TY - JOUR

T1 - Stability results for sets of uniqueness in binary tomography

AU - Dulio, Paolo

AU - Pagani, Silvia M.C.

AU - Pagani, Silvia Maria Carla

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

KW - tomography

KW - uniqueness of reconstruction

KW - tomography

KW - uniqueness of reconstruction

UR - http://hdl.handle.net/10807/125573

UR - https://www.matec-conferences.org/articles/matecconf/pdf/2016/39/matecconf_cscc2016_02046.pdf

U2 - 10.1051/matecconf/20167602046

DO - 10.1051/matecconf/20167602046

M3 - Conference article

SN - 2261-236X

SP - N/A-N/A

JO - MATEC Web of Conferences

JF - MATEC Web of Conferences

T2 - 20th International Conference on Circuits, Systems, Communications and Computers (CSCC 2016)

Y2 - 14 July 2016 through 17 July 2016

ER -