aspects of total variation regularized l1 function approximation the total variation based image denoising model of rudin osher and fatemi phys d 60 1992 pp 259 268 has been generalized and modified in many ways in the literature one of these modifications is to use the l1 norm as the fidelity term we study the interesting consequences of this modification especially from the point of view of geometric properties of its solutions it turns out to have interesting new implications for data driven scale selection and multiscale image decomposition

eigenvalues and degree deviation in graphs abstract let g be a graph with n vertices and m edges and let g 1 g n g be the eigenvalues of its adjacency matrix set s g u v g d u 2 m n we prove that s 2 g 2 n 2 2 m g 2 m n s g in addition we derive similar inequalities for bipartite g we also prove that the inequality k g n k 2 g 1 2 2 s g holds for every k 2 n finally we prove that for every graph g of order n n g n g 1 s 2 g 2 n 3 we show that these inequalities are tight up to a constant factor

maximum entropy and the nearly black object summary maximum entropy me inversion is a non linear inversion technique for inverse problems where the object to be recovered is known to be positive it has been applied in areas ranging from radio astronomy to various forms of spectroscopy sometimes with dramatic success in some cases me has attained an order of magnitude finer resolution and or an order of magnitude smaller noise level than that obtainable by standard linear methods the dramatic successes all seem to occur in cases where the object to be recovered is nearly black essentially zero in the vast majority of samples we show that near blackness is required both for signal to noise enhancements and for superresolution however other methods in particular minimum 1 norm reconstruction may exploit near blackness to an even greater extent

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

bayesian reconstructions from emission tomography data using a modified em algorithm a novel method of reconstruction from single photon emission computerized tomography data is proposed this method builds on the expectation maximization em approach to maximum likelihood reconstruction from emission tomography data but aims instead at maximum posterior probability estimation which takes account of prior belief about smoothness in the isotope concentration a novel modification to the em algorithm yields a practical method the method is illustrated by an application to data from brain scans

on the unification of line processes outlier rejection and robust statistics with applications in early vision the modeling of spatial discontinuities for problems such as surface recovery segmentation image reconstruction and optical flow has been intensely studied in computer vision while line process models of discontinuities have received a great deal of attention there has been recent interest in the use of robust statistical techniques to account for discontinuities this paper unifies the two approaches to achieve this we generalize the notion of a line process to that of an analog outlier process and show how a problem formulated in terms of outlier processes can be viewed in terms of robust statistics we also characterize a class of robust statistical problems for which an equivalent outlier process formulation exists and give a straightforward method for converting a robust estimation problem into an outlier process formulation we show how prior assumptions about the spatial structure of outliers can be expressed as constraints on the recovered analog outlier processes and how traditional continuation methods can be extended to the explicit outlier process formulation these results indicate that the outlier process approach provides a general framework which subsumes the traditional line process approaches as well as a wide class of robust estimation problems examples in surface reconstruction image segmentation and optical flow are presented to illustrate the use of outlier processes and to show how the relationship between outlier processes and robust statistics can be exploited an appendix provides a catalog of common robust error norms and their equivalent outlier process formulations

a multi scale vectorial l τ tv framework for color image restoration a general multi scale vectorial total variation model with spatially adapted regularization parameter for color image restoration is introduced in this paper this total variation model contains an l data fidelity for any c 1 2 the use of a spatial dependent regularization parameter improves the reconstruction of features in the image as well as an adequate smoothing for the homogeneous parts the automated adaptation of this regularization parameter is made according to local statistical characteristics of the noise which contaminates the image the corresponding multiscale vectorial total variation model is solved by fenchel duality and inexact semismooth newton techniques numerical results are presented for the cases 1 and 2 which reconstruct images contaminated with salt and pepper noise and gaussian noise respectively

distance spectra of graphs a survey abstract in 1971 graham and pollack established a relationship between the number of negative eigenvalues of the distance matrix and the addressing problem in data communication systems they also proved that the determinant of the distance matrix of a tree is a function of the number of vertices only since then several mathematicians were interested in studying the spectral properties of the distance matrix of a connected graph computing the distance characteristic polynomial and its coefficients was the first research subject of interest thereafter the eigenvalues attracted much more attention in the present paper we report on the results related to the distance matrix of a graph and its spectral properties

complete multipartite graphs are determined by their distance spectra abstract in this paper we prove that the complete multipartite graphs are determined by their distance spectra which confirms the conjecture proposed by lin hong wang and shu 2013 7 although it is well known that the complete multipartite graphs cannot be determined by their adjacency spectra

