an mrf model based approach to simultaneous recovery of depth and restoration from defocused images in this paper we propose a map markov random field mrf based scheme for recovering the depth and the focused image of a scene from two defocused images the space variant blur parameter and the focused image of the scene are both modeled as mrfs and their map estimates are obtained using simulated annealing the scheme is amenable to the incorporation of smoothness constraints on the spatial variations of the blur parameter as well as the scene intensity it also allows for inclusion of line fields to preserve discontinuities the performance of the proposed scheme is tested on synthetic as well as real data and the estimates of the depth are found to be better than that of the existing window based depth from defocus technique the quality of the space variant restored image of the scene is quite good even under severe space varying blurring conditions

blur identification by the method of generalized cross validation the point spread function psf of a blurred image is often unknown a priori the blur must first be identified from the degraded image data before restoring the image generalized cross validation gcv is introduced to address the blur identification problem the gcv criterion identifies model parameters for the blur the image and the regularization parameter providing all the information necessary to restore the image experiments are presented which show that gvc is capable of yielding good identification results a comparison of the gcv criterion with maximum likelihood ml estimation shows the gcv often outperforms ml in identifying the blur and image model parameters

principal warps thin plate splines and the decomposition of deformations the decomposition of deformations by principal warps is demonstrated the method is extended to deal with curving edges between landmarks this formulation is related to other applications of splines current in computer vision how they might aid in the extraction of features for analysis comparison and diagnosis of biological and medical images in indicated

new universality classes in one dimensional o n invariant spin models with an n parametric action an action with n parameters which generalizes the o n rpn 1 model is considered in one dimension for general n we use asymptotic expansion techniques to determine where the model becomes critical and show that for the actions considered there exists a family of hypersurfaces whose asymptotic behavior determines a one parameter family of new universality classes they interpolate between the o n vector model class and the rpn 1 model class furthermore continuum limits are discussed including the exceptional case n 2

a direct method for sparse least squares problems with lower and upper bounds a direct method is developed for solving linear least squares problems mathop min left ax b right 2 limits x wherea is large and sparse and the solution is subject to lower and upper boundsl x u the problem is initially transformed to upper triangular form by a sparseqr factorization an active set algorithm is then used the key step is the stable updating of ther factor associated with the columns ofa corresponding to the free variables when theq factor is not available for this a new method is developed which uses the semi normal equations and iterative refinement

on sampling continuous aperture distributions for discrete planar arrays the theory of sampling continuous distributions for the purpose of determining planar array excitation coefficients is examined the cause of pattern degradation associated with conventional sampling is identified and a new method called integrated sampling is introduced which provides superior results implementation details are given for the specific case of a rectangular grid planar array with a roughly circular boundary numerical examples are provided for both uniform and taylor distributions in order to perform comparative studies and to demonstrate the advantages of the new technique

estimation of positive definite m matrices and structure learning for attractive gaussian markov random fields abstract consider a random vector with finite second moments if its precision matrix is an m matrix then all partial correlations are non negative if that random vector is additionally gaussian the corresponding markov random field gmrf is called attractive we study estimation of m matrices taking the role of inverse second moment or precision matrices using sign constrained log determinant divergence minimization we also treat the high dimensional case with the number of variables exceeding the sample size the additional sign constraints turn out to greatly simplify the estimation problem we provide evidence that explicit regularization is no longer required to solve the resulting convex optimization problem we propose an algorithm based on block coordinate descent in which each sub problem can be recast as non negative least squares problem illustrations on both simulated and real world data are provided

more on coupling coefficients for the most degenerate representations of so n we present explicit closed form expressions for the general group theoretical factor appearing in the topology of a high temperature expansion of so n symmetric lattice models this object which is closely related to 6j symbols for the most degenerate representation of so n is discussed in detail

