TY - JOUR
T1 - Exact reconstruction analysis of log-sum minimization for compressed sensing
AU - Shen, Yanning
AU - Fang, Jun
AU - Li, Hongbin
PY - 2013
Y1 - 2013
N2 - The fact that fewer measurements are needed by log-sum minimization for sparse signal recovery than the L1-minimization has been observed by extensive experiments. Nevertheless, such a benefit brought by the use of the log-sum penalty function has not been rigorously proved. This paper provides a theoretical justification for adopting the log-sum as an alternative sparsity-encouraging function. We prove that minimizing the log-sum penalty function subject to Az = y is able to yield the exact solution, provided that a certain condition is satisfied. Specifically, our analysis suggests that, for a properly chosen regularization parameter, exact reconstruction can be attained when the restricted isometry constant δ3k is smaller than one, which presents a less restrictive isometry condition than that required by the conventional L1-type methods.
AB - The fact that fewer measurements are needed by log-sum minimization for sparse signal recovery than the L1-minimization has been observed by extensive experiments. Nevertheless, such a benefit brought by the use of the log-sum penalty function has not been rigorously proved. This paper provides a theoretical justification for adopting the log-sum as an alternative sparsity-encouraging function. We prove that minimizing the log-sum penalty function subject to Az = y is able to yield the exact solution, provided that a certain condition is satisfied. Specifically, our analysis suggests that, for a properly chosen regularization parameter, exact reconstruction can be attained when the restricted isometry constant δ3k is smaller than one, which presents a less restrictive isometry condition than that required by the conventional L1-type methods.
KW - Compressed sensing
KW - Iterative reweighted algorithms
KW - Log-sum minimization
UR - http://www.scopus.com/inward/record.url?scp=84886642795&partnerID=8YFLogxK
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U2 - 10.1109/LSP.2013.2285579
DO - 10.1109/LSP.2013.2285579
M3 - Article
AN - SCOPUS:84886642795
SN - 1070-9908
VL - 20
SP - 1223
EP - 1226
JO - IEEE Signal Processing Letters
JF - IEEE Signal Processing Letters
IS - 12
M1 - 6631489
ER -