TY - GEN
T1 - Expander codes over reals, Euclidean sections, and compressed sensing
AU - Guruswami, Venkatesan
AU - Lee, James R.
AU - Wigderson, Avi
PY - 2009
Y1 - 2009
N2 - 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 sub-exponential 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.
AB - 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 sub-exponential 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.
UR - http://www.scopus.com/inward/record.url?scp=77949660150&partnerID=8YFLogxK
U2 - 10.1109/ALLERTON.2009.5394536
DO - 10.1109/ALLERTON.2009.5394536
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AN - SCOPUS:77949660150
SN - 9781424458714
T3 - 2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009
SP - 1231
EP - 1234
BT - 2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009
T2 - 2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009
Y2 - 30 September 2009 through 2 October 2009
ER -