fast nonnegative matrix factorization an active set like method and comparisons nonnegative matrix factorization nmf is a dimension reduction method that has been widely used for numerous applications including text mining computer vision pattern discovery and bioinformatics a mathematical formulation for nmf appears as a nonconvex optimization problem and various types of algorithms have been devised to solve the problem the alternating nonnegative least squares anls framework is a block coordinate descent approach for solving nmf which was recently shown to be theoretically sound and empirically efficient in this paper we present a novel algorithm for nmf based on the anls framework our new algorithm builds upon the block principal pivoting method for the nonnegativity constrained least squares problem that overcomes a limitation of the active set method we introduce ideas that efficiently extend the block principal pivoting method within the context of nmf computation our algorithm inherits the convergence property of the anls framework and can easily be extended to other constrained nmf formulations extensive computational comparisons using data sets that are from real life applications as well as those artificially generated show that the proposed algorithm provides state of the art performance in terms of computational speed

maximum correntropy criterion for robust face recognition in this paper we present a sparse correntropy framework for computing robust sparse representations of face images for recognition compared with the state of the art l1norm based sparse representation classifier src which assumes that noise also has a sparse representation our sparse algorithm is developed based on the maximum correntropy criterion which is much more insensitive to outliers in order to develop a more tractable and practical approach we in particular impose nonnegativity constraint on the variables in the maximum correntropy criterion and develop a half quadratic optimization technique to approximately maximize the objective function in an alternating way so that the complex optimization problem is reduced to learning a sparse representation through a weighted linear least squares problem with nonnegativity constraint at each iteration our extensive experiments demonstrate that the proposed method is more robust and efficient in dealing with the occlusion and corruption problems in face recognition as compared to the related state of the art methods in particular it shows that the proposed method can improve both recognition accuracy and receiver operator characteristic roc curves while the computational cost is much lower than the src algorithms

fast approximations of shift variant blur image deblurring is essential in high resolution imaging e g astronomy microscopy or computational photography shift invariant blur is fully characterized by a single point spread function psf blurring is then modeled by a convolution leading to efficient algorithms for blur simulation and removal that rely on fast fourier transforms however in many different contexts blur cannot be considered constant throughout the field of view and thus necessitates to model variations of the psf with the location these models must achieve a trade off between the accuracy that can be reached with their flexibility and their computational efficiency several fast approximations of blur have been proposed in the literature we give a unified presentation of these methods in the light of matrix decompositions of the blurring operator we establish the connection between different computational tricks that can be found in the literature and the physical sense of corresponding approximations in terms of equivalent psfs physically based approximations being preferable we derive an improved approximation that preserves the same desirable low complexity as other fast algorithms while reaching a minimal approximation error comparison of theoretical properties and empirical performances of each blur approximation suggests that the proposed general model is preferable for approximation and inversion of a known shift variant blur

representation of electromagnetic fields over arbitrary surfaces by a finite and nonredundant number of samples it is shown that the electromagnetic em field radiated or scattered by bounded sources can be accurately represented over a substantially arbitrary surface by a finite number of samples even when the observation domain is unbounded the number of required samples is nonredundant and essentially coincident with the number of degrees of freedom of the field this result relies on the extraction of a proper phase factor from the field expression and on the use of appropriate coordinates to parameterize the domain it is demonstrated that the number of degrees of freedom is independent of the observation domain and depends only on the source geometry the case of spheroidal sources and observation domains with rotational symmetry is analyzed in detail and the particular cases of spherical and planar sources are explicitly considered for these geometries precise and fast sampling algorithms of central type are presented which allow an efficient recovery of em fields from a nonredundant finite number of samples such algorithms are stable with respect to random errors affecting the data

optimal design of multichannel equalizers for the structural similarity index the optimization of multichannel equalizers is studied for the structural similarity ssim criteria the closed form formula is provided for the optimal equalizer when the mean of the source is zero the formula shows that the equalizer with maximal ssim index is equal to the one with minimal mean square error mse multiplied by a positive real number which is shown to be equal to the inverse of the achieved ssim index the relation of the maximal ssim index to the minimal mse is also established for given blurring filters and fixed length equalizers an algorithm is also presented to compute the suboptimal equalizer for the general sources various numerical examples are given to demonstrate the effectiveness of the results

