invariant subspaces dilation theory and the structure of the predual of a dual algebra i on etudie la structure des preduaux d algebres d operateurs on obtient un nouveau theoreme de sous espace invariant on trouve des proprietes concernant le treillis sous espace invariant de l operateur decalage de bergman

new pocs algorithms for regularization of inverse problems abstract ill posed problems described by first kind fredholm equations appear in many interesting practical cases in engineering or mathematical physics such as deconvolution and require regularization techniques to get adequate solutions this paper presents under a projection operators onto convex sets pocs framework to introduce the needed regularization operations a series of non adaptive and adaptive pocs regularization algorithms which offer as main advantages besides including previously proposed methods a lower computational load and the possibility of including any kind of constraints linear and nonlinear a series of simulation examples serve to appreciate the high performance of the proposed techniques in a typical problem recovering the discontinuites of a sequence showing sharp edges

operators similar to their restrictions to invariant subspaces abstract an operator t on a separable infinite dimensional banach space x is called crystal like if for each nonzero invariant subspace m of t there exists a positive number r such that t m the restriction of t to m is similar to rt in this paper we investigate some elementary properties of crystal like operators such as the spectrum cyclicity strong irreducibility essential similarity reflectivity and the commutativity of the commutant

equations of fuzzy relations defined on fuzzy subsects abstract in this paper some results of the theory of fuzzy relation equations are generalized when we consider fuzzy relations defined on fuzzy sets instead of crisp sets if the extension of classical definitions for composition of relations 12 13 is not straightforward we provide suitables counterexamples illustrating the necessity of change in definitions we find the greatest or the least solutions of fuzzy relation equations with different types of compositions like the sup t inf t inf or sup compositions

a cooperative recurrent neural network for solving l1 estimation problems with general linear constraints the constrained l1 estimation is an attractive alternative to both the unconstrained l1 estimation and the least square estimation in this letter we propose a cooperative recurrent neural network crnn for solving l1 estimation problems with general linear constraints the proposed crnn model combines four individual neural network models automatically and is suitable for parallel implementation as a special case the proposed crnn includes two existing neural networks for solving unconstrained and constrained l1 estimation problems respectively unlike existing neural networks with penalty parameters for solving the constrained l1 estimation problem the proposed crnn is guaranteed to converge globally to the exact optimal solution without any additional condition compared with conventional numerical algorithms the proposed crnn has a low computational complexity and can deal with the l1 estimation problem with degeneracy several applied examples show that the proposed crnn can obtain more accurate estimates than several existing algorithms

on the construction of fuzzy eigen solutions in given regions we consider the eigen set problem for fuzzy relations in a given region fuzzy interval using convenient means from the theory of posets we are able to determine the greatest and the minimal elements of the set of eigen solutions whereby the results are different for convergent and oscillating relations numerical examples for illustration are given

eigen fuzzy number sets in this paper we extend certain results of sanchez resolution of eigen fuzzy sets equations fuzzy sets and systems 1 1978 69 75 to the context of fuzzy numbers a slight modification of the dubois prade definition of fuzzy numbers is used

discrete time neural network for fast solving large linear l_ 1 estimation problems and its application to image restoration there is growing interest in solving linear l1 estimation problems for sparsity of the solution and robustness against non gaussian noise this paper proposes a discrete time neural network which can calculate large linear l1 estimation problems fast the proposed neural network has a fixed computational step length and is proved to be globally convergent to an optimal solution then the proposed neural network is efficiently applied to image restoration numerical results show that the proposed neural network is not only efficient in solving degenerate problems resulting from the nonunique solutions of the linear l1 estimation problems but also needs much less computational time than the related algorithms in solving both linear l1 estimation and image restoration problems

resolution enhancement of tomographic images using the row action projection method the row action projection rap method is used to increase the spatial resolution of images reconstructed via the filtered back projection fbp algorithm an implementation of rap is introduced which is computationally efficient and facilitates local adaptation of the projection operators the local mean value as well as minimum and maximum bounds are used as constraints the method is proposed to provide zoom in capability which yields a high resolution estimate of a specified region of the image computer simulations demonstrate the new method to be very effective in recovering high order spectral components of designated regions of the reconstructed image

the feasible solution in signal restoration the feasible solution to the signal restoration problem is defined as the one which satisfies all constraints which can be imposed on the true solution a very important set of constraints can be obtained by examining the statistics of the noise these and other constraints can be described as closed convex sets thus projection onto closed convex sets is the numerical method used to obtain a feasible solution examples of this method demonstrate its usefulness in one and two dimensional signal restoration the limitations of the method are discussed

cooperative recurrent neural networks for the constrained l_ 1 estimator the constrained least absolute deviation l1 estimator is an attractive alternative to both the unconstrained l1 estimator and the least square estimator this paper introduces a constrained l1 method and proposes two cooperative recurrent neural networks crnns for the constrained l1 estimator unlike existing cooperative neural networks the proposed two crnns have a novel weighting cooperation scheme to integrate individual neural network information automatically as a special case the proposed continuous time crnn includes the existing continuous time neural network for unconstrained l1 estimator compared with existing continuous time neural networks for the constrained l1 estimator the proposed continuous time crnn has a lower model complexity and the finite time convergence to the exact optimal solution without any additional condition furthermore compared with existing numerical algorithms for the constrained l1 estimator in addition to a low computational complexity the proposed two crnns are suitable for parallel implementation and can deal with the l1 estimation problem with degeneracy the proposed two crnns are applied to parameter estimation problems under non gaussian noise environments simulation results demonstrate that the proposed crnns are indeed effective in dealing with the l1 estimation problem with nonunique solutions and in obtaining a better solution than relevant algorithms

