Title :
Oblique pursuits for compressed sensing with random anisotropic measurements
Author :
Kiryung Lee ; Bresler, Yoram ; Junge, Marius
Author_Institution :
Dept. of ECE, Univ. of Illinois at Urbana-Champaign, Urbana, IL, USA
Abstract :
Compressed sensing enables universal, simple, and reduced-cost acquisition by exploiting a sparse signal model. Most notably, recovery of the signal by computationally efficient algorithms is guaranteed for certain random measurement models, which satisfy the so-called isotropy property. However, in real-world applications, this property is often not satisfied. We propose two related changes in the existing framework for the anisotropic case: (i) a generalized RIP called the restricted biorthogonality property (RBOP); and (ii) correspondingly modified versions of existing greedy pursuit algorithms, which we call oblique pursuits. Oblique pursuits provide recovery guarantees via the RBOP without requiring the isotropy property; hence, these recovery guarantees apply to practical acquisition schemes. Numerical results show that oblique pursuits also perform better than their conventional counterparts.
Keywords :
compressed sensing; cost reduction; greedy algorithms; RBOP; RIP; compressed sensing; greedy pursuit algorithm; isotropy property; oblique pursuit; random anisotropic measurement; random measurement model; restricted biorthogonality property; sparse signal model; Computational modeling; Dictionaries; Information theory; Matching pursuit algorithms; Pursuit algorithms; Transforms; Vectors;
Conference_Titel :
Information Theory Proceedings (ISIT), 2013 IEEE International Symposium on
Conference_Location :
Istanbul
DOI :
10.1109/ISIT.2013.6620346