snakes active contour models a snake is an energy minimizing spline guided by external constraint forces and influenced by image forces that pull it toward features such as lines and edges snakes are active contour models they lock onto nearby edges localizing them accurately scale space continuation can be used to enlarge the capture region surrounding a feature snakes provide a unified account of a number of visual problems including detection of edges lines and subjective contours motion tracking and stereo matching we have used snakes successfully for interactive interpretation in which user imposed constraint forces guide the snake near features of interest

multichannel blind image deconvolution using the bussgang algorithm spatial and multiresolution approaches this work extends the bussgang blind equalization algorithm to the multichannel case with application to image deconvolution problems we address the restoration of images with poor spatial correlation as well as strongly correlated natural images the spatial nonlinearity employed in the final estimation step of the bussgang algorithm is developed according to the minimum mean square error criterion in the case of spatially uncorrelated images for spatially correlated images the nonlinearity design is rather conducted using a particular wavelet decomposition that detecting lines edges and higher order structures carries out a task analogous to those of the preattentive stage of the human visual system experimental results pertaining to restoration of motion blurred text images out of focus spiky images and blurred natural images are reported

exact duality transformations for sigma models and gauge theories we present an exact duality transformation in the framework of statistical mechanics for various lattice models with non abelian global or local symmetries the transformation applies to sigma models with variables in a compact lie group g with global g g symmetry the chiral model and with variables in coset spaces g h and a global g symmetry for example the nonlinear o n or rpn models in any dimension d 1 it is also available for lattice gauge theories with local gauge symmetry in dimensions d 2 and for the models obtained from minimally coupling a sigma model of the type mentioned above to a gauge theory the duality transformation maps the strong coupling regime of the original model to the weak coupling regime of the dual model transformations are available for the partition function for expectation values of fundamental variables correlators and generalized wilson loops and for expectation values in the dual model which correspond in the original formulation to certain ratios of partition

an effective deterministic procedure for the synthesis of shaped beams by means of uniform amplitude linear sparse arrays a rigorous deterministic approach is proposed for the mask constrained power pattern synthesis of shaped beams through one dimensional sparse arrays having uniform amplitude excitations and variable phases the approach includes the well known density taper procedure as a special case the corresponding technique which exploits an analytical formulation of the problem and convex programming routines results in fast computation and is able to achieve optimal solutions without recurring to any global optimization numerical results assessing the capabilities of the proposed design method are provided opening the way to the development of an effective approach for the synthesis of circularly symmetric shaped beams via uniformly excited circular ring arrays

signal matching through scale space given a collection of similar signals that have been deformed with respect to each other the general signal matching problem is to recover the deformation we formulate the problem as the minimization of an energy measure that combines a smoothness term and a similarity term the minimization reduces to a dynamic system governed by a set of coupled first order differential equations the dynamic system finds an optimal solution at a coarse scale and then tracks it continuously to a fine scale among the major themes in recent work on visual signal matching have been the notions of matching as constrained optimization of variational surface reconstruction and of coarse to fine matching our solution captures these in a precise succinct and unified form results are presented for one dimensional signals a motion sequence and a stereo pair

blind image restoration by anisotropic regularization this paper presents anisotropic regularization techniques to exploit the piecewise smoothness of the image and the point spread function psf in order to mitigate the severe lack of information encountered in blind restoration of shift invariantly and shift variantly blurred images the new techniques which are derived from anisotropic diffusion adapt both the degree and direction of regularization to the spatial activities and orientations of the image and the psf this matches the piecewise smoothness of the image and the psf which may be characterized by sharp transitions in magnitude and by the anisotropic nature of these transitions for shift variantly blurred images whose underlying psfs may differ from one pixel to another we parameterize the psf and then apply the anisotropic regularization techniques this is demonstrated for linear motion blur and out of focus blur alternating minimization is used to reduce the computational load and algorithmic complexity

regularization of inverse visual problems involving discontinuities inverse problems such as the reconstruction problems that arise in early vision tend to be mathematically ill posed through regularization they may be reformulated as well posed variational principles whose solutions are computable standard regularization theory employs quadratic stabilizing functionals that impose global smoothness constraints on possible solutions discontinuities present serious difficulties to standard regularization however since their reconstruction requires a precise spatial control over the smoothing properties of stabilizers this paper proposes a general class of controlled continuity stabilizers which provide the necessary control over smoothness these nonquadratic stabilizing functionals comprise multiple generalized spline kernels combined with noncontinuous continuity control functions in the context of computational vision they may be thought of as controlled continuity constraints these generic constraints are applicable to visual reconstruction problems that involve both continuous regions and discontinuities for which global smoothness constraints fail