an algorithm for the minimization of mixed l sub 1 and l sub 2 norms with application to bayesian estimation the regularizing functional approach is widely used in many estimation problems in practice the solution is defined as one minimum point of a suitable functional the main part of which accounts for the underlying physical model whereas the regularizing part represents some prior information about the unknowns in the bayesian interpretation one has a maximum a posteriori map estimator in which the main and regularizing parts are represented respectively by likelihood and prior distributions when either the prior or likelihood is a laplace distribution and the other is a gaussian distribution one is led to consider functionals that include both absolute and square norms the authors present a characterization of the minimum points of such functionals together with a descent type algorithm for numerical computations the results of monte carlo simulations are also reported

scale space and edge detection using anisotropic diffusion a new definition of scale space is suggested and a class of algorithms used to realize a diffusion process is introduced the diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing rather than interregion smoothing it is shown that the no new maxima should be generated at coarse scales property of conventional scale space is preserved as the region boundaries in the approach remain sharp a high quality edge detector which successfully exploits global information is obtained experimental results are shown on a number of images parallel hardware implementations are made feasible because the algorithm involves elementary local operations replicated over the image

identification of concurrent harmonic and inharmonic vowels a test of the theory of harmonic cancellation and enhancement the improvement of identification accuracy of concurrent vowels with differences in fundamental frequency f0 is usually attributed to mechanisms that exploit harmonic structure to decide whether identification is aided primarily by selecting the target vowel on the basis of its harmonic structure harmonic enhancement or removing the interfering vowel on the basis of its harmonic structure harmonic cancellation pairs of synthetic vowels each of which was either harmonic or inharmonic were presented to listeners for identification responses for each vowel were scored according to the vowel s harmonicity and that of the vowel that accompanied it for a given target identification was better by about 3 for a harmonic ground unless the target was also harmonic with the same f0 this supports the cancellation hypothesis identification was worse for harmonic than for inharmonic targets by 3 8 this does not support the enhancement hypothesis when both vowels were harmonic identificatio

graph realizations associated with minimizing the maximum eigenvalue of the laplacian in analogy to the absolute algebraic connectivity of fiedler we study the problem of minimizing the maximum eigenvalue of the laplacian of a graph by redistributing the edge weights via semidefinite duality this leads to a graph realization problem in which nodes should be placed as close as possible to the origin while adjacent nodes must keep a distance of at least one we prove three main results for a slightly generalized form of this embedding problem first given a set of vertices partitioning the graph into several or just one part the barycenter of each part is embedded on the same side of the affine hull of the set as the origin second there is an optimal realization of dimension at most the tree width of the graph plus one and this bound is best possible in general finally bipartite graphs possess a one dimensional optimal embedding

proof of a conjecture involving the second largest d eigenvalue and the number of triangles abstract let g be a connected graph of order n with tr triangles and d be the distance matrix of g let 1 d 2 d n d be the d eigenvalue of the graph g fajtlowicz 1998 4 conjectured that 2 d tr when the independent number g 2 in this paper the conjecture is confirmed and the extremal graph when the equality holds is characterized

modeling the identification of concurrent vowels with different fundamental frequencies human listeners are better able to identify two simultaneous vowels if the fundamental frequencies of the vowels are different a computational model is presented which for the first time is able to simulate this phenomenon at least qualitatively the first stage of the model is based upon a bank of bandpass filters and inner hair cell simulators that simulate approximately the most relevant characteristics of the human auditory periphery the output of each filter hair cell channel is then autocorrelated to extract pitch and timbre information the pooled autocorrelation function acf based on all channels is used to derive a pitch estimate for one of the component vowels from a signal composed of two vowels individual channel acfs showing a pitch peak at this value are combined and used to identify the first vowel using a template matching procedure the acfs in the remaining channels are then combined and used to identify the second vowel model recognition performance shows a rapid improvement in

suggested formulae for calculating auditory filter bandwidths and excitation patterns recent estimates of auditory filter shape are used to derive a simple formula relating the equivalent rectangular bandwidth erb of the auditory filter to center frequency the value of the auditory filter bandwidth continues to decrease as center frequency decreases below 500 hz a formula is also given relating erb rate to frequency finally a method is described for calculating excitation patterns from filter shapes

on the second largest distance eigenvalue of a block graph abstract bapat and sivasubramanian 4 proved a formula for the inverse of the distance matrix of a block graph by the result of bapat and sivasubramanian we give an upper bound for the second largest distance eigenvalue of a uniform block graph using this we determine all block graphs whose second largest distance eigenvalues are at most 1 2

a generalized gaussian image model for edge preserving map estimation the authors present a markov random field model which allows realistic edge modeling while providing stable maximum a posterior map solutions the model referred to as a generalized gaussian markov random field ggmrf is named for its similarity to the generalized gaussian distribution used in robust detection and estimation the model satisfies several desirable analytical and computational properties for map estimation including continuous dependence of the estimate on the data invariance of the character of solutions to scaling of data and a solution which lies at the unique global minimum of the a posteriori log likelihood function the ggmrf is demonstrated to be useful for image reconstruction in low dosage transmission tomography

