding we then propose a pointwise estimator for undecimated filterbank transforms which consists of subband adaptive thresholding functions with signal dependent thresholds that are globally optimized in the image domain we finally demonstrate the potential of the proposed approach through extensive comparisons with state of the art techniques that are specifically tailored to the estimation of poisson intensities we also present denoising results obtained on real images of low count fluorescence microscopy

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

design of par constrained sequences for mimo channel estimation via majorization minimization communication systems and radars widely employ sequences of low peak to average power ratio par or unimodulus to meet the hardware constraints and maximize the power efficiency numerous works have probed the unimodular sequence design especially attempting to obtain good correlation properties regarding channel estimation however sequences of such properties do not necessarily qualify for the mission and tailored unimodular sequences for the specific criterion concerned are more desirable when we have access to the prior knowledge of the channel impulse response in this paper we formulate the problem of unimodular sequence design by optimizing minimum mean square error and conditional mutual information respectively the problems turn out nonconvex and we develop efficient algorithms based on the majorization minimization framework with convergence guaranteed more general we also examine optimal sequence design with low par constraints numerical examples demonstrate the improved results of mean square error signal to noise ratio and conditional mutual information by using our proposed training sequences with the efficiency of the derived algorithms illustrated

hermitian completely positive matrices abstract in this paper we introduce the hermitian completely positive hcp matrix which has a hermitian completely positive hcp decomposition with all real and imaginary parts of the decomposition vectors being nonnegative some properties of the hermitian completely positive matrix are given a semidefinite algorithm is also proposed for checking whether a hermitian matrix is hcp or not if a matrix is not hcp a certificate for it can be obtained if it is an hcp decomposition can be obtained

needles and straw in haystacks empirical bayes estimates of possibly sparse sequences an empirical bayes approach to the estimation of possibly sparse sequences observed in gaussian white noise is set out and investigated the prior considered is a mixture of an atom of probability at zero and a heavy tailed density y with the mixing weight chosen by marginal maximum likelihood in the hope of adapting between sparse and dense sequences if estimation is then carried out using the posterior median this is a random thresholding procedure other thresholding rules employing the same threshold can also be used probability bounds on the threshold chosen by the marginal maximum likelihood approach lead to overall risk bounds over classes of signal sequences of length n allowing for sparsity of various kinds and degrees the signal classes considered are nearly black sequences where only a proportion is allowed to be nonzero and sequences with normalized p norm bounded by for 0 and 0 1 simulations show excellent performance for appropriately chosen functions y the method is computationally tractable and software is available the extension to a modified thresholding method relevant to the estimation of very sparse sequences is also considered

wavelet domain filtering for photon imaging systems many imaging systems rely on photon detection as the basis of image formation one of the major sources of error in these systems is poisson noise due to the quantum nature of the photon detection process unlike additive gaussian white noise the variance of poisson noise is proportional to the underlying signal intensity and consequently separating signal from noise is a very difficult task in this paper we perform a novel gedankenexperiment to devise a new wavelet domain filtering procedure for noise removal in photon imaging systems the filter adapts to both the signal and the noise and balances the trade off between noise removal and excessive smoothing of image details designed using the statistical method of cross validation the filter is simultaneously optimal in a small sample predictive sum of squares sense and asymptotically optimal in the mean square error sense the filtering procedure has a simple interpretation as a joint edge detection estimation process moreover we derive an efficient algorithm for performing the filtering that has the same order of complexity as the fast wavelet transform itself the performance of the new filter is assessed with simulated data experiments and tested with actual nuclear medicine imagery

natural exponential families with quadratic variance functions statistical theory the normal poisson gamma binomial negative binomial and nefghs distributions are the six univariate natural exponential families nef with quadratic variance functions qvf this sequel to morris 1982 treats certain statistical topics that can be handled within this unified nef qvf formulation including unbiased estimation bhattacharyya and cramer rao lower bounds conditional distributions and moments quadratic regression conjugate prior distributions moments of conjugate priors and posterior distributions empirical bayes and g 2 minimax marginal distributions and their moments parametric empirical bayes and characterizations