a flexible new technique for camera calibration we propose a flexible technique to easily calibrate a camera it only requires the camera to observe a planar pattern shown at a few at least two different orientations either the camera or the planar pattern can be freely moved the motion need not be known radial lens distortion is modeled the proposed procedure consists of a closed form solution followed by a nonlinear refinement based on the maximum likelihood criterion both computer simulation and real data have been used to test the proposed technique and very good results have been obtained compared with classical techniques which use expensive equipment such as two or three orthogonal planes the proposed technique is easy to use and flexible it advances 3d computer vision one more step from laboratory environments to real world use

two stage nonnegative sparse representation for large scale face recognition this paper proposes a novel nonnegative sparse representation approach called two stage sparse representation tsr for robust face recognition on a large scale database based on the divide and conquer strategy tsr decomposes the procedure of robust face recognition into outlier detection stage and recognition stage in the first stage we propose a general multisubspace framework to learn a robust metric in which noise and outliers in image pixels are detected potential loss functions including l1 l2 1 and correntropy are studied in the second stage based on the learned metric and collaborative representation we propose an efficient nonnegative sparse representation algorithm to find an approximation solution of sparse representation according to the l1 ball theory in sparse representation the approximated solution is unique and can be optimized efficiently then a filtering strategy is developed to avoid the computation of the sparse representation on the whole large scale dataset moreover theoretical analysis also gives the necessary condition for nonnegative least squares technique to find a sparse solution extensive experiments on several public databases have demonstrated that the proposed tsr approach in general achieves better classification accuracy than the state of the art sparse representation methods more importantly a significant reduction of computational costs is reached in comparison with sparse representation classifier this enables the tsr to be more suitable for robust face recognition on a large scale dataset

continuum limits and exact finite size scaling functions for one dimensional o n invariant spin models we solve exactly the general one dimensionalo n invariant spin model taking values in the spheresn 1 with nearest neighbor interactions in finite volume with periodic boundary conditions by an expansion in hyperspherical harmonics the possible continuum limits are discussed for a general one parameter family of interactions and an infinite number of universality classes is found for these classes we compute the finite size scaling functions and the leading corrections to finite size scaling a special two parameter family of interactions which includes the mixed isovector isotensor model is also treated and no additional universality classes appear in the appendices we give new formulae for the clebsch gordan coefficients and 6 j symbols of theo n group and some new generalizations of the poisson summation formula these may be of independent interest

identification and restoration of noisy blurred images using the expectation maximization algorithm a maximum likelihood approach to the blur identification problem is presented the expectation maximization algorithm is proposed to optimize the nonlinear likelihood function in an efficient way in order to improve the performance of the identification algorithm low order parametric image and blur models are incorporated into the identification method the resulting iterative technique simultaneously identifies and restores noisy blurred images

a unified approach to superresolution and multichannel blind deconvolution this paper presents a new approach to the blind deconvolution and superresolution problem of multiple degraded low resolution frames of the original scene we do not assume any prior information about the shape of degradation blurs the proposed approach consists of building a regularized energy function and minimizing it with respect to the original image and blurs where regularization is carried out in both the image and blur domains the image regularization based on variational principles maintains stable performance under severe noise corruption the blur regularization guarantees consistency of the solution by exploiting differences among the acquired low resolution images several experiments on synthetic and real data illustrate the robustness and utilization of the proposed technique in real applications

nonparametric rotations for sphere sphere regression regression of data represented as points on a hypersphere has traditionally been treated using parametric families of transformations that include the simple rigid rotation as an important special

