adsorption of pulled directed paths in a slanted boundary in this paper the generating function free energy and phase diagram of a class of models of directed paths related to the models of paths adsorbing in the boundary y nx n 2 for and pulled by a vertical force in its endpoint are determined these models are related to the special classes of models of random walks in the quarter plane and which interact with the x axis generating functions are determined by solving a functional recurrence using the kernel method and are algebraic the generating function is determined for general values of n and the solutions for n 1 and n 2 are examined explicitly together with the derivation of the phase diagram and locations of critical curves three phases including a free or bulk phase an adsorbed phase and a ballistic or stretched phase are identified and the nature of the transitions between these phases are examined order parameters are defined and asymptotic expressions are determined for the critical adsorption surface as a function of the pulling force some of these results are also briefly generalized to arbitrary values of n

analysis of spatial smoothing with uniform circular arrays we analyze spatial smoothing with uniform circular arrays ucas in particular we study the performance of the root music with smoothing in the presence of correlated sources finite data perturbations and errors in the transformed steering vector that arise due to some approximations made while extending the root music and smoothing to uca expressions are derived for the asymptotic performance of the root music with smoothing applied to the transformed uca data an attempt has been made to bring out the impact of both the forward and forward backward smoothing we consider ucas with isotropic as well as directional sensors in our study computer simulations are provided to demonstrate the usefulness of the analysis

iterative weighted maximum likelihood denoising with probabilistic patch based weights image denoising is an important problem in image processing since noise may interfere with visual or automatic interpretation this paper presents a new approach for image denoising in the case of a known uncorrelated noise model the proposed filter is an extension of the nonlocal means nl means algorithm introduced by buades which performs a weighted average of the values of similar pixels pixel similarity is defined in nl means as the euclidean distance between patches rectangular windows centered on each two pixels in this paper a more general and statistically grounded similarity criterion is proposed which depends on the noise distribution model the denoising process is expressed as a weighted maximum likelihood estimation problem where the weights are derived in a data driven way these weights can be iteratively refined based on both the similarity between noisy patches and the similarity of patches extracted from the previous estimate we show that this iterative process noticeably improves the denoising performance especially in the case of low signal to noise ratio images such as synthetic aperture radar sar images numerical experiments illustrate that the technique can be successfully applied to the classical case of additive gaussian noise but also to cases such as multiplicative speckle noise the proposed denoising technique seems to improve on the state of the art performance in that latter case

spatial covariance based downlink beamforming in an sdma mobile radio system on the downlink of an sdma mobile radio system different users who share the same frequency band and time slot have to be spatially separated by beamforming in this paper we analyze an approach to jointly calculate weights in such a way that all users receive their signal with a given signal to noise and interference ratio the computations are based on spatial covariance matrices which describe the user specific channels averaged over the fast fading the presented algorithm succeeds in minimizing the array transmit power while spatially separating the users no matter which rank their spatial covariance matrices have but since it needs to solve a complex nonlinear constrained optimization problem several approximations of this algorithm are presented and compared to each other on the basis of array power complexity and convergence

performance analysis of the optimum beamformer in the presence of correlated sources and its behavior under spatial smoothing in this paper we first study the signal cancellation and interference rejection effects of the optimum constrained least squares or minimum variance beamformer in the presence of partially and fully correlated interfering sources in particular we derive expressions for the output power and the gain in the interference direction of the beamformer in terms of the source powers correlation and the sensor noise power and show quantitatively the penalties arising from increasing correlation in several scenarios of interest next we show that spatial smoothing progressively decorrelates the sources at a rate that depends on the spacing and directions of the sources and thus relate the degree of smoothing to the improvement in signal cancellation and interference rejection behavior provided by spatial smoothing results of computer simulations are included to support our analysis

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

forces in motzkin paths in a wedge entropic forces in models of motzkin paths in a wedge geometry are considered as models of forces in polymers in confined geometries a motzkin path in the square lattice is a path from the origin to a point in the line y x while it never visits sites below this line and it is constrained to give unit length steps only in the north and east directions and steps of length in the north east direction motzkin path models may be generalized to ensembles of ne oriented paths above the line y rx where r 0 is an irrational number these are paths giving east north and north east steps from the origin in the square lattice and confined to the r wedge formed by the y axis and the line y rx the generating function gr of these paths is not known but if r 1 then i determine its radius of convergence to be and if r 0 1 then tr 1 3 the entropic force the path exerts on the line y rx may be computed from this an asymptotic expression for the force for large values of r is given by in terms of the vertex angle of the r wedge the moment of the force about the origin has leading terms as 0 and f 0 if 4 2 moreover numerical integration of the force shows that the total work done by closing the wedge is 1 085 07 lattice units an alternative ensemble of ne oriented paths may be defined by slightly changing the generating function gr in this model it is possible to determine closed form expressions for the limiting free energy and the force the leading term in an asymptotic expansions for this force agrees with the leading term in the asymptotic expansion of the above model and the subleading term only differs by a factor of 2

