signal recovery with certain involved convex data fidelity constraints this paper proposes an optimization framework that can efficiently deal with convex data fidelity constraints onto which the metric projections are difficult to compute although such an involved data fidelity constraint is expected to play an important role in signal recovery under non gaussian noise contamination the said difficulty precludes existing algorithms from solving convex optimization problems with the constraint to resolve this dilemma we introduce a fixed point set characterization of involved data fidelity constraints based on a certain computable quasi nonexpansive mapping this characterization enables us to mobilize the hybrid steepest descent method to solve convex optimization problems with such a constraint the proposed framework can handle a variety of involved data fidelity constraints in a unified manner without geometric approximation to them in addition it requires no computationally expensive procedure such as operator inversion and inner loop as applications of the proposed framework we provide image restoration under several types of non gaussian noise contamination with illustrative examples

a new twist two step iterative shrinkage thresholding algorithms for image restoration iterative shrinkage thresholding 1st algorithms have been recently proposed to handle a class of convex unconstrained optimization problems arising in image restoration and other linear inverse problems this class of problems results from combining a linear observation model with a nonquadratic regularizer e g total variation or wavelet based regularization it happens that the convergence rate of these 1st algorithms depends heavily on the linear observation operator becoming very slow when this operator is ill conditioned or ill posed in this paper we introduce two step 1st twist algorithms exhibiting much faster convergence rate than 1st for ill conditioned problems for a vast class of nonquadratic convex regularizers lscrp norms some besov norms and total variation we show that twist converges to a minimizer of the objective function for a given range of values of its parameters for noninvertible observation operators we introduce a monotonic version of twist mtwist although the convergence proof does not apply to this scenario we give experimental evidence that mtwist exhibits similar speed gains over ist the effectiveness of the new methods are experimentally confirmed on problems of image deconvolution and of restoration with missing samples

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

proximal thresholding algorithm for minimization over orthonormal bases the notion of soft thresholding plays a central role in problems from various areas of applied mathematics in which the ideal solution is known to possess a sparse decomposition in some orthonormal basis using convex analytical tools we extend this notion to that of proximal thresholding and investigate its properties providing in particular several characterizations of such thresholders we then propose a versatile convex variational formulation for optimization over orthonormal bases that covers a wide range of problems and we establish the strong convergence of a proximal thresholding algorithm to solve it numerical applications to signal recovery are demonstrated

a splitting based iterative algorithm for accelerated statistical x ray ct reconstruction statistical image reconstruction using penalized weighted least squares pwls criteria can improve image quality in x ray computed tomography ct however the huge dynamic range of the statistical weights leads to a highly shift variant inverse problem making it difficult to precondition and accelerate existing iterative algorithms that attack the statistical model directly we propose to alleviate the problem by using a variable splitting scheme that separates the shift variant and nearly invariant components of the statistical data model and also decouples the regularization term this leads to an equivalent constrained problem that we tackle using the classical method of multipliers framework with alternating minimization the specific form of our splitting yields an alternating direction method of multipliers admm algorithm with an inner step involving a nearly shift invariant linear system that is suitable for fft based preconditioning using cone type filters the proposed method can efficiently handle a variety of convex regularization criteria including smooth edge preserving regularizers and non smooth sparsity promoting ones based on the l1 norm and total variation numerical experiments with synthetic and real in vivo human data illustrate that cone filter preconditioners accelerate the proposed admm resulting in fast convergence of admm compared to conventional nonlinear conjugate gradient ordered subsets and state of the art mfista split bregman algorithms that are applicable for ct

efficient robust conditional random fields conditional random fields crfs are a flexible yet powerful probabilistic approach and have shown advantages for popular applications in various areas including text analysis bioinformatics and computer vision traditional crf models however are incapable of selecting relevant features as well as suppressing noise from noisy original features moreover conventional optimization methods often converge slowly in solving the training procedure of crfs and will degrade significantly for tasks with a large number of samples and features in this paper we propose robust crfs rcrfs to simultaneously select relevant features an optimal gradient method ogm is further designed to train rcrfs efficiently specifically the proposed rcrfs employ the ell 1 norm of the model parameters to regularize the objective used by traditional crfs therefore enabling discovery of the relevant unary features and pairwise features of crfs in each iteration of ogm the gradient direction is determined jointly by the current gradient together with the historical gradients and the lipschitz constant is leveraged to specify the proper step size we show that an ogm can tackle the rcrf model training very efficiently achieving the optimal convergence rate o 1 k vphantom r r 2 where k is the number of iterations this convergence rate is theoretically superior to the convergence rate o 1 k of previous first order optimization methods extensive experiments performed on three practical image segmentation tasks demonstrate the efficacy of ogm in training our proposed rcrfs

perturbation method for condensation of eigenproblems a perturbation method using a correction in transformation is presented to improve the condensation solution the method proved to be effective and is recommended as a postprocessor of the condensation

penalized maximum likelihood image reconstruction using space alternating generalized em algorithms most expectation maximization em type algorithms for penalized maximum likelihood image reconstruction converge slowly particularly when one incorporates additive background effects such as scatter random coincidences dark current or cosmic radiation in addition regularizing smoothness penalties or priors introduce parameter coupling rendering intractable the m steps of most em type algorithms this paper presents space alternating generalized em sage algorithms for image reconstruction which update the parameters sequentially using a sequence of small hidden data spaces rather than simultaneously using one large complete data space the sequential update decouples the m step so the maximization can typically be performed analytically we introduce new hidden data spaces that are less informative than the conventional complete data space for poisson data and that yield significant improvements in convergence rate this acceleration is due to statistical considerations not numerical overrelaxation methods so monotonic increases in the objective function are guaranteed we provide a general global convergence proof for sage methods with nonnegativity constraints

spatially adapted total variation model to remove multiplicative noise multiplicative noise removal based on total variation tv regularization has been widely researched in image science in this paper inspired by the spatially adapted methods for denoising gaussian noise we develop a variational model which combines the tv regularizer with local constraints it is also related to a tv model with spatially adapted regularization parameters the automated selection of the regularization parameters is based on the local statistical characteristics of some random variable the corresponding subproblem can be efficiently solved by the augmented lagrangian method numerical examples demonstrate that the proposed algorithm is able to preserve small image details whereas the noise in the homogeneous regions is sufficiently removed as a consequence our method yields better denoised results than those of the current state of the art methods with respect to the signal to noise ratio values

the three dimensional euler equations where do we stand the three dimensional euler equations have stood for a quarter of a millenium as a challenge to mathematicians and physicists while much has been discovered the nature of solutions is still largely a mystery this paper surveys some of the issues such as singularity formation that have cost so much effort in the last 25 years in this light we review the beale kato majda theorem and its consequences and then list some of the results of numerical experiments that have been attempted a different line of endeavour focuses on work concerning the pressure hessian and how it may be used and modelled the euler equations are finally discussed in terms of their membership of a class of general lagrangian evolution equations using hamilton s quaternions these are reformulated in an elegant manner to describe the motion and rotation of fluid particles c 2007 elsevier b v all rights reserved