on distance matrices and laplacians we consider distance matrices of certain graphs and of points chosen in a rectangular grid formulae for the inverse and the determinant of the distance matrix of a weighted tree are obtained results concerning the inertia and the determinant of the distance matrix of an unweighted unicyclic graph are proved if d is the distance matrix of a tree then we obtain certain results for a perturbation of d 1 as an example it is shown that if l is the laplacian matrix of an arbitrary connected graph then d 1 l 1 is an entrywise positive matrix we consider the distance matrix of a subset of a rectangular grid of points in the plane if we choose m k 1 points not containing a closed path in an m k grid then a formula for the determinant of the distance matrix of such points is obtained

a regularization framework for robust dimensionality reduction with applications to image reconstruction and feature extraction dimensionality reduction has many applications in pattern recognition machine learning and computer vision in this paper we develop a general regularization framework for dimensionality reduction by allowing the use of different functions in the cost function this is especially important as we can achieve robustness in the presence of outliers it is shown that optimizing the regularized cost function is equivalent to solving a nonlinear eigenvalue problem under certain conditions which can be handled by the self consistent field scf iteration moreover this regularization framework is applicable in unsupervised or supervised learning by defining the regularization term which provides some types of prior knowledge of projected samples or projected vectors it is also noted that some linear projection methods can be obtained from this framework by choosing different functions and imposing different constraints finally we show some applications of our framework by various data sets including handwritten characters face images uci data and gene expression data

local strong homogeneity of a regularized estimator this paper deals with regularized pointwise estimation of discrete signals which contain large strongly homogeneous zones where typically they are constant or linear or more generally satisfy a linear equation the estimate is defined as the minimizer of an objective function combining a quadratic data fidelity term and a regularization prior term the latter term is the sum of the values obtained by applying a potential function pf to each component called a difference of a linear transform of the signal minimizers of functions of this form arise in various settings in statistics and optimization the features exhibited by such an estimate are closely related to the shape of the pf our goal is to determine estimators providing solutions which involve large strongly homogeneous zones where more precisely the differences are null in spite of the noise corrupting the data to this end we require that the strongly homogeneous zones recovered by the estimator be insensitive to any variation of th

fast weighted tv denoising via an edge driven metric abstract in this paper we propose a new fast weighted total variation denoising approach where we introduce edge driven weights in the standard tv discrete regularizer and a non euclidean metric in the discrepancy term induced by a positive definite matrix b strictly related to the weights in this way the fidelity constraint is adapted according to edgeness of each pixel the corresponding minimization problem is iteratively solved by using the split bregman strategy in which due to the particular choice of the structure of the positive definite matrix involved in the measure of the fidelity term the optimality conditions imposed for the computation of the minimum are reduced to simple assignments since all variables are decoupled for its solution we propose a fast weighted total variation fwtv algorithm and moreover we prove its convergence several experiments demonstrate that the fwtv algorithm outperforms both in terms of accuracy and execution times the performance of the weighted split bregman denoising approach where the l 2 norm is used in order to measure the fidelity term in the case of synthetic images the proposed algorithm is better respect to the best state of art algorithms but the methods not based on tv minimization give better performances with respect to our proposal in the case of natural images

convergence rates for exponentially ill posed inverse problems with impulsive noise this paper is concerned with exponentially ill posed operator equations with additive impulsive noise on the right hand side i e the noise is large on a small part of the domain and small or zero outside it is well known that tikhonov regularization with an l 1 data fidelity term outperforms tikhonov regularization with an l 2 fidelity term in this case this effect has recently been explained and quantified for the case of finitely smoothing operators here we extend this analysis to the case of infinitely smoothing forward operators under standard sobolev smoothness assumptions on the solution i e exponentially ill posed inverse problems it turns out that high order polynomial rates of convergence in the size of the support of large noise can be achieved rather than the poor logarithmic convergence rates typical for exponentially ill posed problems the main tools of our analysis are banach spaces of analytic functions and interpolation type inequalities for such spaces we discuss two examp

