Archivio della ricerca dell'Università di Modena e Reggio Emiliahttps://iris.unimore.itIl sistema di repository digitale IRIS acquisisce, archivia, indicizza, conserva e rende accessibili prodotti digitali della ricerca.Mon, 09 Dec 2019 05:53:29 GMT2019-12-09T05:53:29Z10551An alternating minimization method for blind deconvolution from Poisson datahttp://hdl.handle.net/11380/1009714Titolo: An alternating minimization method for blind deconvolution from Poisson data
Abstract: Blind deconvolution is a particularly challenging inverse problem since information on both the desired target and the acquisition system have to be inferred from the measured data. When the collected data are affected by Poisson noise, this problem is typically addressed by the minimization of the Kullback-Leibler divergence, in which the unknowns are sought in particular feasible sets depending on the a priori information provided by the specific application. If these sets are separated, then the resulting constrained minimization problem can be addressed with an inexact alternating strategy. In this paper we apply this optimization tool to the problem of reconstructing astronomical images from adaptive optics systems, and we show that the proposed approach succeeds in providing very good results in the blind deconvolution of nondense stellar clusters.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/11380/10097142014-01-01T00:00:00ZOn the constrained minimization of smooth Kurdyka– Lojasiewicz functions with the scaled gradient projection methodhttp://hdl.handle.net/11380/1100005Titolo: On the constrained minimization of smooth Kurdyka– Lojasiewicz functions with the scaled gradient projection method
Abstract: The scaled gradient projection (SGP) method is a first-order optimization method applicable to the constrained minimization of smooth functions and exploiting a scaling matrix
multiplying the gradient and a variable steplength parameter to improve the convergence of the scheme. For a general nonconvex function, the limit points of the sequence generated by SGP have been proved to be stationary, while in the convex case and with some restrictions on the choice of the scaling matrix the sequence itself converges to a constrained minimum point. In this paper we extend these convergence results by showing that the SGP sequence converges to a limit point provided that the objective function satisfies the Kurdyka– Lojasiewicz property at each point of its domain and its gradient is Lipschitz continuous.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/11380/11000052016-01-01T00:00:00ZAn alternating minimization method for blind deconvolution in astronomyhttp://hdl.handle.net/11380/1059917Titolo: An alternating minimization method for blind deconvolution in astronomy
Abstract: Blind deconvolution is the problem of image deblurring when both the original object and the blur are unknown. In this work, we show a particular astronomical imaging problem, in which p images of the same astronomical object are acquired and convolved with p different Point Spread Functions (PSFs). According to the maximum likelihood approach, this becomes a constrained minimization problem with p+1 blocks of variables, whose objective function is globally non convex. Thanks to the separable structure of the constraints, the problem can be treated by means of an inexact alternating minimization method whose limit points are stationary for the function. This method has been tested on some realistic datasets and the numerical results are hereby reported to show its effectiveness on both sparse and diffuse astronomical objects.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/11380/10599172014-01-01T00:00:00ZSpace-D: a software for nonnegative image deconvolution from sparse Fourier datahttp://hdl.handle.net/11380/694062Titolo: Space-D: a software for nonnegative image deconvolution from sparse Fourier data
Abstract: This code deals with image restoration problems where the data are nonuniform samples of the Fourier transform of the unknown object. We propose a practical algorithm, based on the gradient projection method, to compute a regularized solution in the discrete case. The key point in our deconvolution-based approach is that the fast Fourier transform can be employed in the algorithm implementation without the need of preprocessing the data.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/11380/6940622010-01-01T00:00:00ZA novel gradient projection approach for Fourier-based image restorationhttp://hdl.handle.net/11380/644689Titolo: A novel gradient projection approach for Fourier-based image restoration