designing unimodular codes via quadratic optimization the np hard problem of optimizing a quadratic form over the unimodular vector set arises in radar code design scenarios as well as other active sensing and communication applications to tackle this problem which we call unimodular quadratic program uqp several computational approaches are devised and studied power method like iterations are introduced for local optimization of uqp furthermore a monotonically error bound improving technique merit is proposed to obtain the global optimum or a local optimum of uqp with good sub optimality guarantees the provided sub optimality guarantees are case dependent and may outperform the 4 approximation guarantee of semi definite relaxation several numerical examples are presented to illustrate the performance of the proposed method the examples show that for several cases including rank deficient matrices the proposed methods can solve uqps efficiently in the sense of sub optimality guarantee and computational time

variable selection using svm based criteria we propose new methods to evaluate variable subset relevance with a view to variable selection relevance criteria are derived from support vector machines and are based on weight vector w 2 or generalization error bounds sensitivity with respect to a variable experiments on linear and non linear toy problems and real world datasets have been carried out to assess the effectiveness of these criteria results show that the criterion based on weight vector derivative achieves good results and performs consistently well over the datasets we used

minimum risk wavelet shrinkage operator for poisson image denoising the pixel values of images taken by an image sensor are said to be corrupted by poisson noise to date multiscale poisson image denoising techniques have processed haar frame and wavelet coefficients the modeling of coefficients is enabled by the skellam distribution analysis we extend these results by solving for shrinkage operators for skellam that minimizes the risk functional in the multiscale poisson image denoising setting the minimum risk shrinkage operator of this kind effectively produces denoised wavelet coefficients with minimum attainable l 2 error

feature scaling for kernel fisher discriminant analysis using leave one out cross validation kernel fisher discriminant analysis kfd is a successful approach to classification it is well known that the key challenge in kfd lies in the selection of free parameters such as kernel parameters and regularization parameters here we focus on the feature scaling kernel where each feature individually associates with a scaling factor a novel algorithm named fs kfd is developed to tune the scaling factors and regularization parameters for the feature scaling kernel the proposed algorithm is based on optimizing the smooth leave one out error via a gradient descent method and has been demonstrated to be computationally feasible fs kfd is motivated by the following two fundamental facts the leave one out error of kfd can be expressed in closed form and the step function can be approximated by a sigmoid function empirical comparisons on artificial and benchmark data sets suggest that fs kfd improves kfd in terms of classification accuracy

constructing binary sequences with good correlation properties an efficient analytical computational interplay binary sequence sets with asymptotically optimal auto cross correlation peak sidelobe level psl growth have been known in the literature for a long time and their construction has been studied both analytically and numerically in contrast it has been a long standing problem whether we can construct a family of binary sequences whose auto correlation psl grows in an optimal manner in this paper we devise a construction method of binary sequences with asymptotically optimal psl growth from the sequence sets with good correlation properties a key component of the design follows from the observation that if the psl of the sequence set grows optimally or nearly optimally then the psl of the constructed binary sequence will experience a similar growth as a consequence the proposed construction is simple to implement and is shown to be accomplished in polynomial time with such a construction we not only bridge the gap between analytical construction and computational search but also pave the way to settle the long standing design problem of binary sequences with an optimal growth of the auto correlation psl

a multirate dsp model for estimation of discrete probability density functions the problem of estimating a probability density function pdf from measurements has been widely studied by many researchers even though much work has been done in the area of pdf estimation most of it was focused on the continuous case we propose a new model based approach for modeling and estimating discrete probability density functions or probability mass functions this approach is based on multirate signal processing theory and it has several advantages over the conventional histogram method we illustrate the pdf estimation procedure and analyze the statistical properties of the pdf estimates based on this model a novel scheme is introduced that can be used for estimating the pdf in the presence of noise furthermore the proposed ideas are extended to the more general case of estimating multivariate pdfs finally we also consider practical issues such as optimizing the coefficients of a digital filter which is an integral part of the model this allows us to apply the proposed model to solve real world problems simulation results are given where appropriate in order to demonstrate the ideas

multiscale poisson data smoothing summary the paper introduces a framework for non linear multiscale decompositions of poisson data that have piecewise smooth intensity curves the key concept is conditioning on the sum of the observations that are involved in the computation of a given multiscale coefficient within this framework most classical wavelet thresholding schemes for data with additive homoscedastic noise can be used any family of wavelet transforms orthogonal biorthogonal or second generation can be incorporated in this framework our second contribution is to propose a bayesian shrinkage approach with an original prior for coefficients of this decomposition as such the method combines the advantages of the haar fisz transform with wavelet smoothing and bayesian multiscale likelihood models with additional benefits such as extendability towards arbitrary wavelet families simulations show an important reduction in average squared error of the output compared with the present techniques of anscombe or fisz variance stabilization or multiscale likelihood modelling

