first order phase transition of triangulated surfaces on a spherical core abstract we study an intrinsic curvature model defined on fixed connectivity triangulated lattices enclosing a spherical core by using the canonical monte carlo simulation technique we find that the model undergoes a discontinuous transition of shape transformation between the smooth state and a collapsed state even when the core radius r is sufficiently large the transition depends on r the origin of the multitude of transitions is considered to be a degeneracy of the collapsed states we also find that the gaussian bond potential s 1 n which is the sum of bond length squares discontinuously changes at the transition the discontinuity in s 1 n implies a possibility of large fluctuations of the distance between lipids or the density of lipids in biological membranes such as giant vesicles or liposomes enclosing some materials

convergence of an iterative method for total variation denoising in total variation denoising one attempts to remove noise from a signal or image by solving a nonlinear minimization problem involving a total variation criterion several approaches based on this idea have recently been shown to be very effective particularly for denoising functions with discontinuities this paper analyzes the convergence of an iterative method for solving such problems the iterative method involves a lagged diffusivity approach in which a sequence of linear diffusion problems are solved global convergence in a finite dimensional setting is established and local convergence properties including rates and their dependence on various parameters are examined

folding transition of the triangular lattice in a discrete three dimensional space a vertex model introduced by m bowick p di francesco o golinelli and e guitter nucl phys b 450 463 1995 describing the folding of the triangular lattice onto the face centered cubic lattice has been studied in the hexagon approximation of the cluster variation method the model describes the behavior of a polymerized membrane in a discrete three dimensional space we have introduced a curvature energy and a symmetry breaking field and studied the phase diagram of the resulting model by varying the curvature energy parameter a first order transition has been found between a flat and a folded phase for any value of the symmetry breaking field textcopyright 1996 the american physical society

acceleration methods for total variation based image denoising in this paper we apply a fixed point method to solve the total variation based image denoising problem an algebraic multigrid method is used to solve the corresponding linear equations krylov subspace acceleration is adopted to improve convergence in the fixed point iteration a good initial guess for this outer iteration at finest grid is obtained by combining fixed point iteration and geometric multigrid interpolation successively from the coarsest grid to the finest grid numerical experiments demonstrate that this method is efficient and robust even for images with large noise to signal ratios

globally convergent iterative numerical schemes for nonlinear variational image smoothing and segmentation on a multiprocessor machine we investigate several iterative numerical schemes for nonlinear variational image smoothing and segmentation implemented in parallel a general iterative framework subsuming these schemes is suggested for which global convergence irrespective of the starting point can be shown we characterize various edge preserving regularization methods from the image processing literature involving auxiliary variables as special cases of this general framework as a by product global convergence can be proven under conditions slightly weaker than these stated in the literature efficient krylov subspace solvers for the linear parts of these schemes have been implemented on a multiprocessor machine the performance of these parallel implementations has been assessed and empirical results concerning convergence rates and speed up factors are reported

on effective methods for implicit piecewise smooth surface recovery this paper considers the problem of reconstructing a piecewise smooth model function from given measured data the data are compared to a field which is given as a possibly nonlinear function of the model a regularization functional is added which incorporates the a priori knowledge that the model function is piecewise smooth and may contain jump discontinuities regularization operators related to total variation tv are therefore employed two popular methods are modified tv and huber s function both contain a parameter which must be selected the huber variant provides a more natural approach for selecting its parameter and we use this to propose a scheme for both methods our selected parameter depends both on the resolution and on the model average roughness thus it is determined adaptively its variation from one iteration to the next yields additional information about the progress of the regularization process the modified tv operator has a smoother generating function nonetheless we obtain a huber variant with comparable and occasionally better performance for large problems e g high resolution the resulting reconstruction algorithms can be tediously slow we propose two mechanisms to improve efficiency the first is a multilevel continuation approach aimed mainly at obtaining a cheap yet good estimate for the regularization parameter and the solution the second is a special multigrid preconditioner for the conjugate gradient algorithm used to solve the linearized systems encountered in the procedures for recovering the model function

a parallel proximal algorithm for anisotropic total variation minimization total variation tv is a one of the most popular regularizers for stabilizing the solution of ill posed inverse problems this paper proposes a novel proximal gradient algorithm for minimizing tv regularized least squares cost functionals unlike traditional methods that require nested iterations for computing the proximal step of tv our algorithm approximates the latter with several simple proximals that have closed form solutions we theoretically prove that the proposed parallel proximal method achieves the tv solution with arbitrarily high precision at a global rate of converge that is equivalent to the fast proximal gradient methods the results in this paper have the potential to enhance the applicability of tv for solving very large scale imaging inverse problems

efficient multiplicative noise removal method using isotropic second order total variation to overcome and reduce the undesirable staircase effect commonly met in the total variation tv regularization based multiplicative noise removal methods a novel multiplicative noise removal model based on isotropic second order total variation isotv is proposed under the maximum a posteriori map framework under the spectral decomposition framework the isotv is first transformed into an equivalent formulation as a novel weighted l 1 l 2 mixed norm of the second order image derivatives then an efficient alternating iterative algorithm is designed to solve the proposed model finally we prove in detail the convergence of the proposed algorithm a set of experiments on both standard and medical images show that the proposed isotv method yields state of the art results both in terms of peak signal to noise ratio psnr and image perception quality specifically the proposed isotv method can better reduce the staircase effect and preserve image edges more sharpness with medical applications

density matrix formulation for quantum renormalization groups a generalization of the numerical renormalization group procedure used first by wilson for the kondo problem is presented it is shown that this formulation is optimal in a certain sense as a demonstration of the effectiveness of this approach results from numerical real space renormalization group calculations for heisenberg chains are presented

