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.Tue, 20 Aug 2019 14:54:33 GMT2019-08-20T14:54:33Z10541An 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/11380/10097142014-01-01T00:00:00ZAlternating minimization for Poisson blind deconvolution in astronomyhttp://hdl.handle.net/11380/1033316Titolo: Alternating minimization for Poisson blind deconvolution in astronomy
Abstract: Although the continuous progresses in the design of devices which reduce the distorting effects of an optical system, a correct model of the point spread function (PSF) is often unavailable and in general it has to be estimated manually from a measured image. As an alternative to this approach, one can address the so-called blind deconvolution problem, in which the reconstruction of both the target distribution and the model is performed simultaneously by considering the minimization of a fit-to-data function in which both the object and the PSF are unknown. Due to the strong ill-posedness of the resulting inverse problem, suitable a priori information are needed to recover a meaningful solution, which can be included in the minimization problem under the form of constraints on the unknowns. In this work we consider a recent optimization algorithm for the solution of the blind deconvolution problem from data affected by Poisson noise, and we propose a strategy to automatically select its parameters based on a measure of the optimality condition violation. Some numerical simulations on astronomical images show that the proposed approach allows to provide reconstructions very close to those obtained by manually optimizing the algorithm parameters.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/11380/10333162014-01-01T00:00:00ZAn 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/11380/10599172014-01-01T00:00:00ZGradient projection approaches for optimization problems in image deblurring and denoisinghttp://hdl.handle.net/11380/618316Titolo: Gradient projection approaches for optimization problems in image deblurring and denoising
Abstract: Gradient type methods are widely used approaches for nonlinearprogramming in image processing, due to their simplicity, low memory requirement and ability to provide medium-accurate solutions without excessive computational costs. In this work we discuss some improved gradient projection methods for constrained optimization problems in image deblurring and denoising. Crucial feature of these approaches is the combination of special steplength rules and scaled gradient directions, appropriately designed to achieve a better convergence rate. Convergence results are given by exploiting monotone or nonmonotone line-search strategies along the feasible direction. The effectiveness of the algorithms is evaluated on the problems arising from the maximum likelihood approach to the deconvolution of images and from the edge-preserving removal of Poisson noise. Numerical results obtained by facing large scale problems involving images of several mega-pixels on graphics processors are also reported.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/11380/6183162009-01-01T00:00:00ZOn 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/11380/11000052016-01-01T00:00:00ZA scaled gradient projection method for Bayesian learning in dynamical systemshttp://hdl.handle.net/11380/1063508Titolo: A scaled gradient projection method for Bayesian learning in dynamical systems
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/11380/10635082015-01-01T00:00:00ZA 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/11380/6446892010-01-01T00:00:00ZA blind deconvolution method for ground based telescopes and Fizeau interferometershttp://hdl.handle.net/11380/1065549Titolo: A blind deconvolution method for ground based telescopes and Fizeau interferometers
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/11380/10655492015-01-01T00:00:00ZNew convergence results for the scaled gradient projection methodhttp://hdl.handle.net/11380/1070364Titolo: New convergence results for the scaled gradient projection method
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/11380/10703642015-01-01T00:00:00ZImage Reconstruction from Nonuniform Fourier Datahttp://hdl.handle.net/11380/651635Titolo: Image Reconstruction from Nonuniform Fourier Data
Abstract: In many scientific frameworks (e.g., radio and high energy astronomy, medical imaging) the data at one's disposal are encoded in the form of sparse and nonuniform samples of the desired unknown object's Fourier Transform. From the numerical point of view, reconstructing an image from sparse Fourier data is an ill-posed inverse problem in the sense of Hadamard, since there are infinite possible images which match the available Fourier samples. Moreover, the irregular distribution of such samples in the frequency space makes the use of any FFT-based reconstruction algorithm impossible, unless an interpolation and resampling (also known as gridding) procedure is previously applied to the original data. However, if the distribution of the Fourier samples in the frequency space is particularly irregular and/or the signal-to-noise ratio is poor, then the gridding step might either distort the information enclosed in the data or amplify the noise level on the re-sampled data with the result of artefacts formation and undesirable effects in the corresponding reconstructed image.This talk will deal with a different approach to the reconstruction of an image from a nonuniform sampling of its Fourier transform which acts straightly on the data without interpolation and re-sampling operations, exploiting in this way the real nature of the data themselves. In particular, we show that the minimization of the data discrepancy is equivalent to a deconvolution problem with a suitable kernel and we address its solution by means of a gradient projection method with an adaptive steplength parameter, chosen via an alternation of the two Barzilai–Borwein rules. Since the objective function involves a convolution operator, the algorithm can be effectively implemented exploiting the Fast Fourier Transform. The proposed algorithm is tested in a real-world problem, namely the restoration of X-ray images of the Sun during the solar flares by means of the datasets provided by the NASA RHESSI satellite.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/11380/6516352011-01-01T00:00:00Z