Reconstruction of the measurable sets in the two dimensional plane by two projections
Takashi Takiguchi · Journal of Physics Conference Series · 2007
We discuss the reconstruction of the measurable plane sets from their two projections. Reconstruction of a measurable plane set F ⊂ 2 with λ 2 ( F ) < ∞ from its orthogonal projections is well studied, where λ i ; is the Lebesgue measure on i , i = 1, 2. In this paper we first discuss generalization of the known results in the frame of general two projections. The main purpose is to study, for any measurable plane set F , whether there are suitable two angles such that F is uniquely reconstructed from the pair of its projections in that two directions. We give an example to show that this problem is negatively solved.