branched polymer to inflated transition of self avoiding fluid surfaces abstract we study phase transition of self avoiding fluid surface model on dynamically triangulated lattices using the monte carlo simulation technique we report the continuous transition between the branched polymer and inflated phases at p 0 where p p in p out is the pressure difference between the inner and outer sides of the surface this transition is characterized by almost discontinuous change of the enclosed volume vs the variations of the bending rigidity and the pressure difference p no surface fluctuation transition accompanies this transition up to the surface with the number of vertices n 2562

bayesian video dejittering by the bv image model line jittering or random horizontal displacement in video images occurs when the synchronization signals are corrupted in video storage media or by electromagnetic interference in wireless video transmission the goal of intrinsic video dejittering is to recover the ideal video directly from the observed jittered and often noisy frames the existing approaches in the literature are mostly based on local or semilocal filtering techniques and autoregressive image models and are complemented by various image processing tools in this paper based on the statistical rationale of bayesian inference we propose the first variational dejittering model based on the bounded variation bv image model which is global clean and self contained and intrinsically combines dejittering with denoising the mathematical properties of the model are studied based on the direct method of calculus of variations we design one effective algorithm and present its computational implementation based on techniques from numeri

generalized higher degree total variation hdtv regularization we introduce a family of novel image regularization penalties called generalized higher degree total variation hdtv these penalties further extend our previously introduced hdtv penalties which generalize the popular total variation tv penalty to incorporate higher degree image derivatives we show that many of the proposed second degree extensions of tv are special cases or are closely approximated by a generalized hdtv penalty additionally we propose a novel fast alternating minimization algorithm for solving image recovery problems with hdtv and generalized hdtv regularization the new algorithm enjoys a tenfold speed up compared with the iteratively reweighted majorize minimize algorithm proposed in a previous paper numerical experiments on 3d magnetic resonance images and 3d microscopy images show that hdtv and generalized hdtv improve the image quality significantly compared with tv

bergman spaces with exponential weights abstract in this paper we introduce a kind of bergman space a p on the unit disk d with exponential weights which cover those defined by borichev et al 2007 6 we obtain upper and lower bound estimates on the bergman kernel as an application we discuss the bergman projection and duality

a convergent overlapping domain decomposition method for total variation minimization in this paper we are concerned with the analysis of convergent sequential and parallel overlapping domain decomposition methods for the minimization of functionals formed by a discrepancy term with respect to the data and a total variation constraint to our knowledge this is the first successful attempt of addressing such a strategy for the nonlinear nonadditive and nonsmooth problem of total variation minimization we provide several numerical experiments showing the successful application of the algorithm for the restoration of 1d signals and 2d images in interpolation inpainting problems respectively and in a compressed sensing problem for recovering piecewise constant medical type images from partial fourier ensembles

noise suppression by removing singularities a method is proposed for suppressing gaussian noise by extracting local singularities the method is based on truncating riemann series decomposition whose components naturally characterize different orders of holder regularity the approach yields a single step filtering technique whose performance is comparable to three step wavelet decomposition and thresholding techniques

deconvolution based partial volume correction in raclopride pet and monte carlo comparison to mr based method abstract in this work we evaluated three iterative deconvolution algorithms and compared their performance to partial volume pv correction based on structural imaging in brain positron emission tomography pet using a database of monte carlo simulated images we limited our interest to quantitative radioligand pet imaging particularly to 11c raclopride and striatal imaging the studied deconvolution methods included richardson lucy reblurred van cittert and reblurred van cittert with the total variation regularization we studied the bias and variance of the regional estimates of binding potential bp values and the accuracy of regional tacs as a function of the applied image processing the resolution noise tradeoff in parametric bp images was addressed as well the regional bp values and tacs obtained by deconvolution were almost as accurate than those by structural imaging based pv correction gtm method when the ideal volumes of interests vois were used to extract tacs from the images for deconvolution methods the ideal vois were slightly eroded from the exact anatomical voi to limit the bias due to tissue fraction effect which is not corrected for by deconvolution based methods for the gtm method the ideal vois were the exact anatomical vois the bp values and tacs by deconvolution were less affected by segmentation and registration errors than those with the gtm based pv correction the bp estimates and tacs with deconvolution based pv correction were more accurate than bps and tacs derived without pv correction the parametric images obtained by the deconvolution based pv correction showed considerably improved resolution with only slightly increased noise level compared to the case with no pv correction the reblurred van cittert method was the best of the studied deconvolution methods we conclude that the deconvolution is an interesting alternative to structural imaging based pv correction as it leads to quantification results of similar accuracy and it is less prone to registration and segmentation errors than structural imaging based pv correction moreover pv corrected parametric images can be readily computed based on deconvolved dynamic images

mathematical models for local nontexture inpaintings dedicated to stanley osher on the occasion of his 60th birthday abstract inspired by the recent work of bertalmio et al on digital inpaintings siggraph 2000 we develop general mathematical models for local inpaintings of nontexture images on smooth regions inpaintings are connected to the harmonic and biharmonic extensions and inpainting orders are analyzed for inpaintings involving the recovery of edges we study a variational model that is closely connected to the classical total variation tv denoising model of rudin osher and fatemi phys d 60 1992 pp 259 268 other models are also discussed based on the mumford shah regularity comm pure appl math xlii 1989 pp 577 685 and curvature driven diffusions cdd of chan and shen j visual comm image rep 12 2001 the broad applications of the inpainting models are demonstrated through restoring scratched old photos disocclusion in vision analysis text removal digital zooming and edge based image coding

