TY - GEN

T1 - Frame scalability in dynamical sampling

AU - Aceska, Roza

AU - Kim, Yeon Hyang

N1 - Funding Information:
The authors thank to the anonymous referees for their valuable comments and suggestions on the earlier version of this manuscript. Kim was supported by the Central Michigan UniversityFRCEResearchType AGrant#C48143.Aceska was supported by the Ball State University Aspire Research Award#I601-16.
Publisher Copyright:
© 2017 IEEE.

PY - 2017/9/1

Y1 - 2017/9/1

N2 - Let H be the finite dimensional Hilbert space ℝn or ℂn. We consider a subset G ⊂ H and a dynamical operator A : H → H. The collection equation is called a dynamical system, where L = (L1,..., Lp) is a vector of non-negative integers. Under certain conditions FGL(A) is a frame for H; in such a case, we call this system a dynamical frame, generated by operator A and set G. A frame is a spanning set of a Hilbert space and a tight frame is a special case of a frame which admits a reconstruction formula similar to that of an orthonormal basis. Because of this simple formulation of reconstruction, tight frames are employed in many applications. Given a spanning set of vectors in H satisfying a certain property, one can manipulate the length of the vectors to obtain a tight frame. Such a spanning set is called a scalable frame. In this contribution, we study the relations between the operator A, the set G and the number of iterations L which ensure that the dynamical system FGL (A) is a scalable frame.

AB - Let H be the finite dimensional Hilbert space ℝn or ℂn. We consider a subset G ⊂ H and a dynamical operator A : H → H. The collection equation is called a dynamical system, where L = (L1,..., Lp) is a vector of non-negative integers. Under certain conditions FGL(A) is a frame for H; in such a case, we call this system a dynamical frame, generated by operator A and set G. A frame is a spanning set of a Hilbert space and a tight frame is a special case of a frame which admits a reconstruction formula similar to that of an orthonormal basis. Because of this simple formulation of reconstruction, tight frames are employed in many applications. Given a spanning set of vectors in H satisfying a certain property, one can manipulate the length of the vectors to obtain a tight frame. Such a spanning set is called a scalable frame. In this contribution, we study the relations between the operator A, the set G and the number of iterations L which ensure that the dynamical system FGL (A) is a scalable frame.

UR - http://www.scopus.com/inward/record.url?scp=85031704485&partnerID=8YFLogxK

U2 - 10.1109/SAMPTA.2017.8024349

DO - 10.1109/SAMPTA.2017.8024349

M3 - Conference contribution

AN - SCOPUS:85031704485

T3 - 2017 12th International Conference on Sampling Theory and Applications, SampTA 2017

SP - 41

EP - 45

BT - 2017 12th International Conference on Sampling Theory and Applications, SampTA 2017

A2 - Anbarjafari, Gholamreza

A2 - Kivinukk, Andi

A2 - Tamberg, Gert

PB - Institute of Electrical and Electronics Engineers Inc.

Y2 - 3 July 2017 through 7 July 2017

ER -