a generalized accelerated proximal gradient approach for total variation based image restoration this paper proposes a generalized accelerated proximal gradient gapg approach for solving total variation tv based image restoration problems the gapg algorithm generalizes the original apg algorithm by replacing the lipschitz constant with an appropriate positive definite matrix resulting in faster convergence for tv based image restoration problems we further introduce two auxiliary variables that approximate the partial derivatives constraints on the variables can easily be imposed without modifying the algorithm much and the tv regularization can be either isotropic or anisotropic as compared with the recently developed apg based methods for tv based image restoration i e monotone version of the two step iterative shrinkage thresholding algorithm mtwist and monotone version of the fast ist algorithm mfista our gapg is much simpler as it does not require to solve an image denoising subproblem moreover the convergence rate of o k 2 is maintained by our gapg where k is the number of iterations the cost of each iteration in gapg is also lower as a result in our experiments our gapg approach can be much faster than mtwist and mfista the experiments also verify that our gapg converges faster than the original apg and mtwist when they solve identical problems

blowup or no blowup the interplay between theory and numerics the question of whether the 3d incompressible euler equations can develop a finite time singularity from smooth initial data has been an outstanding open problem in fluid dynamics and mathematics recent studies indicate that the local geometric regularity of vortex lines can lead to dynamic depletion of vortex stretching guided by the local non blowup theory we have performed large scale computations of the 3d euler equations on some of the most promising blowup candidates our results show that there is tremendous dynamic depletion of vortex stretching the local geometric regularity of vortex lines and the anisotropic solution structure play an important role in depleting the nonlinearity dynamically and thus prevents a finite time blowup

automatic choice of measurement locations for dynamic testing this paper examines the problem of choosing an optimum set of measurement locations for experimental modal testing and suggests criteria whereby the suitability of the chosen locations can be assessed two methods of coordinate selection are used one based on guyan reduction and the other on the fisher information matrix each begins with a detailed finite element model of the structure being tested both procedures reduce this model by one degree of freedom at a time until the number of degrees of freedom in the reduced model equals the number of measurement locations required the choice of the eliminated coordinates is generally automatic and the coordinates of the reduced model are those used for modal testing

total nuclear variation and jacobian extensions of total variation for vector fields we explore a class of vectorial total variation vtv measures formed as the spatial sum of a pixel wise matrix norm of the jacobian of a vector field we give a theoretical treatment that indicates that while color smearing and affine coupling bias often reported as gray scale bias are typically cited as drawbacks for vtv these are actually fundamental to smoothing vector direction i e smoothing hue and saturation in color images additionally we show that encouraging different vector channels to share a common gradient direction is equivalent to minimizing jacobian rank we thus propose total nuclear variation tnv and since nuclear norm is the convex envelope of matrix rank we argue that tnv is the optimal convex regularizer for enforcing shared directions we also propose extended jacobians which use larger neighborhoods than the conventional finite difference operator and we discuss efficient vtv optimization algorithms in simple color image denoising experiments tnv outperformed other common vtv regularizers and was further improved by using extended jacobians tnv was also competitive with the method of non local means often outperforming it by 0 25 to 2 db when using extended jacobians

multiplicative noise removal using variable splitting and constrained optimization multiplicative noise also known as speckle noise models are central to the study of coherent imaging systems such as synthetic aperture radar and sonar and ultrasound and laser imaging these models introduce two additional layers of difficulties with respect to the standard gaussian additive noise scenario 1 the noise is multiplied by rather than added to the original image 2 the noise is not gaussian with rayleigh and gamma being commonly used densities these two features of multiplicative noise models preclude the direct application of most state of the art algorithms which are designed for solving unconstrained optimization problems where the objective has two terms a quadratic data term log likelihood reflecting the additive and gaussian nature of the noise plus a convex possibly nonsmooth regularizer e g a total variation or wavelet based regularizer prior in this paper we address these difficulties by 1 converting the multiplicative model into an additive one by taking logarithms as proposed by some other authors 2 using variable splitting to obtain an equivalent constrained problem and 3 dealing with this optimization problem using the augmented lagrangian framework a set of experiments shows that the proposed method which we name midal multiplicative image denoising by augmented lagrangian yields state of the art results both in terms of speed and denoising performance

improved denoising via poisson mixture modeling of image sensor noise this paper describes a study aimed at comparing the real image sensor noise distribution to the models of noise often assumed in image denoising designs a quantile analysis in pixel wavelet transform and variance stabilization domains reveal that the tails of poisson signal dependent gaussian and poisson gaussian models are too short to capture real sensor noise behavior a new poisson mixture noise model is proposed to correct the mismatch of tail behavior based on the fact that noise model mismatch results in image denoising that undersmoothes real sensor data we propose a mixture of poisson denoising method to remove the denoising artifacts without affecting image details such as edge and textures experiments with real sensor data verify that denoising for real image sensor data is indeed improved by this new technique

3d euler equations and ideal mhd mapped to regular systems probing the finite time blowup hypothesis abstract we prove by an explicit construction that solutions to incompressible 3d euler equations defined in the periodic cube 0 l 3 can be mapped bijectively to a new system of equations whose solutions are globally regular we establish that the usual beale kato majda criterion for finite time singularity or blowup of a solution to the 3d euler system is equivalent to a condition on the corresponding regular solution of the new system in the hypothetical case of euler finite time singularity we provide an explicit formula for the blowup time in terms of the regular solution of the new system the new system is amenable to being integrated numerically using similar methods as in euler equations we propose a method to simulate numerically the new regular system and describe how to use this to draw robust and reliable conclusions on the finite time singularity problem of euler equations based on the conservation of quantities directly related to energy and circulation the method of mapping to a regular system can be extended to any fluid equation that admits a beale kato majda type of theorem e g 3d navier stokes 2d and 3d magnetohydrodynamics and 1d inviscid burgers we discuss briefly the case of 2d ideal magnetohydrodynamics in order to illustrate the usefulness of the mapping we provide a thorough comparison of the analytical solution versus the numerical solution in the case of 1d inviscid burgers equation

sampling based uncertainty quantification in deconvolution of x ray radiographs abstract in imaging applications that focus on quantitative analysis such as x ray radiography in the security sciences it is necessary to be able to reliably estimate the uncertainties in the processing algorithms applied to the image data and deconvolving the system blur out of the image is usually an essential step in this work we solve the deconvolution problem within a bayesian framework for edge enhancing reconstruction with uncertainty quantification the likelihood is a normal approximation to the poisson likelihood and the prior is generated from a classical total variation regularized poisson deconvolution samples from the corresponding posterior distribution are computed using a markov chain monte carlo approach giving a pointwise measure of uncertainty in the reconstructed signal we demonstrate the results on real data used to calibrate a high energy x ray source and show that this approach gives reconstructions as good as classical regularization methods while mitigating many of their drawbacks

a kalman filter approach for denoising and deblurring 3 d microscopy images this paper proposes a new method for removing noise and blurring from 3d microscopy images the main contribution is the definition of a space variant generating model of a 3 d signal which is capable to stochastically describe a wide class of 3 d images unlike other approaches the space variant structure allows the model to consider the information on edge locations if available a suitable description of the image acquisition process including blurring and noise is then associated to the model a state space realization is finally derived which is amenable to the application of standard kalman filter as an image restoration algorithm the so obtained method is able to remove at each spatial step both blur and noise via a linear minimum variance recursive one shot procedure which does not require the simultaneous processing of the whole image numerical results on synthetic and real microscopy images confirm the merit of the approach

