1,721,164 research outputs found
A two-steps inexact-Newton method for atmospheric remote sensing
No full textIn this paper we deal with regularization procedures for the nonlinear inverse problem of atmospheric profile retrievals from measurements of electromagnetic radiations. Since the inverse problem is severely ill-posed, Newton's linearization gives unsatisfactory results. In that case the linearized system is ill-conditioned, and its resolutions is very sensitive to the noise of input data. Here we propose an outer-inner two-steps iterative algorithm which belongs to the general class of inexact Newton method. The outer iteration is the Newton method and the inner iteration is the truncated Landweber one. In particular, truncated Landweber method regularizes the resolution of any outer Newton linearized step. The mathematical formulation of the 1-d problem is analyzed and the algorithm is described. Numerical experiments are performed, and the results are compared with the classical (i.e., one-step) Landweber method for nonlinear inverse problems
Approach to regularization preconditioners for image processing
No full textPreconditioning techniques for linear systems are widely used in order to speed up the convergence of iterative methods. Unfortunately, linear systems arising in image processing are highly ill-conditioned and preconditioners often give bad results, since the noise components on the data are strongly amplified already at the early iterations. In this work, we propose filtering strategies which allow to obtain preconditioners with regularization features for Toeplitz systems of image deblurring. Regularization preconditioners are able to speed up the convergence in the space less sensitive to the noise and, simultaneously, they slow down the restoration from components mainly corrupted by noise. A 2-d numerical simulation concerning astronomical image deblurring confirms the effectiveness of the arguments
Block splitting least square regularization for structured matrices arising in nonlinear microwave imaging
No full textA classification scheme for regularizing preconditioners, with application to Toeplitz systems
No full textAbstractPreconditioning techniques for linear systems are widely used in order to speed up the convergence of iterative methods. If the linear system is generated by the discretization of an ill-posed problem, preconditioning may lead to wrong results, since components related to noise on input data are amplified. Using basic concepts from the theory of inverse problems, we identify a class of preconditioners which acts as a regularizing tool. In this paper we study relationships between this class and previously known circulant preconditioners for ill-conditioned Hermitian Toeplitz systems. In particular, we deal with the low-pass filtered optimal preconditioners and with a recent family of superoptimal preconditioners. We go on to describe a set of preconditioners endowed with particular regularization properties, whose effectiveness is supported by several numerical tests
Regularized fast multiple-image deconvolution for LBT
No full textAbstractIn this paper we study a fast deconvolution technique for the image restoration problem of the Large Binocular Telescope (LBT) interferometer. Since LBT provides several blurred and noisy images of the same object, it requires the use of multiple-image deconvolution methods in order to produce a unique image with high resolution. Hence the restoration process is basically a linear ill-posed problem, with overdetermined system and data corrupted by several components of noise.Here the preconditioned conjugate gradient method is used to obtain regularized reconstructions within few iterations. In particular, we study the effectiveness of some preconditioners which have been previously proposed for discrete ill-posed problems. These preconditioners can be considered as regularizing tools since they are able to increase the speed of convergence without amplifying the reconstruction from components with high noise. A wide set of numerical tests will confirm the useful properties of the technique
A class of filtering superoptimal preconditioners for highly ill-conditioned linear systems
No full textPopular preconditioners for conjugate gradient methods often reveal poor regularization properties that make them useless for very ill-conditioned linear systems arising in inverse problems. Recent results have awakened the interest towards the Tyrtyshnikov superoptimal preconditioners since it has been demonstrated that they exhibit good filtering capabilities. Here, in order to improve the regularizing behaviour, we generalize the definition of superoptimal preconditioner. Later on, by means of this more general definition, we develop a particular family of preconditioners for Toeplitz highly ill-conditioned linear systems
Il tempo della forma e della sostanza
No full textRappresentazine teatrale di carattere scientifico al "Festival della Scienza 2014" di Genova. Un insolito logico matematico e i suoi ospiti coinvolgono il pubblico in un viaggio tra sogni e realtà, dove la ricerca del rigore formale del primo si scontra con la leggerezza del senso comune. Sarà il pretesto per parlare di logica, di tempo, di dimostrazioni e di dimostrabilità, concetti che da sempre hanno affascinato generazioni di pensatori, e che sono alla base dei più importanti risultati scientifici del secolo scorso. Fino ad entrare, in punta di piedi e con semplicità, nel Teorema di incompletezza di Kurt Gödel, uno dei più grandi logici di sempre,
ed avere così la garanzia che "non tutto ciò che è vero è dimostrabile"
Precondizionatori regolarizzanti per equazioni lineari mal poste e applicazione alla ricostruzione di immagini
No full textA large scale iterative regularization inexact Newton method for nonlinear imaging applications
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