performance analysis of the minimum variance beamformer we present an analysis of the signal to interference plus noise ratio sinr at the output of the minimum variance beamformer the analysis is based on the assumption that the signals and noise are gaussian and that the number of samples is large compared to the array size and it yields an explicit expression for the sinr in terms of the different parameters affecting the performance including signal to noise ratio snr interference to noise ratio inr signal to interference ratio sir angular separation between the desired signal and the interference array size and shape correlation between the desired signal and the interference and finite sample size

constrained least squares design of 2 d fir filters we consider the design of 2 d linear phase finite impulse response fir filters according to the least squares ls error criterion subject to equality and or inequality constraints since we use a frequency domain formulation these constraints can be used to explicitly prescribe frequency dependent error tolerances the maximum minimum or fixed values of the frequency response at certain points and or regions our method combines lagrange multiplier and kuhn tucker theory to solve a much wider class of problems than do standard methods it allows arbitrary compromises between the ls and the equiripple design

finite data performance analysis of mvdr beamformer with and without spatial smoothing the finite data performance of a minimum variance distortionless response mvdr beamformer is analyzed with and without spatial smoothing using first order perturbation theory in particular expressions are developed for the mean values of the power gain in any direction of interest the output power and the norm of the weight error vector as a function of the number of snapshots and the number of smoothing steps it is shown that in general the smoothing in addition to decorrelating the sources can alleviate the effects of finite data perturbations the above expressions are reduced to the case in which no spatial smoothing is used these expressions are valid for an arbitrary array and for arbitrarily correlated signals for this case an expression for the variance of the power gain is also developed for a single interference case it is shown explicitly how the snr spacing of the interference from the desired signal and the correlation between them influence the beamformer performance simulations verify the usefulness of the theoretical expressions

on the performance analysis of the mvdr beamformer in the presence of correlated interference expressions are developed that describe the output of an adaptive array based on the minimum variance distortionless response mvdr beamformer when multiple correlated interfering signals are present such signals may arise in certain multipath scenarios or in the case of smart jamming previous analyses considered only the case of single correlated interferer three scenarios of interest are examined very high signal to noise ratio snr moderately high snr and very low snr the analysis is based on simpler linear algebra concepts and generalizes a number of previously reported results proved for special cases in addition a modification of mvdr beamforming based on total least squares is introduced as a means of mitigating the sensitivity of the mvdr beamformer to uncertainties in element positions pointing angle etc

applications of cumulants to array processing iii blind beamforming for coherent signals for pt ii see ibid vol 43 no 7 p 1663 7 1995 we provide a cumulant based blind beamforming method for recovery of statistically independent narrowband source signals in the presence of coherent or perfectly correlated multipath propagation our method is based on the fact that for a blind beamformer the presence of coherent multipaths is equivalent to the case of independent sources with a different steering matrix our approach is applicable to any array configuration having unknown response signal sources must have nonzero fourth order cumulants there is no need to estimate the directions of arrival our method maximizes signal to interference plus noise ratio sinr a comparable result does not exist using just second order statistics

parallel spatial processing a cure for signal cancellation in adaptive arrays a spatial processing algorithm with parallel structure is presented for the prevention of signal caneellation phenomena in conventional adaptive arrays this algorithm basically uses a parallel structure with a spatial averaging effect to combat coherent jamming it results in a spatially smoothed maximum likelihood estimate of the desired signal when the adaptive beamformer converges simulations have been conducted which verify the effectiveness of the proposed structure

chain polymers near an adsorbing surface we present improved estimates of critical exponents for 3d polymers near a plane adsorbing surface the improvements were possible by simulating rather long chains up to n 2000 by means of a new algorithm apart from minor but significant adjustments in the location of the tricritical point and in the various gamma exponents our main result is that the crossover exponent for critical adsorption is compatible with phi 1 2 this is much lower than previous estimates and suggests that this exponent might be superuniversal

structure texture image decomposition modeling algorithms and parameter selection this paper explores various aspects of the image decomposition problem using modern variational techniques we aim at splitting an original image f into two components u and where u holds the geometrical information and holds the textural information the focus of this paper is to study different energy terms and functional spaces that suit various types of textures our modeling uses the total variation energy for extracting the structural part and one of four of the following norms for the textural part l2 g l1 and a new tunable norm suggested here for the first time based on gabor functions apart from the broad perspective and our suggestions when each model should be used the paper contains three specific novelties first we show that the correlation graph between u and may serve as an efficient tool to select the splitting parameter second we propose a new fast algorithm to solve the tv l1 minimization problem and third we introduce the theory and design tools for the tv gabor model

nonlinear scale space with spatially varying stopping time a general scale space algorithm is presented for denoising signals and images with spatially varying dominant scales the process is formulated as a partial differential equation with spatially varying time the proposed adaptivity is semi local and is in conjunction with the classical gradient based diffusion coefficient designed to preserve edges the new algorithm aims at maximizing a local snr measure of the denoised image it is based on a generalization of a global stopping time criterion presented recently by the author and colleagues most notably the method works well also for partially textured images and outperforms any selection of a global stopping time given an estimate of the noise variance the procedure is automatic and can be applied well to most natural images