regularization parameter selection for nonlinear iterative image restoration and mri reconstruction using gcv and sure based methods regularized iterative reconstruction algorithms for imaging inverse problems require selection of appropriate regularization parameter values we focus on the challenging problem of tuning regularization parameters for nonlinear algorithms for the case of additive possibly complex gaussian noise generalized cross validation gcv and weighted mean squared error mse approaches based on stein s unbiased risk estimate sure need the jacobian matrix of the nonlinear reconstruction operator representative of the iterative algorithm with respect to the data we derive the desired jacobian matrix for two types of nonlinear iterative algorithms a fast variant of the standard iterative reweighted least squares method and the contemporary split bregman algorithm both of which can accommodate a wide variety of analysis and synthesis type regularizers the proposed approach iteratively computes two weighted sure type measures predicted sure and projected sure which require knowledge of noise variance 2 and gcv which does not need 2 for these algorithms we apply the methods to image restoration and to magnetic resonance image mri reconstruction using total variation and an analysis type l1 regularization we demonstrate through simulations and experiments with real data that minimizing predicted sure and projected sure consistently lead to near mse optimal reconstructions we also observe that minimizing gcv yields reconstruction results that are near mse optimal for image restoration and slightly suboptimal for mri theoretical derivations in this paper related to jacobian matrix evaluations can be extended in principle to other types of regularizers and reconstruction algorithms

restoration of color images by vector valued bv functions and variational calculus we analyze a variational problem for the recovery of vector valued functions and compute its numerical solution the data of the problem are a small set of complete samples of the vector valued function and some significant incomplete information where the former are missing the incomplete information is assumed as the result of a distortion with values in a lower dimen sional manifold for the recovery of the function we minimize a functional which is formed by the discrepancy with respect to the data and total variation regularization constraints we show the existence of minimizers in the space of vector valued bounded variation functions for the computa tion of minimizers we provide a stable and efficient method first we approximate the functional by coercive functionals on w 1 2 in terms of convergence then we realize approximations of minimiz ers of the latter functionals by an iterative procedure to solve the pde system of the corresponding euler lagrange equations the numerical implementation comes naturally by finite element dis cretization we apply the algorithm to the restoration of color images from limited color information and gray levels where the colors are missing the numerical experiments show that this scheme is very fast and robust the reconstruction capabilities of the model are shown also from very limited randomly distributed color data several examples are included from the real restoration problem of a mantegna s art frescoes in italy

blind source separation using temporal predictability a measure of temporal predictability is defined and used to separate linear mixtures of signals given any set of statistically independent source signals it is conjectured here that a linear mixture of those signals has the following property the temporal predictability of any signal mixture is less than or equal to that of any of its component source signals it is shown that this property can be used to recover source signals from a set of linear mixtures of those signals by finding an un mixing matrix that maximizes a measure of temporal predictability for each recovered signal this matrix is obtained as the solution to a generalized eigenvalue problem such problems have scaling characteristics of o n3 where n is the number of signal mixtures in contrast to independent component analysis the temporal predictability method requires minimal assumptions regarding the probability density functions of source signals it is demonstrated that the method can separate signal mixtures in which each mixture is a linear combination of source signals with supergaussian subgaussian and gaussian probability density functions and on mixtures of voices and music

crumpling transition of the triangular lattice without open edges effect of a modified folding rule folding of the triangular lattice in a discrete three dimensional space is investigated by means of the transfer matrix method this model was introduced by bowick and co workers as a discretized version of the polymerized membrane in thermal equilibrium the folding rule constraint is incompatible with the periodic boundary condition and the simulation has been made under the open boundary condition in this paper we propose a modified constraint which is compatible with the periodic boundary condition technically the restoration of translational invariance leads to a substantial reduction in the transfer matrix size treating the cluster sizes l ensuremath le 7 we analyze the singularities of the crumpling transitions for a wide range of the bending rigidity k we observe a series of the crumpling transitions at k 0 206 2 ensuremath 0 32 1 and ensuremath 0 76 10 at each transition point we estimate the latent heat as q 0 356 30 0 08 3 and 0 05 5 respectively

noise removal using fourth order partial differential equation with applications to medical magnetic resonance images in space and time we introduce a new method for image smoothing based on a fourth order pde model the method is tested on a broad range of real medical magnetic resonance images both in space and time as well as on nonmedical synthesized test images our algorithm demonstrates good noise suppression without destruction of important anatomical or functional detail even at poor signal to noise ratio we have also compared our method with related pde models

phase retrieval through regularization for seismic problems abstractthe most advanced data processing imaging algorithms aim at optimizing a suitably defined cost function consisting of a data misfit term posed in the data domain and a regularization term for strong phase errors in the data however such algorithms fail to achieve an acceptable solution because they force us to match the incorrect phase information to remedy this deficiency we replaced the time domain misfit term by a fourier magnitude fidelity term to recover the desired signal from just the amplitude spectrum of the observations such a problem is known as phase retrieval and it is a subject of interest for those who cannot measure the phase information about the system under study the proposed phase retrieval problem is solved by a fast iterative shrinkage thresholding algorithm and it is used to tackle two common phase problems arising in seismic processing data recovery in the presence of residual static shifts and deconvolution with a missing wavelet phase under sparsity constrain

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

convergence of a fixed point iteration method for the osv model in image processing image denoising and texture extraction are important problems in which many new methods recently have been developed one of the most important models is the osv model s osher a sole l vese image decomposition and restoration using total variation minimization and the h 1 norm multiscale model simul a siam interdisciplinary j 1 3 2003 349 370 which is constructed by the total variation and h 1 norm this paper proves the existence of the minimizer of the functional from the osv model and analyzes the convergence of an iterative method for solving the problems our iteration method is constructed by a fixed point iteration on the fourth order partial differential equation from the computation of the associated euler lagrange equation and the limit of our iterations satisfies the minimizer of the functional from the osv model in numerical experiments we compare the numerical results of our works with those of the rof model l i rudin s osher e fatemi nonlinear total variation based noise removal algorithms phys d 60 1992 259 268

identification of discontinuous parameters in flow equations a problem of identifying possibly discontinuous diffusion coefficients in parabolic equations is considered general theorems on existence and convergence of galerkin approximations are proved in l 1 setting classes of functions of bounded variation are discussed and the variation estimates are obtained a double discretization method with the variations constraints is used in two and three dimensional problems and the numerical experiments are presented