minimizers of cost functions involving nonsmooth data fidelity terms application to the processing of outliers we present a theoretical study of the recovery of an unknown vector x in mathbb r p such as a signal or an image from noisy data y in mathbb r q by minimizing with respect to x a regularized cost function cal f x y psi x y alpha phi x where psi is a data fidelity term phi is a smooth regularization term and alpha 0 is a parameter typically psi x y ax y 2 where a is a linear operator the data fidelity terms psi involved in regularized cost functions are generally smooth functions only a few papers make an exception to this and they consider restricted situations nonsmooth data fidelity terms are avoided in image processing in spite of this we consider both smooth and nonsmooth data fidelity terms our goal is to capture essential features exhibited by the local minimizers of regularized cost functions in relation to the smoothness of the data fidelity term in order to fix the context of our study we consider psi x y sum i psi a i tx y i where a i t are the rows of a and psi is cal c m on mathbb r setminus 0 we show that if psi 1 0 psi 1 0 then typical data y give rise to local minimizers hat x of cal f y which fit exactly a certain number of the data entries there is a possibly large set hat h of indexes such that a i t hat x y i for every i in hat h in contrast if psi is smooth on mathbb r for almost every y the local minimizers of cal f y do not fit any entry of y thus the possibility that a local minimizer fits some data entries is due to the nonsmoothness of the data fidelity term this is a strong mathematical property which is useful in practice by way of application we construct a cost function allowing aberrant data outliers to be detected and to be selectively smoothed our numerical experiments advocate the use of nonsmooth data fidelity terms in regularized cost functions for special purposes in image and signal processing

digital filters as absolute norm regularizers a variational formulation of the digital filtering problem based on a certain regularizing functional is presented in particular the special case where the regularizing functional is defined by means of l sub 1 norm is considered and a characterization of its minima is presented it is shown that for a certain class of signals one solution to the regularization problem can be obtained by means of a suitable recursive median filter some examples and a possible extension of the variational approach are also discussed

upper bounds on the spectral radius of book free and or k2 l free graphs abstract the spectral radius g of a graph g is the largest eigenvalue of its adjacency matrix let b k denote a book with k pages in this paper we generalize a result of lu et al m lu h liu f tian a new upper bound for the spectral radius of graphs with girth at least 5 linear algebra appl 414 2006 512 516 on the upper bound for the spectral radius of connected graphs with girth at least 5 to connected b k 1 k 2 l 1 free graphs g of order n with maximum degree as follows g k l k l 2 4 4 l n 1 2 with equality if and only if g is a strongly regular graph with parameters k l this implies sharp upper bounds for book free or k 2 l free graphs

a property of the minimum vectors of a regularizing functional defined by means of the absolute norm we consider a regularizing functional defined by means of the l sub 1 norm where the regularization is obtained using first differences as is well known such a functional can be put in relation with recursive median filters of appropriate window length we show that at least one of the minima is reached at a vector whose components have values over the same discrete set of the given signal this suggests a simple method to refine the approximate solution to the regularization problem which can be obtained with recursive median filters of increasing order we also report an example of application where the refinement method is employed for a signal detection problem

waveform interactions and the segregation of concurrent vowels two experiments investigated the effects of small values of fundamental frequency difference f0 on the identification of concurrent vowels as f0 s get smaller mechanisms that exploit them must necessarily fail and the pattern of breakdown may tell which mechanisms are used by the auditory system small f0 s also present a methodological difficulty if the stimulus is shorter than the beat period its spectrum depends on which part of the beat pattern is sampled a different starting phase might produce a different experimental outcome and the experiment may lack generality the first experiment explored the effects of f0 s as small as 0 4 the smallest f0 conditions were synthesized with several starting phases obtained by gating successive segments of the beat pattern an improvement in identification was demonstrated for f0 s as small as 0 4 for all segments differences between segments or starting phase were also observed but when averaged over vowel pairs they were of small magnitude

sharp upper bounds on the spectral radius of graphs abstract let g be a simple connected graph with n vertices m edges and degree sequence d 1 d 2 d n the spectral radius g of graph g is the largest eigenvalue of its adjacency matrix in this paper we present some sharp upper bounds of the spectral radius in terms of the degree sequence of graphs

non lipschitz ell_ p regularization and box constrained model for image restoration nonsmooth nonconvex regularization has remarkable advantages for the restoration of piecewise constant images constrained optimization can improve the image restoration using a priori information in this paper we study regularized nonsmooth nonconvex minimization with box constraints for image restoration we present a computable positive constant for using nonconvex nonsmooth regularization and show that the difference between each pixel and its four adjacent neighbors is either 0 or larger than in the recovered image moreover we give an explicit form of for the box constrained image restoration model with the non lipschitz nonconvex lp norm 0 p 1 regularization our theoretical results show that any local minimizer of this imaging restoration problem is composed of constant regions surrounded by closed contours and edges numerical examples are presented to validate the theoretical results and show that the proposed model can recover image restoration results very well

deblurring of color images corrupted by impulsive noise we consider the problem of restoring a multichannel image corrupted by blur and impulsive noise e g salt and pepper noise using the variational framework we consider the l1 fidelity term and several possible regularizers in particular we use generalizations of the mumford shah ms functional to color images and gamma convergence approximations to unify deblurring and denoising experimental comparisons show that the ms stabilizer yields better results with respect to beltrami and total variation regularizers color edge detection is a beneficial by product of our methods

