The recovery of an unknown density function from the knowledge of its projections is the aim of tomography. In many cases, considering the problem from a discrete perspective is more convenient than employing a continuous approach: discrete tomography, and in particular binary tomography, is therefore exploited. One of the main goals of tomography is guaranteeing that the produced output coincides with the scanned object, namely, one wants to achieve uniqueness of reconstruction, even when only a few directions, from which projections are taken, are employed. Relying on a theoretical result stating that special sets of just four lattice directions are enough to uniquely reconstruct a binary grid, we prove that such sets are stable, in the sense that a small discrete perturbation of the components of the directions returns sets which again ensure uniqueness of reconstruction. Examples are provided.

Dulio, P., Pagani, S. M. C., Stability results for sets of uniqueness in binary tomography, Paper (Corfu', 14-17 July 2016), <<MATEC WEB OF CONFERENCES>>, 2016; (76): N/A-N/A.[doi: 10.1051/matecconf/20167602046] [http://hdl.handle.net/10807/125573]

Stability results for sets of uniqueness in binary tomography

Dulio, Paolo;Pagani, Silvia M. C.
2016

Abstract

The recovery of an unknown density function from the knowledge of its projections is the aim of tomography. In many cases, considering the problem from a discrete perspective is more convenient than employing a continuous approach: discrete tomography, and in particular binary tomography, is therefore exploited. One of the main goals of tomography is guaranteeing that the produced output coincides with the scanned object, namely, one wants to achieve uniqueness of reconstruction, even when only a few directions, from which projections are taken, are employed. Relying on a theoretical result stating that special sets of just four lattice directions are enough to uniquely reconstruct a binary grid, we prove that such sets are stable, in the sense that a small discrete perturbation of the components of the directions returns sets which again ensure uniqueness of reconstruction. Examples are provided.
Inglese
20th International Conference on Circuits, Systems, Communications and Computers (CSCC 2016)
Corfu'
Paper
14-lug-2016
17-lug-2016
Dulio, P., Pagani, S. M. C., Stability results for sets of uniqueness in binary tomography, Paper (Corfu', 14-17 July 2016), <<MATEC WEB OF CONFERENCES>>, 2016; (76): N/A-N/A.[doi: 10.1051/matecconf/20167602046] [http://hdl.handle.net/10807/125573]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10807/125573
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