fourth order partial differential equations for noise removal a class of fourth order partial differential equations pdes are proposed to optimize the trade off between noise removal and edge preservation the time evolution of these pdes seeks to minimize a cost functional which is an increasing function of the absolute value of the laplacian of the image intensity function since the laplacian of an image at a pixel is zero if the image is planar in its neighborhood these pdes attempt to remove noise and preserve edges by approximating an observed image with a piecewise planar image piecewise planar images look more natural than step images which anisotropic diffusion second order pdes uses to approximate an observed image so the proposed pdes are able to avoid the blocky effects widely seen in images processed by anisotropic diffusion while achieving the degree of noise removal and edge preservation comparable to anisotropic diffusion although both approaches seem to be comparable in removing speckles in the observed images speckles are more visible in images processed by the proposed pdes because piecewise planar images are less likely to mask speckles than step images and anisotropic diffusion tends to generate multiple false edges speckles can be easily removed by simple algorithms such as the one presented in this paper

variational phase imaging using the transport of intensity equation we introduce a variational phase retrieval algorithm for the imaging of transparent objects our formalism is based on the transport of intensity equation tie which relates the phase of an optical field to the variation of its intensity along the direction of propagation tie practically requires one to record a set of defocus images to measure the variation of intensity we first investigate the effect of the defocus distance on the retrieved phase map based on our analysis we propose a weighted phase reconstruction algorithm yielding a phase map that minimizes a convex functional the method is nonlinear and combines different ranges of spatial frequencies depending on the defocus value of the measurements in a regularized fashion the minimization task is solved iteratively via the alternating direction method of multipliers our simulations outperform commonly used linear and nonlinear tie solvers we also illustrate and validate our method on real microscopy data of hela cells

an algorithm for image removals and decompositions without inverse matrices partial differential equation pde based methods in image processing have been actively studied in the past few years one of the effective methods is the method based on a total variation introduced by rudin oshera and fatemi rof l i rudin s osher e fatemi nonlinear total variation based noise removal algorithms physica d 60 1992 259 268 this method is a well known edge preserving model and an useful tool for image removals and decompositions unfortunately this method has a nonlinear term in the equation which may yield an inaccurate numerical solution to overcome the nonlinearity a fixed point iteration method has been widely used the nonlinear system based on the total variation is induced from the rof model and the fixed point iteration method to solve the rof model is introduced by dobson and vogel d c dobson c r vogel convergence of an iterative method for total variation denoising siam j numer anal 34 5 1997 1779 1791 however some methods had to compute inverse matrices which led to roundoff error to address this problem we developed an efficient method for solving the rof model we make a sequence like richardson s method by using a fixed point iteration to evade the nonlinear equation this approach does not require the computation of inverse matrices the main idea is to make a direction vector for reducing the error at each iteration step in other words we make the next iteration to reduce the error from the computed error and the direction vector we describe that our method works well in theory in numerical experiments we show the results of the proposed method and compare them with the results by d dobson and c vogel and then we confirm the superiority of our method

in vivo impedance imaging with total variation regularization we show that electrical impedance tomography eit image reconstruction algorithms with regularization based on the total variation tv functional are suitable for in vivo imaging of physiological data this reconstruction approach helps to preserve discontinuities in reconstructed profiles such as step changes in electrical properties at interorgan boundaries which are typically smoothed by traditional reconstruction algorithms the use of the tv functional for regularization leads to the minimization of a nondifferentiable objective function in the inverse formulation this cannot be efficiently solved with traditional optimization techniques such as the newton method we explore two implementations methods for regularization with the tv functional the lagged diffusivity method and the primal dual interior point method pd ipm first we clarify the implementation details of these algorithms for eit reconstruction next we analyze the performance of these algorithms on noisy simulated data finally we show reconstructed eit images of in vivo data for ventilation and gastric emptying studies in comparison to traditional quadratic regularization tv regulariza tion shows improved ability to reconstruct sharp contrasts

a posteriori error control for the binary mumford shah model the binary mumford shah model is a widespread tool for image segmentation and can be considered as a basic model in shape optimization with a broad range of applications in computer vision ranging from basic segmentation and labeling to object reconstruction this paper presents robust a posteriori error estimates for a natural error quantity namely the area of the non properly segmented region to this end a suitable strictly convex and non constrained relaxation of the originally non convex functional is investigated and repin s functional approach for a posteriori error estimation is used to control the numerical error for the relaxed problem in the l norm in combination with a suitable cut out argument a fully practical estimate for the area mismatch is derived this estimate is incorporated in an adaptive meshing strategy two different adaptive primal dual finite element schemes and the most frequently used finite difference discretization are investigated and compared numerical experiments show qualitative and quantitative properties of the estimates and demonstrate their usefulness in practical applications

deterministic edge preserving regularization in computed imaging many image processing problems are ill posed and must be regularized usually a roughness penalty is imposed on the solution the difficulty is to avoid the smoothing of edges which are very important attributes of the image in this paper we first give conditions for the design of such an edge preserving regularization under these conditions we show that it is possible to introduce an auxiliary variable whose role is twofold first it marks the discontinuities and ensures their preservation from smoothing second it makes the criterion half quadratic the optimization is then easier we propose a deterministic strategy based on alternate minimizations on the image and the auxiliary variable this leads to the definition of an original reconstruction algorithm called artur some theoretical properties of artur are discussed experimental results illustrate the behavior of the algorithm these results are shown in the field of 2d single photon emission tomography but this method can be applied in a large number of applications in image processing

convergence of fixed point iteration for deblurring and denoising problem abstract to solve deblurring and denoising problem we present a proof of the global and linear convergence of fixed point iteration as well as an estimate for the rate of convergence is given we show the equivalence among three different iterative methods half quadratic regularization iteration based on bergman distance weiszfeld s method