image restoration by convex projections using adaptive constraints and the l sub 1 norm a new projection method based on the row action projection rap algorithm for image restoration is presented the new implementation is computationally attractive and facilitates local adaption of projection operators the local mean and the least l sub 1 norm set of solutions are used as constraints computer simulations illustrate the new methods to be very competitive in restoring missing spectral components of a degraded image

tomographic image reconstruction from incomplete view data by convex projections and direct fourier inversion we consider the problem of reconstructing cat imagery by the direct fourier method dfm when not all view data are available to restore the missing information we use the method of projections onto convex sets pocs pocs is a recursive image restoration technique that finds a solution consistent with the measured data and a priori known constraints in both the space and fourier domain because dfm reconstruction is a frequency domain technique it is ideally matched to pocs restoration when for one reason or another we are forced to generate an image from a less than complete set of view data we design and apply an algorithm prdf which interpolates extrapolates the missing fourier domain information by pocs and reconstructs an image by dfm a simulated human thorax cross section is restored and reconstructed the restorations using pocs are compared with the gerchberg papoulis extrapolation method and shown to be superior applications of prdf to other types of medical imaging modalities are discussed

t eigen fuzzy sets abstract this paper concerns the study of the solutions of sup t equations such that atr a where t is a triangular norm and r is a fuzzy relation by generalizing a result from sanchez 12 we determine the greatest t eigen fuzzy set of a fuzzy relation a t eigen fuzzy set of r being a fuzzy set a which is a solution of atr a we also study some algebraic properties for the class of the t eigen sets of a fuzzy relation and for the set of fuzzy relations leaving invariant a given fuzzy set finally properties related with the transitive closure are established

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

quasitriangular small compact strongly irreducible let t be a bounded linear operator acting on a separable infinite dimensional hilbert space let be a positive number in this article we prove that the perturbation of t by a compact operator k with k 0 be given is there a compact operator k with k such that t k is strongly irreducible

iterative algorithms for large partitioned linear systems with applications to image reconstruction abstract we present a unifying framework for a wide class of iterative methods in numerical linear algebra in particular the class of algorithms contains kaczmarz s and richardson s methods for the regularized weighted least squares problem with weighted norm the convergence theory for this class of algorithms yields as corollaries the usual convergence conditions for kaczmarz s and richardson s methods the algorithms in the class may be characterized as being group iterative and incorporate relaxation matrices as opposed to a single relaxation parameter we show that some well known iterative methods of image reconstruction fall into the class of algorithms under consideration and are thus covered by the convergence theory we also describe a novel application to truly three dimensional image reconstruction

processing in relational structures fuzzy relational equations abstract the paper provides an overview of methodology for processing fuzzy information in relational structures completed in terms of fuzzy relational equations the origin and the central role of relational calculus in general and fuzzy sets in particular is explained with special emphasis paid to its role and representation capabilities it is pointed out that fuzzy relational equations play a significant role as a platform for a uniform development of techniques in fuzzy sets many of the problems and frameworks developed in fuzzy sets so far can be easily translated into the language of fuzzy relational equations which immediately takes a significant advantage of their solid well developed formalisms techniques and clarity of exposition we will study the role of approximate solutions to fuzzy relational equations as a convenient tool to handle probabilistic type of uncertainty moreover those solutions can easily explain the origin and generate a way in which fuzzy sets of higher generality such as for instance type 2 sets interval valued sets can be algorithmically determined finally we study the role of equations in diverse fields of applications making use of an ample framework of general systems theory

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

studies in fuzzy relations over fuzzy subsets in this paper a generalisation of fuzzy relations is introduced fuzzy relations are defined on fuzzy subsets properties like ordered reflexivity symmetry transitity transitive closures of such generalised relations and operations on them are discussed

image restoration by the method of convex projections part 2 applications and numerical results the image restoration theory discussed in a previous paper by youla and webb 1 is applied to a simulated image and the results compared with the well known method known as the gerchberg papoulis algorithm the results show that the method of image restoration by projection onto convex sets by providing a convenient technique for utilizing a priori information performs significantly better than the gerchberg papoulis method

a compact cooperative recurrent neural network for computing general constrained l_1 norm estimators recently cooperative recurrent neural networks for solving three linearly constrained l 1 estimation problems were developed and applied to linear signal and image models under non gaussian noise environments for wide applications this paper proposes a compact cooperative recurrent neural network crnn for calculating general constrained l 1 norm estimators it is shown that the proposed crnn converges globally to the constrained l 1 norm estimator without any condition the proposed crnn includes three existing crnns as its special cases unlike the three existing crnns the proposed crnn is easily applied and can deal with the nonlinear elliptical sphere constraint moreover when computing the general constrained l 1 norm estimator the proposed crnn has a fast convergence speed due to low computational complexity simulation results confirm further the good performance of the proposed crnn

adaptive image restoration with artifact suppression using the theory of convex projections the authors develop an iterative adaptive space variant restoration incorporating both regularization and artifact suppression constraints the algorithm is formulated using the method of projections onto convex sets pocs they introduce a closed convex regularization constraint set called the partial wiener solution set projection onto this set forces the solution to be equal to the wiener solution over a predetermined set of frequencies that lie outside the neighborhoods of the zeros of the degradation transfer function in the neighborhoods of the zeros the wiener solution contains significant errors that contribute to artifacts hence in these neighborhoods the wiener solution is discarded and the missing frequency components are determined so that the entire solution is consistent with the artifact suppression constraints and other a priori information the proposed artifact suppression constraints bound the norm of the variation of the image from its local mean using regionally adaptive bounds the high quality of the resulting restorations is noteworthy