gradient based optimization of hyperparameters many machine learning algorithms can be formulated as the minimization of a training criterion that involves a hyperparameter this hyperparameter is usually chosen by trial and error with a model selection criterion in this article we present a methodology to optimize several hyperparameters based on the computation of the gradient of a model selection criterion with respect to the hyperparameters in the case of a quadratic training criterion the gradient of the selection criterion with respect to the hyperparameters is efficiently computed by backpropagating through a cholesky decomposition in the more general case we show that the implicit function theorem can be used to derive a formula for the hyperparameter gradient involving second derivatives of the training criterion

parametric empirical bayes inference theory and applications abstract this article reviews the state of multiparameter shrinkage estimators with emphasis on the empirical bayes viewpoint particularly in the case of parametric prior distributions some successful applications of major importance are considered recent results concerning estimates of error and confidence intervals are described and illustrated with data

window based example selection in learning vector quantization a variety of modifications have been employed to learning vector quantization lvq algorithms using either crisp or soft windows for selection of data although these schemes have been shown in practice to improve performance a theoretical study on the influence of windows has so far been limited here we rigorously analyze the influence of windows in a controlled environment of gaussian mixtures in high dimensions concepts from statistical physics and the theory of online learning allow an exact description of the training dynamics yielding typical learning curves convergence properties and achievable generalization abilities we compare the performance and demonstrate the advantages of various algorithms including lvq 2 1 generalized lvq glvq learning from mistakes lfm and robust soft lvq rslvq we find that the selection of the window parameter highly influences the learning curves but not surprisingly the asymptotic performances of lvq 2 1 and rslvq although the prototypes of lvq 2 1 exhibit divergent behavior the resulting decision boundary coincides with the optimal decision boundary thus yielding optimal generalization ability

multiscale variance stabilization via maximum likelihood this article proposes maximum likelihood approaches for multiscale variance stabilization mvs tranforms for independently and identically distributed data for two mvs transforms we present new unified theoretical results on their jacobians which are a key component of the likelihood the new results provide i a deeper theoretical understanding of the transforms and ii the ability to compute the likelihood in linear time compared to previous numerical methods which required quadratic effort the new mvs transforms are shown empirically to compare favourably to the well known box cox transform and almost dominate it we show how the new transforms like box cox can facilitate simpler models by an example involving the famous wool data

optimizing resources in model selection for support vector machine tuning support vector machine svm hyperparameters is an important step in achieving a high performance learning machine it is usually done by minimizing an estimate of generalization error based on the bounds of the leave one out loo such as radius margin bound and on the performance measures such as generalized approximate cross validation gacv empirical error etc these usual automatic methods used to tune the hyperparameters require an inversion of the gram schmidt matrix or a resolution of an extra quadratic programming problem in the case of a large data set these methods require the addition of huge amounts of memory and a long cpu time to the already significant resources used in svm training in this paper we propose a fast method based on an approximation of the gradient of the empirical error along with incremental learning which reduces the resources required both in terms of processing time and of storage space we tested our method on several benchmarks which produced promising results confirming our approach furthermore it is worth noting that the gain time increases when the data set is large

a feasible method for optimization with orthogonality constraints minimization with orthogonality constraints e g x top x i and or spherical constraints e g vert x vert 2 1 has wide applications in polynomial optimization combinatorial optimization eigenvalue problems sparse pca p harmonic flows 1 bit compressive sensing matrix rank minimization etc these problems are difficult because the constraints are not only non convex but numerically expensive to preserve during iterations to deal with these difficulties we apply the cayley transform a crank nicolson like update scheme to preserve the constraints and based on it develop curvilinear search algorithms with lower flops compared to those based on projections and geodesics the efficiency of the proposed algorithms is demonstrated on a variety of test problems in particular for the maxcut problem it exactly solves a decomposition formulation for the sdp relaxation for polynomial optimization nearest correlation matrix estimation and extreme eigenvalue problems the proposed algorithms run very fast and return solutions no worse than those from their state of the art algorithms for the quadratic assignment problem a gap 0 842 to the best known solution on the largest problem tai256c in qaplib can be reached in 5 min on a typical laptop

