Title :
On minimal scalings of scalable frames
Author :
Domagalski, Rachel ; Yeon Hyang Kim ; Narayan, Sivaram K.
Author_Institution :
Dept. of Math., Central Michigan Univ., Mount Pleasant, MI, USA
Abstract :
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.
Keywords :
redundancy; signal reconstruction; minimal scaling; orthogonal partitioning property; orthonormal basis; reconstruction formula; redundant system; scalable frame construction; tight frame; unit-norm frame; Electronic mail; Image reconstruction; Linear algebra; Scalability; Standards; Symmetric matrices;
Conference_Titel :
Sampling Theory and Applications (SampTA), 2015 International Conference on
Conference_Location :
Washington, DC
DOI :
10.1109/SAMPTA.2015.7148857