a general framework for regularized similarity based image restoration any image can be represented as a function defined on a weighted graph in which the underlying structure of the image is encoded in kernel similarity and associated laplacian matrices in this paper we develop an iterative graph based framework for image restoration based on a new definition of the normalized graph laplacian we propose a cost function which consists of a new data fidelity term and regularization term derived from the specific definition of the normalized graph laplacian the normalizing coefficients used in the definition of the laplacian and associated regularization term are obtained using fast symmetry preserving matrix balancing this results in some desired spectral properties for the normalized laplacian such as being symmetric positive semidefinite and returning zero vector when applied to a constant image our algorithm comprises of outer and inner iterations where in each outer iteration the similarity weights are recomputed using the previous estimate and the updated objective function is minimized using inner conjugate gradient iterations this procedure improves the performance of the algorithm for image deblurring where we do not have access to a good initial estimate of the underlying image in addition the specific form of the cost function allows us to render the spectral analysis for the solutions of the corresponding linear equations in addition the proposed approach is general in the sense that we have shown its effectiveness for different restoration problems including deblurring denoising and sharpening experimental results verify the effectiveness of the proposed algorithm on both synthetic and real examples

stiffening of fluid membranes due to thermal undulations density matrix renormalization group study it has been considered that the effective bending rigidity of fluid membranes should be reduced by thermal undulations however recent thorough investigation by pinnow and helfrich revealed the significance of measure factors for the partition sum accepting the local curvature as a statistical measure they found that fluid membranes are stiffened macroscopically in order to examine this remarkable idea we performed extensive ab initio simulations for a fluid membrane we set up a transfer matrix that is diagonalized by means of the density matrix renormalization group our method has an advantage in that it allows us to survey various statistical measures as a consequence we found that the effective bending rigidity flows toward strong coupling under the choice of local curvature as a statistical measure on the contrary for other measures such as normal displacement and tilt angle we found a clear tendency toward softening

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

nested conjugate gradient algorithm with nested preconditioning for non linear image restoration we develop a novel optimization algorithm which we call nested non linear conjugate gradient cg algorithm nncg for image restoration based on quadratic data fitting and smooth non quadratic regularization the algorithm is constructed as a nesting of two conjugate gradient iterations the outer iteration is constructed as a preconditioned non linear cg algorithm the preconditioning is performed by the inner cg iteration that is linear the inner cg iteration which performs preconditioning for outer cg iteration itself is accelerated by an another fft based non iterative preconditioner we prove that the method converges to a stationary point for both convex and non convex regularization functionals we demonstrate experimentally that proposed method outperforms the well known majorization minimization method used for convex regularization and a non convex inertial proximal method for non convex regularization functional

stability results on interpolation scales of quasi banach spaces and applications we investigate the stability of fredholm properties on interpolation scales of quasi banach spaces this analysis is motivated by problems arising in pde s and several applications are presented

localization and compactness of operators on fock spaces abstract for 0 p let f p be the fock space induced by a weight function satisfying d d c 0 in this paper given p 0 1 we introduce the concept of weakly localized operators on f p we characterize the compact operators in the algebra generated by weakly localized operators as an application for 0 p we prove that an operator t in the algebra generated by bounded toeplitz operators with bmo symbols is compact on f p if and only if its berezin transform satisfies certain vanishing property at in the classical fock space we extend the axler zheng condition on linear operators t which ensures t is compact on f p for all possible 0 p

fft based preconditioners for toeplitz block least squares problems discretized two dimensional deconvolution problems arising e g in image restoration and seismic tomography can be formulated as least squares computations min b tx 2 where t is often a large scale rectangular toeplitz block matrix the authors consider solving such block least squares problems by the preconditioned conjugate gradient algorithm using square nonsingular circulant block and related preconditioners constructed from the blocks of the rectangular matrix t preconditioning with such matrices allows efficient implementation using the one dimensional or two dimensional fast fourier transform fft two block preconditioners related to those proposed by t chan and j olkin for square nonsingular toeplitz block systems are derived and analyzed it is shown that for important classes of t the singular values of the preconditioned matrix are clustered around one this extends the authors earlier work on preconditioners for toeplitz least squares iterations for one dimensiona

majorization minimization algorithms for wavelet based image restoration standard formulations of image signal deconvolution under wavelet based priors regularizers lead to very high dimensional optimization problems involving the following difficulties the non gaussian heavy tailed wavelet priors lead to objective functions which are nonquadratic usually nondifferentiable and sometimes even nonconvex the presence of the convolution operator destroys the separability which underlies the simplicity of wavelet based denoising this paper presents a unified view of several recently proposed algorithms for handling this class of optimization problems placing them in a common majorization minimization mm framework one of the classes of algorithms considered when using quadratic bounds on nondifferentiable log priors shares the infamous singularity issue si of iteratively re weighted least squares irls algorithms the possibility of having to handle infinite weights which may cause both numerical and convergence issues in this paper we prove several new results which strongly support the claim that the si does not compromise the usefulness of this class of algorithms exploiting the unified mm perspective we introduce a new algorithm resulting from using bounds for nonconvex regularizers the experiments confirm the superior performance of this method when compared to the one based on quadratic majorization finally an experimental comparison of the several algorithms reveals their relative merits for different standard types of scenarios

an infeasible primal dual algorithm for total bounded variation based inf convolution type image restoration in this paper a primal dual algorithm for total bounded variation tv type image restoration is analyzed and tested analytically it turns out that employing a global boldsymbol l s regularization with 1 s leq 2 in the dual problem results in a local smoothing of the tv regularization term in the primal problem the local smoothing can alternatively be obtained as the infimal convolution of the ell r norm with r 1 s 1 1 and a smooth function in the case r s 2 this results in gauss tv type image restoration the globalized primal dual algorithm introduced in this paper works with generalized derivatives converges locally at a superlinear rate and is stable with respect to noise in the data in addition it utilizes a projection technique which reduces the size of the linear system that has to be solved per iteration a comprehensive numerical study ends the paper