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

new algorithms for designing unimodular sequences with good correlation properties unimodular i e constant modulus sequences with good autocorrelation properties are useful in several areas including communications and radar the integrated sidelobe level isl of the correlation function is often used to express the goodness of the correlation properties of a given sequence in this paper we present several cyclic algorithms for the local minimization of isl related metrics these cyclic algorithms can be initialized with a good existing sequence such as a golomb sequence a frank sequence or even a pseudo random sequence to illustrate the performance of the proposed algorithms we present a number of examples including the design of sequences that have virtually zero autocorrelation sidelobes in a specified lag interval and of long sequences that could hardly be handled by means of other algorithms previously suggested in the literature

wavelet shrinkage for natural exponential families with quadratic variance functions we propose a wavelet shrinkage methodology for univariate natural exponential families with quadratic variance functions covering the gaussian poisson gamma binomial negative binomial and generalised hyperbolic secant distributions simulation studies for poisson and binomial data are used to illustrate the usefulness of the proposed methodology and comparisons are made with other methods available in the literature we also present applications to datasets arising from high energy astrophysics and from epidemiology

this is spiral tap sparse poisson intensity reconstruction algorithms theory and practice observations in many applications consist of counts of discrete events such as photons hitting a detector which cannot be effectively modeled using an additive bounded or gaussian noise model and instead require a poisson noise model as a result accurate reconstruction of a spatially or temporally distributed phenomenon f from poisson data y cannot be effectively accomplished by minimizing a conventional penalized least squares objective function the problem addressed in this paper is the estimation of f from y in an inverse problem setting where the number of unknowns may potentially be larger than the number of observations and f admits sparse approximation the optimization formulation considered in this paper uses a penalized negative poisson log likelihood objective function with nonnegativity constraints since poisson intensities are naturally nonnegative in particular the proposed approach incorporates key ideas of using separable quadratic approximations to the objective function at each iteration and penalization terms related to l1 norms of coefficient vectors total variation seminorms and partition based multiscale estimation methods

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

blind ml detection of orthogonal space time block codes efficient high performance implementations orthogonal space time block codes ostbcs have attracted much attention owing to their simple code construction maximal diversity gain and low maximum likelihood ml detection complexity when channel state information csi is available at the receiver this paper addresses the problem of ml ostbc detection with unknown csi focusing on the binary and quaternary psk constellations we show that blind ml ostbc detection can be simplified to a boolean quadratic program bqp from an optimization viewpoint the bqp is still a computationally hard problem and we propose two alternatives for dealing with this inherent complexity first we consider the semidefinite relaxation sdr approach which leads to a suboptimal but accurate blind ml detection algorithm with an affordable worst case computational cost we also consider the sphere decoding approach which leads to an exact blind ml detection algorithm that remains computationally expensive in the worst case but generally incurs a reasonable average computational cost for the two algorithms we study implementation methods that can significantly reduce the computational complexity simulation results indicate that the two blind ml detection algorithms are competitive in that the bit error performance of the two algorithms is almost the same and is noticeably better than that of some other existing blind detectors moreover numerical studies show that the sdr algorithm provides better complexity performance than the sphere decoder in the worst case sense and vice versa in the average sense

skellam shrinkage wavelet based intensity estimation for inhomogeneous poisson data the ubiquity of integrating detectors in imaging and other applications implies that a variety of real world data are well modeled as poisson random variables whose means are in turn proportional to an underlying vector valued signal of interest in this article we first show how the so called skellam distribution arises from the fact that haar wavelet and filterbank transform coefficients corresponding to measurements of this type are distributed as sums and differences of poisson counts we then provide two main theorems on skellam shrinkage one showing the near optimality of shrinkage in the bayesian setting and the other providing for unbiased risk estimation in a frequentist context these results serve to yield new estimators in the haar transform domain including an unbiased risk estimate for shrinkage of haar fisz variance stabilized data along with accompanying low complexity algorithms for inference we conclude with a simulation study demonstrating the efficacy of our skellam shrinkage estimators both for the standard univariate wavelet test functions as well as a variety of test images taken from the image processing literature confirming that they offer some performance improvements over existing alternatives