maximum likelihood estimation of a class of non gaussian densities with application to i sub p deconvolution the properties of the maximum likelihood estimator of the generalized p gaussian gpg probability density function from n independent identically distributed samples is investigated especially in the context of the deconvolution problem under gpg white noise specifically the properties in the estimator are first described independently of the application then the solution of the above mentioned deconvolution problem is obtained as the solution of a minimum norm problem in an l sub p normed space it is shown that such minimum norm solution is the maximum likelihood estimate of the system function parameters and that such an estimate is unbiased with the lower bound of the variance of the error equal to the cramer rao lower bound and the upper bound derived from the concept of a generalized inverse the results are illustrated by computer simulations

salt and pepper noise removal by median type noise detectors and detail preserving regularization this paper proposes a two phase scheme for removing salt and pepper impulse noise in the first phase an adaptive median filter is used to identify pixels which are likely to be contaminated by noise noise candidates in the second phase the image is restored using a specialized regularization method that applies only to those selected noise candidates in terms of edge preservation and noise suppression our restored images show a significant improvement compared to those restored by using just nonlinear filters or regularization methods only our scheme can remove salt and pepper noise with a noise level as high as 90

nonideal sampling and regularization theory shannon s sampling theory and its variants provide effective solutions to the problem of reconstructing a signal from its samples in some shift invariant space which may or may not be bandlimited in this paper we present some further justification for this type of representation while addressing the issue of the specification of the best reconstruction space we consider a realistic setting where a multidimensional signal is prefiltered prior to sampling and the samples are corrupted by additive noise we adopt a variational approach to the reconstruction problem and minimize a data fidelity term subject to a tikhonov like continuous domain l2 regularization to obtain the continuous space solution we present theoretical justification for the minimization of this cost functional and show that the globally minimal continuous space solution belongs to a shift invariant space generated by a function generalized b spline that is generally not bandlimited when the sampling is ideal we recover some of the classical smoothing spline estimators the optimal reconstruction space is characterized by a condition that links the generating function to the regularization operator and implies the existence of a b spline like basis to make the scheme practical we specify the generating functions corresponding to the most popular families of regularization operators derivatives iterated laplacian as well as a new generalized one that leads to a new brand of matern splines we conclude the paper by proposing a stochastic interpretation of the reconstruction algorithm and establishing an equivalence with the minimax and minimum mean square error mmse wiener solutions of the generalized sampling problem

constrained restoration and the recovery of discontinuities the linear image restoration problem is to recover an original brightness distribution x sup 0 given the blurred and noisy observations y kx sup 0 b where k and b represent the point spread function and measurement error respectively this problem is typical of ill conditioned inverse problems that frequently arise in low level computer vision a conventional method to stabilize the problem is to introduce a priori constraints on x sup 0 and design a cost functional h x over images x which is a weighted average of the prior constraints regularization term and posterior constraints data term the reconstruction is then the image x which minimizes h a prominent weakness in this approach especially with quadratic type stabilizers is the difficulty in recovering discontinuities the authors therefore examine prior smoothness constraints of a different form which permit the recovery of discontinuities without introducing auxiliary variables for marking the location of jumps and suspending the constraints in their vicinity in this sense discontinuities are addressed implicitly rather than explicitly

properties of l1 tgv2 the one dimensional case abstract we study properties of solutions to second order total generalized variation tgv 2 regularized l 1 fitting problems in dimension one special attention is paid to the analysis of the structure of the solutions their regularity and the effect of the regularization parameters

image reconstruction and restoration overview of common estimation structures and problems developments in the theory of image reconstruction and restoration over the past 20 or 30 years are outlined particular attention is paid to common estimation structures and to practical problems not properly solved yet the problem of image reconstruction and restoration is first formulated some of the current regularization approaches used to solve the problem are then described the concepts of a priori information and compound criterion are introduced a bayesian interpretation of the regularization techniques is given which clarifies the role of the tuning parameters and indicates how they could be estimated the practical aspects of computing the solution first when the hyperparameters are known and second when they must be estimated are then considered conclusions are drawn and points that still need to be investigated are outlined

singular integrals image smoothness and the recovery of texture in image deblurring total variation tv image deblurring is a pde based technique that preserves edges but often eliminates vital small scale information or em texture this phenomenon reflects the fact that most natural images are not of bounded variation the present paper reconsiders the image deblurring problem in lipschitz spaces lambda alpha p q wherein a wide class of nonsmooth images can be accommodated a new and fast fft based deblurring method is developed that can recover texture in cases where tv deblurring fails completely singular integrals such as the poisson kernel are used to create an effective new image analysis tool that can calibrate the lack of smoothness in an image it is found that a rich class of images in lambda alpha 1 infty cap lambda beta 2 infty with 0 2 alpha beta 0 7 the poisson kernel is then used to regularize the deblurring problem by appropriately constraining its solutions in lambda alpha 2 infty spaces leading to new l2 error bounds

