English

Restricted Conformal Property of Compressive Sensing

Information Theory 2014-08-26 v1 math.IT

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.

Cite

@article{arxiv.1408.5543,
  title  = {Restricted Conformal Property of Compressive Sensing},
  author = {Tao Cheng},
  journal= {arXiv preprint arXiv:1408.5543},
  year   = {2014}
}

Comments

11 pages, 4 figures

R2 v1 2026-06-22T05:37:45.332Z