hessian based norm regularization for image restoration with biomedical applications we present nonquadratic hessian based regularization methods that can be effectively used for image restoration problems in a variational framework motivated by the great success of the total variation tv functional we extend it to also include second order differential operators specifically we derive second order regularizers that involve matrix norms of the hessian operator the definition of these functionals is based on an alternative interpretation of tv that relies on mixed norms of directional derivatives we show that the resulting regularizers retain some of the most favorable properties of tv i e convexity homogeneity rotation and translation invariance while dealing effectively with the staircase effect we further develop an efficient minimization scheme for the corresponding objective functions the proposed algorithm is of the iteratively reweighted least square type and results from a majorization minimization approach it relies on a problem specific preconditioned conjugate gradient method which makes the overall minimization scheme very attractive since it can be applied effectively to large images in a reasonable computational time we validate the overall proposed regularization framework through deblurring experiments under additive gaussian noise on standard and biomedical images

new methods of controlled total variation reduction for digital functions we consider the functional of total variation for functions of either one or two discrete variables we introduce a new principle for construction of evolution processes that gradually reduce the total variation of a function the method is derived from analysis of relaxation of the functional along the directions given by the haar wavelets an approach that does not require regularization of either the functional or its singular gradient we further present a rigorous analysis of the analytical properties of the resulting evolution schemes the purely discrete theory grows out of universal observations about the relation between the total variation and the haar functions an additional advantage of the method is that it can be directly implemented as an effective numerical procedure moreover it can be intertwined in a natural way with a nonlinear phase space filtering which further increases control of the deformation of a signal finally we report that the algorithms can be used as remarkable tools for signal processing and image enhancement

properties and refinements of the fused lasso we consider estimating an unknown signal both blocky and sparse which is corrupted by additive noise we study three interrelated least squares procedures and their asymptotic properties the first procedure is the fused lasso put forward by friedman et al ann appl statist 1 2007 302 332 which we modify into a different estimator called the fused adaptive lasso with better properties the other two estimators we discuss solve least squares problems on sieves one constrains the maximal l 1 norm and the maximal total variation seminorm and the other restricts the number of blocks and the number of nonzero coordinates of the signal we derive conditions for the recovery of the true block partition and the true sparsity patterns by the fused lasso and the fused adaptive lasso and we derive convergence rates for the sieve estimators explicitly in terms of the constraining parameters

total variation and high order total variation adaptive model for restoring blurred images with cauchy noise abstract in this paper we propose a novel model to restore an image corrupted by blur and cauchy noise the model is composed of a data fidelity term and two regularization terms including total variation and high order total variation total variation provides well preserved edge features but suffers from staircase effects in smooth regions whereas high order total variation can alleviate staircase effects moreover we introduce a strategy for adaptively selecting regularization parameters we develop an efficient alternating minimization algorithm for solving the proposed model numerical examples suggest that the proposed method has the advantages of better preserving edges and reducing staircase effects

a two step model for image denoising using a duality strategy and surface fitting in order to alleviate the staircase effect or the edge blurring in the course of the image denoising we propose a two step model based on the duality strategy in fact this strategy follows the observation that the dual variable of the restored image can be looked at as the normal vector so we first obtain the dual variable and then reconstruct the image by fitting the dual variable following the augmented lagrangian strategy we propose a projection gradient method for solving this two step model we also give some convergence analyses of the proposed projection gradient method several numerical experiments are tested to compare our proposed model with the rof model and the llt model

design of steerable filters for feature detection using canny like criteria we propose a general approach for the design of 2d feature detectors from a class of steerable functions based on the optimization of a canny like criterion in contrast with previous computational designs our approach is truly 2d and provides filters that have closed form expressions it also yields operators that have a better orientation selectivity than the classical gradient or hessian based detectors we illustrate the method with the design of operators for edge and ridge detection we present some experimental results that demonstrate the performance improvement of these new feature detectors we propose computationally efficient local optimization algorithms for the estimation of feature orientation we also introduce the notion of shape adaptable feature detection and use it for the detection of image corners

hessian schatten norm regularization for linear inverse problems we introduce a novel family of invariant convex and non quadratic functionals that we employ to derive regularized solutions of ill posed linear inverse imaging problems the proposed regularizers involve the schatten norms of the hessian matrix which are computed at every pixel of the image they can be viewed as second order extensions of the popular total variation tv semi norm since they satisfy the same invariance properties meanwhile by taking advantage of second order derivatives they avoid the staircase effect a common artifact of tv based reconstructions and perform well for a wide range of applications to solve the corresponding optimization problems we propose an algorithm that is based on a primal dual formulation a fundamental ingredient of this algorithm is the projection of matrices onto schatten norm balls of arbitrary radius this operation is performed efficiently based on a direct link we provide between vector projections onto norm balls and matrix projections onto schatten norm balls finally we demonstrate the effectiveness of the proposed methods through experimental results on several inverse imaging problems with real and simulated data

folding of the triangular lattice in a discrete three dimensional space density matrix renormalization group study folding of the triangular lattice in a discrete three dimensional space is investigated numerically such discrete folding has come about through theoretical investigation since bowick and co workers introduced it as a simplified model for the crumpling of the phantom polymerized membranes so far it has been analyzed with the hexagon approximation of the cluster variation method cvm however the possible systematic error of the approximation was not fully estimated in fact it has been known that the transfer matrix calculation is limited in the tractable strip widths l ensuremath leqslant 6 aiming to surmount this limitation we utilized the density matrix renormalization group thereby we succeeded in treating strip widths up to l 29 which admit reliable extrapolations to the thermodynamic limit our data indicate an onset of a discontinuous crumpling transition with the latent heat substantially larger than the cvm estimate it is even larger than the latent heat of the planar two dimensional folding as first noticed by the preceding cvm study that is contrary to our naive expectation the discontinuous character of the transition is even promoted by the enlargement of the embedding space dimensions we also calculated the folding entropy which appears to lie within the best analytical bound obtained previously via combinatorics arguments