nonparametric regression in exponential families most results in nonparametric regression theory are developed only for the case of additive noise in such a setting many smoothing techniques including wavelet thresholding methods have been developed and shown to be highly adaptive in this paper we consider nonparametric regression in exponential families with the main focus on the natural exponential families with a quadratic variance function which include for example poisson regression binomial regression and gamma regression we propose a unified approach of using a mean matching variance stabilizing transformation to turn the relatively complicated problem of nonparametric regression in exponential families into a standard homoscedastic gaussian regression problem then in principle any good nonparametric gaussian regression procedure can be applied to the transformed data to illustrate our general methodology in this paper we use wavelet block thresholding to construct the final estimators of the regression function the procedures are easily implementable both theoretical and numerical properties of the estimators are investigated the estimators are shown to enjoy a high degree of adaptivity and spatial adaptivity with near optimal asymptotic performance over a wide range of besov spaces the estimators also perform well numerically

adapting to unknown smoothness via wavelet shrinkage abstract we attempt to recover a function of unknown smoothness from noisy sampled data we introduce a procedure sureshrink that suppresses noise by thresholding the empirical wavelet coefficients the thresholding is adaptive a threshold level is assigned to each dyadic resolution level by the principle of minimizing the stein unbiased estimate of risk sure for threshold estimates the computational effort of the overall procedure is order n log n as a function of the sample size n sureshrink is smoothness adaptive if the unknown function contains jumps then the reconstruction essentially does also if the unknown function has a smooth piece then the reconstruction is essentially as smooth as the mother wavelet will allow the procedure is in a sense optimally smoothness adaptive it is near minimax simultaneously over a whole interval of the besov scale the size of this interval depends on the choice of mother wavelet we know from a previous paper by the authors that traditional smoot

code design to optimize radar detection performance under accuracy and similarity constraints this paper deals with the design of coded waveforms which optimize radar performances in the presence of colored gaussian disturbance we focus on the class of linearly coded pulse trains and determine the optimum radar code according to the following criterion maximization of the detection performance under a control on the region of achievable doppler estimation accuracies and imposing a similarity constraint with a prefixed radar code this last constraint is tantamount to requiring a similarity between the ambiguity functions of the devised waveform and of the pulse train encoded with the prefixed sequence the resulting optimization problem is nonconvex and quadratic in order to solve it we propose a technique with polynomial computational complexity based on the relaxation of the original problem into a semidefinite program thus the best code is determined through a rank one decomposition of an optimal solution of the relaxed problem at the analysis stage we assess the performance of the new encoding technique in terms of detection performance region of achievable doppler estimation accuracies and ambiguity function

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

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

bayesian multiscale models for poisson processes abstract i introduce a class of bayesian multiscale models bmsm s for one dimensional inhomogeneous poisson processes the focus is on estimating the discretized intensity function underlying the process unlike the usual transform based approach at the heart of most wavelet based methods for gaussian data these bmsm s are constructed using recursive dyadic partitions rdp s within an entirely likelihood based framework each rdp may be associated with a binary tree and a new multiscale prior distribution is introduced for the unknown intensity through the placement of mixture distributions at each of the nodes of the tree the concept of model mixing is then applied to a complete collection of such trees in addition to allowing for the inclusion of full location scale information in the model this last step also is fundamental both in inducing stationarity in the prior distribution and in enabling a given intensity function to be approximated at the resolution of the data under squared error lo

complex quadratic optimization and semidefinite programming in this paper we study the approximation algorithms for a class of discrete quadratic optimization problems in the hermitian complex form a special case of the problem that we study corresponds to the max 3 cut model used in a recent paper of goemans and williamson j comput system sci 68 2004 pp 442 470 we first develop a closed form formula to compute the probability of a complex valued normally distributed bivariate random vector to be in a given angular region this formula allows us to compute the expected value of a randomized with a specific rounding rule solution based on the optimal solution of the complex semidefinite programming relaxation problem in particular we present an m 2 1 cos frac 2 pi m 8 pi approximation algorithm and then study the limit of that model in which the problem remains np hard we show that if the objective is to maximize a positive semidefinite hermitian form then the randomization rounding procedure guarantees a worst case performance ratio of pi 4 approx 0 7854 which is better than the ratio of 2 pi approx 0 6366 for its counterpart in the real case due to nesterov furthermore if the objective matrix is real valued positive semidefinite with nonpositive off diagonal elements then the performance ratio improves to 0 9349