self avoiding walks with geometrical constraints we consider self avoiding walks on ad dimensional hypercubic lattice confined to a slab geometry and confined to a half space we present a proof of the existence of a connective constant for the slab geometry and review some corresponding results for the half space we also discuss the way in which scaling arguments can be used to give stronger but nonrigorous results

a novel power bearing approach and asymptotically optimum estimator for target motion analysis the problem of target motion analysis tma has been extensively investigated using bearing only bo doppler bearing db and other measurement data for radio frequency rf emitters signal powers follow the well known path loss law that can be utilized to aid localization and target tracking in bo tma leading to the novel power bearing pb approach as proposed in this paper our main contribution lies in the proof of the asymptotic optimality of the total least squares tls algorithm for pb tma under some mild condition the cramer rao lower bound crlb is employed to demonstrate the performance improvements of the pb tma over the bo tma our work shows the promise of the pb tma approach for rf signals

forces in square lattice directed paths in a wedge a square lattice directed path confined to a wedge with vertex angle exerts an entropic force f on the wedge we show that this is a repulsive force of magnitude this force is determined by examining the combinatorial properties of the directed path and by determining the exact entropic contribution to the free energy in the limit as the path length goes to infinite

decorrelation performance of deese and spatial smoothing techniques for direction of arrival problems second order spatial analysis methods for array signal processing have been shown to yield high resolution by exploiting specific eigenstructure properties of the array output covariance matrix however when some of the signals are coherent these covariance based methods face serious difficulties produced by smaller rank in this correspondence a theoretical expression is derived for the effective correlation coefficient between sources after processing when using spatial smoothing and a new scheme of space diversity called deese decomposition de l espace source estime monte carlo simulations have been used to compare deese and spatial smoothing and to show the advantages of using deese when noise is present

performance of spatial smoothing algorithms for correlated sources the problem of identifying the angles of arrival of a set of plane waves impinging on a narrowband array of sensors and related spectral analysis problems have been addressed with a large number of algorithms one of the most popular techniques is the multiple signal classification music the major shortcoming of the music algorithm is that it performs poorly when the sources are highly correlated fortunately two algorithms exist to overcome this problem spatial smoothing ss and forward backward spatial smoothing fbss the performance of the ss technique depends on signal bearings and spatial separation for the same smoothing fbss can offer improved performance but this depends on the signal phases numerical results for the variance of the algorithms are given to illustrate the points made

on the equivalence of soft wavelet shrinkage total variation diffusion total variation regularization and sides soft wavelet shrinkage total variation tv diffusion tv regularization and a dynamical system called sides are four useful techniques for discontinuity preserving denoising of signals and images in this paper we investigate under which circumstances these methods are equivalent in the one dimensional case first we prove that haar wavelet shrinkage on a single scale is equivalent to a single step of space discrete tv diffusion or regularization of two pixel pairs in the translationally invariant case we show that applying cycle spinning to haar wavelet shrinkage on a single scale can be regarded as an absolutely stable explicit discretization of tv diffusion we prove that space discrete tv diffusion and tv regularization are identical and that they are also equivalent to the sides system when a specific force function is chosen afterwards we show that wavelet shrinkage on multiple scales can be regarded as a single step diffusion filtering or regularization of the laplacian pyramid of the signal we analyze possibilities to avoid gibbs like artifacts for multiscale haar wavelet shrinkage by scaling the thresholds finally we present experiments where hybrid methods are designed that combine the advantages of wavelets and pde variational approaches these methods are based on iterated shift invariant wavelet shrinkage at multiple scales with scaled thresholds

ica based artifact correction improves spatial localization of adaptive spatial filters in meg abstract beamformers are one of the most common inverse models currently used in the estimation of source activity from magnetoencephelography meg data they rely on a minimization of total power while constraining the gain in the voxel of interest resulting in the suppression of background noise nonetheless in cases where background noise is strong compared to the source of interest or when many sources are present the ability of the beamformer to detect and accurately localize weak sources is reduced in visual paradigms two main background sources can substantially impact an accurate estimation of weaker sources ocular artifacts are orders of magnitude higher than neural sources making it difficult for the beamformer to effectively suppress them primary visual activations also result in strong signals that can impede localization of weak sources in this paper we systematically evaluated how neural visual and non neural eye heart sources affect the localization accuracy of frontal and medial temporal sources in visual tasks these sources are of tremendous interest in learning and memory studies as well as in clinical settings alzheimer s epilepsy and are typically difficult to localize robustly in meg empirical data from two tasks active learning and control were used to evaluate our analysis techniques global field power calculations showed multiple time periods where active learning was significantly different from response selection with dominant sources converging to the eyes extensive leakage of eye activity into frontal and visual that evoked responses into parietal cortices was also observed contributions from ocular activity to the reconstructed time series were indiscernible from task based recruitment of frontal sources in the original data removing artifacts eye movements cardiac and muscular by means of independent component analysis ica led to a significant improvement in detection and localization of frontal and medial temporal sources we verified our results by using simulations of sources placed in frontal and medial temporal regions with various types of background noise eye heart and visual we report that the detection and localization accuracy of frontal and medial temporal sources with beamformer techniques is highly dependent on the magnitude and location of background sources and that removing artifacts can substantially improve the beamformer s performance

