Restricted conformal property of compressive sensing

Author

Tao Cheng

Author_Institution

Dept. of Mech., Guangxi Univ. of Sci. & Technol., Liuzhou, China

fYear

2014

Firstpage

152

Lastpage

161

Abstract

Energy and direction are tow basic properties of a vector. A discrete signal is a vector in nature. RIP of compressive sensing can not show the direction information of a signal but show the energy information of a signal. Hence, RIP is not complete. Orthogonal matrices can preserve angles and lengths. Preservation of length can show energies of signals like RIP do; and preservation of angle can show directions of signals. Therefore, Restricted Conformal Property (RCP) is proposed according to preservation of angle. RCP can show the direction of a signal just as RIP shows the energy of a signal. RCP is important supplement and development of RIP. Tow different proofs of RCP are given, namely, RCP_JL and RCP_IP.

Keywords

compressed sensing; matrix algebra; RCP_IP; RCP_JL; RIP; angle preservation; compressive sensing; direction information; discrete signal; energy information; orthogonal matrices; restricted conformal property; restricted isometry property; Compressed sensing; Eigenvalues and eigenfunctions; Energy measurement; Gold; Remote sensing; Sparse matrices; Vectors; Compressive sensing (CS); Johnson-Lindenstrauss (JL); Restricted Conformal Property (RCP); direction; energy; inner product (IP); measurement and reconstruction matrices; restricted isometry property (RIP);

fLanguage

English

Publisher

ieee

Conference_Titel

Wavelet Active Media Technology and Information Processing (ICCWAMTIP), 2014 11th International Computer Conference on

Print_ISBN

978-1-4799-7207-4

Type

conf

DOI

10.1109/ICCWAMTIP.2014.7073381

Filename

7073381