TY - GEN
T1 - On minimal scalings of scalable frames
AU - Domagalski, Rachel
AU - Kim, Yeon Hyang
AU - Narayan, Sivaram K.
N1 - Publisher Copyright:
© 2015 IEEE.
PY - 2015/7/2
Y1 - 2015/7/2
N2 - A tight frame in Rn is a redundant system which has a reconstruction formula similar to that of an orthonormal basis. For a unit-norm frame F = {fi}ki=1, a scaling is a vector c = (c(l)..., c(k)) ε Rk≥0 such that {c(i)fi}ki=1 is a tight frame in Rn. If a scaling c exists, we say that F is a scalable frame. A scaling c is a minimal scaling if {fi: c{i) > 0} has no proper scalable subframes. In this paper, we present the uniqueness of the orthogonal partitioning property of any set of minimal scalings and provide a construction of scalable frames by extending the standard orthonormal basis of Rn.
AB - A tight frame in Rn is a redundant system which has a reconstruction formula similar to that of an orthonormal basis. For a unit-norm frame F = {fi}ki=1, a scaling is a vector c = (c(l)..., c(k)) ε Rk≥0 such that {c(i)fi}ki=1 is a tight frame in Rn. If a scaling c exists, we say that F is a scalable frame. A scaling c is a minimal scaling if {fi: c{i) > 0} has no proper scalable subframes. In this paper, we present the uniqueness of the orthogonal partitioning property of any set of minimal scalings and provide a construction of scalable frames by extending the standard orthonormal basis of Rn.
UR - http://www.scopus.com/inward/record.url?scp=84941063113&partnerID=8YFLogxK
U2 - 10.1109/SAMPTA.2015.7148857
DO - 10.1109/SAMPTA.2015.7148857
M3 - Conference contribution
AN - SCOPUS:84941063113
T3 - 2015 International Conference on Sampling Theory and Applications, SampTA 2015
SP - 91
EP - 95
BT - 2015 International Conference on Sampling Theory and Applications, SampTA 2015
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 11th International Conference on Sampling Theory and Applications, SampTA 2015
Y2 - 25 May 2015 through 29 May 2015
ER -