Acta mathematica scientia, Series B >
ON THE STABILITY OF FUSION FRAMES (FRAMES OF SUBSPACES)
Received date: 2008-07-12
Revised date: 2010-03-29
Online published: 2011-07-20
A frame is an orthonormal basis-like collection of vectors in a Hilbert space, but need not be a basis or orthonormal. A fusion frame (frame of subspaces) is a frame-like collection of subspaces in a Hilbert space, thereby constructing a frame for the whole space
by joining sequences of frames for subspaces. Moreover the notion of fusion frames provide a framework for applications and providing efficient and robust information processing algorithms.In this paper we study the conditions under which removing an element from a fusion frame, again we obtain another fusion frame. We give another proof of [5, Corollary 3.3(iii)] with extra information about the bounds.
Mohammad Sadegh Asgari . ON THE STABILITY OF FUSION FRAMES (FRAMES OF SUBSPACES)[J]. Acta mathematica scientia, Series B, 2011 , 31(4) : 1633 -1642 . DOI: 10.1016/S0252-9602(11)60349-4
[1] Asgari M S, Khosravi A. Frames and bases of subspaces in Hilbert spaces. J Math Anal Appl, 2005, 308: 541–553
[2] Asgari M S, Khosravi A. Frames of subspaces and approximation of the inverse frame operator. Houston J Math, 2007, 33(3): 907–920
[3] Casazza P G, Kovacevic J. Equal-norm tight frames with erasures. Adv Compt Math, 2003, 18: 387–430
[4] Casazza P G, Kutyniok G. Frames of subspaces//Wavelets, Frames and Operator Theory (College Park, MD, 2003). Contemp Math, 345. Providence, RI: Amer Math Soc, 2004: 87–113
[5] Casazza P G, Kutyniok G. Robustness of fusion frames under erasures of subspaces and of local frame vectors. Contemp Math, 2008, 464: 149–160
[6] Casazza P G, Kutyniok G, Li S. Fusion frames and distributed processing. Appl Comput Harmon Anal, 2008, 25(1): 114–132
[7] Casazza P G, Kutyniok G, Li S, Rozell C J. Modeling sensor networks with fusion frames//Wavelets XII. Prof of SPIE, 2007
[8] Christensen O. An Introduction to Frames and Riesz Bases. Boston: Birkhauser, 2003
[9] Christensen O. Frames and pseudo-inverses. Appl Comput Harmon Anal, 1995, 195: 401–414
[10] Daubechies I, Grossmann A, Meyer Y. Painless nonorthogonal expansions. J Math Phys, 1986, 27: 1271–1283
[11] Ding J. On the perturbation of the reduced minimum modulus of bounded linear operators. Appl Math Comput, 2003, 140: 69–75
[12] Duffin R J, Schaeffer A C. A class of nonharmonic Fourier series. Trans Amer Math Soc, 1952, 72(2): 341–366
[13] Feichtinger H G, Strohmer T, eds. Gabor Analysis and Algorithms: Theory and Applications. Boston, MA: Birkhauser Inc, 1998
[14] Fornasier M. Quasi-orthogonal decompositions of structured frames. J Math Anal Appl, 2004, 289: 180–199
[15] Gabor D. Theory of communications. J Inst Electr Eg London, 1946, 93(3): 429–457
[16] Han D, Larson D R. Frames, bases and group representations. Mem Amer Math Soc, 2000, 147(697)
[17] Sun W. G-frames and G-Riesz bases. J Math Anal Appl, 2006, 322: 437–452
/
| 〈 |
|
〉 |