improvement on the iterated irs method for structural eigensolutions iterated improved reduced system iirs technique is a model reduction or condensation method by repeatedly updating a transformation matrix an improvement on this dynamic condensation technique is proposed in this paper to modify the iterative transformation matrix and achieve faster convergence meanwhile connection between the present algorithm and the subspace iteration method sim is demonstrated a proof of the convergence property is also presented applications of the method to two numerical examples have demonstrated that the proposed method can obtain the lowest eigensolutions of structures more accurately and efficiently as compared with the current iirs

finite time blow up for a 1d model of 2d boussinesq system the 2d conservative boussinesq system describes inviscid incompressible buoyant fluid flow in a gravity field the possibility of finite time blow up for solutions of this system is a classical problem of mathematical hydrodynamics we consider a 1d model of the 2d boussinesq system motivated by a particular finite time blow up scenario we prove that finite time blow up is possible for the solutions to the model system

on the eddy resolving capability of high order discontinuous galerkin approaches to implicit les under resolved dns of euler turbulence we present estimates of spectral resolution power for under resolved turbulent euler flows obtained with high order discontinuous galerkin dg methods the 1 rule based on linear dispersion diffusion analysis introduced by moura et al 2015 10 is here adapted for 3d energy spectra and validated through the inviscid taylor green vortex problem the 1 rule estimates the wavenumber beyond which numerical diffusion induces an artificial dissipation range on measured energy spectra as the original rule relies on standard upwinding different riemann solvers are tested very good agreement is found for solvers which treat the different physical waves in a consistent manner relatively good agreement is still found for simpler solvers the latter however displayed spurious features attributed to the inconsistent treatment of different physical waves it is argued that in the limit of vanishing viscosity such features might have a significant impact on robustness and solution quality the estimates proposed are regarded as useful guidelines for no model dg based simulations of free turbulence at very high reynolds numbers

a variational approach to removing multiplicative noise this paper focuses on the problem of multiplicative noise removal we draw our inspiration from the modeling of speckle noise by using a map estimator we can derive a functional whose minimizer corresponds to the denoised image we want to recover although the functional is not convex we prove the existence of a minimizer and we show the capability of our model on some numerical examples we study the associated evolution problem for which we derive existence and uniqueness results for the solution we prove the convergence of an implicit scheme to compute the solution

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

poisson inverse problems in this paper we focus on nonparametric estimators in inverse problems for poisson processes involving the use of wavelet decompositions adopting an adaptive wavelet galerkin discretization we find that our method combines the well known theoretical advantages of wavelet vaguelette decompositions for inverse problems in terms of optimally adapting to the unknown smoothness of the solution together with the remarkably simple closed form expressions of galerkin inversion methods adapting the results of barron and sheu ann statist 19 1991 1347 1369 to the context of log intensity functions approximated by wavelet series with the use of the kullback leibler distance between two point processes we also present an asymptotic analysis of convergence rates that justifies our approach in order to shed some light on the theoretical results obtained and to examine the accuracy of our estimates in finite samples we illustrate our method by the analysis of some simulated examples

direct approach in inverse problems for dynamic systems a direct and effective approach is presented for the inverse problem of dynamic structural systems which is related to structural optimization system identification and damage detection the structural modifications are sought for the characteristic changes assigned from the design goals or modal measurements a finite element method is used for the system analysis and inverse problem mathematical programming techniques are applied for the minimization of the deviation of the finite element model from the desired inverse system along with an objective function of least structural change the modal method is based on the perturbation equations of a set of selected degrees of freedom and the energy equation associated with the frequency change the mode shape change is expressed as the sum of the baseline mode shape and complementary vector which plays a very important role in the search for the inverse solution the linear perturbation equation is employed to get an initial approximation which can be improved through iterations with the nonlinear perturbation equation the proposed method does not involve the system reduction therefore it is believed to be superior to conventional methods which suffer from the residual error due to transformation of the eigenproblem

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

accelerated edge preserving image restoration without boundary artifacts to reduce blur in noisy images regularized image restoration methods have been proposed that use nonquadratic regularizers like l1 regularization or total variation that suppress noise while preserving edges in the image most of these methods assume a circulant blur periodic convolution with a blurring kernel that can lead to wraparound artifacts along the boundaries of the image due to the implied periodicity of the circulant model using a noncirculant model could prevent these artifacts at the cost of increased computational complexity in this paper we propose to use a circulant blur model combined with a masking operator that prevents wraparound artifacts the resulting model is noncirculant so we propose an efficient algorithm using variable splitting and augmented lagrangian al strategies our variable splitting scheme when combined with the al framework and alternating minimization leads to simple linear systems that can be solved noniteratively using fast fourier transforms ffts eliminating the need for more expensive conjugate gradient type solvers the proposed method can also efficiently tackle a variety of convex regularizers including edge preserving e g total variation and sparsity promoting e g l1 norm regularizers simulation results show fast convergence of the proposed method along with improved image quality at the boundaries where the circulant model is inaccurate

a nonlinear primal dual method for total variation based image restoration we present a new method for solving total variation tv minimization problems in image restoration the main idea is to remove some of the singularity caused by the nondifferentiability of the quantity nabla u in the definition of the tv norm before we apply a linearization technique such as newton s method this is accomplished by introducing an additional variable for the flux quantity appearing in the gradient of the objective function which can be interpreted as the normal vector to the level sets of the image u our method can be viewed as a primal dual method as proposed by conn and overton a primal dual interior point method for minimizing a sum of euclidean norms preprint 1994 and andersen ph d thesis odense university denmark 1995 for the minimization of a sum of euclidean norms in addition to possessing local quadratic convergence experimental results show that the new method seems to be globally convergent

platelets a multiscale approach for recovering edges and surfaces in photon limited medical imaging the nonparametric multiscale platelet algorithms presented in this paper unlike traditional wavelet based methods are both well suited to photon limited medical imaging applications involving poisson data and capable of better approximating edge contours this paper introduces platelets localized functions at various scales locations and orientations that produce piecewise linear image approximations and a new multiscale image decomposition based on these functions platelets are well suited for approximating images consisting of smooth regions separated by smooth boundaries for smoothness measured in certain holder classes it is shown that the error of m term platelet approximations can decay significantly faster than that of m term approximations in terms of sinusoids wavelets or wedgelets this suggests that platelets may outperform existing techniques for image denoising and reconstruction fast platelet based maximum penalized likelihood methods for photon limited image denoising deblurring and tomographic reconstruction problems are developed because platelet decompositions of poisson distributed images are tractable and computationally efficient existing image reconstruction methods based on expectation maximization type algorithms can be easily enhanced with platelet techniques experimental results suggest that platelet based methods can outperform standard reconstruction methods currently in use in confocal microscopy image restoration and emission tomography

