Reconstructing random pictures
| Autor: | Narayanan, Bhargav, Yap, Corrine |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Given a random binary picture $P_n$ of size $n$, i.e., an $n\times n$ grid filled with zeros and ones uniformly at random, when is it possible to reconstruct $P_n$ from its $k$-deck, i.e., the multiset of all its $k\times k$ subgrids? We demonstrate ``two-point concentration'' for the reconstruction threshold by showing that there is an integer $k_c(n) \sim (2 \log n)^{1/2}$ such that if $k > k_c$, then $P_n$ is reconstructible from its $k$-deck with high probability, and if $k < k_c$, then with high probability, it is impossible to reconstruct $P_n$ from its $k$-deck. The proof of this result uses a combination of interface-exploration arguments and entropic arguments. Comment: 11 figures, 18 pages; improved exposition of Section 3 proofs |
| Databáze: | arXiv |
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