Abstract: This work deals with the ill-posed inverse problem of reconstructing a two-dimensional image of an unknownobject starting from sparse and nonuniform measurements of its Fourier Transform. In particular, if we consider a prioriinformation about the target image (e.g., the nonnegativity of the pixels), this inverse problem can be reformulated as aconstrained optimization problem, in which the stationary points of the objective function can be viewed as the solutionsof a deconvolution problem with a suitable kernel. We propose a fast and effective gradient-projection iterative algorithmto provide regularized solutions of such a deconvolution problem by early stopping the iterations. Preliminary results on areal-world application in astronomy are presented.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/11380/6446892010-01-01T00:00:00ZThe scaled gradient projection method: an application to nonconvex optimizationhttp://hdl.handle.net/11380/1070951Titolo: The scaled gradient projection method: an application to nonconvex optimization
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/11380/10709512015-01-01T00:00:00ZApplication of cyclic block generalized gradient projection methods to Poisson blind deconvolutionhttp://hdl.handle.net/11380/1073401Titolo: Application of cyclic block generalized gradient projection methods to Poisson blind deconvolution
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/11380/10734012015-01-01T00:00:00ZNonnegative image reconstruction from sparse Fourier data: a new deconvolution algorithmhttp://hdl.handle.net/11380/641680Titolo: Nonnegative image reconstruction from sparse Fourier data: a new deconvolution algorithm
Abstract: This paper deals with image restoration problems where the data are nonuniform samples of the Fourier transform of the unknown object. We study the inverse problem in both semidiscrete and fully discrete formulations, and our analysis leads to an optimization problem involving the minimization of the data discrepancy under nonnegativity constraints. In particular we show that such problem is equivalent to a deconvolution problem in the image space. We propose a practical algorithm, based on the gradient projection method, to compute a regularized solution in the discrete case. The key point in our deconvolution-based approach is that the Fast Fourier Transform can be employed in the algorithm implementation without the need of preprocessing the data. A numerical experimentation on simulated and real datafrom the NASA RHESSI mission is also performed.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/11380/6416802010-01-01T00:00:00ZHestenes method for symmetric indefinite systems in interior-point methodhttp://hdl.handle.net/11380/452955Titolo: Hestenes method for symmetric indefinite systems in interior-point method
Abstract: This paper deals with the analysis and the solution of the Karush-Kuhn-Tucker (KKT) system that arises at each iteration of an Interior-Point (IP) method for minimizing a nonlinear function subject to equality and inequality constraints.This system is generally large and sparse and it can be reduced so that the coefficient matrix is still sparse, symmetric and indefinite, with size equal to the number of the primal variables and of the equality constraints. Instead of transforming this reduced system to a quasidefinite form by regularization techniques used in available codes on IP methods, under standard assumptions on the nonlinear problem, the system can be viewed as the optimality Lagrange conditions for a linear equality constrained quadratic programming problem, so that Hestenes multipliers' method can be applied. Numerical experiments on elliptic control problems with boundary and distributed control show the effectiveness of Hestenes scheme as inner solver for IP methods.
Thu, 01 Jan 2004 00:00:00 GMThttp://hdl.handle.net/11380/4529552004-01-01T00:00:00ZAn inexact Newton method combined with Hestenes multipliers' scheme for the solution of Karush-Kuhn-Tucker systemshttp://hdl.handle.net/11380/452951Titolo: An inexact Newton method combined with Hestenes multipliers' scheme for the solution of Karush-Kuhn-Tucker systems
Abstract: In this work a Newton interior-point method for the solution of Karush-Kuhn-Tucker systems is presented.A crucial feature of this iterative method is the solution, at each iteration, of the inner subproblem. This subproblem is a linear-quadratic programming problem, that can solved approximately by an inner iterative method such as the Hestenes multipliers' method.A deep analysis on the choices of the parameters of the method (perturbation and damping parameters) has been done.The global convergence of the Newton interior-point method is proved when it is viewed as an inexact Newton method for the solution of nonlinear systems with restriction on the sign of some variables.The Newton interior-point method is numerically evaluated on large scale test problems arising from elliptic optimal control problems which show the effectiveness of the approach.
Sat, 01 Jan 2005 00:00:00 GMThttp://hdl.handle.net/11380/4529512005-01-01T00:00:00Z