dynamic condensation method for structural eigenvalue analysis an improved dynamic condensation approach is presented for accurate calculation of structural eigenproperties the approach is iterative the kept and reduced degrees of freedom in the approach are related through a condensation matrix that is used to form a condensed eigenvalue problem an initial condensation matrix can be defined in terms of the system submatrices the eigenproperties calculated in an iterative step are utilized to update the condensation matrix matrix inversions or gaussian eliminations are avoided in the updating process by employing the orthogonality of the eigenvectors the process of updating the condensation matrix and the eigenvalue problem is repeated until a desired convergence in the eigenvalues is achieved usually a few iterations are quite adequate iterations for both the lower as well as the higher modes can be performed as the condensation matrices for the two sets of modes are very simply related numerical examples are presented to show the applicability of the proposed approach several methods that have been used in practice to select the kept degrees of freedom for condensing are also evaluated numerically with respect to their effectiveness in providing accurate estimates of the eigenproperties with a minimum number of iterations

a new multiplicative denoising variational model based on m th root transformation in coherent imaging systems such as the synthetic aperture radar sar the observed images are contaminated by multiplicative noise due to the edge preserving feature of the total variation tv variational models with tv regularization have attracted much interest in removing multiplicative noise however the fidelity term of the variational model based on maximum a posteriori estimation is not convex and so it is usually difficult to find a global solution hence the logarithmic function is used to transform the nonconvex variational model to the convex one in this paper instead of using the log we exploit the th root function to relax the nonconvexity of the variational model an algorithm based on the augmented lagrangian function which has been applied to solve the log transformed convex variational model can be applied to solve our proposed model however this algorithm requires solving a subproblem which does not have a closed form solution at each iteration hence we propose to adapt the linearized proximal alternating minimization algorithm which does not require inner iterations for solving the subproblems in addition the proposed method is very simple and highly parallelizable thus it is efficient to remove multiplicative noise in huge sar images the proposed model for multiplicative noise removal shows overall better performance than the convex model based on the log transformation

an efficient nonconvex regularization for wavelet frame and total variation based image restoration in order to improve the quality of the image many works impose explicit priors on the solution to regularize the ill posed inverse problem in this paper we propose a hybrid variational model which takes advantages of the wavelet tight frame model and the total variation model for image restoration the core of the method is a new nonconvex penalty function that is designed for efficient minimization by means of the firm thresholding and soft shrinkage operations we address the proposed optimization problem by converting it to a constrained problem with variable splitting and using the alternating direction method of multipliers numerical examples for image restoration are given to show that the proposed method outperforms some existing methods in terms of the peak signal to noise ratio and structural similarity index

parallel proximal algorithm for image restoration using hybrid regularization regularization approaches have demonstrated their effectiveness for solving ill posed problems however in the context of variational restoration methods a challenging question remains namely how to find a good regularizer while total variation introduces staircase effects wavelet domain regularization brings other artefacts e g ringing however a tradeoff can be made by introducing a hybrid regularization including several terms not necessarily acting in the same domain e g spatial and wavelet transform domains while this approach was shown to provide good results for solving deconvolution problems in the presence of additive gaussian noise an important issue is to efficiently deal with this hybrid regularization for more general noise models to solve this problem we adopt a convex optimization framework where the criterion to be minimized is split in the sum of more than two terms for spatial domain regularization isotropic or anisotropic total variation definitions using various gradient filters are considered an accelerated version of the parallel proximal algorithm is proposed to perform the minimization some difficulties in the computation of the proximity operators involved in this algorithm are also addressed in this paper numerical experiments performed in the context of poisson data recovery show the good behavior of the algorithm as well as promising results concerning the use of hybrid regularization techniques

relaxing tight frame condition in parallel proximal methods for signal restoration a fruitful approach for solving signal deconvolution problems consists of resorting to a frame based convex variational formulation in this context parallel proximal algorithms and related alternating direction methods of multipliers have become popular optimization techniques to approximate iteratively the desired solution until now in most of these methods either lipschitz differentiability properties or tight frame representations were assumed in this paper it is shown that it is possible to relax these assumptions by considering a class of non necessarily tight frame representations thus offering the possibility of addressing a broader class of signal restoration problems in particular it is possible to use non necessarily maximally decimated filter banks with perfect reconstruction which are common tools in digital signal processing the proposed approach allows us to solve both frame analysis and frame synthesis problems for various noise distributions in our simulations it is applied to the deconvolution of data corrupted with poisson noise or laplacian noise by using non tight discrete dual tree wavelet representations and filter bank structures

an accurate error estimator for guyan reduction the objective of this study is to develop an error estimator that accurately predicts relative eigenvalue errors in finite element models reduced by guyan reduction we present a derivation procedure for the error estimator in which kidder s transformation matrix for guyan reduction is employed we demonstrate the excellent performance of the proposed error estimator through various numerical examples rectangular plate cylindrical panel hyperboloid panel and shaft shaft interaction problems c

sensor placement methodologies for dynamic testing two methods are presented for structural sensor placement the first scheme selects the most linearly independent impulse responses at all candidate sensor locations from a gram schmidt orthogonalization procedure the second scheme is based on a principal component analysis and iteratively removes sensors that do not contribute significant information to the fisher information matrix furthermore use of a model reduction criterion is proposed to address the optimality issue several sensor placement methods were implemented to compare results and were applied to an euler bernoulli beam and a cantilevered frame structure it is shown that the proposed frequency criterion appears to be a selective criterion for choosing optimum sensor locations finally the optimum measurement locations from several of the methods studied yield acceptable results based on data from an experimental study on the frame structure

on the convergence of a distributed augmented lagrangian method for nonconvex optimization in this paper we propose a distributed algorithm for optimization problems that involve a separable possibly nonconvex objective function subject to convex local constraints and linear coupling constraints the method is based on the accelerated distributed augmented lagrangians adal algorithm that was recently developed by the authors to address convex problems here we extend this line of work in two ways first we establish convergence of the method to a local minimum of the problem using assumptions that are common in the analysis of nonconvex optimization methods to the best of our knowledge this is the first work that shows convergence to local minima specifically for a distributed augmented lagrangian al method applied to nonconvex optimization problems distributed al methods are known to perform very well when used to solve convex problems second we propose a more general and decentralized rule to select the stepsizes of the method this improves on the authors original adal method where the stepsize selection used global information at initialization numerical results are included to verify the correctness and efficiency of the proposed distributed method

proximal linearized alternating direction method for multiplicative denoising multiplicative noise naturally appears in coherent imaging systems such as synthetic aperture radar due to the edge preserving feature of total variation tv variational models with tv regularization show good performance for multiplicative denoising recently proposed augmented lagrangian frameworks with the gauss seidel method are efficient for solving multiplicative denoising variational models with tv but recent algorithms based on the augmented lagrangian require inner iterations or an inverse involving the laplacian operator at each iteration in this paper we propose efficient algorithms for tv regularized convex variational models our proposed algorithms do not require any inner iteration or the inverse involving the laplacian operator by using a linearization scheme and a proximal function we establish global convergence under a lipschitz continuous assumption on the gradient of the fidelity term when a correction step is used numerical results show that our proposed algorithms overall