a comparison of block pivoting and interior point algorithms for linear least squares problems with nonnegative variables in this paper we discuss the use of block principal pivoting and predictor corrector methods for the solution of large scale linear least squares problems with nonnegative variables nvlsq we also describe two implementations of these algorithms that are based on the normal equations and corrected seminormal equations csne approaches we show that the method of normal equations should be employed in the implementation of the predictor corrector algorithm this type of approach should also be used in the implementation of the block principal pivoting method but a switch to the csne method may be useful in the last iterations of the algorithm computational experience is also included in this paper and shows that both the predictor corrector and the block principal pivoting algorithms are quite efficient to deal with large scale nvlsq problems

critical behavior in a quasi d dimensional spin model we study a classical spin model more precisely a class of models with o n symmetry that can be viewed as a simplified d dimensional lattice model it is equivalent to a non translationinvariant one dimensional model and contains the dimensionality d as a parameter that need not be an integer the critical dimension turns out to be 2 just as in the usual translation invariant models we study the phase structure critical phenomena and spontaneous symmetry breaking furthermore we compute the perturbation expansion to low order with various boundary conditions in our simplified models a number of questions can be answered that remain controversial in the translation invariant models such as the asymptoticity of the perturbation expansion and the role of super instantons we find that perturbation theory produces the right asymptotic expansion in dimension d 2 only with special boundary conditions finally the model allows a test of the percolation ideas of patrascioiu and seiler

a super resolution framework for high accuracy multiview reconstruction we present a variational framework to estimate super resolved texture maps on a 3d geometry model of a surface from multiple images given the calibrated images and the reconstructed geometry the proposed functional is convex in the super resolution texture using a conformal atlas of the surface we transform the model from the curved geometry to the flat charts and solve it using state of the art and provably convergent primal dual algorithms in order to improve image alignment and quality of the texture we extend the functional to also optimize for a normal displacement map on the surface as well as the camera calibration parameters since the sub problems for displacement and camera parameters are non convex we revert to relaxation schemes in order to robustly estimate a minimizer via sequential convex programming experimental results confirm that the proposed super resolution framework allows to recover textured models with significantly higher level of detail than the individual input images

theta functions modular invariance and strings we use quillen s theorem and algebraic geometry to investigate the modular transformation properties of some quantities of interest in string theory in particular we show that the spin structure dependence of the chiral dirac determinant on a riemann surface is given by riemann s theta function we use this result to investigate the modular invariance of multiloop heterotic string amplitudes

perfect blind restoration of images blurred by multiple filters theory and efficient algorithms we address the problem of restoring an image from its noisy convolutions with two or more unknown finite impulse response fir filters we develop theoretical results about the existence and uniqueness of solutions and show that under some generically true assumptions both the filters and the image can be determined exactly in the absence of noise and stably estimated in its presence we present efficient algorithms to estimate the blur functions and their sizes these algorithms are of two types subspace based and likelihood based and are extensions of techniques proposed for the solution of the multichannel blind deconvolution problem in one dimension we present memory and computation efficient techniques to handle the very large matrices arising in the two dimensional 2 d case once the blur functions are determined they are used in a multichannel deconvolution step to reconstruct the unknown image the theoretical and practical implications of edge effects and weakly exciting images are examined finally the algorithms are demonstrated on synthetic and real data

blind identification of multichannel fir blurs and perfect image restoration despite its practical importance in image processing and computer vision blind blur identification and blind image restoration have so far been addressed under restrictive assumptions such as all pole stationary image models blurred by zero or minimum phase point spread functions relying upon diversity availability of a sufficient number of multiple blurred images we develop blind fir blur identification and order determination schemes apart from a minimal persistence of the excitation condition also present with nonblind setups the inaccessible input image is allowed to be deterministic or random and of unknown color of distribution with the blurs satisfying a certain co primeness condition in addition we establish existence and uniqueness results which guarantee that single input multiple output fir blurred images can be restored blindly though perfectly in the absence of noise using linear fir filters results of simulations employing the blind order determination blind blur identification and blind image restoration algorithms are presented when the snr is high direct image restoration is found to yield better results than indirect image restoration which employs the estimated blurs in low snr indirect image restoration performs well while the direct restoration results vary with the delay but improve with larger equalizer orders

