Expander codes over reals, Euclidean sections, and compressed sensing
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
Pseudorandom financial derivatives
Proceedings of the 12th ACM conference on Electronic commerce
Deterministic construction of a high dimensional lp section in l1n for any p
Proceedings of the forty-third annual ACM symposium on Theory of computing
| Hi-index | 0.01 |
We give an explicit (in particular, deterministic polynomial time) construction of subspaces X⊆ℝN of dimension (1−o(1))N such that for every x∈X, $$(\log N)^{ - O(\log \log \log N)} \sqrt N \left\| x \right\|_2 \leqslant \left\| x \right\|_1 \leqslant \sqrt N \left\| x \right\|_2 $$. Through known connections between such Euclidean sections of ℓ1 and compressed sensing matrices, our result also gives explicit compressed sensing matrices for low compression factors for which basis pursuit is guaranteed to recover sparse signals. Our construction makes use of unbalanced bipartite graphs to impose local linear constraints on vectors in the subspace, and our analysis relies on expansion properties of the graph. This is inspired by similar constructions of error-correcting codes.