TY - GEN
T1 - Adaptive sensing using deterministic partial Hadamard matrices
AU - Haghighatshoar, S.
AU - Abbe, E.
AU - Telatar, E.
PY - 2012
Y1 - 2012
N2 - This paper investigates the construction of deterministic measurement matrices preserving the entropy of a random vector with a given probability distribution. In particular, it is shown that for a random vector with i.i.d. discrete components, this is achieved by selecting a subset of rows of a Hadamard matrix such that (i) the selection is deterministic (ii) the fraction of selected rows is vanishing. In contrast, it is shown that for a random vector with i.i.d. continuous components, no entropy preserving measurement matrix allows dimensionality reduction. These results are in agreement with the results of Wu-Verdu on almost lossless analog compression and provide a low-complexity measurement matrix. The proof technique is based on a polar code martingale argument and on a new entropy power inequality for integer-valued random variables.
AB - This paper investigates the construction of deterministic measurement matrices preserving the entropy of a random vector with a given probability distribution. In particular, it is shown that for a random vector with i.i.d. discrete components, this is achieved by selecting a subset of rows of a Hadamard matrix such that (i) the selection is deterministic (ii) the fraction of selected rows is vanishing. In contrast, it is shown that for a random vector with i.i.d. continuous components, no entropy preserving measurement matrix allows dimensionality reduction. These results are in agreement with the results of Wu-Verdu on almost lossless analog compression and provide a low-complexity measurement matrix. The proof technique is based on a polar code martingale argument and on a new entropy power inequality for integer-valued random variables.
KW - Analog compression
KW - Compressed sensing
KW - Entropy power inequality
KW - Entropy-preserving matrices
UR - http://www.scopus.com/inward/record.url?scp=84867544968&partnerID=8YFLogxK
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U2 - 10.1109/ISIT.2012.6283598
DO - 10.1109/ISIT.2012.6283598
M3 - Conference contribution
AN - SCOPUS:84867544968
SN - 9781467325790
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 1842
EP - 1846
BT - 2012 IEEE International Symposium on Information Theory Proceedings, ISIT 2012
T2 - 2012 IEEE International Symposium on Information Theory, ISIT 2012
Y2 - 1 July 2012 through 6 July 2012
ER -