iterative shrinkage approach to restoration of optical imagery the problem of reconstruction of digital images from their degraded measurements is regarded as a problem of central importance in various fields of engineering and imaging sciences in such cases the degradation is typically caused by the resolution limitations of an imaging device in use and or by the destructive influence of measurement noise specifically when the noise obeys a poisson probability law standard approaches to the problem of image reconstruction are based upon using fixed point algorithms which follow the methodology first proposed by richardson and lucy the practice of using these methods however shows that their convergence properties tend to deteriorate at relatively high noise levels accordingly in the present paper a novel method for denoising and or deblurring of digital images corrupted by poisson noise is introduced the proposed method is derived under the assumption that the image of interest can be sparsely represented in the domain of a linear transform consequently a shrinkage based iterative procedure is proposed which guarantees the solution to converge to the global maximizer of an associated maximum a posteriori criterion it is shown in a series of computer simulated experiments that the proposed method outperforms a number of existing alternatives in terms of stability precision and computational efficiency

efficient computation of the binary vector that maximizes a rank deficient quadratic form the maximization of a full rank quadratic form over the binary alphabet can be performed through exponential complexity exhaustive search however if the rank of the form is not a function of the problem size then it can be maximized in polynomial time by introducing auxiliary spherical coordinates we show that the rank deficient quadratic form maximization problem is converted into a double maximization of a linear form over a multidimensional continuous set the multidimensional set is partitioned into a polynomial size set of regions which are associated with distinct candidate binary vectors and the optimal binary vector belongs to the polynomial size set of candidate vectors thus the size of the candidate set is reduced from exponential to polynomial we also develop an algorithm that constructs the polynomial size candidate set in polynomial time and show that it is fully parallelizable and rank scalable finally we demonstrate the efficiency of the proposed algorithm in the context of adaptive spreading code design

orthonormal bases of compactly supported wavelets we construct orthonormal bases of compactly supported wavelets with arbitrarily high regularity the order of regularity increases linearly with the support width we start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction the construction then follows from a synthesis of these different approaches

on meeting the peak correlation bounds in this paper we study the problem of meeting peak periodic or aperiodic correlation bounds for complex valued sets of sequences to this end the welch levenstein and exponential bounds on the peak inner product of sequence sets are considered and used to provide compound peak correlation bounds in both periodic and aperiodic cases the peak aperiodic correlation bound is further improved by using the intrinsic dimension deficiencies associated with its formulation in comparison to the compound bound the new aperiodic bound contributes an improvement of more than 35 for some specific values of the sequence length n and set cardinality m we study the tightness of the provided bounds by using both analytical and computational tools in particular novel algorithms based on alternating projections are devised to approach a given peak periodic or aperiodic correlation bound several numerical examples are presented to assess the tightness of the provided correlation bounds as well as to illustrate the effectiveness of the proposed methods for meeting these bounds

monotone empirical bayes estimators based on more informative samples abstract an empirical bayes estimator is constructed for the case of nonidentical components coming from an exponential family of distributions that is closed under convolution examples are the normal poisson and binomial distributions the construction is based on robbins approach to empirical bayes estimation and generalizes results of o bryan and stijnen and van houwelingen the method is elaborated for the normal and poisson case and examples are given that show that this approach gives results comparable to those from the nonparametric maximum likelihood approach of laird

wavelets ridgelets and curvelets for poisson noise removal in order to denoise poisson count data we introduce a variance stabilizing transform vst applied on a filtered discrete poisson process yielding a near gaussian process with asymptotic constant variance this new transform which can be deemed as an extension of the anscombe transform to filtered data is simple fast and efficient in very low count situations we combine this vst with the filter banks of wavelets ridgelets and curvelets leading to multiscale vsts ms vsts and nonlinear decomposition schemes by doing so the noise contaminated coefficients of these ms vst modified transforms are asymptotically normally distributed with known variances a classical hypothesis testing framework is adopted to detect the significant coefficients and a sparsity driven iterative scheme reconstructs properly the final estimate a range of examples show the power of this ms vst approach for recovering important structures of various morphologies in very low count images these results also demonstrate that the ms vst approach is competitive relative to many existing denoising methods

