Re-projection without Reconstruction

Dimitri Pertin (1, 2) , Nicolas Normand (1)

1 IRCCyN - Institut de Recherche en Communications et en Cybernétique de Nantes
2 Rozo Systems

Discrete tomography focuses on image representation by its discrete projections, and the related inversion algorithms (or image reconstruction). Our study is based on redundant representations (considering more than just few projections). We propose a new approach to compute further redundancy (i.e. new projections) from a set of existing projections. While this technique relies on the geometric properties of ghosts, which are elements of the 2D image that sum to zero following some projection directions, we show an equivalent method using 1D convolutions, thus avoiding the explicit image reconstruction. This technique has interesting applications in distributed storage systems, where the use of redundancy data is key for system reliability.

Mots clés: discrete tomography; redundancy; convolution; storage; ghost

Domaines: Informatique [cs]; Théorie de l'information et codage [math.IT]; Géométrie algorithmique [cs.CG]

Dimitri Pertin, Nicolas Normand. Re-projection without Reconstruction. 9ème Journées du Groupe de travail de Géométrie Discrète, Reims Image 2014, Nov 2014, Reims, France. pp.43. ⟨hal-01164872⟩