TY - GEN

T1 - Use of tight frames for optimized compressed sensing

AU - Tsiligianni, Evaggelia

AU - Kondi, Lisimachos P.

AU - Katsaggelos, Aggelos K

PY - 2012/11/27

Y1 - 2012/11/27

N2 - Compressed sensing (CS) theory relies on sparse representations in order to recover signals from an undersampled set of measurements. The sensing mechanism is described by the projection matrix, which should possess certain properties to guarantee high quality signal recovery, using efficient algorithms. Although the major breakthrough in compressed sensing results is obtained for random matrices, recent efforts have shown that CS performance could be improved with optimized non-random projections. Designing matrices that satisfy CS theoretical requirements is closely related to the construction of equiangular tight frames, a problem that has applications in various scientific fields like sparse approximations, coding, and communications. In this paper, we employ frame theory and propose an algorithm for the optimization of the projection matrix that improves sparse signal recovery.

AB - Compressed sensing (CS) theory relies on sparse representations in order to recover signals from an undersampled set of measurements. The sensing mechanism is described by the projection matrix, which should possess certain properties to guarantee high quality signal recovery, using efficient algorithms. Although the major breakthrough in compressed sensing results is obtained for random matrices, recent efforts have shown that CS performance could be improved with optimized non-random projections. Designing matrices that satisfy CS theoretical requirements is closely related to the construction of equiangular tight frames, a problem that has applications in various scientific fields like sparse approximations, coding, and communications. In this paper, we employ frame theory and propose an algorithm for the optimization of the projection matrix that improves sparse signal recovery.

KW - Compressed sensing

KW - Grassmannian frames

KW - tight frames

UR - http://www.scopus.com/inward/record.url?scp=84869772120&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84869772120&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84869772120

SN - 9781467310680

T3 - European Signal Processing Conference

SP - 1439

EP - 1443

BT - Proceedings of the 20th European Signal Processing Conference, EUSIPCO 2012

T2 - 20th European Signal Processing Conference, EUSIPCO 2012

Y2 - 27 August 2012 through 31 August 2012

ER -