constant modulus mimo radar waveform design with minimum peak sidelobe transmit beampattern this paper addresses the problem of minimum peak sidelobe transmit beampattern design for colocated multiple input multiple output radar systems two new methods are proposed to achieve it via designing constant modulus cm waveforms directly one is to maximize the ratio of the minimum mainlobe level to the peak sidelobe level psl without specifying pattern masks and another is to minimize psl under the mainlobe ripple and unspecified waveform modulus constraints the resultant optimization problems are difficult to solve due to the coupled numerator and denominator of the quadratic fractional programming problem formulation in the former and double sided quadratic constraints and unknown waveform modulus in the latter for the former we decouple the numerator and denominator by equivalent transformation and introduction of boundary type auxiliary variables in order that feasible methods are derived to tackle them independently and efficiently for the latter we simplify the coupled double sided quadratic constraints on the same waveform vector into those on different single auxiliary variables to tackle the corresponding nonconvex optimization problem numerical examples show that the proposed algorithms can attain sufficient low peak sidelobe beampattern levels under the cm constraints

patch based nonlocal functional for denoising fluorescence microscopy image sequences we present a nonparametric regression method for denoising 3 d image sequences acquired via fluorescence microscopy the proposed method exploits the redundancy of the 3 d time information to improve the signal to noise ratio of images corrupted by poisson gaussian noise a variance stabilization transform is first applied to the image data to remove the dependence between the mean and variance of intensity values this preprocessing requires the knowledge of parameters related to the acquisition system also estimated in our approach in a second step we propose an original statistical patch based framework for noise reduction and preservation of space time discontinuities in our study discontinuities are related to small moving spots with high velocity observed in fluorescence video microscopy the idea is to minimize an objective nonlocal energy functional involving spatio temporal image patches the minimizer has a simple form and is defined as the weighted average of input data taken in spatially varying neighborhoods the size of each neighborhood is optimized to improve the performance of the pointwise estimator the performance of the algorithm which requires no motion estimation is then evaluated on both synthetic and real image sequences using qualitative and quantitative criteria

bayesian tree structured image modeling using wavelet domain hidden markov models wavelet domain hidden markov models have proven to be useful tools for statistical signal and image processing the hidden markov tree hmt model captures the key features of the joint probability density of the wavelet coefficients of real world data one potential drawback to the hmt framework is the need for computationally expensive iterative training to fit an hmt model to a given data set e g using the expectation maximization algorithm we greatly simplify the hmt model by exploiting the inherent self similarity of real world images the simplified model specifies the hmt parameters with just nine meta parameters independent of the size of the image and the number of wavelet scales we also introduce a bayesian universal hmt uhmt that fixes these nine parameters the uhmt requires no training of any kind while extremely simple we show using a series of image estimation denoising experiments that these new models retain nearly all of the key image structure modeled by the full hmt finally we propose a fast shift invariant hmt estimation algorithm that outperforms other wavelet based estimators in the current literature both visually and in mean square error

multiscale likelihood analysis and complexity penalized estimation we describe here a framework for a certain class of multiscale likelihood factorizations wherein in analogy to a wavelet decomposition of an l 2 function a given likelihood function has an alternative representation as a product of conditional densities reflecting information in both the data and the parameter vector localized in position and scale the framework is developed as a set of sufficient conditions for the existence of such factorizations formulated in analogy to those underlying a standard multiresolution analysis for wavelets and hence can be viewed as a multiresolution analysis for likelihoods we then consider the use of these factorizations in the task of nonparametric complexity penalized likelihood estimation we study the risk properties of certain thresholding and partitioning estimators and demonstrate their adaptivity and near optimality in a minimax sense over a broad range of function spaces based on squared hellinger distance as a loss function in particular our results provide an illustration of how properties of classical wavelet based estimators can be obtained in a single unified framework that includes models for continuous count and categorical data types

ambiguity function shaping for cognitive radar via complex quartic optimization in this paper we propose a cognitive approach to design phase only modulated waveforms sharing a desired range doppler response the idea is to minimize the average value of the ambiguity function of the transmitted signal over some range doppler bins which are identified exploiting a plurality of knowledge sources from a technical point of view this is tantamount to optimizing a real and homogeneous complex quartic order polynomial with a constant modulus constraint on each optimization variable after proving some interesting properties of the considered problem we devise a polynomial time waveform optimization procedure based on the maximum block improvement mbi method and the theory of conjugate partial symmetric conjugate super symmetric fourth order tensors at the analysis stage we assess the performance of the proposed technique showing its capability to properly shape the range doppler response of the transmitted waveform