a statistical multiscale framework for poisson inverse problems this paper describes a statistical multiscale modeling and analysis framework for linear inverse problems involving poisson data the framework itself is founded upon a multiscale analysis associated with recursive partitioning of the underlying intensity a corresponding multiscale factorization of the likelihood induced by this analysis and a choice of prior probability distribution made to match this factorization by modeling the splits in the underlying partition the class of priors used here has the interesting feature that the noninformative member yields the traditional maximum likelihood solution other choices are made to reflect prior belief as to the smoothness of the unknown intensity adopting the expectation maximization em algorithm for use in computing the maximum a posteriori map estimate corresponding to our model we find that our model permits remarkably simple closed form expressions for the em update equations the behavior of our em algorithm is examined and it is shown that convergence to the global map estimate can be guaranteed applications in emission computed tomography and astronomical energy spectral analysis demonstrate the potential of the new approach

iterative reweighted total generalized variation based poisson noise removal model total generalized variation tgv regularization model is one of the most effective methods for denoising and eliminating staircase effect however the tgv regularization model tends to blur edges as the existence of high order derivative in order to avoid the staircase effect while alleviating the edge blurring an iterative reweighted tgv based poisson noise removal model is presented under the assumption that each pixel of noisy image follows a poisson distribution the weight function incorporated in the tgv regularization term is derived from the expectation maximization em algorithm we design a new iterative weighted primal dual algorithm which is an improvement of the classic iterative reweighted algorithm numerical experimental results show the better performance of our model in removing noise effectively while preserving edges and eliminating staircase effect

sparse poisson noisy image deblurring deblurring noisy poisson images has recently been a subject of an increasing amount of works in many areas such as astronomy and biological imaging in this paper we focus on confocal microscopy which is a very popular technique for 3 d imaging of biological living specimens that gives images with a very good resolution several hundreds of nanometers although degraded by both blur and poisson noise deconvolution methods have been proposed to reduce these degradations and in this paper we focus on techniques that promote the introduction of an explicit prior on the solution one difficulty of these techniques is to set the value of the parameter which weights the tradeoff between the data term and the regularizing term only few works have been devoted to the research of an automatic selection of this regularizing parameter when considering poisson noise therefore it is often set manually such that it gives the best visual results we present here two recent methods to estimate this regularizing parameter and we first propose an improvement of these estimators which takes advantage of confocal images following these estimators we secondly propose to express the problem of the deconvolution of poisson noisy images as the minimization of a new constrained problem the proposed constrained formulation is well suited to this application domain since it is directly expressed using the antilog likelihood of the poisson distribution and therefore does not require any approximation we show how to solve the unconstrained and constrained problems using the recent alternating direction technique and we present results on synthetic and real data using well known priors such as total variation and wavelet transforms among these wavelet transforms we specially focus on the dual tree complex wavelet transform and on the dictionary composed of curvelets and an undecimated wavelet transform

numerical simulations of possible finite time singularities in the incompressible euler equations comparison of numerical methods abstract the numerical simulation of the 3d incompressible euler equations is analyzed with respect to different integration methods the numerical schemes we considered include spectral methods with different strategies for dealiasing and two variants of finite difference methods based on this comparison a kida pelz like initial condition is integrated using adaptive mesh refinement and estimates on the necessary numerical resolution are given this estimate is based on analyzing the scaling behavior similar to the procedure in critical phenomena and present simulations are put into perspective

a new nonconvex approach for image restoration with gamma noise abstract in this paper a new total generalized variational tgv model for restoring images with multiplicative noise is proposed which contains a nonconvex fidelity term and a tgv term we use a difference of convex functions algorithm dca to deal with the proposed model for multiplicative noise removal there exist many models and algorithms most of which focus on convex approximation so that numerical algorithms with guaranteed convergence can be designed unlike these algorithms we use the dca algorithm to remove multiplicative noise by numerical experiments it is shown that the proposed approach leads to a better solution compared with the gradient projection algorithm for solving the classic multiplicative noise removal models we prove that the sequence generated by the dca algorithm converges to a stationary point which satisfies the first order optimality condition finally we demonstrate the performance of our whole scheme by numerical examples a comparison with other methods is provided as well numerical results demonstrate that the proposed algorithm significantly outperforms some previous methods for multiplicative gamma noise removal

poisson intensity estimation for tomographic data using a wavelet shrinkage approach we consider a two dimensional 2 d problem of positron emission tomography pet where the random mechanism of the generation of the tomographic data is modeled by poisson processes the goal is to estimate the intensity function which corresponds to emission density using the wavelet vaguelette decomposition wvd we propose an estimator based on thresholding of empirical vaguelette coefficients which attains the minimax rates of convergence on besov function classes furthermore we construct an adaptive estimator which attains the optimal rate of convergence up to a logarithmic term

computing nearly singular solutions using pseudo spectral methods in this paper we investigate the performance of pseudo spectral methods in computing nearly singular solutions of fluid dynamics equations we consider two different ways of removing the aliasing errors in a pseudo spectral method the first one is the traditional 2 3 dealiasing rule the second one is a high 36th order fourier smoothing which keeps a significant portion of the fourier modes beyond the 2 3 cut off point in the fourier spectrum for the 2 3 dealiasing method both the 1d burgers equation and the 3d incompressible euler equations are considered we demonstrate that the pseudo spectral method with the high order fourier smoothing gives a much better performance than the pseudo spectral method with the 2 3 dealiasing rule moreover we show that the high order fourier smoothing method captures about 12 15 more effective fourier modes in each dimension than the 2 3 dealiasing method for the 3d euler equations the gain in the effective fourier codes for the high order fourier smoothing method can be as large as 20 over the 2 3 dealiasing method another interesting observation is that the error produced by the high order fourier smoothing method is highly localized near the region where the solution is most singular while the 2 3 dealiasing method tends to produce oscillations in the entire domain the high order fourier smoothing method is also found be very stable dynamically no high frequency instability has been observed in the case of the 3d euler equations the energy is conserved up to at least six digits of accuracy throughout the computations 2007 elsevier inc all rights reserved

a hybrid optimization method for multiplicative noise and blur removal the main contribution of this paper is to propose a new hybrid optimization method for the multiplicative noise and blur removal problem a degraded image can often be recovered efficiently by minimizing an objective function which consists of a data fidelity term and a regularization term in the paper we apply the quadratic penalty function method combined with the alternating direction method to minimize the corresponding objective function numerical experiments are presented to demonstrate the effectiveness of the proposed method experimental results illustrate the state of the art performance of the proposed method to handle multiplicative noise and blur removal problem

efficient method for dynamic condensation of nonclassically damped vibration systems dynamic condensation methods have been widely used to reduce the number of degrees of freedom of finite element models most of them however are valid for undamped systems an efficient iterative approach for the dynamic condensation of nonclassically damped systems is proposed the classical subspace iteration method for undamped models is extended to nonclassically damped models then a governing equation for the dynamic condensation matrix in state space is derived from the extended subspace iteration two iterative schemes are proposed to solve the governing equation because the dynamic condensation matrix is independent of the system matrices and the eigenpairs eigenvalues and eigenvectors of the reduced model it is unnecessary to compute them in every iteration this makes the present method much more computationally efficient than those approaches proposed in the past the convergence of the proposed approach is also proven two numerical examples one discrete mass damper spring system and one floating raft isolation system are included to demonstrate the convergence of the present method the results show that the convergence of the present method is much faster than the previous approaches especially when the dynamic characteristics of the reduced model are very close to the full model