bayesian blind deconvolution from differently exposed image pairs photographs acquired under low lighting conditions require long exposure times and therefore exhibit significant blurring due to the shaking of the camera using shorter exposure times results in sharper images but with a very high level of noise in this paper we address the problem of utilizing two such images in order to obtain an estimate of the original scene and present a novel blind deconvolution algorithm for solving it we formulate the problem in a hierarchical bayesian framework by utilizing prior knowledge on the unknown image and blur and also on the dependency between the two observed images by incorporating a fully bayesian analysis the developed algorithm estimates all necessary model parameters along with the unknown image and blur such that no user intervention is needed moreover we employ a variational bayesian inference procedure which allows for the statistical compensation of errors occurring at different stages of the restoration and also provides uncertainties of the estimates experimental results with synthetic and real images demonstrate that the proposed method provides very high quality restoration results and compares favorably to existing methods even though no user supervision is needed

on eigenstructure based direct multichannel blind image restoration existing eigenstructure based direct multichannel blind image restoration techniques include nullspace based and direct deconvolver estimation techniques the nullspace based approach can be formulated as an optimization problem we show that this formulation implies a new subspace based approach that uses matrix operations this new approach has the same advantages as the nullspace based one but requires less computational complexity under some mild conditions its complexity is equal to that of the fft furthermore the relation among the nullspace based approach the direct deconvolver estimation and the new subspace based approach is studied

multichannel blind deconvolution of spatially misaligned images existing multichannel blind restoration techniques assume perfect spatial alignment of channels correct estimation of blur size and are prone to noise we developed an alternating minimization scheme based on a maximum a posteriori estimation with a priori distribution of blurs derived from the multichannel framework and a priori distribution of original images defined by the variational integral this stochastic approach enables us to recover the blurs and the original image from channels severely corrupted by noise we observe that the exact knowledge of the blur size is not necessary and we prove that translation misregistration up to a certain extent can be automatically removed in the restoration process

explicit ringing removal in image deblurring in this paper we present a simple yet effective image deblurring method to produce ringing free deblurred images our work is inspired by the observation that large scale deblurring ringing artifacts are measurable through a multi resolution pyramid of low pass filtering of the blurred deblurred image pair we propose to model such a quantification as a convex cost function and minimize it directly in the deblurring process in order to reduce ringing regardless of its cause an efficient primal dual algorithm is proposed as a solution to this optimization problem since the regularization is more biased toward ringing patterns the details of the reconstructed image are prevented from over smoothing an inevitable source of ringing is sensor saturation which can be detected costlessly contrary to most other sources of ringing however dealing with the saturation effect in deblurring introduces a non linear operator in optimization problem in this paper we also introduce a linear approximation as a solution to handling saturation in the proposed deblurring method as a result of these steps we significantly enhance the quality of the deblurred images experimental results and quantitative evaluations demonstrate that the proposed method performs favorably against state of the art image deblurring methods

robust all in focus super resolution for focal stack photography we present an unconventional image super resolution algorithm targeting focal stack images contrary to previous works which align multiple images with sub pixel accuracy for image super resolution we analyze the correlation among the differently focused narrow depth of field images in a focal stack to infer high resolution details for image super resolution in order to accurately model the defocus kernels at different depths we use a cubic interpolation to parameterize the projection of defocus kernels and apply the radon transform to accurately reconstruct the defocus kernels at arbitrary depth in the image super resolution we utilize the multi image deconvolution method with a l 1 norm regularization to suppress noise and ringing artifacts we have also extended the depth of field of our inputs to produce an all in focus super resolution image the effectiveness of our algorithm is demonstrated with the quantitative analysis using synthetic examples and the qualitative analysis using real world examples

parameter estimation in bayesian high resolution image reconstruction with multisensors we consider the estimation of the unknown parameters for the problem of reconstructing a high resolution image from multiple undersampled shifted degraded frames with subpixel displacement errors we derive mathematical expressions for the iterative calculation of the maximum likelihood estimate of the unknown parameters given the low resolution observed images these iterative procedures require the manipulation of block semi circulant bsc matrices that is block matrices with circulant blocks we show how these bsc matrices can be easily manipulated in order to calculate the unknown parameters finally the proposed method is tested on real and synthetic images