generating set search methods for piecewise smooth problems we consider a direct search approach for solving nonsmooth minimization problems where the objective function is locally lipschitz continuous and piecewise continuously differentiable on a finite family of polyhedra a generating set search method is proposed which is named structured because the structure of the set of nondifferentiability near the current iterate is exploited to define the search directions at each iteration some numerical results are presented to validate the approach

extremal digraphs with given clique number abstract we classify those digraphs with a given number of vertices and a given clique number that maximize the perron root of the adjacency matrix

fast nonconvex nonsmooth minimization methods for image restoration and reconstruction nonconvex nonsmooth regularization has advantages over convex regularization for restoring images with neat edges however its practical interest used to be limited by the difficulty of the computational stage which requires a nonconvex nonsmooth minimization in this paper we deal with nonconvex nonsmooth minimization methods for image restoration and reconstruction our theoretical results show that the solution of the nonconvex nonsmooth minimization problem is composed of constant regions surrounded by closed contours and neat edges the main goal of this paper is to develop fast minimization algorithms to solve the nonconvex nonsmooth minimization problem our experimental results show that the effectiveness and efficiency of the proposed algorithms

the maximum spectral radius of c4 free graphs of given order and size suppose that g is a graph with n vertices and m edges and let be the spectral radius of its adjacency matrix recently we showed that if g has no 4 cycle then 2 n 1 with equality if and only if g is the friendship graph here we prove that if m 9 and g has no 4 cycle then 2 m with equality if g is a star for 4 m 8 this assertion fails

a unified approach to statistical tomography using coordinate descent optimization over the past years there has been considerable interest in statistically optimal reconstruction of cross sectional images from tomographic data in particular a variety of such algorithms have been proposed for maximum a posteriori map reconstruction from emission tomographic data while map estimation requires the solution of an optimization problem most existing reconstruction algorithms take an indirect approach based on the expectation maximization em algorithm we propose a new approach to statistically optimal image reconstruction based on direct optimization of the map criterion the key to this direct optimization approach is greedy pixel wise computations known as iterative coordinate decent icd we propose a novel method for computing the icd updates which we call icd newton raphson we show that icd newton raphson requires approximately the same amount of computation per iteration as em based approaches but the new method converges much more rapidly in our experiments typically five to ten iterations other advantages of the icd newton raphson method are that it is easily applied to map estimation of transmission tomograms and typical convex constraints such as positivity are easily incorporated

a detection statistic for random valued impulse noise this paper proposes an image statistic for detecting random valued impulse noise by this statistic we can identify most of the noisy pixels in the corrupted images combining it with an edge preserving regularization we obtain a powerful two stage method for denoising random valued impulse noise even for noise levels as high as 60 simulation results show that our method is significantly better than a number of existing techniques in terms of image restoration and noise detection

geometry of total variation regularized l p model in this paper the geometry and scale selection properties of the total variation tv regularized l p model are rigorously analyzed some intrinsic features different from the tv l 1 model are derived and demonstrated numerical algorithms based on recent developed augmented lagrangian methods are implemented and numerical results consistent with the theoretical results are provided

on the distance spectrum of graphs abstract let g be a connected graph and d g be the distance matrix of g suppose that 1 d 2 d n d are the d eigenvalues of g in this paper we characterize all connected graphs with n d 2 furthermore we characterize all connected graphs of diameter 2 with exactly three d eigenvalues when 1 d is not an integer we also conjecture that the complete k partite graph is determined by its d spectrum

on the convergence of nonconvex minimization methods for image recovery nonconvex nonsmooth regularization method has been shown to be effective for restoring images with neat edges fast alternating minimization schemes have also been proposed and developed to solve the nonconvex nonsmooth minimization problem the main contribution of this paper is to show the convergence of these alternating minimization schemes based on the kurdyka ojasiewicz property in particular we show that the iterates generated by the alternating minimization scheme converges to a critical point of this nonconvex nonsmooth objective function we also extend the analysis to nonconvex nonsmooth regularization model with box constraints and obtain similar convergence results of the related minimization algorithm numerical examples are given to illustrate our convergence analysis

