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

UR - http://www.scopus.com/inward/citedby.url?scp=84867544968&partnerID=8YFLogxK

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 -