Leírás
The first part of the lecture deals with the problem:
Let $A = \{(i,j) \in \mathbb{Z}^2: 0 \leq i < m, 0 \leq j < n\}$ and $f: A \to \mathbb{R}$ an unknown function.
Let $D = \{(a_i,b_i)\}_{i=1}^d$ be a set of coprime integers ('directions').
Suppose all the (discrete) line sums of $f$ in the directions of $D$ are given.
Compute all functions $g : A \to \mathbb{R}$ with the same line sums as $f$.
The case $D=\{(1,0), (0,1)\}$ represents the classical case that all row and column sums are given.
The second part indicates how a restricted number of errors in the line sums can be corrected.
Such problems are studied in discrete tomography which in contrast to computed tomography requires only a small number of directions.
This concerns joint work with Matthew Ceko, Lajos Hajdu and Silvia Pagani.