an effective method for solving nonlinear equations and its application the linearized partial differential equation from the nonlinear partial differential equation which was proposed by rudin osher and fatemi l i rudin s osher and e fatemi nonlinear total variation based noise removal algorithms for solving image decomposition was introduced by chambolle a chambolle an algorithm for total variation minimization and applications and r acar and c r vogel r acar and c r vogel analysis of bounded variation penalty methods for ill posed problems in this paper we propose a method for solving the linearized partial differential equation and we show numerical results for denoising which demonstrate a significant improvement over other previous works

future polynomial regularization of ill posed volterra equations we examine a new discrete method for regularizing ill posed volterra problems unlike many classical regularization techniques such as tikhonov regularization this method preserves the volterra causal nature of the problem allowing the regularized solution to be produced sequentially in near real time as data arrives we analyze the method and for an important class of volterra problems prove that regularized solutions converge to the true solution at the best possible rate with respect to error in the data in fact the future polynomial regularization method discussed here may be applied to quite general operator equations provided that the operator may be discretized by a lower triangular matrix of toeplitz type this enlarges the class of operator equations that may be approximated using the method but it also introduces degenerate situations in which the future polynomial method is no more regularizing than an ordinary discretization method we characterize these degenerate cases and argue that we are unlikely to see them for the problems of interest here in particular such degeneracies cannot occur for the class of volterra problems for which we are able to prove the future polynomial method converges finally we present numerical evidence that this method works well in the recovery of sharp and discontinuous features in the true solution features that can be oversmoothed by classical regularization techniques

an efficient linear solver for nonlinear parameter identification problems in this paper we study some efficient numerical methods for parameter identifications in elliptic systems the proposed numerical methods are conducted iteratively and each iteration involves only solving positive definite linear algebraic systems although the original inverse problems are ill posed and highly nonlinear the positive definite systems can be naturally preconditioned with their corresponding block diagonal matrices numerical experiments are presented to illustrate the efficiency of the proposed algorithms

folding transition of the triangular lattice we study the problem of folding of the regular triangular lattice in the presence of bending rigidity k and magnetic field h conjugate to the local normal vectors to the triangles a numerical study of the transfer matrix of the problem shows the existence of three first order transition lines in the k h plane separating three phases a folded phase a phase frozen in the completely flat configuration with all normal vectors pointing up and its mirror image all normal vectors pointing down at zero magnetic field a first order folding transition is found at a positive value k c 0 11 1 of the bending rigidity corresponding to a triple point in the phase diagram

reconstruction of wavelet coefficients using total variation minimization we propose a model to reconstruct wavelet coefficients using a total variation minimization algorithm the approach is motivated by wavelet signal denoising methods where thresholding small wavelet coefficients leads to pseudo gibbs artifacts by replacing these thresholded coefficients by values minimizing the total variation our method performs a nearly artifact free signal denoising in this paper we detail the algorithm based on a subgradient descent combining a projection on a linear space the convergence of the algorithm is established and numerical experiments are reported

iterative image restoration combining total variation minimization and a second order functional a noise removal technique using partial differential equations pdes is proposed here it combines the total variational tv filter with a fourth order pde filter the combined technique is able to preserve edges and at the same time avoid the staircase effect in smooth regions a weighting function is used in an iterative way to combine the solutions of the tv filter and the fourth order filter numerical experiments confirm that the new method is able to use less restrictive time step than the fourth order filter numerical examples using images with objects consisting of edge flat and intermediate regions illustrate advantages of the proposed model

on the convergence of the lagged diffusivity fixed point method in total variation image restoration in this paper we show that the lagged diffusivity fixed point algorithm introduced by vogel and oman in siam j sci comput 17 1996 pp 227 238 to solve the problem of total variation denoising proposed by rudin osher and fatemi in phys d 60 1992 pp 259 268 is a particular instance of a class of algorithms introduced by voss and eckhardt in computing 25 1980 pp 243 251 whose origins can be traced back to weiszfeld s original work for minimizing a sum of euclidean lengths tohoku math j 43 1937 pp 355 386 there have recently appeared several proofs for the convergence of this algorithm g aubert et al technical report 94 01 informatique signaux et systemes de sophia antipolis 1994 a chambolle and p l lions technical report 9509 ceremade 1995 and d c dobson and c r vogel siam j numer anal 34 1997 pp 1779 1791 here we present a proof of the global and linear convergence using the framework introduced in h voss and u eckhart computing 25 1980 pp 243 251 and give a bound for the convergence rate of the fixed point iteration that agrees with our experimental results these results are also valid for suitable generalizations of the fixed point algorithm

latent heat calculation of the three dimensional q 3 4 and 5 potts models by the tensor product variational approach three dimensional 3d q state potts models q 3 4 and 5 are studied by the tensor product variational approach which is a recently developed variational method for 3d classical lattice models the variational state is given by a 2d product of local factors and is improved by way of self consistent calculations assisted by the corner transfer matrix renormalization group it should be noted that no a priori condition is imposed for the local factor transition temperatures and latent heats are calculated from the observations of thermodynamic functions in both ordered and disordered phases

robustness improvement of hyperspectral image unmixing by spatial second order regularization the acquisition of hundreds of images of a scene each at a different wavelength is known as hyperspectral imaging this high amount of data allows the extraction of much more information from hyperspectral images compared with conventional color images the forward looking imaging approach emerged from remote sensing but is still not very widespread in industrial and other practical applications spectral unmixing in particular aims at the determination of the components present in a scene as well as the abundance to which each component contributes this information is valuable for instance when discrimination tasks are to be performed involving not only spectral but also spatial information was found to have the potential to improve the unmixing results several publications use spatial first order regularization closely related to the total variation approach to incorporate this spatial information like in classical image processing this approach favors piecewise constant pixel transitions this is why it was proposed in the literature to use second order regularization instead of first order to approach piecewise linear transitions therefore we introduce hessian based regularization to hyperspectral unmixing and propose an algorithm to calculate the regularized result we use simulated data and images measured in our laboratory to show that both the first and second order approaches share many properties and produce similar results the second order approach however is more robust and thus more accurate in finding the minimum both methods smoothen the images in the case of supervised unmixing i e the component spectra are known beforehand and enhance unsupervised unmixing when the spectra are not known