optimal parameter selection for the alternating direction method of multipliers admm quadratic problems the alternating direction method of multipliers admm has emerged as a powerful technique for large scale structured optimization despite many recent results on the convergence properties of admm a quantitative characterization of the impact of the algorithm parameters on the convergence times of the method is still lacking in this paper we find the optimal algorithm parameters that minimize the convergence factor of the admm iterates in the context of l 2 regularized minimization and constrained quadratic programming numerical examples show that our parameter selection rules significantly outperform existing alternatives in the literature

tensor based formulation and nuclear norm regularization for multienergy computed tomography the development of energy selective photon counting x ray detectors allows for a wide range of new possibilities in the area of computed tomographic image formation under the assumption of perfect energy resolution here we propose a tensor based iterative algorithm that simultaneously reconstructs the x ray attenuation distribution for each energy we use a multilinear image model rather than a more standard stacked vector representation in order to develop novel tensor based regularizers in particular we model the multispectral unknown as a three way tensor where the first two dimensions are space and the third dimension is energy this approach allows for the design of tensor nuclear norm regularizers which like its 2d counterpart is a convex function of the multispectral unknown the solution to the resulting convex optimization problem is obtained using an alternating direction method of multipliers approach simulation results show that the generalized tensor nuclear norm can be used as a standalone regularization technique for the energy selective spectral computed tomography problem and when combined with total variation regularization it enhances the regularization capabilities especially at low energy images where the effects of noise are most prominent

a nonstationary accelerating alternating direction method for frame based poissonian image deblurring abstract poissonian image deblurring problem has been an attractive research subject in many areas of imaging science and engineering in order to obtain accurate restorations one has to run several times to manually select a good value of a regularization parameter in many models in this paper we first propose an optimization model by combining a new data fitting term with a frame based analysis regularizer and a nonnegative constraint a discrepancy principle based nonstationary accelerating alternating direction method called dp naadm is then proposed to solve the optimization model without estimating the regularization parameter numerical results show that dp naadm provides competitive restoration results compared to the well known poisson image deconvolution by augmented lagrangian method called pidal also dp naadm provides better restorations in terms of both accuracy and visual quality than the discrepancy principle based pidal method

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

pure let image deconvolution we propose a non iterative image deconvolution algorithm for data corrupted by poisson or mixed poisson gaussian noise many applications involve such a problem ranging from astronomical to biological imaging we parameterize the deconvolution process as a linear combination of elementary functions termed as linear expansion of thresholds this parameterization is then optimized by minimizing a robust estimate of the true mean squared error the poisson unbiased risk estimate each elementary function consists of a wiener filtering followed by a pointwise thresholding of undecimated haar wavelet coefficients in contrast to existing approaches the proposed algorithm merely amounts to solving a linear system of equations which has a fast and exact solution simulation experiments over different types of convolution kernels and various noise levels indicate that the proposed method outperforms the state of the art techniques in terms of both restoration quality and computational complexity finally we present some results on real confocal fluorescence microscopy images and demonstrate the potential applicability of the proposed method for improving the quality of these images

insight into the dynamic condensation technique of non classically damped models the dynamic condensation technique fully depends on the definition and computational scheme of the dynamic condensation matrix four definitions for the dynamic condensation matrix in the single mode m mode response dependent dynamic condensation and modal reduction of non classically damped models are presented they are respectively defined as the relations of the single eigenvector m eigenvectors p eigenvectors and responses between the master and the slave degrees of freedom using the complex mode superposition technique the response dependent dynamic condensation matrix may be interpreted as any mode including whole mode m mode p mode and single mode dependent condensation matrix computational equations for the dynamic condensation matrix are derived for each of definitions after the proper introduction of the assumptions for the single mode and the response dependent dynamic condensation the same computational equation is obtained from the former three definitions in the modal reduction the dynamic condensation matrix is directly computed from the eigenvector matrix of full model because the eigenvector matrix of the non classically damped models is generally complex the complex numerical operations are required in the commonly used expression an alternative expression is derived in which only the real numerical operations are necessary furthermore it is proven that the dynamic condensation matrix and the reduced system matrices resulted from the modal reduction all have real values

parallel mr image reconstruction using augmented lagrangian methods magnetic resonance image mri reconstruction using sensitivity encoding sense requires regularization to suppress noise and aliasing effects edge preserving and sparsity based regularization criteria can improve image quality but they demand computation intensive nonlinear optimization in this paper we present novel methods for regularized mri reconstruction from undersampled sensitivity encoded data sense reconstruction using the augmented lagrangian al framework for solving large scale constrained optimization problems we first formulate regularized sense reconstruction as an unconstrained optimization task and then convert it to a set of equivalent constrained problems using variable splitting we then attack these constrained versions in an al framework using an alternating minimization method leading to algorithms that can be implemented easily the proposed methods are applicable to a general class of regularizers that includes popular edge preserving e g total variation and sparsity promoting e g norm of wavelet coefficients criteria and combinations thereof numerical experiments with synthetic and in vivo human data illustrate that the proposed al algorithms converge faster than both general purpose optimization algorithms such as nonlinear conjugate gradient ncg and state of the art mfista

convergence acceleration of iterative modal reduction methods an accelerated method is presented for the iterative condensation of eigenproblems the present study was motivated by the improved reduction system and the succession level approximate reduction sar the reduction procedures are supplemented with the second order approximation in the series expansion of the system transformation the reduced equation of an equivalent system and the transformation matrix are updated in an iterative manner in addition systematicderivation andcomparisonoftheequationsinvolvedin variouscondensationshave been sought thematrixupdateincorporatesnotonlyinverseiteration butalsosubspacetransformation implicitly theseriesexpansion canbeconsideredasrepeatedupdatesofthetransformationmatrixthroughinverseiteration the solution accuracy is sensitive to the selection of the degrees of freedom for which sequential elimination or energy method may be preferable when a poor selection causes a sudden failure of the updatemethod the hybrid dynamic condensation can be used the method of sar is closely related to the hybrid dynamic condensation nomenclature as kss i 1 mss in eq 10 bpp bsp submatrices for inertia force in eq 68 dg mg i 1 kg dynamic matrix in eq 13 ke me equivalent structural matrices in eq 26 kg mg reduced matrices in guyan s condensation kr mr structural matrices reduced through tr kx mx structural matrices reduced through tx k ka b stiffness matrix and submatrices m ma b mass matrix and submatrices p number of primary degrees of freedom q pp modal matrix for generalized coordinates r residual error in eigenproblem s number of secondary degrees of freedom t exact transformation matrix in eq 22 ti matrices in series of eqs 15 and 18 tp system transformation matrix tr approximate transformation matrix tx improved transformation matrix in eq 40 t0 transformation in guyan s condensation t k frequency dependent transformation in eq 3 x p improved modal matrix x pp xsp submatrices of x p e convergence tolerance k p

