Boundary Ghosts for Discrete Tomography
Tóm tắt
Discrete tomography reconstructs an image of an object on a grid from its discrete projections along relatively few directions. When the resulting system of linear equations is under-determined, the reconstructed image is not unique. Ghosts are arrays of signed pixels that have zero sum projections along these directions; they define the image pixel locations that have non-unique solutions. In general, the discrete projection directions are chosen to define a ghost that has minimal impact on the reconstructed image. Here we construct binary boundary ghosts, which only affect a thin string of pixels distant from the object centre. This means that a large portion of the object around its centre can be uniquely reconstructed. We construct these boundary ghosts from maximal primitive ghosts, configurations of
$$2^N$$
connected binary (
$$\pm 1$$
) points over N directions. Maximal ghosts obfuscate image reconstruction and find application in secure storage of digital data.
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