towards artifact free characterization of surface topography using complex wavelets and total variation minimization a hybrid method based on dual tree complex wavelet transform and total variation minimization is proposed for erasure of undesirable artifacts that arise in the existing wavelet based methods in surface metrology the complex wavelet transform provides approximate shift invariance and good directional selectivity and attempts to solve the weakness of real discrete wavelet methods reconstruct the complex wavelet coefficients using a total variation minimization principle to eliminate the wavelet shape artifacts and the pseudo gibbs artifacts near the discontinuities which are caused when thresholding small wavelet coefficients by replacing these thresholded complex wavelet coefficients by optimal values that minimize the total variation the method performs a close artifact free surface characterization numerical experiments using a series of typical engineering and bioengineering surfaces demonstrate the remarkable potential of the methodology

fredholm toeplitz operators with vmo symbols and the duality of generalized fock spaces with small exponents we characterize fredholmness of toeplitz operators acting on generalized fock spaces of the n dimensional complex space for symbols in the space of vanishing mean oscillation vmo our results extend the recent characterizations for toeplitz operators on standard weighted fock spaces to the setting of generalized weight functions and also allow for unbounded symbols in vmo for the first time another novelty is the treatment of small exponents 0 p 1 which to our knowledge has not been seen previously in the study of the fredholm properties of toeplitz operators on any function spaces we accomplish this by describing the dual of the generalized fock spaces with small exponents

flat histogram monte carlo simulations of triangulated fixed connectivity surface models using the wang landau flat histogram monte carlo fhmc simulation technique we were able to study two types of triangulated spherical surface models in which the two dimensional extrinsic curvature energy is assumed in the hamiltonian the gaussian bond potential is also included in the hamiltonian of the first model but it is replaced by a hard wall potential in the second model the results presented in this paper are in good agreement with the results previously reported by our group the transition of surface fluctuations and collapsing transition were studied using the canonical metropolis monte carlo simulation technique and were found to be of the first order the results obtained in this paper also show that the fhmc technique can be successfully applied to triangulated surface models it is non trivial whether the technique is applicable or not to surface models because the simulations are performed on relatively large surfaces

variational approach for edge preserving regularization using coupled pdes this paper deals with edge preserving regularization for inverse problems in image processing we first present a synthesis of the main results we have obtained in edge preserving regularization by using a variational approach we recall the model involving regularizing functions spl phi and we analyze the geometry driven diffusion process of this model in the three dimensional 3 d case then a half quadratic theorem is used to give a very simple reconstruction algorithm after a critical analysis of this model we propose another functional to minimize for edge preserving reconstruction purposes it results in solving two coupled partial differential equations pdes one processes the intensity the other the edges we study the relationship with similar pde systems in particular with the functional proposed by ambrosio tortorelli 1990 1992 in order to approach the mumford shah 1989 functional developed in the segmentation application experimental results on synthetic and real images are presented

high order total variation based image restoration the total variation tv denoising method is a pde based technique that preserves edges well but has the sometimes undesirable staircase effect namely the transformation of smooth regions ramps into piecewise constant regions stairs in this paper we present an improved model constructed by adding a nonlinear fourth order diffusive term to the euler lagrange equations of the variational tv model our technique substantially reduces the staircase effect while preserving sharp jump discontinuities edges we show numerical evidence of the power of resolution of this novel model with respect to the tv model in some 1d and 2d numerical examples

subspace correction methods for total variation and ell_1 minimization this paper is concerned with the numerical minimization of energy functionals in hilbert spaces involving convex constraints coinciding with a seminorm for a subspace the optimization is realized by alternating minimizations of the functional on a sequence of orthogonal subspaces on each subspace an iterative proximity map algorithm is implemented via oblique thresholding which is the main new tool introduced in this work we provide convergence conditions for the algorithm in order to compute minimizers of the target energy analogous results are derived for a parallel variant of the algorithm applications are presented in domain decomposition methods for degenerate elliptic pdes arising in total variation minimization and in accelerated sparse recovery algorithms based on ell 1 minimization we include numerical examples which show efficient solutions to classical problems in signal and image processing

toeplitz operators on the segal bargmann space in this paper we give a complete characterization of those functions on 2n dimensional euclidean space for which the berezin toeplitz quantizations admit a symbol calculus modulo the compact operators the functions in question are characterized by a condition of small oscillation at infinity

the cutoff method for the numerical computation of nonnegative solutions of parabolic pdes with application to anisotropic diffusion and lubrication type equations the cutoff method which cuts off the values of a function less than a given number is studied for the numerical computation of nonnegative solutions of parabolic partial differential equations a convergence analysis is given for a broad class of finite difference methods combined with cutoff for linear parabolic equations two applications are investigated linear anisotropic diffusion problems satisfying the setting of the convergence analysis and nonlinear lubrication type equations for which it is unclear if the convergence analysis applies the numerical results are shown to be consistent with the theory and in good agreement with existing results in the literature the convergence analysis and applications demonstrate that the cutoff method is an effective tool for use in the computation of nonnegative solutions cutoff can also be used with other discretization methods such as collocation finite volume finite element and spectral methods and for the computation of positive solutions

rate of convergence of regularization procedures and finite element approximations for the total variation flow we derive rates of convergence for regularization procedures characterized by a parameter and finite element approximations of the total variation flow which arises from image processing geometric analysis and materials sciences practically useful error estimates which depend on open image in new window only in low polynomial orders are established for the proposed fully discrete finite element approximations as a result scaling laws which relate mesh parameters to the regularization parameter are also obtained numerical experiments are provided to validate the theoretical results and show efficiency of the proposed numerical methods