a hybrid convex variational model for image restoration we propose a new hybrid model for variational image restoration using an alternative diffusion switching non quadratic function with a parameter the parameter is chosen adaptively so as to minimize the smoothing near the edges and allow the diffusion to smooth away from the edges this model belongs to a class of edge preserving regularization methods proposed in the past the f function formulation this involves a minimizer to the associated energy functional we study the existence and uniqueness of the energy functional of the model using real and synthetic images we show that the model is effective in image restoration

efficient diffusion coefficient for image denoising diffusion coefficient has an important role in the performance of partial differential equation pde based image denoising techniques commonly the classical perona malik pm diffusion coefficient is widely used in pde based noise removal algorithms in this paper pm diffusion coefficient is analyzed regarding to its flux based on the analysis pm flux for regions where the gradient magnitude is higher than smoothing threshold may lead to undesirable blurring effect and edge displacement to address these issues the image is divided into three segments based on the gradient magnitude regions where the gradient is lower than the smoothing threshold regions where the gradient is between the smoothing threshold and inflection point of flux and regions where the gradient magnitude is higher than inflection point we define the conditions that should be considered in these three segments then a diffusion coefficient satisfying all these conditions is computed experimental results confirm the performance of the proposed method with regard to peak signal to noise ratio psnr mean structural similarity mssim universal quality index uqi visual information fidelity vif feature similarity fsim information content weighted ssim iw ssim and visual quality

optimal spatial adaptation for patch based image denoising a novel adaptive and patch based approach is proposed for image denoising and representation the method is based on a pointwise selection of small image patches of fixed size in the variable neighborhood of each pixel our contribution is to associate with each pixel the weighted sum of data points within an adaptive neighborhood in a manner that it balances the accuracy of approximation and the stochastic error at each spatial position this method is general and can be applied under the assumption that there exists repetitive patterns in a local neighborhood of a point by introducing spatial adaptivity we extend the work earlier described by buades et al which can be considered as an extension of bilateral filtering to image patches finally we propose a nearly parameter free algorithm for image denoising the method is applied to both artificially corrupted white gaussian noise and real images and the performance is very close to and in some cases even surpasses that of the already published denoising methods

polygons and stars in a slit geometry the authors consider self avoiding polygons uniform 3 stars and uniform 4 stars weakly embeddable in the square lattice and confined between two parallel lines y 0 and y l they show rigorously that the connective constants of these three structures provided that the corresponding limits exist are all strictly less than the connective constant kappa l of self avoiding walks with the same geometrical constraint they also derive lower bounds on the connective constants of uniform 3 stars and 4 stars these bounds appear to be strong at least for small l

the performance of the least mean squares algorithm combined with spatial smoothing many practical signal environments involve correlation between desired and undesired signals causing narrowband adaptive array beamformers to exhibit signal cancellation spatial smoothing is a technique that can perform beamforming in such environments this method can be incorporated into an adaptive algorithm such as least mean squares lms possibly altering the well known performance characteristics of the algorithm we discuss methods for combining spatial smoothing with the lms algorithm in an array with a generalized side lobe canceler gsc structure the first of these methods is an electronic version of mechanically dithering the array we show that this well known method obeys a set of nonhomogeneous dynamical equations resulting in a limit cycle that increases the misadjustment of the algorithm the previously reported parallel spatial processing algorithm is also shown to have this increased misadjustment we then introduce two methods that do not suffer from this misadjustment increase we compare the methods computational complexity and performance in terms of stability and steady state behavior including weight misadjustment gsc output power and signal to noise ratio snr in conclusion we find that the limit cycle of the first method can be avoided without any increase in complexity by using one of the new methods

scale selection for compact scale space representation of vector valued images this paper investigates the scale selection problem for nonlinear diffusion scale spaces this topic comprises the notions of localization scale selection and scale space discretization for the former we present a new approach it aims at maximizing the image content s presence by finding the scale that has a maximum correlation with the noise free image for the latter we propose to adapt the optimal diffusion stopping time criterion of mrazek and navara in such a way that it may identify multiple scales of importance

