Near-Optimal Sparse Recovery in the L1 Norm
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Almost Euclidean subspaces of ℓ1N VIA expander codes
Combinatorica
IEEE Transactions on Information Theory - Part 1
IEEE Transactions on Information Theory
Decoding by linear programming
IEEE Transactions on Information Theory
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Classical results from the 1970's state that w.h.p. a random subspace of N-dimensional Euclidean space of proportional (linear in N) dimension is "well-spread" in the sense that vectors in the subspace have their l2 mass smoothly spread over a linear number of coordinates. Such well-spread subspaces are intimately connected to low distortion embeddings, compressed sensing matrices, and error-correction over reals. We describe a construction inspired by expander/Tanner codes that can be used to produce well-spread subspaces of Ω(N) dimension using sub-linear randomness (or in subexponential time). These results were presented in our paper [10]. We also discuss the connection of our subspaces to compressed sensing, and describe a near-linear time iterative recovery algorithm for compressible signals.