two level scheme for selection of primary degrees of freedom and semi analytic sensitivity based on the reduced system a number of approximate techniques have been developed to calculate the eigenvalues in a reduced manner these schemes approximate the lower eigenvalues that represent the global behavior of the structures the present study proposes a two level condensation scheme tlcs this scheme consists of two steps in the first step the candidate elements are selected for constructing the reduced system by energy estimation in the second step primary degrees of freedom are selected by sequential elimination from the candidate degrees of freedom linked to the selected elements through the first step the proposed method saves computational cost effectively and recovers eigenvalues of the full system with high accuracy from the lowest to the truncated range of frequency moreover besides the accuracies of the eigenvalue well constructed reduced system assures the accuracy of sensitivity of the eigenvalue compared to full system in this paper the semi analytic design sensitivity of eigenvalues is obtained by the rigid body separation technique in reduced system for the sensitivity calculation the eigenvectors obtained from the reduced system are transformed into global system field numerical examples demonstrate the reliability of the eigenvalue and its sensitivity obtained by the reduced system through the comparison with conventional sensitivity schemes

improvement of reduction method combined with sub domain scheme in large scale problem for a few decades various approximate techniques have been developed to calculate the eigenvalues in a reduced manner in order to construct reliable reduced systems it is essential to select the proper primary degrees of freedom pdofs unless the pdofs are selected properly the selection of pdofs might be localized and the eigenvalue prediction might emphasize excessively the lower modes or lose the important modes moreover sometimes it takes considerable amount of computing time to construct a reduced system in large scale problem these troubles in constructing reduced system can be avoided by applying reduction scheme in sub domain level after dividing global system into a number of subdomains reduced system which has only the pdofs is constructed in each sub domain this paper presents new algorithms to construct efficient reduction system through three different schemes they are version 1 version 2 and version 3 systems the version 3 system is constructed by combining the advantages of the version 1 and the version 2 systems numerical examples demonstrate that the proposed version 3 method saves computational cost effectively and provides a reduced system which can predict accurate eigenvalues of global system

edge preserving pet image reconstruction using trust optimization transfer iterative image reconstruction for positron emission tomography can improve image quality by using spatial regularization the most commonly used quadratic penalty often oversmoothes sharp edges and fine features in reconstructed images while nonquadratic penalties can preserve edges and achieve higher contrast recovery existing optimization algorithms such as the expectation maximization em and preconditioned conjugate gradient pcg algorithms work well for the quadratic penalty but are less efficient for high curvature or nonsmooth edge preserving regularizations this paper proposes a new algorithm to accelerate edge preserving image reconstruction by using two strategies trust surrogate and optimization transfer descent trust surrogate approximates the original penalty by a smoother function at each iteration but guarantees the algorithm to descend monotonically optimization transfer descent accelerates a conventional optimization transfer algorithm by using conjugate gradient and line search results of computer simulations and real 3 d data show that the proposed algorithm converges much faster than the conventional em and pcg for smooth edge preserving regularization and can also be more efficient than the current state of art algorithms for the nonsmooth ell 1 regularization

proximal admm for multi channel image reconstruction in spectral x ray ct the development of spectral x ray computed tomography ct using binned photon counting detectors has received great attention in recent years and has enabled selective imaging of contrast agents loaded with k edge materials a practical issue in implementing this technique is the mitigation of the high noise levels often present in material decomposed sinogram data in this work the spectral x ray ct reconstruction problem is formulated within a multi channel mc framework in which statistical correlations between the decomposed material sinograms can be exploited to improve image quality specifically a mc penalized weighted least squares pwls estimator is formulated in which the data fidelity term is weighted by the mc covariance matrix and sparsity promoting penalties are employed this allows the use of any number of basis materials and is therefore applicable to photon counting systems and k edge imaging to overcome numerical challenges associated with use of the full covariance matrix as a data fidelity weight a proximal variant of the alternating direction method of multipliers is employed to minimize the mc pwls objective function computer simulation and experimental phantom studies are conducted to quantitatively evaluate the proposed reconstruction method

improvement in model reduction schemes using the system equivalent reduction expansion process the serep produces an exact reduced model however this method requires knowledge of the full system eigenvectors an extension of this method was presented that uses only the mode shapes of a reduced system the reduced system mode shapes can be obtained from any reduction procedure including guyan for example results from a simulation of a cantilevered euler bernoulli beam validated the technique it was shown that the method improved upon the guyan and the irs reduction methods provided that a proper set of master dof were chosen

structural system identification using degree of freedom based reduction and hierarchical clustering algorithm abstract a system identification method has been proposed to validate finite element models of complex structures using measured modal data finite element method is used for the system identification as well as the structural analysis in perturbation methods the perturbed system is expressed as a combination of the baseline structure and the related perturbations the changes in dynamic responses are applied to determine the structural modifications so that the equilibrium may be satisfied in the perturbed system in practical applications the dynamic measurements are carried out on a limited number of accessible nodes and associated degrees of freedom the equilibrium equation is in principle expressed in terms of the measured master primary and unmeasured slave secondary degrees of freedom only the specified degrees of freedom are included in the equation formulation for identification and the unspecified degrees of freedom are eliminated through the iterative improved reduction scheme a large number of system parameters are included as the unknown variables in the system identification of large scaled structures the identification problem with large number of system parameters requires a large amount of computation time and resources in the present study a hierarchical clustering algorithm is applied to reduce the number of system parameters effectively numerical examples demonstrate that the proposed method greatly improves the accuracy and efficiency in the inverse problem of identification

on finite time singularity and global regularity of an axisymmetric model for the 3d euler equations in comm pure appl math 62 4 502 564 2009 hou and lei proposed a 3d model for the axisymmetric incompressible euler and navier stokes equations with swirl this model shares a number of properties of the 3d incompressible euler and navier stokes equations in this paper we prove that the 3d inviscid model with an appropriate neumann robin or dirichlet robin boundary condition will develop a finite time singularity in an axisymmetric domain we also provide numerical confirmation for our finite time blowup results we further demonstrate that the energy of the blowup solution is bounded up to the singularity time and the blowup mechanism for the mixed dirichlet robin boundary condition is essentially the same as that for the energy conserving homogeneous dirichlet boundary condition finally we prove that the 3d inviscid model has globally smooth solutions for a class of large smooth initial data with some appropriate boundary condition both the analysis and the results we obtain here improve the previous work in a rectangular domain by hou et al adv math 230 607 641 2012 in several respects

restoration of poissonian images using alternating direction optimization much research has been devoted to the problem of restoring poissonian images namely for medical and astronomical applications however the restoration of these images using state of the art regularizers such as those based upon multiscale representations or total variation is still an active research area since the associated optimization problems are quite challenging in this paper we propose an approach to deconvolving poissonian images which is based upon an alternating direction optimization method the standard regularization or maximum a posteriori map restoration criterion which combines the poisson log likelihood with a nonsmooth convex regularizer log prior leads to hard optimization problems the log likelihood is nonquadratic and nonseparable the regularizer is nonsmooth and there is a nonnegativity constraint using standard convex analysis tools we present sufficient conditions for existence and uniqueness of solutions of these optimization problems for several types of regularizers total variation frame based analysis and frame based synthesis we attack these problems with an instance of the alternating direction method of multipliers admm which belongs to the family of augmented lagrangian algorithms we study sufficient conditions for convergence and show that these are satisfied either under total variation or frame based analysis and synthesis regularization the resulting algorithms are shown to outperform alternative state of the art methods both in terms of speed and restoration accuracy

remarks on the breakdown of smooth solutions for the 3 d euler equations the authors prove that the maximum norm of the vorticity controls the breakdown of smooth solutions of the 3 d euler equations in other words if a solution of the euler equations is initially smooth and loses its regularity at some later time then the maximum vorticity necessarily grows without bound as the critical time approaches equivalently if the vorticity remains bounded a smooth solution persists