a proximal iteration for deconvolving poisson noisy images using sparse representations we propose an image deconvolution algorithm when the data is contaminated by poisson noise the image to restore is assumed to be sparsely represented in a dictionary of waveforms such as the wavelet or curvelet transforms our key contributions are as follows first we handle the poisson noise properly by using the anscombe variance stabilizing transform leading to a nonlinear degradation equation with additive gaussian noise second the deconvolution problem is formulated as the minimization of a convex functional with a data fidelity term reflecting the noise properties and a nonsmooth sparsity promoting penalty over the image representation coefficients e g lscr1 norm an additional term is also included in the functional to ensure positivity of the restored image third a fast iterative forward backward splitting algorithm is proposed to solve the minimization problem we derive existence and uniqueness conditions of the solution and establish convergence of the iterative algorithm finally a gcv based model selection procedure is proposed to objectively select the regularization parameter experimental results are carried out to show the striking benefits gained from taking into account the poisson statistics of the noise these results also suggest that using sparse domain regularization may be tractable in many deconvolution applications with poisson noise such as astronomy and microscopy

quadratic optimization with similarity constraint for unimodular sequence synthesis this paper considers unimodular sequence synthesis under similarity constraint for both the continuous and discrete phase cases a computationally efficient iterative algorithm for the continuous phase case ia cpc is proposed to sequentially optimize the quadratic objective function the quadratic optimization problem is turned into multiple one dimensional optimization problems with closed form solutions for the discrete phase case we present an iterative block optimization algorithm specifically we partition the design variables into k blocks and then we sequentially optimize each block via exhaustive search while fixing the remaining k 1 blocks finally we evaluate the computational costs and performance gains of the proposed algorithms in comparison with power method like and semidefinite relaxation related techniques

computational design of sequences with good correlation properties in this paper we introduce a computational framework based on an iterative twisted approximation itrox and a set of associated algorithms for various sequence design problems the proposed computational framework can be used to obtain sequences or complementary sets of sequences possessing good periodic or aperiodic correlation properties and in an extended form to construct zero or low correlation zone sequences furthermore as constrained e g finite alphabets are of interest in many applications we introduce a modified version of our general framework that can be useful in these cases several applications of itrox are studied and numerical examples focusing on the construction of real valued and binary sequences are provided to illustrate the performance of itrox for each application

a doppler robust max min approach to radar code design this correspondence considers the problem of robust waveform design in the presence of colored gaussian disturbance under a similarity and an energy constraint we resort to a max min approach where the worst case detection performance over the possible doppler shifts is optimized with respect to the radar waveform under the previously mentioned constraints the resulting optimization problem is a non convex quadratically constrained quadratic program qcqp with an infinite number of constraints which is np hard in general and typically difficult to solve hence we propose an algorithm with a polynomial computational complexity to generate a good sub optimal solution for the aforementioned qcqp the analysis conducted in comparison with some known radar waveforms shows that the sub optimal solutions by the algorithm lead to high quality radar signals

nonconvex phase synchronization we estimate n phases angles from noisy pairwise relative phase measurements the task is modeled as a nonconvex least squares optimization problem it was recently shown that this problem can be solved in polynomial time via convex relaxation under some conditions on the noise in this paper under similar but more restrictive conditions we show that a modified version of the power method converges to the global optimum this is simpler and empirically faster than convex approaches empirically they both succeed in the same regime further analysis shows that in the same noise regime as previously studied second order necessary optimality conditions for this quadratically constrained quadratic program are also sufficient despite nonconvexity

support value based stent graft marker detection with the development of the fluoroscopic roentgenographic stereophotogrammetric analysis frsa it is possible to make the three dimensional 3d dynamics of stent graft the stent graft markers however are identified manually in this paper we present a robust solution for automatic detection of stent graft marker projections in frsa x ray images several directional support value dsv filters and the directional support value transform dsvt method are studied based on the dsv of the dsvt a support value matrix is constructed and the determinant of this matrix is then defined as the markerness measure the corresponding multi scale correlations of the rescaled markerness measures are computed for enhancing the multi scale marker response peaks while suppressing the effects of stent grafts and poisson noise the marker spots are subsequently located by finding the local maximum of the correlated markerness measures the conditional variance stabilizer cvs is further integrated into this framework for removing poisson noises performance comparisons are carried out among the proposed dsvt the cvs dsvt local threshold operation lto and the frequently adopted spot detectors including the morphological grayscale opening top hat filter mth wavelet multiscale products wmp and multiscale variance stabilizing transform msvst methods the results from experiments on synthetic as well as real frsa x ray image data show that the proposed cvs dsvt method performs better than other detectors in terms of the free response receiver operation characteristic froc curves