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Improved Bounds on RIP for Generalized Orthogonal Matching Pursuit by Satpathi, Siddhartha; Das, Rajib Lochan; Chakraborty, Mrityunjoy is a scholarly article available to read on EtoBox.

What is Improved Bounds on RIP for Generalized Orthogonal Matching Pursuit about?

Generalized Orthogonal Matching Pursuit (gOMP) is a natural extension of OMP algorithm where unlike OMP, it may select $N (\geq1)$ atoms in each iteration. In this paper, we demonstrate that gOMP can successfully reconstruct a $K$-sparse signal from a compressed measurement $ {\bf y}={\bf \Phi x}$ by $K^{th}$ iteration if the sensing matrix ${\bf \Phi}$ satisfies restricted isometry property (RIP) of order $NK$ where $\delta_{NK} < \frac {\sqrt{N}}{\sqrt{K}+2\sqrt{N}}$. Our bound offers an improvement over the very recent result shown in \cite{wang_2012b}. Moreover, we present another bound for gOMP of order $NK+1$ with $\delta_{NK+1} < \frac {\sqrt{N}}{\sqrt{K}+\sqrt{N}}$ which exactly relates to the near optimal bound of $\delta_{K+1} < \frac {1}{\sqrt{K}+1}$ for OMP (N=1) as shown in \cite{wang_2012a}.

Author

Satpathi, Siddhartha; Das, Rajib Lochan; Chakraborty, Mrityunjoy

Published

2013

Language

EN