mask constrained power synthesis of linear arrays with even excitations an existing effective approach for the synthesis of linear arrays providing power patterns lying in arbitrary masks is extended to the case where an even distribution is required on element excitations the approach consists of a linear programming optimization plus a polynomial factorization and it allows one to deal with a considerably reduced computational burden with respect to the previous approaches by so doing it is now possible to solve problems that cannot be successfully tackled by the previous techniques an extension of the overall strategy to the synthesis of fields guaranteeing optimal performances in terms of directivity or ripple in the main beam region is also given

computational experience with a primal dual interior point method for linear programming abstract a new comprehensive implementation of a primal dual algorithm for linear programming is described it allows for easy handling of simple bounds on the primal variables and incorporates free variables which have not previously been included in a primal dual implementation we discuss in detail a variety of computational issues concerning the primal dual implementation and barrier methods for linear programming in general we show that in a certain way lustig s method for obtaining feasibility is equivalent to newton s method this demonstrates that the method is in some sense the natural way to reduce infeasibility the role of the barrier parameter in computational practice is studied in detail numerical results are given for the entire expanded netlib test set for the basic algorithm and its variants as well as version 5 3 of minos

optimal synthesis of circularly symmetric shaped beams the problem of the optimal power pattern synthesis of circularly symmetric shaped beams is addressed and solved in particular an existence criterion is provided to test a priori i e without solving the overall synthesis problem if a non superdirective source of given size can radiate or not a circularly symmetric power pattern lying in a given arbitrary mask in the affirmative case the proposed approach guarantees the achievement of the optimal solution i e that of maximum directivity or minimum size by using convex optimization techniques in general a number of equivalent source distributions i e radiating the same power pattern do exist which can be explicitly determined in a deterministic way numerical examples concerning applications of actual interest support the given theory and confirm the effectiveness of the developed synthesis procedure

structured least squares problems and robust estimators a novel approach is proposed to provide robust and accurate estimates for linear regression problems when both the measurement vector and the coefficient matrix are structured and subject to errors or uncertainty a new analytic formulation is developed in terms of the gradient flow of the residual norm to analyze and provide estimates to the regression the presented analysis enables us to establish theoretical performance guarantees to compare with existing methods and also offers a criterion to choose the regularization parameter autonomously theoretical results and simulations in applications such as blind identification multiple frequency estimation and deconvolution show that the proposed technique outperforms alternative methods in mean squared error for a significant range of signal to noise ratio values

the non parametric sub pixel local point spread function estimation is a well posed problem most medium to high quality digital cameras dslrs acquire images at a spatial rate which is several times below the ideal nyquist rate for this reason only aliased versions of the cameral point spread function psf can be directly observed yet it can be recovered at a sub pixel resolution by a numerical method since the acquisition system is only locally stationary this psf estimation must be local this paper presents a theoretical study proving that the sub pixel psf estimation problem is well posed even with a single well chosen observation indeed theoretical bounds show that a near optimal accuracy can be achieved with a calibration pattern mimicking a bernoulli 0 5 random noise the physical realization of this psf estimation method is demonstrated in many comparative experiments we use an algorithm to accurately estimate the pattern position and its illumination conditions once this accurate registration is obtained the local psf can be directly computed by inverting a well conditioned linear system the psf estimates reach stringent accuracy levels with a relative error of the order of 2 to 5 to the best of our knowledge such a regularization free and model free sub pixel psf estimation scheme is the first of its kind

a numerically stable solver for positive semidefinite quadratic programs based on nonnegative least squares this paper proposes a new algorithm for solving convex quadratic programs qp subject to linear inequality and equality constraints the method extends an approach recently proposed by the author for solving strictly convex qp s using nonnegative least squares by making it numerically more robust and able to handle also the nonstrictly convex case equality constraints and warm starting from an initial guess robustness is achieved by introducing an outer proximal point iteration scheme that regularizes the problem without altering the solution and by adaptively weighting the least squares problems encountered while solving the problem the performance of the resulting qp solver in terms of speed and robustness in the single precision arithmetic is assessed against other optimization algorithms tailored to embedded model predictive control applications