modeling the perception of concurrent vowels vowels with different fundamental frequencies if two vowels with different fundamental frequencies f0 s are presented simultaneously and monaurally listeners often hear two talkers producing different vowels on different pitches this paper describes the evaluation of four computational models of the auditory and perceptual processes which may underlie this ability each model involves four stages i frequency analysis using an auditory filter bank ii determination of the pitches present in the stimulus iii segregation of the competing speech sources by grouping energy associated with each pitch to create two derived spectral patterns and iv classification of the derived spectral patterns to predict the probabilities of listeners vowel identification responses the place models carry out the operations of pitch determination and spectral segregation by analyzing the distribution of rms levels across the channels of the filter bank the place time models carry out these operations by analyzing the periodicities in the wavef

efficient minimization methods of mixed l 2 l 1 and l 1 l 1 norms for image restoration image restoration problems are often solved by finding the minimizer of a suitable objective function usually this function consists of a data fitting term and a regularization term for the least squares solution both the data fitting and the regularization terms are in the ell 2 norm in this paper we consider the least absolute deviation lad solution and the least mixed norm lmn solution for the lad solution both the data fitting and the regularization terms are in the ell 1 norm for the lmn solution the regularization term is in the ell 1 norm but the data fitting term is in the ell 2 norm since images often have nonnegative intensity values the proposed algorithms provide the option of taking into account the nonnegativity constraint the lmn and lad solutions are formulated as the solution to a linear or quadratic programming problem which is solved by interior point methods at each iteration of the interior point method a structured linear system must be solved the preconditioned conjugate gradient method with factorized sparse inverse preconditioners is employed to solve such structured inner systems experimental results are used to demonstrate the effectiveness of our approach we also show the quality of the restored images using the minimization of mixed ell 2 ell 1 and ell1 ell 1 norms is better than that using only the ell 2 norm

a local update strategy for iterative reconstruction from projections a method for bayesian reconstruction which relies on updates of single pixel values rather than the entire image at each iteration is presented the technique is similar to gauss seidel gs iteration for the solution of differential equations on finite grids the computational cost per iteration of the gs approach is found to be approximately equal to that of gradient methods for continuously valued images gs is found to have significantly better convergence at modes representing high spatial frequencies in addition gs is well suited to segmentation when the image is constrained to be discretely valued it is shown that bayesian segmentation using gs iteration produces useful estimates at much lower signal to noise ratios than required for continuously valued reconstruction the convergence properties of gradient ascent and gs for reconstruction from integral projections are analyzed and simulations of both maximum likelihood and maximum a posteriori cases are included

pde based random valued impulse noise removal based on new class of controlling functions this paper is concerned with partial differential equation pde based image denoising for random valued impulse noise we introduce the notion of eni the abbreviation for edge pixels noisy pixels and interior pixels that denotes the number of homogeneous pixels in a local neighborhood and is significantly different for edge pixels noisy pixels and interior pixels we redefine the controlling speed function and the controlling fidelity function to depend on eni according to our two controlling functions the diffusion and fidelity process at edge pixels noisy pixels and interior pixels can be selectively carried out furthermore a class of second order improved and edge preserving pde denoising models is proposed based on the two new controlling functions in order to deal with random valued impulse noise reliably we demonstrate the performance of the proposed pdes via application to five standard test images corrupted by random valued impulse noise with various noise levels and comparison with the related second order pde models and the other special filtering methods for random valued impulse noise our two controlling functions are extended to automatically other pde models

convergence rates for inverse problems with impulsive noise we study inverse problems f f g with perturbed right hand side g rm obs corrupted by so called impulsive noise i e noise which is concentrated on a small subset of the domain of definition of g it is well known that tikhonov type regularization with an mathbf l 1 data fidelity term yields significantly more accurate results than tikhonov regularization with classical mathbf l 2 data fidelity terms for this type of noise the purpose of this paper is to provide a convergence analysis explaining this remarkable difference in accuracy our error estimates significantly improve previous error estimates for tikhonov regularization with mathbf l 1 fidelity term in the case of impulsive noise we present numerical results which are in good agreement with the predictions of our analysis

simultaneous higher order optical flow estimation and decomposition we study the estimation and decomposition of optical flows from highly nonrigid motions to this end recent methods from image decomposition into structural and textural parts are combined with variational optical flow estimation the approaches we suggest amount to minimizing discrete convex functionals using second order cone programming higher order regularization is necessary in order to accurately recover important flow structure like vortices and to incorporate key physical properties such as vanishing divergence for proper discretization we apply the finite mimetic difference method which preserves the identities fulfilled by the continuous differential operators numerical examples demonstrate the feasibility of the complex approaches

on the spectral radius of graphs with a given domination number we characterize the graphs which achieve the maximum value of the spectral radius of the adjacency matrix in the sets of all graphs with a given domination number and graphs with no isolated vertices and a given domination number

a new upper bound for the spectral radius of graphs with girth at least 5 let g be a simple connected graph with v g v1 v 2 v n and girth at least 5 let be the maximum degree of g in this paper we present a new sharp upper bound for the spectral radius of g as follows