2 d bauer factorization the extension to the 2 d case of the bauer formulation of the spectral factorization is given the relation to the 2 d generalization of the levinson algorithm by marzetta leads to a proof of the convergence of the method the problems of the practical implementation are discussed

applications of second order cone programming in a second order cone program socp a linear function is minimized over the intersection of an affine set and the product of second order quadratic cones socps are nonlinear convex problems that include linear and convex quadratic programs as special cases but are less general than semidefinite programs sdps several efficient primaldual interior point methods for socp have been developed in the last few years after reviewing the basic theory of socps we describe general families of problems that tan be recast as socps these include robust linear programming and robust leastsquares problems problems involving sums or maxima of norms or with convex hyperbolic constraints we discuss a variety of engineering applications such as filter design antenna array weight design truss design and grasping forte optimization in robotics we describe an efficient primaldual interior point method for solving socps which shares many of the features of primaldual interior point methods for linear program

shaped beam synthesis of real antenna arrays via finite element method floquet modal analysis and convex programming a shaped beam synthesis methodology for planar arrays with control of the ripple amplitude in the shaped region and constraints on the sidelobe and cross polar levels is proposed in this paper a previously developed synthesis formulation for designing finite impulse response fir filters by transforming a nonconvex synthesis problem to a convex optimization scheme enforcing conjugate symmetric excitation weights is extended to real and coupled radiating elements of complex geometry taking into account mutual coupling effects the optimization procedure is integrated with a finite array approach simulating different array environments this approach is based on the infinite array model through a floquet modal and general scattering matrix gsm based analysis where the periodic radiating element is characterized from a hybrid and full wave analysis procedure combining the fem modal analysis and domain decomposition technique numerical results of different synthesized beam patterns are presented for arrays of open ended apertures and microstrip antennas

beamforming in the presence of correlated arrivals using structured correlation matrix expressions are derived for the snr signal to noise ratio at the output of two antenna array processors in the presence of correlated arrivals and the effect on the output snr of the magnitude and the phase of the correlation the number of elements in the array the direction of the level of the interference source and the level of the uncorrelated noise is investigated the two processes considered are the optimal element space processor esp and the optimal postbeamformer interference canceller pic the pic processes the signal by forming two beams and adjusting the weights of one beam in contrast to the esp where the signals from all the elements are weighted and all the weights are adjusted a method is proposed for decorrelating the correlated sources and an analytical expression is derived to show the decorrelation effect of the proposed technique for a line array of equispaced elements numerical examples are included

a directed walk model of a long chain polymer in a slit with attractive walls we present the exact solutions of various directed walk models of polymers confined to a slit and interacting with the walls of the slit via an attractive potential we consider three geometric constraints on the ends of the polymer and concentrate on the long chain limit apart from the general interest in the effect of geometrical confinement this can be viewed as a two dimensional model of steric stabilization and sensitized flocculation of colloidal dispersions we demonstrate that the large width limit admits a phase diagram that is markedly different from the one found in a half plane geometry even when the polymer is constrained to be fixed at both ends on one wall we are not able to find a closed form solution for the free energy for finite width at all values of the interaction parameters but we can calculate the asymptotic behaviour for large widths everywhere in the phase plane this allows us to find the force between the walls induced by the polymer and hence the regions of the plane where either steric stabilization or sensitized flocculation would occur

directed paths in a wedge models of directed paths have been used extensively in the scientific literature to model linear polymers in this paper we examine a directed path model of a linear polymer in a confining geometry a wedge we are particularly interested in cn the number of directed lattice paths of length n steps which take steps in the north east and south east directions and are confined in the wedge y x p where p is an integer we examine the case p 2 in detail and show that the generating function satisfies a functional equation with quartic kernel we give a formal solution by using the kernel method show that this model is not d finite and determine asymptotics to leading order for cn in particular the number of paths of length n in the wedge y x 2 is given by where the constant 0 67874 can be determined to arbitrary accuracy with little computational effort

adaptive single snapshot beamforming a new concept for the rejection of nonstationary and coherent interferers an approach to adaptive beamforming adaptive reconstruction of a desired signal in the presence of interferers and noise that uses just a single snapshot to calculate the antenna weights is presented as in previous studies a structured and grouped array of sensor elements is assumed the concept exploits the induced special data structure which can be described as a generalized rank one eigenvalue problem and can be solved by means of a linear overdetermined system solver arbitrary signal statistics are allowed and no difficulties with nonstationary and coherent interferers arise furthermore the algorithm does not exhibit any transient behavior simulations verify its good performance in comparison with the optimum beamformer

sensor array signal processing via a procrustes rotations based eigenanalysis of the esprit data pencil the authors propose the procrustes rotation based esprit algorithm pro esprit for estimating characteristic parameters associated with a scene of radiating sources given data derived from two identical sensor arrays the x and y arrays which are displaced relative to one another pro esprit uses the inherent redundancy built into the esprit array system to compensate for deviations from the ideal array model this redundancy is manifested by two fundamental properties of the noiseless x and y data matrices comprising the esprit data pencil a they have the same row space the signal subspace and 2 they have the same column space the source subspace these properties are utilized by invoking two primary tools 1 the solution to the procrustes problem for optimally approximating an invariant subspace rotation and 2 the total least squares method for perturbing each of two estimates of a common subspace in a minimal fashion until the two perturbed spaces are the same

