TY - GEN
T1 - Relation between exact and robust recovery for F-minimization
T2 - 2013 IEEE International Symposium on Information Theory, ISIT 2013
AU - Liu, Jingbo
AU - Jin, Jian
AU - Gu, Yuantao
PY - 2013
Y1 - 2013
N2 - Recent work in compressed sensing has shown the possibility reducing the number of measurements via non-convex optimization methods. Most of these methods can be studied in the general framework called 'F-minimization', for which the relation between the noiseless exact recovery condition (ERC) and noisy robust recovery condition (RRC) was not fully understood. In this paper, we associate each set of nulls spaces of the measurement matrices satisfying ERC/RRC as a subset of a Grassmannian, and show that the RRC set is exactly the interior of the ERC set. Then, a previous result of the equivalence of ERC and RRC for lp-minimization follows easily as a special case. We also show under some mild but necessary additional assumption that the ERC and RRC sets differ by a set of measure zero.
AB - Recent work in compressed sensing has shown the possibility reducing the number of measurements via non-convex optimization methods. Most of these methods can be studied in the general framework called 'F-minimization', for which the relation between the noiseless exact recovery condition (ERC) and noisy robust recovery condition (RRC) was not fully understood. In this paper, we associate each set of nulls spaces of the measurement matrices satisfying ERC/RRC as a subset of a Grassmannian, and show that the RRC set is exactly the interior of the ERC set. Then, a previous result of the equivalence of ERC and RRC for lp-minimization follows easily as a special case. We also show under some mild but necessary additional assumption that the ERC and RRC sets differ by a set of measure zero.
UR - http://www.scopus.com/inward/record.url?scp=84890351373&partnerID=8YFLogxK
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U2 - 10.1109/ISIT.2013.6620348
DO - 10.1109/ISIT.2013.6620348
M3 - Conference contribution
AN - SCOPUS:84890351373
SN - 9781479904464
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 859
EP - 863
BT - 2013 IEEE International Symposium on Information Theory, ISIT 2013
Y2 - 7 July 2013 through 12 July 2013
ER -