spectral radius of digraphs with given dichromatic number abstract let d be a digraph with vertex set v d a partition of v d into k acyclic sets is called a k coloring of d the minimum integer k for which there exists a k coloring of d is the dichromatic number d of the digraph d denote g n k the set of the digraphs of order n with the dichromatic number k 2 in this note we characterize the digraph which has the maximal spectral radius in g n k our result generalizes the result of 8 by feng et al

a faster algorithm solving a generalization of isotonic median regression and a class of fused lasso problems many applications in the areas of production signal processing economics bioinformatics and statistical learning involve a given partial order on certain parameters and a set of noisy observations of the parameters the goal is to derive estimated values of the parameters that satisfy the partial order that minimize the loss of deviations from the given observed values a prominent application of this setup is the well known isotonic regression problem where the partial order is a total order a commonly studied isotonic regression problem is the isotonic median regression imr where the loss function is a sum of absolute value functions on the deviations of the estimated values from the observation values we present here the most efficient algorithm to date for a generalization of imr with any convex piecewise linear loss function as well as for variant models that include ell 1 norm penalty separation regularization functions in the objective on the violation of the total order constraints suc

the l 1 potts functional for robust jump sparse reconstruction we investigate the nonsmooth and nonconvex l 1 potts functional in discrete and continuous time we show gamma convergence of discrete l 1 potts functionals toward their continuous counterpart and obtain a convergence statement for the corresponding minimizers as the discretization gets finer for the discrete l 1 potts problem we introduce an o n 2 time and o n space algorithm to compute an exact minimizer we apply l 1 potts minimization to the problem of recovering piecewise constant signals from noisy measurements f it turns out that the l 1 potts functional has a quite interesting blind deconvolution property in fact we show that mildly blurred jump sparse signals are reconstructed by minimizing the l 1 potts functional furthermore for strongly blurred signals and a known blurring operator we derive an iterative reconstruction algorithm

structural source identification using a generalized tikhonov regularization abstract this paper addresses the problem of identifying mechanical exciting forces from vibration measurements the proposed approach is based on a generalized tikhonov regularization that allows taking into account prior information on the measurement noise as well as on the main characteristics of sources to identify like its sparsity or regularity to solve such a regularization problem efficiently a generalized iteratively reweighted least squares girls algorithm is introduced proposed numerical and experimental validations reveal the crucial role of prior information in the quality of the source identification and the performance of the girls algorithm

image deblurring in the presence of impulsive noise consider the problem of image deblurring in the presence of impulsive noise standard image deconvolution methods rely on the gaussian noise model and do not perform well with impulsive noise the main challenge is to deblur the image recover its discontinuities and at the same time remove the impulse noise median based approaches are inadequate because at high noise levels they induce nonlinear distortion that hampers the deblurring process distinguishing outliers from edge elements is difficult in current gradient based edge preserving restoration methods the suggested approach integrates and extends the robust statistics line process half quadratic and anisotropic diffusion points of view we present a unified variational approach to image deblurring and impulse noise removal the objective functional consists of a fidelity term and a regularizer data fidelity is quantified using the robust modified l 1 norm and elements from the mumford shah functional are used for regularization we show that the mumford shah regularizer can be viewed as an extended line process it reflects spatial organization properties of the image edges that do not appear in the common line process or anisotropic diffusion this allows to distinguish outliers from edges and leads to superior experimental results

on the distance spectral radius of some graphs abstract for a connected graph the distance spectral radius is the largest eigenvalue of its distance matrix in this paper we determine the unique graph with minimum distance spectral radius among all connected graphs of order n with a given diameter moreover we determine the unique graph with maximum distance spectral radius among the catacondensed hexagonal systems with h hexagons

parametric maximum flow algorithms for fast total variation minimization this report studies the global minimization of anisotropically discretized total variation tv energies with an l p in particular l 1 and l 2 fidelity term using parametric maximum flow algorithms to minimize s t cut representations of these energies the tv l 2 model also known as the rudin osher fatemi rof model is suitable for restoring images contaminated by gaussian noise while the tv l 1 model is able to remove impulsive noise from grayscale images and perform multiscale decompositions of them preliminary numerical results on large scale two dimensional ct and three dimensional brain mr images are presented to illustrate the effectiveness of these approaches

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

bounds on graph eigenvalues i abstract we prove three results about the spectral radius g of a graph g a let t r n be the r partite turan graph of order n if g is a k r 1 free graph of order n then g t r n unless g t r n b for most irregular graphs g of order n and size m g 2 m n 1 2 m 2 n c let 0 k l if g is a graph of order n with no k 2 k k 1 and no k 2 l 1 then g min g k l 1 k l 1 2 4 l n 1 2