estimation of optimal pde based denoising in the snr sense this paper is concerned with finding the best partial differential equation based denoising process out of a set of possible ones we focus on either finding the proper weight of the fidelity term in the energy minimization formulation or on determining the optimal stopping time of a nonlinear diffusion process a necessary condition for achieving maximal snr is stated based on the covariance of the noise and the residual part we provide two practical alternatives for estimating this condition by observing that the filtering of the image and the noise can be approximated by a decoupling technique with respect to the weight or time parameters our automatic algorithm obtains quite accurate results on a variety of synthetic and natural images including piecewise smooth and textured ones we assume that the statistics of the noise were previously estimated no a priori knowledge regarding the characteristics of the clean image is required a theoretical analysis is carried out where several snr performance bounds are established for the optimal strategy and for a widely used method wherein the variance of the residual part equals the variance of the noise

new results for directed vesicles and chains near an attractive wall in this paper we present new exact results for single fully directed walks and fully directed vesicles near an attractive wall this involves a novel method of solution for these types of problems the major advantage of this method is that it unlike many other single walker methods generalizes to an arbitrary number of walkers the method of solution involves solving a set of partial difference equations with a bethe ansatz the solution is expressed as a constant term formula which evaluates to sums of products of binomial coefficients the vesicle critical temperature is found at which a binding transition takes place and the asymptotic forms of the associated partition functions are found to have three different entropic exponents depending on whether the temperature is above below or at its critical value the expected number of monomers adsorbed onto the surface is found to become proportional to the vesicle length at temperatures below critical scaling functions near the critical point are determined

2 d wilson spectral factorization g wilson s method of spectral factorization 1969 is considered for generalization to the two dimensional 2 d case for practical implementation finite order approximants to the 2 d spectral factors of infinite order are obtained although stability or convergence cannot be guaranteed in general justifications are given for the success of the proposed generalization illustrative examples are given to support the conclusions

self avoiding walks in wedges the authors consider the number of self avoiding walks confined to a subset zd f of the d dimensional hypercubic lattice zd such that the coordinates x1 x2 xd of each vertex in the walk satisfy x1 or 0 and 0 or xk or fk x1 for k 2 3 d they show that if fk x to infinity as x to infinity the connective constant of walks in zd f is identical to the convective constant of walks in zd they also explore conditions on fk which lead to a smaller connective constant for walks in zd f and in particular consider walks between two parallel d 1 dimensional hyperplanes finally they contrast some of these results with recent work by grimmett on percolation on subsets of the square lattice

monte carlo sure a black box optimization of regularization parameters for general denoising algorithms we consider the problem of optimizing the parameters of a given denoising algorithm for restoration of a signal corrupted by white gaussian noise to achieve this we propose to minimize stein s unbiased risk estimate sure which provides a means of assessing the true mean squared error mse purely from the measured data without need for any knowledge about the noise free signal specifically we present a novel monte carlo technique which enables the user to calculate sure for an arbitrary denoising algorithm characterized by some specific parameter setting our method is a black box approach which solely uses the response of the denoising operator to additional input noise and does not ask for any information about its functional form this therefore permits the use of sure for optimization of a wide variety of denoising algorithms we justify our claims by presenting experimental results for sure based optimization of a series of popular image denoising algorithms such as total variation denoising wavelet soft thresholding and wiener filtering smoothing splines in the process we also compare the performance of these methods we demonstrate numerically that sure computed using the new approach accurately predicts the true mse for all the considered algorithms we also show that sure uncovers the optimal values of the parameters in all cases

improved adaptive nulling of coherent interference without spatial smoothing a new scheme for adaptive nulling in the presence of coherent interference is proposed that finds the weight vector using a nonsquare correlation matrix without spatial smoothing conventional schemes which use square matrices correspond to specific cases of the new method it allows us to increase the dimension of the weight vector such that the nulling capability is enhanced theoretic performance analysis is made showing that the output signal to interference ratio sinr of such a beamformer is proportional to the weight dimension for sidelobe interference simulation results confirm this

fast bilateral filtering for denoising large 3d images a fast implementation of bilateral filtering is presented which is based on an optimal expansion of the filter kernel into a sum of factorized terms these terms are computed by minimizing the expansion error in the mean square error sense this leads to a simple and elegant solution in terms of eigenvectors of a square matrix in this way the bilateral filter is applied through computing a few gaussian convolutions for which very efficient algorithms are readily available moreover the expansion functions are optimized for the histogram of the input image leading to improved accuracy it is shown that this further optimization it made possible by removing the commonly deployed constrain of shiftability of the basis functions experimental validation is carried out in the context of digital rock imaging results on large 3d images of rock samples show the superiority of the proposed method with respect to other fast approximations of bilateral filtering

