Luca Zanni

University of Modena and Reggio Emilia

82Publications

16H-index

1,182Citations

Publications 82

Newest*
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Abstract The role of the steplength selection strategies in gradient methods has been widely investigated in the last decades. Starting from the work of Barzilai and Borwein (1988), many efficient steplength rules have been designed, that contributed to make the gradient approaches an effective tool for the large-scale optimization problems arising in important real-world applications. Most of these steplength rules have been thought in unconstrained optimization, with the aim of exploiting some...

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Reconstruction of 3D X-ray CT images from reduced sampling by a scaled gradient projection algorithm*
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We propose a scaled gradient projection algorithm for the reconstruction of 3D X-ray tomographic images from limited data. The problem arises from the discretization of an ill-posed integral problem and, due to the incompleteness of the data, has infinite possible solutions. Hence, by following a regularization approach, we formulate the reconstruction problem as the nonnegatively constrained minimization of an objective function given by the sum of a fit-to-data term and a smoothed differentiab...

Estimated H-index: 12

Estimated H-index: 12

Estimated H-index: 16

Abstract The seminal paper by Barzilai and Borwein (1988) has given rise to an extensive investigation, leading to the development of effective gradient methods. Several steplength rules have been first designed for unconstrained quadratic problems and then extended to general nonlinear optimization problems. These rules share the common idea of attempting to capture, in an inexpensive way, some second-order information. However, the convergence theory of the gradient methods using the previous ...

Published on Jan 1, 2018

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Published on Oct 1, 2017

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In this paper we address the problem of estimating the phase from color images acquired with differential–interference–contrast microscopy. In particular, we consider the nonlinear and nonconvex optimization problem obtained by regularizing a least–squares–like discrepancy term with an edge–preserving functional, given by either the hypersurface potential or the total variation one. We investigate the analytical properties of the resulting objective functions, proving the existence of minimum po...

Published on Jan 1, 2017

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Published on Sep 19, 2016

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The DIC image is formed by the interference of two orthogonally polarized beams that have a lateral displacement (called shear) and are phase shifted relatively one to each other. The resulting image has a 3D high contrast appearance, which can be enhanced by introducing a uniform phase difference between the beams (called bias).

Accelerated gradient-based methods for phase estimation in differential-interference-contrast microscopy*
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Published on Sep 13, 2016

Estimated H-index: 3

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In the last forty years, differential-interference-contrast (DIC) microscopy has gained popularity in biomedical research as an effective optical microscopy technique used to observe unstained transparent specimens under a transmitted-light configuration. The DIC image formation is caused by the interference of two orthogonally polarized beams, which are laterally split of a few tenths of a micrometer by a Wollaston prism, phase shifted when passing through different materials across the specime...

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