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

a new eigensolution of structures via dynamic condensation dynamic condensation or model reduction is a commonly used algorithm to fast estimate some low eigenvalues and corresponding eigenvectors of structures by reducing the order of the original structural model to a smaller one this paper proposes a new eigensolution technique via iterated dynamic condensation the technique retains all the inertia terms associated with the removed degrees of freedom in an iterated form which generates the reduced mass matrix similar to that obtained in the guyan reduction method with a frequency dependent perturbed term the corresponding eigenvalues and eigenvectors of interest are obtained as those of the guyan reduction method with perturbations by using an eigensensitivity based iterative method the effectiveness and accuracy of the proposed technique are numerically verified by using a steel frame and the garteur structure

alternating direction method of multiplier for tomography with nonlocal regularizers the ordered subset expectation maximization osem algorithm approximates the gradient of a likelihood function using a subset of projections instead of using all projections so that fast image reconstruction is possible for emission and transmission tomography such as spect pet and ct however osem does not significantly accelerate reconstruction with computationally expensive regularizers such as patch based nonlocal nl regularizers because the regularizer gradient is evaluated for every subset we propose to use variable splitting to separate the likelihood term and the regularizer term for penalized emission tomographic image reconstruction problem and to optimize it using the alternating direction method of multiplier admm we also propose a fast algorithm to optimize the admm parameter based on convergence rate analysis this new scheme enables more sub iterations related to the likelihood term we evaluated our admm for 3 d spect image reconstruction with a patch based nl regularizer that uses the fair potential function our proposed admm improved the speed of convergence substantially compared to other existing methods such as gradient descent em and osem using de pierro s approach and the limited memory broyden fletcher goldfarb shanno algorithm

a truncated nuclear norm regularization method based on weighted residual error for matrix completion low rank matrix completion aims to recover a matrix from a small subset of its entries and has received much attention in the field of computer vision most existing methods formulate the task as a low rank matrix approximation problem a truncated nuclear norm has recently been proposed as a better approximation to the rank of matrix than a nuclear norm the corresponding optimization method truncated nuclear norm regularization tnnr converges better than the nuclear norm minimization based methods however it is not robust to the number of subtracted singular values and requires a large number of iterations to converge in this paper a tnnr method based on weighted residual error tnnr wre for matrix completion and its extension model etnnr wre are proposed tnnr wre assigns different weights to the rows of the residual error matrix in an augmented lagrange function to accelerate the convergence of the tnnr method the etnnr wre is much more robust to the number of subtracted singular values than the tnnr wre tnnr alternating direction method of multipliers and tnnr accelerated proximal gradient with line search methods experimental results using both synthetic and real visual data sets show that the proposed tnnr wre and etnnr wre methods perform better than tnnr and iteratively reweighted nuclear norm irnn methods

accelerated regularized estimation of mr coil sensitivities using augmented lagrangian methods several magnetic resonance parallel imaging techniques require explicit estimates of the receive coil sensitivity profiles these estimates must be accurate over both the object and its surrounding regions to avoid generating artifacts in the reconstructed images regularized estimation methods that involve minimizing a cost function containing both a data fit term and a regularization term provide robust sensitivity estimates however these methods can be computationally expensive when dealing with large problems in this paper we propose an iterative algorithm based on variable splitting and the augmented lagrangian method that estimates the coil sensitivity profile by minimizing a quadratic cost function our method admm circ reformulates the finite differencing matrix in the regularization term to enable exact alternating minimization steps we also present a faster variant of this algorithm using intermediate updating of the associated lagrange multipliers numerical experiments with simulated and real data sets indicate that our proposed method converges approximately twice as fast as the preconditioned conjugate gradient method over the entire field of view these concepts may accelerate other quadratic optimization problems

a dictionary learning approach for poisson image deblurring the restoration of images corrupted by blur and poisson noise is a key issue in medical and biological image processing while most existing methods are based on variational models generally derived from a maximum a posteriori map formulation recently sparse representations of images have shown to be efficient approaches for image recovery following this idea we propose in this paper a model containing three terms a patch based sparse representation prior over a learned dictionary the pixel based total variation regularization term and a data fidelity term capturing the statistics of poisson noise the resulting optimization problem can be solved by an alternating minimization technique combined with variable splitting extensive experimental results suggest that in terms of visual quality peak signal to noise ratio value and the method noise the proposed algorithm outperforms state of the art methods

wavelet decomposition approaches to statistical inverse problems summary a wide variety of scientific settings involve indirect noisy measurements where one faces a linear inverse problem in the presence of noise primary interest is in some function f t but data are accessible only about some linear transform corrupted by noise the usual linear methods for such inverse problems do not perform satisfactorily when f t is spatially inhomogeneous one existing nonlinear alternative is the wavelet vaguelette decomposition method based on the expansion of the unknown f t in wavelet series in the vaguelette wavelet decomposition method proposed here the observed data are expanded directly in wavelet series the performances of various methods are compared through exact risk calculations in the context of the estimation of the derivative of a function observed subject to noise a result is proved demonstrating that with a suitable universal threshold somewhat larger than that used for standard denoising problems both the wavelet based approaches have an ideal spatial adaptivity property

geometric statistics in turbulence the author presents results regarding certain average properties of incompressible fluids derived from the equations of motion the author estimates the average dissipation rate the average dimension of level sets the role played by the field of direction of vorticity in the three dimensional euler and navier stokes equations is discussed and a class of two dimensional equations that are useful models of incompressible dynamics is described the author presents results concerning scaling exponents in turbulence

element based node selection method for reduction of eigenvalue problems dynamic analysis of structural systems requires a considerable amount of computing time because the dynamic behavior of a structure is dominated by lower modes all of the eigenvalues of the system need not be calculated the previously proposed methods approximate the eigenvalues of a global system but they take great amount of computing time to construct a reduced system an element level energy estimation technique is proposed to construct a reduced finite element model through several examples it is demonstrated that the proposed method effectively saves computational time and accurately predicts the eigenvalues of a global system

energy method for selection of degrees of freedom in condensation an analytical method is presented for the selection of degrees of freedom in condensation of eigenproblems the method isbasedon theenergiesassociatedwiththedegrees offreedom in theeigenmodesofstructuralsystems for theenergyestimationritzvectorsarecalculated usingthestiffnessandmassmatrices theenergiesaddedthrough themodesortheweighted rowsum oftheenergy distribution matrix can be used asan effective guideline on which degrees of freedom should be retained in the analysis another approach of sequential selection can be employed in which a e nite number of new degrees of freedom with the largest energy are taken in each mode and the e nal union becomes the analysis set the energy of the selected degrees of freedom or the column sum of the matrix can beused to predict thesolution accuracy in each mode the erroranalysisshowsthattheperturbation in eigenvalue is related with the energy of the degrees of freedom the row and column sums indicate the completeness of the selected set and give a clue to how many degrees of freedom to be included the energy criterion has shown that the conventional practice of choosing translational degrees of freedom is appropriate only for the lowest modes numerical investigations were performed to test the convergence criterion the energy method proved to work well for typical example problems