statistical mechanics of directed models of polymers in the square lattice directed square lattice models of polymers and vesicles have received considerable attention in the recent mathematical and physical sciences literature these are idealized geometric directed lattice models introduced to study phase behaviour in polymers and include dyck paths partially directed paths directed trees and directed vesicles models directed models are closely related to models studied in the combinatorics literature and are often exactly solvable they are also simplified versions of a number of statistical mechanics models including the self avoiding walk lattice animals and lattice vesicles the exchange of approaches and ideas between statistical mechanics and combinatorics have considerably advanced the description and understanding of directed lattice models and this will be explored in this review the combinatorial nature of directed lattice path models makes a study using generating function approaches most natural in contrast the statistical mechanics approach would introduce partition functions and free energies and then investigate these using the general framework of critical phenomena generating function and statistical mechanics approaches are closely related for example questions regarding the limiting free energy may be approached by considering the radius of convergence of a generating function and the scaling properties of thermodynamic quantities are related to the asymptotic properties of the generating function in this review the methods for obtaining generating functions and determining free energies in directed lattice path models of linear polymers is presented these methods include decomposition methods leading to functional recursions as well as the temperley method that is implemented by creating a combinatorial object one slice at a time a constant term formulation of the generating function will also be reviewed the thermodynamic features and critical behaviour in models of directed paths may be informative about the underlying properties that determine phase diagrams for wider classes of models including physical models of polymers of particular interest are adsorption and collapse transitions in models of polymers and copolymers the properties of thermodynamic quantities in those models are described by tricritical scaling this is reviewed for directed path models and the generating function approaches can be used to apply tricritical scaling to models of adsorbing inflating and collapsing directed lattice paths critical exponents for a variety of models can be obtained in this manner and with it a better understanding and a classification of the models

multidimensional recursive filters via a helix wind a wire onto a cylinder to create a helix i show that a filter on the 1 d space of the wire mimics a 2 d filter on the cylindrical surface thus 2 d convolution can be done with a 1 d convolution program i show some examples of 2 d recursive filtering also called 2 d deconvolution or 2 d polynomial division in 2 d as in 1 d the computational advantage of recursive filters is the speed with which they propagate information over long distances we can estimate 2 d prediction error filters pefs that are assured of being stable for 2 d recursion such 2 d and 3 d recursions are general purpose preconditioners that vastly speed the solution of a wide class of geophysical estimation problems the helix transformation also enables use of the partial differential equation of wave extrapolation as though it were an ordinary differential equation

l sub 2 and l sub 1 beamformers recursive implementation and performance analysis studies array beamformers as optimal waveform estimators the authors apply an inverse problem formulation presenting an integrated design to quadratic l sub 2 and least absolute value l sub 1 beamformers the general solution of the l sub 2 beamformers is parameterized by a regularizing parameter that weights the confidence placed by the designer on prior knowledge versus the quality of the measurements this regularizing parameter is used to establish an equivalence between alternative l sub 2 beamformers the authors then develop time recursive implementations of the l sub 2 and l sub 1 beamformers the performance of these beamformers is studied next the authors show that 1 in the presence of correlated arrivals the mmse beamformer uses constructively the correlation between incoming signals in reconstructing the estimated field while rejecting the uncorrelated returns and 2 the l sub 1 beamformer has the ability to adjust itself to unexpected noise conditions because it is considerably more robust than the l sub 2 beamformers to unmodeled impulsive noise or to the occurrence of malfunctioning sensors the analysis is confirmed by simulated studies

a note on spatially weighted subarray covariance averaging schemes in spatial smoothing the effective correlation among the impinging sources goes to zero only asymptotically with the number of subarrays k takao and n kimura ibid vol ap 35 p 1389 96 dec 1987 and a paulraj et al ieee j ocean eng vol oe 12 p 163 72 jan 1987 proposed toeplitzization and adaptively weighted subarray covariance averaging methods respectively wherein the impinging sources are perfectly decorrelated whenever the number of subarrays exceeds a minimum value while both methods achieve the same result the formulations of the two methods are different the present work first suggests an alternate formulation of the same problem and then compares the three methods showing that the solutions obtained by them are equivalent

convex programming design of linear and nonlinear phase wideband blocking filters blocking filters are commonly used in array processing to excise targets from data when suitable target free training data is not available a drawback is the reduction of the effective size of the array by the order of the filter motivating a search for the smallest filter that meets the design specifications common linear phase approaches lead to convex optimization and efficient global solutions but can be inefficient when the phase of the blocking filter is unimportant although direct magnitude response optimization is nonconvex in general for narrowband linear arrays optimal magnitude blocking filters can be found using constrained optimization followed by spectral factorization this approach cannot be directly applied to wideband arrays as finite support spectral factors do not generally exist in higher dimensions instead a procedure is presented in which an approximate multidimensional spectral factor of an optimized spectral density is used as a target response in a second optimization stage linear and nonlinear phase solutions are found and compared for both narrowband and wideband notch filters with the nonlinear phase outperforming the linear phase in both notch width and passband error the various optimizations are performed using second order cone programming an efficient class of convex optimization

performance analysis of an improved music doa estimator this paper addresses the statistical performance of subspace doa estimation using a sensor array in the asymptotic regime where the number of samples and sensors both converge to infinity at the same rate improved subspace doa estimators were derived termed as g music in previous works and were shown to be consistent and asymptotically gaussian distributed in the case where the number of sources and their doa remain fixed in this case which models widely spaced doa scenarios it is proved in the present paper that the traditional music method also provides doa consistent estimates having the same asymptotic variances as the g music estimates the case of doa that are spaced of the order of a beamwidth which models closely spaced sources is also considered it is shown that g music estimates are still able to consistently separate the sources while this is no longer the case for the music ones the asymptotic variances of g music estimates are also evaluated

on the choice of the parameters for anisotropic diffusion in image processing anisotropic diffusion filtering is highly dependent on some crucial parameters such as the conductance function the gradient threshold parameter and the stopping time of the iterative process the various alternative options at each stage of the algorithm are examined and evaluated and the best choice is selected an automatic stopping criterion is proposed that takes into consideration the quality of the preserved edges as opposed to just the level of smoothing achieved the proposed scheme is evaluated with the help of real and simulated images and compared with other state of the art schemes using objective criteria

iterative solvers for image denoising with diffusion models a comparative study abstract in this paper we propose and compare the use of two iterative solvers using the crank nicolson finite difference method to address the task of image denoising via partial differential equations pdes models such as regularized perona malik equation or c model and bazan model bilateral filter based model the solvers which are considered in this paper are the successive over relaxation sor and an advanced solver known as hybrid bi conjugate gradient stabilized hybrid bicgstab method from numerical experiments it is found that the crank nicolson method with hybrid bicgstab iterative solver produces better results and is more efficient than sor and already existing in terms of mssim and psnr

variational denoising of partly textured images by spatially varying constraints denoising algorithms based on gradient dependent regularizers such as nonlinear diffusion processes and total variation denoising modify images towards piecewise constant functions although edge sharpness and location is well preserved important information encoded in image features like textures or certain details is often compromised in the process of denoising we propose a mechanism that better preserves fine scale features in such denoising processes a basic pyramidal structure texture decomposition of images is presented and analyzed a first level of this pyramid is used to isolate the noise and the relevant texture components in order to compute spatially varying constraints based on local variance measures a variational formulation with a spatially varying fidelity term controls the extent of denoising over image regions our results show visual improvement as well as an increase in the signal to noise ratio over scalar fidelity term processes this type of processing can be used for a variety of tasks in partial differential equation based image processing and computer vision and is stable and meaningful from a mathematical viewpoint

experimental and theoretical comparison of some algorithms for beamforming in single receiver adaptive arrays adaptive null steering in single receiver adaptive arrays is discussed the single receiver structure allows only output power for a given set of weights to be measured the problem then is to adaptively adjust the weights of the antenna array based on output power measurements only so as to reject interference signals while maintaining a fixed response in a given look direction the authors determine the optimal beamformer weights in a single step by estimating the covariance matrix of the array sensor outputs using a weight perturbation technique based on this covariance matrix estimate three different approaches for finding the beamformer weights are studied the first corresponds to a sample matrix inversion scheme with the sample covariance matrix replaced by the one obtained from the perturbation estimation method while in the second approach the weights are determined using an eigenvalue decomposition of the covariance matrix estimate in the third approach the directions of arrival doas of the incoming wavefronts are first estimated and then in a second step the beamformer weights are calculated from the doa estimates the advantage of the third approach is that this method is not affected by correlation between the different sources

peak constrained least squares optimization we presented the basic concepts for peak constrained least squares pcls optimization in previous papers we present advanced pcls optimization concepts in this paper this paper discusses only a few of the many ways that pcls design problems can be formulated we believe that the pcls optimality criterion can be customized to fit virtually any practical application for example pcls optimization can readily be used to design equalizers in the prefilter equalizer or interpolated fir implementations of filters

a note on redundancy averaging it is well known that the performance of direction of arrival estimation and beamforming algorithms degrades in the presence of correlated signals since techniques like spatial and weighted smoothing which were developed for decorrelating the signals suffer from reduced effective aperture several authors have recently proposed redundancy averaging as an alternative spatial averaging method considering a two source signal model and the asymptotic case the authors show analytically that this technique results in an eigenstructure which is inconsistent with that of the underlying signal model in particular the resulting signal subspace fills up the whole m dimensional space where m is the array size and the resulting covariance matrix is not guaranteed to be nonnegative definite it is shown that complete decorrelation is not possible with this method even if the array size is infinitely large

lossless image compression based on optimal prediction adaptive lifting and conditional arithmetic coding the optimal predictors of a lifting scheme in the general n dimensional case are obtained and applied for the lossless compression of still images using first quincunx sampling and then simple row column sampling in each case the efficiency of the linear predictors is enhanced nonlinearly directional postprocessing is used in the quincunx case and adaptive length postprocessing in the row column case both methods are seen to perform well the resulting nonlinear interpolation schemes achieve extremely efficient image decorrelation we further investigate context modeling and adaptive arithmetic coding of wavelet coefficients in a lossless compression framework special attention is given to the modeling contexts and the adaptation of the arithmetic coder to the actual data experimental evaluation shows that the best of the resulting coders produces better results than other known algorithms for multiresolution based lossless image coding